[
    {
        "image_filename": "designv11_24_0003139_12.539578-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003139_12.539578-Figure1-1.png",
        "caption": "Figure 1. Schematic diagram of the wireless temperature sensor system.",
        "texts": [
            " The objective of our research efforts is to monitor the temperature variation of bearing cages during bearing operation. Smart Structures and Materials 2004: Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems, Shih-Chi Liu, Editor, Proc. of SPIE Vol. 5391 (SPIE, Bellingham, WA, 2004) \u00b7 0277-786X/04/$15 \u00b7 doi: 10.1117/12.539578 368 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/18/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx As shown in Figure 1, our bearing temperature monitoring system consists of a transducer unit, an external data receiver (an antenna), and a central computer. Temperature sensing elements are placed in an electronic transmitter circuit and located on the bearing cage. Data measured during the bearing operation is wirelessly sent via a frequency - modulated (FM) carrier signal to an external receiver. Traditionally, batteries have been widely used to supply power to the portable electronic applications. However, their finite lifetime is a limiting factor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002165_1.1589505-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002165_1.1589505-Figure1-1.png",
        "caption": "Fig. 1 Novel bearing system for artificial joints \u201ea\u2026 and applications in total joint replacement of knee and hip \u201eb\u2026",
        "texts": [
            ", producing a low friction in start-up conditions. Under the assumption that lower friction would result in lower wear, an implant having a biphasic material might reduce the wear during stop-dwell-start-up motion. \u2022 Micro-modifications of the geometry are acceptable from a kinematical standpoint, both for the fixed and mobile prosthetic bearings. \u2022 After joint replacement, the rheologically modified lubricant, called periprosthetic fluid, behaves almost as water ~low viscosity, Newtonian fluid!, A novel bearing system for artificial joints ~Fig. 1~a!! has been proposed @24\u201327#. Here, the micro-pockets are machined on the surface of a rigid component and a biphasic material ~poro-elastic hydrated layer! covers the opposite articulating surface ~Fig. 1~a!!. Considering applications in total joint replacement of knee and hip ~Fig. 1~b!!, the artificial biphasic cartilage ~e.g., hydrogel! covers the tibial plateau, respectively the acetabular cup. Micropockets are machined on the rigid femoral condyle, or femoral head ~Fig. 1~b!!. Hemiarthroplasty can be also included as possible application; it might be done in the hip with micro-pocketcovered femoral head implants and in the knee with micro-pocketcovered femoral condyles. These implants articulate against the natural biphasic cartilage. However, a detailed discussion concerning the joint replacement designs lies beyond the purpose of this paper. In the case of the proposed bearing system ~Fig. 1~a!! a poro-elasto-hydrodynamic regime of lubrication might be developed. The fluid exudes from the biphasic cartilage, fills and pressurizes the micro-pockets @24,25#. Assuming that lower friction would result in lower adhesive wear, and neglecting the fatigue wear ~e.g., biphasic cartilage delamination! as well as the abrasive wear ~which might occur in the case of micro-pockets inadequate design!, the proposed bearing system might be able to reduce the wear rate. Preliminary tests @26,27#, considering the rigid component ~Fig. 1~a!! as a circular plate, with uniformly machined micro-pockets ~100 mm diameter and 25 mm depth! on 7.5 percent and 15 percent of its surface, articulating against artificial cartilage made in polyvinyl alcohol hydrogel, shown an important reduction of the wear factor ~43 percent\u201367 percent!. Maximum wear factor reduction was obtained for polyvinyl alcohol hydrogel with 77 percent water, which had the same fluid content as the natural cartilage @26,27#. This paper presents a theoretical investigation of an idealized artificial joint articulation with micro-pocket-covered component Transactions of the ASME Terms of Use: http://www"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003618_11892960_104-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003618_11892960_104-Figure4-1.png",
        "caption": "Fig. 4. Case for 1}{ lSMin i \u2264 Fig. 5. Case for 21 }{ lSMinl i \u2264<",
        "texts": [
            " The central point is used as an origin to the limit-cycle of the equation (1), and r is a radius derived by adding a half length of the obstacle to a half size of actual robot. Therefore, through the process shown in Fig. 2 and Fig. 3, the limit-cycle path where the robot navigates with avoiding obstacles is generated. For the direction of robot rotating, the robot rotates clockwise(CW) for \u2211\u2211 == > 7 3 3 0 i ii i SS , or the robot rotates counterclockwise(CCW) for , \u2211\u2211 == < 7 3 3 0 i ii i SS . In Fig. 4, where iS denotes the distance of each of ultrasonic sensors. In this paper, the maximum distance is set to 3m. If there is no obstacle detected, the distance of ultrasonic sensor is set to 3m not to 0. To generate a limit-cycle path for obstacles placed on side of the robot, the vector field method is proposed. As shown in Table 1, after selecting the least value among the distance values detected by 8 groups of ultrasonic sensor, we pre-set the angle of avoidance. In Fig. 4 and Fig. 5, robot\u2019s avoidance vector is measured. For ii lSMin \u2264}{ use equation (6), and for 21 }{ lSMinl i \u2264< , use equation (7), where 7 ,6 ,,1 ,0},{ L=iSMin i is the least value among the values detected by ultrasonic waves. The line 1l and 2l are the absolute distance between the robot and the obstacle, which represents the distance where the obstacle influences to robot\u2019s navigation, and the value is selected through experiment. In Fig. 4, the vector coordinate ),( yx TT of avoiding obstacles for 1}{ lSMin i \u2264 , defines ( ) ( )\u03b1 \u03b1 \u00b1= \u00b1= deg deg sin cos iy ix SKT SKT (6) Where K is a constant to decide the magnitude of a vector of avoidance. In Table 1 degiS is an angle of avoidance of }{ iSMin and \u03b1 denotes [ ])/90)(( 112 lSl \u00b0\u2212 , which is an inverse value proportional to the distance 1l , and if }{ iSMin is a distance detected by ultrasonic wave on the left plane, then it takes a negative value (-), if it is detected on the right plane, then it takes a positive value (+)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003258_detc2005-84712-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003258_detc2005-84712-Figure5-1.png",
        "caption": "Figure 5. One-dimensional mode of Wunderlich\u2019s mechanism.",
        "texts": [
            " The kinematic tangent cone Cq0 V ( IK ) = C\u2032 q0 V ( IK ) \u222aC\u2032\u2032 q0 V ( IK ) is the union of a two-dimensional cone C1 q0 V ( IK ) and a onedimensional cone C2 q0 V ( IK ) . II. I-Tangent cone to V : It holds Cq0 V ( IK ) \u223d Cq0 V ( I ) . III. Tangent cone to V : It holds Cq0 V = Cq0 V ( IK ) . IV. Discussion: The kinematic tangent space is a threedimensional vector space. The kinematic tangent cone is the union of a two-dimensional vector space C\u2032 q0 V ( IK ) and a one-dimensional vector space C\u2032\u2032 q0 V ( IK ) . These are the tangent spaces to respectively two- and one-dimensional manifolds (modi). I.e. the mechanism can enter modi with different dimensions. Figure 5 shows a configura- 10 wnloaded From: https://proceedings.asmedigitalcollection.asme.org on 01/04/2019 Terms of Us tion in a mode with \u03b4loc= 1 and figure 6 shows one in a mode with \u03b4loc = 2. Due to \u03b4diff (q0) = 3 and \u03b4loc (q0) = dimCq0 V ( IK ) \u2261 max(dimC\u2032 q0 V ( IK ) , C\u2032\u2032 q0 V ( IK ) ) = 2 the point q0 is singular with deg q0 = 1. The mechanism is kinematotropic. The planar 8-bar mechanism in figure 7 is a combination of a planar 4- and 5-bar mechanism. Shown is the reference configuration q0 = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001349_0954407011528095-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001349_0954407011528095-Figure2-1.png",
        "caption": "Fig. 2 Picture of a band and drum assembly",
        "texts": [
            " This is partly due to the high level of diYculty and partly due to the availability 2 ENGAGEMENT MECHANISMof high quality experimental data. Friction materials for band brakes are often tested in combination with various transmission oils to characterize engagement behaviour Figure 1 illustrates a typical band brake system. It con- sists of a band, a drum, an anchor and a servo assembly.[5\u201313]. However, an interpretation of experimental data can be diYcult without a basic understanding of the The inner surface of the band strap is lined with a porous friction material. Figure 2 shows a picture of a band andengagement process. Most design analyses have been limited to a static estimation of torque capacity based drum assembly. The drum is usually connected to a plan- etary gear set directly. When a shift event is initiated,on Coulomb friction alone [2, 14]. Although many publications exist in squeeze- lm analysis [15, 16 ], appli- hydraulic pressure is applied to the servo assembly. The hydraulic pressure acts against the return spring, strokescations of the theory have been mostly limited to plate- D05800 \u00a9 IMechE 2001Proc Instn Mech Engrs Vol 215 Part D at University of Birmingham on June 5, 2015pid"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002473_s0020-7225(03)00241-6-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002473_s0020-7225(03)00241-6-Figure4-1.png",
        "caption": "Fig. 4. The simple shear test.",
        "texts": [
            " For n < 0 the element shows tensile softening and compressive stiffening. For n \u00bc 1 it shows a linear behaviour and acts like a Hook string which obeys the linear Hook s law in every range of deformation. Fig. 3 shows the relative volume change det\u00f0F\u00de \u00bc dv=dV for nP 0, where dV and dv are initial and current infinitesimal volumes of a material particle. As it is seen, excessive finite elastic deformations results in a zero volume, except for n \u00bc 0. For n < 0 the relative volume change is quite unreasonable and are ignored. Fig. 4 shows a rectangular body undergoing a simple shear deformation. The kinematics of the problem is simply defined in a Lagrangian description as x1 \u00bc X1 \u00fe cX2 x2 \u00bc X2 x3 \u00bc X3 \u00f034\u00de The deformation gradient tensor is F \u00bc 1 c 0 0 1 0 0 0 1 2 4 3 5 \u00f035\u00de There are several methods to compute U one of which has been proposed by Hoger and Carlson [9]: C \u00bc FTF \u00f036\u00de U \u00bc b1\u00f0b2I\u00fe b3C C2\u00de \u00f037\u00de where b1 \u00bc 1=\u00f0I:II III\u00de; b2 \u00bc I :III ; b3 \u00bc I2 II \u00f038\u00de Hence, for simple shear test we have I \u00bc II \u00bc 1\u00fe ffiffiffiffiffiffiffiffiffiffiffiffi 4\u00fe c2 p ; III \u00bc 1 \u00f039\u00de U \u00bc 1ffiffiffiffiffiffiffiffiffiffiffiffi c2 \u00fe 4 p 2 c 0 c c2 \u00fe 2 0 0 0 1 2 4 3 5 \u00f040\u00de Now, if we use constitutive equation (6) for the material behaviour, from Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002175_1.1515333-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002175_1.1515333-Figure8-1.png",
        "caption": "Fig. 8 Sweeping test rig",
        "texts": [
            " Accepting that the maximum stress within a tine is at the mounting point then from Stango @4# the stress at this point is: smax5 2Ey~u12f! l (17) Additionally, the strain energy within the tine may be readily obtained from: U5( n 1 Ui5( n 1 k~u i2u i21!2 (18) DECEMBER 2002, Vol. 124 \u00d5 677 7 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F Practical Investigations To validate the theory a test rig has been developed to analyze and record the performance of large diameter cup brushes in a controlled environment. The test rig ~Fig. 8! has been developed to investigate all the main process variables. An automated test procedure using the graphical programming language in \u2018\u2018Labview\u2019\u2019 has been developed to ensure repeatability of test results. Tests were undertaken at a set rotational speed from zero brush penetration, referenced to the static geometry of the brush ~Fig. 2!. The test procedure can be best summarized using a flow chart ~Fig. 9!. It should be noted that the test data points were recorded both when the brush axial load was being increased and also decreased to allow an analysis of the hysteresis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002512_026635118700200301-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002512_026635118700200301-Figure7-1.png",
        "caption": "Fig. 7. Building formed with two 1200 modules joined on their ends.",
        "texts": [
            " 6 and it can be seen that the minimum width of the collapsed device is also the length of the long side of the element. If this length is made to be 2\u00b74 m then the head room in the central section of the structure is 2\u00b708 m (6 ft 10in) and the building would be suitable for human habitation. In the same manner that the 90\u00b0 modules were connected with a field joint to make a structure with a larger span and greater head room, two 120\u00b0 modules can be connected to form the building illustrated in Fig. 7. In this particular form of building the internal clear width at ground level would be 8\u00b796 m and the head room 4\u00b748 m (again using 2\u00b74 m-long elements). Buildings of this size would appear to be useful as temporary field service hangers for light aircraft and similar applications. The important dimensions for a number of structures using regular isosceles triangles are presented C. G. Foster. S. Krishnakumar in Tables I and 2. In Table I, the dimensions are given for elements with a unit length of long side (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002274_mawe.19860170706-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002274_mawe.19860170706-Figure2-1.png",
        "caption": "Fig. 2. Variation of the coordinate shear stress -cq along the rolling direction Y at a depth into the material of &.",
        "texts": [
            " Alternating Shear Stress Hypothesis (ASH) The alternating shear stress hypothesis is used to represent the extent to which the material is stressed in components subjected to loads in rolling contact. The coordinate shear stress tTY acting in planes parallel to the surface is considered as determining the extent to which the material is loaded [12]. During a rolling process, all the material elements at a depth Z pass through the complete shear stress profile, the shear stress changes between f zzy,. According to the Hertzian theory, the shear stress amplitude increases at first with increasing material depth (Z-axis), reaches a maximum value tzx,, at Z, and then falls again. Figure 2 shows the variation of the coordinate shear stress tZY in the corresponding X-Y plane (Z = Zo) along the rolling direction (Y coordinate). Dealing with the frictionless condition (p = 0) first, it appears that twice the numerical shear stress value is the decisive criterion for the fatigue of the material. The equivalent stress is therefore [12]: a y = 2 IzZ,l (4) The equivalent stress along the Z coordinate is thus given by the maximum shear stress amplitude found in each plane par- ~~ Z. Werkstofftech"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001904_70.988971-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001904_70.988971-Figure1-1.png",
        "caption": "Fig. 1. Manipulator PUMA frames selection.",
        "texts": [
            " \u2022 The three origins coincide with and they are placed at the shoulder joint. \u2022 Axis of is along the first link axis . \u2022 Axis of coincides with axis of . (Both frames coincide when .) \u2022 Axis of is placed along the second link axis and moves with it. Axis is perpendicular to the plane made by and . 2) For the frame , related with the third link, its origin is placed at the elbow joint. Axis is along the third link axis . Finally, is the revolution axis for the third element. The result of the frame selection procedure is shown in Fig. 1. A robot configuration will be given by the orientation of and with respect to and the orientation of with respect to . Each configuration is parameterized with . Taking into account the PUMA kinematic structure, the workspace parameterization is given by choosing spherical coordinates ( ). So, the angular path of and matches and respectively. As it will be shown, our choice will be decisive in order to reduce the computational load corresponding to evaluation of (5). Once the parameterization for and spaces has been established, the function definition will be Due to the robot mechanical structure, this function can be written as (11) where it has been taken into account that the first link does not depend on and DOFs and the second link does not depend on "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003124_3-540-26415-9_80-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003124_3-540-26415-9_80-Figure7-1.png",
        "caption": "Fig. 7. The three-modules star configuration.",
        "texts": [
            " Now, it only has one module on the pitch axis. Therefore, it cannot move forward or backward. But lateral shift or lateral rolling can still be achieved. When lateral rolling is performed, configurations PYP and YPY appears alternatively. Table1 summarizes the conditions needed to perform the different gaits. A sinusoidal wave is used in all the cases except in 2D sinusoidal gait, in which the rotation angle \u03d52 has a constant value. The last configuration tested was a three-modules star, shown in Fig.7. The modules form a star of three points with an angular distance of 1200. The locomotion is achieved by means of sinusoidal waves. It can move on a 2D surface, in three directions, as well as performing rotations in the yaw axis. If two adjacent modules are in phase and the opposite has \u03c6 \u2208 [100, 150], it moves on a straight in the direction of the module out of phase. However, this movement is very surface-dependant. When the increment of phase between the three modules is 120o, for example, \u03c61 = 0, \u03c62 = 120o and \u03c63 = 240o, the robot performs a slow rotation in the yaw axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001765_1350650011543709-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001765_1350650011543709-Figure5-1.png",
        "caption": "Fig. 5 Picture of a remotely powered telemeter installed on the bearing cage",
        "texts": [],
        "surrounding_texts": [
            "In the remotely powered version, two types of inductor coil for power transmission were tested. The first used a surface mount technology (SMT) inductor coil as coil 2, while in the second a loop of copper wire wound all along the periphery of the cage worked as coil 2. The efficiency of power transmission between the two coils is a function of coupling between them. It was found that inductor coil 2 employing a loop of copper wire provided better coupling. The copper loop inductor was able to transmit 25 times more power than the SMT coil.\nThe telemeter mainly consists of a temperature-sensing element, the sensitive capacitor and other electronic components. The telemeter is built separately on a printedcircuit board (PCB) instead of building directly on the cage. The PCB was then installed on the cage using a glueing agent. This construction was adopted for ease of manufacture. The PCB serves as wiring and mounting pads as well as the support for the components. Photolithography was used to develop the PCB and discrete SMT components were mounted on it by soldering.\nPhotolithography was used to develop the pattern of the desired circuit on a flexible copper-coated polyamide circuit board, commercially available and known as Kapton1. The circuit board is available with multiple layers of copper with layers of insulating material separating multiple layers of copper. Because of the simplicity of the telemeter circuit designed for this study, single-layer Kapton was used. A Kapton1 circuit board with 0.3 kg of copper per square metre on a polyamide substrate 0.05 mm thick was used for the telemeter developed for this study.\nThe first step in the process is to design and develop the artwork or the pattern for the desired circuit representing a positive or negative image of the wiring and soldering pads\non a photographic film. While designing the artwork, large sizes of mounting pads are recommended to accommodate dimensional tolerances in the SMT components. To account for the non-uniform nature of the etching process that would follow, the separation between the copper regions in the pattern should be large enough to avoid traces of copper left behind in the etching process. At the same time, the width of copper regions forming connecting wires must be large enough to avoid breaks in the circuit. It was found that the minimum dimension for a width of wire or a gap must be at least 250 \u00edm. The quality of pattern generated depends on the sharpness of edges and lines of pattern on the photographic film. Therefore, the pattern is printed on the photographic film paper using a high-density 2510 dots=inch laser printer. Figure 3 depicts a picture of the circuit pattern prepared on the photographic film.\nThe next step is to transfer the pattern on to the circuit board. For this purpose, the circuit board is completely covered with a layer of an AZ-1518 positive photoresist, a substance that changes its chemical properties after exposure to light. A centrifuge is used to achieve a thin and uniform layer. In the next step called pre-baking, the layer of photoresist is baked in an oven at 60 8C for 30 min before allowing it to cool to ambient temperature for about 30 min. The circuit board is then exposed to ultraviolet light for 120 s through the photographic film, which has the desired circuit pattern. The photographic film acts as a light-blocking mask. The circuit board with the exposed layer of photoresist is now developed in a 1:1 solution of water and AZ developer, a solution of trisodium phosphate, silicic acid and sodium salt in water. Here the portion of the photoresist layer that was not exposed to light is dissolved. The board is then post-baked in the oven at 120 8C for 60 min. This process forms a hard layer on the circuit board in the form of the pattern that was printed on the photographic film. The preceding procedure is carried out under safe sodium light so as to avoid premature exposure of photoresist.\nThe board is then exposed to etching solution at elevated\nJ01201 # IMechE 2001 Proc Instn Mech Engrs Vol 215 Part J\nat Universitats-Landesbibliothek on December 16, 2013pij.sagepub.comDownloaded from",
            "temperature of 45\u201350 8C. The etching solution is a chemical solution of ferric chloride and hydrochloric acid in water, commercially known as electronic circuit etching solution. The part of the copper that is not under the photoresist layer is dissolved and the copper pattern as designed on the photographic film is generated on the board.\nThe SMT components are mounted on the circuit board using standard soldering techniques, although proper care needs to be taken when dealing with discrete size SMT components manually. The exciter coil for the remotely powered telemeter and a receiver antenna are fabricated in the form of loops made of copper wire and mounted on a support and installed around the bearing. Figures 4 and 5 show photographs of the fabricated and installed batterypowered and remotely powered telemeters respectively.\nThe output frequency is monitored using a radio-frequency spectrum analyser connected to the loop antenna. A data acquisition system collects the output from the spectrum analyser at small time intervals of 5\u201315 s.\nThe bearing used in this study for temperature monitoring is a Timken JM205149/JM205110 tapered roller bearing with internal and external diameters of 50 and 90 mm respectively. Tests were conducted with the full complement of rollers in the bearing and also when two-thirds of the 18 rollers were removed. The rollers were removed from the bearing in order to achieve higher contact stresses in the bearing for a given load.\nFigure 6 shows a schematic assembly of the test rig. The test rig is built on a rigid frame that supports an 11.2 kW a.c. motor on the top. The motor shaft turns the inner race of the bearing through a spindle assembly. The outer race of the bearing is fixed to the housing and is mounted on a torsion bar. The housing also contains an oil sump underneath the outer race to supply lubricant to the bearing. The housing and the torsion bar are mounted on a subframe that can be moved vertically along the guide pillars using a hydraulic jack. An axial load of 22 250 N will generate a Hertzian contact stress of 1.725 MPa at the race\u2013roller contact. The axial load is measured using a load cell.\nFigure 7 depicts the details of the torque measurement subassembly. The torsion bar located below the bearing was designed to allow measurement of torque transmitted through the bearing. Two arms 1808 apart extend from either side of the housing. Because of the torque generated in the bearing, the torsion bar twists. The tangential move-\nProc Instn Mech Engrs Vol 215 Part J J01201 # IMechE 2001\nat Universitats-Landesbibliothek on December 16, 2013pij.sagepub.comDownloaded from",
            "ment of the arms is measured with proximity sensors and is calibrated to measure the torque. This system allows for accurate torque measurements down to 0.11 N m.\nCalibration was performed by immersing the telemeter installed on the bearing cage in an oil bath. A hot-plate was used to increase the temperature of the oil bath gradually, while a thermocouple was used to monitor and record the temperature. A radio-frequency spectrum analyser with a\nloop antenna was used to pick up the telemeter output. Figure 8 illustrates a calibration curve for the telemeter used in this study. The results indicate that frequency is a linear function of temperature without any hysteretic effects.\nThe monitored parameters include speed, axial load, torque transmitted, housing temperature and cage temperature. The output from the load cell, proximeters and thermocouples are recorded in a computer using a data acquisition card. The speed is recorded using the frequency drive output while the telemeter frequency for the cage temperature is first analysed in a spectrum analyser and then recorded into the computer. The data acquisition software used in this study is Delphi1.\nThe test bearing is pool lubricated using SAE 30 weight oil. A reservoir underneath the bearing is filled until about 75 per cent of the bearing is submerged in oil at rest. During operation the tapered roller bearing pumps the oil upwards to the top of the bearing housing from where it is drained back into the reservoir underneath the bearing through holes in the housing. A constant supply of lubricant to all parts of the bearing is thus maintained.\nTests were conducted at shaft speeds ranging from 400 to 2400 r=min and axial loads from 2225 to 22 250 N with loads resulting in outer ring peak contact stresses of 1.21\u2013 1.72 GPa. Tests were conducted at constant load and speed, with the bearing initially at room temperature. The operating parameters were recorded during the tests at time intervals of 5\u201315 s. The parameters monitored included cage temperature (measured with the telemeter), housing temperature (measured with a thermocouple) and bearing torque as functions of time.\nJ01201 # IMechE 2001 Proc Instn Mech Engrs Vol 215 Part J\nat Universitats-Landesbibliothek on December 16, 2013pij.sagepub.comDownloaded from"
        ]
    },
    {
        "image_filename": "designv11_24_0001366_20.950989-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001366_20.950989-Figure2-1.png",
        "caption": "Fig. 2. Dimple separation during unload process. An additional torque is produced due to the rotations of gimbal 1 and gimbal 2. A gimbal coefficient is introduced, which is defined as c = ( )=tan (d=l), where and refer to the rotation angle of gimbal 1 and gimbal 2 respectively, d is dimple separation.",
        "texts": [
            " The bonding force and bonding moments , acting on the main suspension may change as the tab climbing on the ramp. The equivalent tab force acting on the main suspension is . The acting force and moments between slider and local suspension are , and respectively, and they consist of three parts, the slider/dimple contact force when dimple is not separated, the gimbal force/moments when dimple is separated, and the limiter contact force/moments when dimple separation is larger than the limiter gap [8]. Fig. 2 shows the gimbal rotation when the dimple is separated. When the rotation angle of gimbal 1 is larger than the rotation angle of gimbal 2 , a positive torque is produced to help the slider increase its pitch angle, otherwise, a negative torque is produced to decrease the pitch angle. Fig. 3 illustrates two types of limiters currently used in industry. The hook limiter prevents slider/dimple separation, while allows the slider rotate along pitch and roll angles freely. The side limiter allows the slider separate from the dimple 0018\u20139464/01$10.00 \u00a9 2001 IEEE for a certain spacing, but prevents further separation. The performances of the two types of limiter will be discussed in the simulation below. The effect of gimbal rotation due to slider/dimple separation is studied. Fig. 4 illustrates the effect of gimbal coefficient on the unload process of a negative tripad slider. When ( , refer to Fig. 2), it is observed that the rear part of the slider contacts with disk, while , the front part of the slider contacts with disk. Smooth unload process is observed when , however, the dimple separation can be as large as 0.384 mm. The reason is that for a negative tripad slider, the negative force center is ahead of slider center, and it is more difficult to release the suction force, when compared with the slider whose negative force center is behind the slider center. Due to the spacing limitation between disks, dimple separation is also restricted"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003447_iros.2006.282145-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003447_iros.2006.282145-Figure2-1.png",
        "caption": "Fig. 2. Three-rotors rigid body and the associated frames",
        "texts": [
            " Furthermore, the constructed controller has satisfactory performance and improves the convergence speed of the closed-loop system compared to other approaches [1] (see Section IV). Section V is devoted to the testbed and experimental results description. The required control vectors (thrust and three torques) are obtained by a simple mechanism consisting of two body-fixed rotors and a tail tilting rotor with fixed-angle blades. The two front rotors rotate in opposite directions and are fixed to the aircraft frame. The tail rotor can be tilted around the E1-axis (Figure 2) using a servo-motor in order to produce a yaw torque. Since the main front rotors are powered by two independent motors, their angular velocities can be controlled to produce the main thrust as well as the roll torque. Finally, the pitch torque is obtained by varying the angular speed of the tail rotor. Modeling the UAV dynamics is a main issue, and the full model of a helicopter is very complex [7]. In most cases, 1-4244-0259-X/06/$20.00 \u00a92006 IEEE the aerial robot is considered as a rigid body incorporating a force/torques generation process. The equations of motion for a rigid body subject to body force F \u2208 R 3 and torque \u03c4 \u2208 R 3 applied to the center of mass G and specified with respect to the body coordinate frame B = (E1, E2, E3) (see Figure 2) are given by the following Newton-Euler equations in the inertial frame I = (Ex, Ey, Ez) [8], [9], [10], [11], [12].{ m\u03be\u0308 = RF \u2212 mgEz I(\u03b7)\u03b7\u0308 = \u03c4 \u2212 C(\u03b7\u0307, \u03b7) (1) where \u03be = (x, y, z) \u2208 R 3 is the position of the center of gravity with respect to the inertial frame I. m \u2208 R specifies the mass, I \u2208 R 3\u00d73 is a pseudo-inertial matrix and C(\u03b7\u0307, \u03b7) is a coriolis/centripetal vector. g represents the gravitational constant and R \u2208 SO(3) is the rotational matrix of the body axes relative to the inertial axes",
            " In the following, we will express these force/moment control vectors in terms of the original control inputs, i.e., the rotation speed of each motor wi, (i = 1, 2, 3) and the tilt angle (\u03b1) of the tail rotor. The force vector is expressed in the rigid body frame B as: F = (0, f3 sin \u03b1, f1 + f2 + f3 cos \u03b1)T = (0, uy, uz)T (2) Let us denote (o1, o2, o3) the application points of the forces (f1, f2, f3) respectively. Therefore, the torque vector MB F generated by these forces in respect to the mass center G can be expressed in B as follows, Figure 2: MB F = Go1 \u00d7 f1 + Go2 \u00d7 f2 + Go3 \u00d7 f3 (3) By developing this expression, we obtain MB F = \u239b \u239d l2(f1 \u2212 f2) \u2212l1(f1 + f2) + l3f3 cos \u03b1 \u2212l3f3 sin \u03b1 \u239e \u23a0 (4) where the li distances are defined in Figure 2. Furthermore, there exists other parasitic moments. Indeed, tilting the tail rotor laterally results in additional small moments. An adverse reaction moment appears when precessing the tail rotor laterally. It depends on the propeller inertia It and on tilt angle acceleration. This moment acts as a rolling moment and can be expressed in B as: Ma.r = (\u2212It\u03b1\u0308, 0, 0)T (5) The gyroscopical effect of tilting the tail rotor induces other moments. Tilting the propellers around the E1-axis, creates a gyroscopic moment which is perpendicular to this axis and to its spin axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003225_1.3111-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003225_1.3111-Figure6-1.png",
        "caption": "Fig. 6 Finite element bladed disk model with tapered blades.",
        "texts": [
            " 2) The relative motion of the tuned modes near the frequency veering contributes to high amplitude mistuned response in the selected degree of freedom. Therefore, it is clear that Eq. (17) provides not only a means for predicting mistuned amplitude magnification with frequency veering, but also a useful tool for understanding how various frequency veering mechanisms affect mistuned forced response. The second numerical example consists of a finite element model of a bladed disk with 18 tapered blades (Fig. 6). The natural frequencies are shown as a function of nodal diameter in Fig. 7. The mode families to be considered here are highlighted by the smaller box in Fig. 7, and the blade mode shapes in these mode families are displayed. Although a frequency veering is not apparent in Fig. 7, the blade mode shapes essentially exchange from zero nodal diameters to nine nodal diameters, indicative of mode interaction behavior consistent with frequency veering. Instead of disk and blade mode interaction, as is often observed with frequency veering, this example consists of interaction between two blade-dominated families of modes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001934_robot.1992.220116-Figure9-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001934_robot.1992.220116-Figure9-1.png",
        "caption": "Figure 9: Exit from a maximal extension placement",
        "texts": [
            " In both cases we claim that the robot has crossed anew trapezoid of A : when the robot has got two legs on the end points of an edge p4p5 of P , the stability polygon must have changed which means that we have crossed an edge of A, since we know the motion go ahead. Suppose now that the robot placement is such that one of its legs is at maximal extension: G is on the circle C ( p 1 ) . Let P' be the polygon obtained from P by deleting the critical site pl . Let the actual placement be p l , p z , a , with G E C ( p l ) . We check in O(1ogn) time if there exists a vertex p4 of P' such that G is contained in the triangle p2,p3 ,p4 (i.e. there exists a vertex of P' in the cone defined by G and the two lines s2 and s3: Figure 9.a). If so, we put the free leg on p4 and lift the back leg on p l . The motion then can go ahead until a new critical placement occurs. Otherwise, call p4, ps the vertices of P' lying on the line issued from pl and tangent to P' and let L1 be the polyfonal chain from p4 to p5 whose edges are edges of P but not of P (Figure 9.b); on the chain L1 we can perform a double binary search to find in O(1og n) time two consecutive vertices p and q such that the triangle p 3 , p , q contains G. It is clear, that p or q is on the same side of the line passing through p3 and . pl as p2 . Assume that this point is p . Then, since G E w p q but G 4 f i p z q , it is plain to observe that G must belong to triangle pplp3 . The robot moves as follows: first the free leg is moved to p , the leg in p2 is put on q , and then the back leg (resting in p1) is lifted"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002472_robot.2002.1014811-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002472_robot.2002.1014811-Figure5-1.png",
        "caption": "Figure 5: Friction cone.",
        "texts": [
            "3 Frictionlimit To prevent slipping down, the foot force vector should stay inside the friction cone. It is preferable that the force vector has some margin from the friction limit so that the robot becomes robust against some disturbances. To evaluate this friction margin, the following index is introduced: where a i k denotes the angle of the force vector of the kth vertex of the left (i = 3)lright (i = 4) foot from the contact normal vector, and aik,\" means the angle of the friction cone as shown in Figure 5 . Note that only legs (i = 3,4) are considered in this index. As the force vector goes closer to the edge of the friction cone, C, becomes larger, meaning that the robot has a smaller friction margin. 3.4 Joint motion range Each joint of the robot has certain motion range. If some of the joints reach the upper or lower limit of that range during the task, the robot might loose the balance and fall down. Therefore, it is preferable that each joint has certain margin from the upperflower bounds of the motion range"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002680_s09-Figure9-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002680_s09-Figure9-1.png",
        "caption": "Figure 9. Test rig for the micro spinner.",
        "texts": [
            " In eccentric conditions, the clearance h of each hypothetical circular thrust bearing is given by the following equation: h = Cr(1 \u2212 \u03b5 cos \u03b8) (14) where Cr is the radial clearance, \u03b5 is the eccentricity ratio and \u03b8 is the angle between the normal to the surface of the hypothetical circular thrust bearings and the direction of eccentricity. Figure 8 shows an example of load capacity and flow rate of a hydroinertia radial gas bearing. The bearing diameter D = 4 mm, length L = 2.4 mm, diameter d of the supply S230 holes d = 0.3 mm and number n of the supply holes n = 8 and supply pressure ps = 150 kPa(G). Load capacity becomes maximum Cr = 28 \u00b5m for \u03b5 = 0.3 and Cr = 35 \u00b5m for \u03b5 = 0.5. Hydroinertia gas bearings are applied to a micro spinner. Figure 9 shows the schematic configuration of the trial micro spinner test rig. The diameter of the spinner (\u00a91 of figure 9) is 4 mm and is driven by an impulse turbine (\u00a92 ) of the same diameter fitted at the end of the spinner. Two radial bearings (\u00a93 ) and a thrust bearing (\u00a94 ) set at the end surface of the spinner opposite to the turbine support the spinner. Rotational speed is measured by an optical sensor (\u00a95 ) and vibration by an eddy current type displacement meter (\u00a96 ). The radial bearings are of the same type as shown in figure 5 and their dimensions are almost the same as shown in figure 8. The spinner is made of stainless steel (Japanese standard SUS420) and the radial bearings are made of ceramics (zirconium)",
            " Figure 10 shows the 3D display of the shaft vibration spectrum. The horizontal axis shows the frequency from 0 to 50 kHz and the diagonal axis shows the rotational speed from 10 to 20 krps. Two vibrations are observed, one is synchronous to the rotational speed (shown by (A) in figure 10) and the other is at the low frequency of about 1 kHz (shown by (B)). The latter is the vibration by whirl motion and its frequency corresponds to the first resonance speed of this bearing\u2013spinner system. As shown in figure 9, radial bearings are set at the ends of the spinner, and the span of the bearing position is rather long compared with the spinner length. Therefore, the first resonance of the spinner\u2013bearing system is cylindrical mode, and the second resonance is conical (tilting) mode. The spinner vibration is detected near the center of the spinner. Thus, only cylindrical mode vibration is observed. Figure 11 shows the waveforms of the spinner at the rotational speed of 10 krps and 20 krps. In addition to the synchronous vibration, whirl vibrations can apparently be seen"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003809_detc2005-84681-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003809_detc2005-84681-Figure8-1.png",
        "caption": "Figure 8: Test configuration and modal identification results.",
        "texts": [
            " For this structure the beam model is not satisfactory and only solid three-dimensional finite element modeling makes it possible to translate the complexity of its dynamic behavior. Moreover, the MAC criterion established on the first three identified bending modes is unsatisfactory (see figure 7). The identification process did not enable an acceptable dynamic characterization of the spindle body and in this case the \"infinitely rigid\" model is retained. ownloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/03/2016 T The rear guide (see figure 8) is the connection between the spindle body and the rotating shaft. It allows axial thermal expansion of the shaft thanks to a ball bush. Measurements present many high frequency modes. However the measurement coherence criterion does not guarantee good identification conditions. Due to the geometrical complexity of the entity the beam model cannot correctly translate dynamic behavior. The results do not enable us to regard this entity as influencing overall spindle behavior. Characterization of the complete spindle unit The modal parameters of the complete spindle result from a combination of the results presented above"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001636_bit.260310904-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001636_bit.260310904-Figure4-1.png",
        "caption": "Figure 4. galactose (product) inhibition. Model mechanism of enzymatic lactose hydrolysis assuming",
        "texts": [
            " CAMFER can be operated essentially in three different modes: diffusional reactor, recycle reactor, and backflush reactor. In the following, these modes will be described in some detail and their theoretically predicted performance compared. Because of the nature of numerical solution, the comparison was made on the basis of one specific model reaction with well-defined kinetics. For this purpose, enzymatic lactose hydrolysis was chosen: @-galactosidase Lactose glucose + galactose It can be modelled by Michaelis-Menten kinetics with product inhibition (Fig. 4). This reaction was studied extensively in our laboratory and the kinetic constants were determined with a considerable degree of accuracy. I7 DIFFUSION REACTOR Substrate solution flows through the inner capillary space lumen, and the biocatalyst is located in the outer porous support structure of the capillary. The reaction process requires diffusion of substrate and products through the membrane. Mass transport to and from the membrane has to be also considered. The asymmetric hollow fiber can be divided into three parts: inner space or lumen (Region l), membrane skin or separation medium (Region 2), and porous structure or support for the membrane skin (Region 3) (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002689_j.mechmachtheory.2004.12.016-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002689_j.mechmachtheory.2004.12.016-Figure2-1.png",
        "caption": "Fig. 2. Representation of a coupler line.",
        "texts": [
            " If the second method is used, all the points Q1, Q2, and Q3 lie on a circle with the point \u00f0Hx=2;Hy=2\u00de as the center. The circle also passes through both points H and origin as shown in Fig. 1. 2 ler point curves of various four-bar bar Order Circularity Number of intersection points With a circle Case no. With a line Case no. R 6 3 6 1 6 7 P 4 1 6 2 4 8 6 3 6 3 6 9 2 0 4 4 2 10 4 1 6 5 4 11 4 2 4 6 4 12 Both methods can be applied to describe the motion of a line on the coupler link. As shown in Fig. 2, a line passing through points D and E is on the coupler link ABDE of the four-bar AoABBo. Both vectors AD ! and BE ! are parallel to each other and perpendicular to the vector DE ! . The point F(x,y) is on the line DE and is nearest to the origin. Therefore, the point F(x,y) can represent this line if the second method is used. The pivoted point Ao is set to be the origin for analysis. The lengths of both input and output links are a and b, respectively. The parameter k is the angle between the vector AD ",
            " The fourth method is to fix the ternary link ABC and treat the problem as a four-bar AAoBoB with a line on the coupler link AoBo. This leads to the Case 13 in Table 3, and six solutions can be derived. The breaking points and the cases related to all these four ways are also summarized and listed in Table 4. An example by using the fourth way is given as follows. Example 2. A 5-link chain is given with the ternary link fixed. The coordinates of these points are A:(0,0),B:(0,35), and C:( 12,25). A line is on the coupler link AoBo and passes through both points D and E. The dimensions, similar to Fig. 2, are jAoDj = 10, jBoEj = 25, and jDEj = 20. The link lengths are jAoAj = a = 20 and jBoBj = b = 27. The line on the coupler link must pass through the fixed point C as well. Sol: As discussed in the third section, two methods can be used to describe the motion of the line on the coupler link AoBo algebraically. For the first method, the equation of the curve is Table Soluti No. 1 2 3 4 5 6 \u00f0\u2018\u00fe m2\u00de3 \u00fe \u00f0 1:037m2 :7800e 1m\u00fe :4563e 2\u00fe :1786\u2018\u00de\u00f0\u20182 \u00fe m2\u00de2 \u00fe \u00f0:5146e 3\u2018 :1639e 3m :2526e 2m2 \u00fe 1:166\u20184 :1142\u20183 \u00fe :6473e 2\u20182 :7222e 2\u2018m :3929e 1m2\u2018\u00fe 3:357m2\u20182 :5969m3\u2018 :6881e 1m\u20182 3:731\u20183m\u00fe :2984e 1m4 \u00fe :5942e 1m3 \u00fe :6807e 5\u00de\u00f0\u20182 \u00fe m2\u00de \u00f0:1243e 12\u00f0 :9800e5m2 \u00fe 5600m \u00fe 140\u2018\u00f0 30: 1750:\u2018\u00fe 1400m\u00de\u00de2\u00de \u00bc 0 The algebraic equation by using the second method is \u00f0x2 \u00fe y2\u00de4 \u00fe \u00f0 :32213x2 \u00fe \u00f0 75:612\u00fe :85902y\u00dex\u00fe 24:081y \u00fe 402:10 :57268y2\u00de\u00f0x2 \u00fe y2\u00de3 \u00fe \u00f037:582x3 \u00fe \u00f0951:92 80:175y\u00dex2 \u00fe \u00f055:121y2 4400:4 1061:8y\u00dex 370:88y2 \u00fe :14688e6\u00fe 2663:4y 20:044y3\u00de\u00f0x2 \u00fe y2\u00de2 \u00fe \u00f0 1096:1x4 \u00fe \u00f016771:\u00fe 1753:8y\u00dex3 \u00fe \u00f010122:y :42459e6 1578:5y2\u00dex2 \u00fe \u00f05767:6y2 \u00fe 701:53y3 \u00fe :28828e6y\u00dex 8729:1y3 :16269e6y2 175:38y4\u00de\u00f0x2 \u00fe y2\u00de \u00fe 4384:6y4 87692:y3x\u00fe :49327e6y2x2 :54807e6yx3 \u00fe :17127e6x4 \u00bc 0 The first equation is combined with a line equation, 12\u2018 + 25m + 1 = 0, to get the solutions, while the second one is combined with a circle, x2 + 12x + y2 25y = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003972_jsen.2005.857881-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003972_jsen.2005.857881-Figure2-1.png",
        "caption": "Fig. 2. Cross section of the sensing structure of an ammonium ion-selective electrode based urea biosensor.",
        "texts": [
            " Based on the research described in this study, urea biosensors can be fabricated when the sensing devices and readout circuits are separated. Furthermore, the separated structures were studied in our research [21]\u2013[24]. Through combining the semiconductor process, it not only minimizes the size of the sensor but also have mass production capabilities, thereby allowing the development of a low cost disposable potentiometric urea biosensor. The general construction of the urea biosensor based on the ammonium ion-selective electrode was shown in Fig. 2. All potentiometric measurements were performed at ambient temperature (about 25 C). Fig. 3 shows the structure of the readout circuit, which was discussed in our research [24]\u2013[26]. The readout circuit was based on an instrumentation amplifier (LT1167) and a commercial Ag/AgCl electrode serving as a reference electrode. All EMF values were recorded against the given Ag/AgCl reference electrode. Before taking measurements, the urea biosensor was first set in the 20-mM Tris-HCl buffer until a stable potential was reached"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002885_j.triboint.2004.01.008-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002885_j.triboint.2004.01.008-Figure3-1.png",
        "caption": "Fig. 3. Hydro-support used in the PWA-lock. The hydro-support consists of a steel hydrostatic bearing with four recesses and is supported by a rubber ring. The hydro-supports slides on an UHMWPE track.",
        "texts": [
            " The support exposes many moving parts (wheels, bearings, load distribution mechanism) to a corros- ive environment, namely (salt) water. . Furthermore, the location of the support under water results in high inspection and maintenance costs. In order to address these drawbacks, an alternative lock-gate support has been developed: a water lubri- cated, hydrostatic thrust bearing sliding on an elastic track, the so-named \u2018hydrosupport\u2019 [1]. The hydro-sup- port is connected to the lock-gate using a flexible rub- ber hinge (Fig. 3). This hinge compensates for any misalignment between the lock-gate and the track, as a result of misalignment during construction or (extra) tilting of the gate during operation. The first application of the hydro-support was the four-recess, circular hydro-support in the new Prins Willem-Alexander lock (PWA-lock) which was put into use in 1995 in the \u2018Oranje\u2019-lock complex near Amsterdam. The hydro-support has been studied previously with respect to the tilting stiffness and the influence of elastic surface deformation on its performance [1\u20135]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001841_095440603321509711-Figure10-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001841_095440603321509711-Figure10-1.png",
        "caption": "Fig. 10 Three-dimensional sketch of the optimal washer shape",
        "texts": [
            " Clearly, they both converge quickly, even though these two design regions are in opposite contact directions. F rom Fig. 9, it can also be seen that the initial deviations of contact stresses are different for both design regions, where the deviation for the upper one is greater than that for the Proc. Instn Mech. Engrs Vol. 217 Part C: J. Mechanical Engineering Science C10902 # IMechE 2003 at UNIV OF PITTSBURGH on March 16, 2015pic.sagepub.comDownloaded from lower one. Eventually, both deviations are close to zero, as expected. Figure 10 shows a sketch of the optimal pro le for the washer design (based on the uni ed criterion). It is worth noting that the gap spacing and the shape of the upper design region are slightly different from those of the lower one. This is simply due to the difference between their initial contact stress statuses. Also, from a visual inspection the washer can be seen to be wedgeshaped with an almost linear slope on the top and a somewhat different linear slope on the bottom. These gradients and the difference between them can be a function of connection geometry and material parameters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000761_s0890-6955(97)00059-x-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000761_s0890-6955(97)00059-x-Figure1-1.png",
        "caption": "Fig. 1. Skeleton of the drag-link drive.",
        "texts": [
            " In this study, it is aimed at proposing optimum designs for partial balancing of the draglink drive [17, 18] by adding disk counterweights for reducing the shaking force and \u2020Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan. \u2021Author to whom correspondence should be addressed. 131 shaking moment. It is a multi-objective function problem. For the problem, the two-phase optimization technique is proposed and applied. A skeleton of the drag-link drive is shown in Fig. 1. Link ADG (also assigned as link 1) is the fixed link, link AB (link 2) is the driver, links BC, CDE, EF are assigned as links 3, 4, and 5, respectively, and the slider is link 6 which is the ram. A reference coordinate is chosen with A as the origin. For link i, ri is the length, mi and Ii are the mass and mass moment of inertia respectively, fi and li are the relative angular and linear positions of the mass center, ui is the angular position of the link measured counterclockwise from the positive X-axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003212_6.2004-5326-Figure9-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003212_6.2004-5326-Figure9-1.png",
        "caption": "Figure 9. Moving-Mass Control Concept",
        "texts": [
            " Figures 7 and 8 show the closed loop simulation results for the discrete-time feedback linearized autopilot. The autopilot performance in all three cases is qualitatively similar. It is important to note that these designs could be improved considerably by iterating on the design parameters. American Institute of Aeronautics and Astronautics 11 IV. Integrated Flight Control System Design for a Moving-Mass Actuated Interceptor Recently, internal mass movement has been proposed as a control methodology for a kinetic warhead (KW) in atmospheric and exo-atmospheric engagements19. As shown in Figure 9, the moving-masses positioned by servos inside the vehicle changes the location of its center of mass relative to the external forces to generate the desired control moments. The moving-mass control concept works equally well in space when the KW is thrusting, or in the atmosphere, when the vehicle experiences aerodynamic forces. An advantage of this actuation technology is that it can be employed in kinetic warheads that have both atmospheric and exo- atmospheric interception capabilities. As discussed in Reference 19, the moving mass actuator controlled kinetic warhead is a high-order coupled nonlinear dynamic system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001788_bf02459024-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001788_bf02459024-Figure5-1.png",
        "caption": "Fig. 5. - The path . . .AIA2A~A4 is consistent with properties 1-9.",
        "texts": [
            " In magnetic hysteresis, the definitions of first-turning-point derivatives of y(xo, Xl, x2, x3 = xl) and of y(xo, xl, x2) corresponds to the concepts of composite irreversible susceptibilities, introduced by Neel for describing <<reptation>> phenomena (11). With a proper choice of variables x and y, properties 1-9 characterize the mathematical structure of the input-output relationships of mostly real static hysteretic systems (ferromagnetism, absorption,...). A natural choice of x and y (11) L. NEEL: J. Phys. Radium, 20, 215 (1959). is that for which x y is a specific energy (12). Properties 1-9 are quite general; for instance, the curve ... A1 A2 A3A4 of fig. 5 is consistent with these properties. In particular <,reptation>, and ,<bascule>, phenomena(~1) are consistent with properties 1-9. Let us remark that all the properties stated in this section are consistent with hysteresis nonlinearities which include not only the irreversible changes of y( t ) but also the reversible ones. 3. - Generalized Preisach model. We shall suppose that the hysteresis region in (x, y)-plane is bounded by a closed loop. We shall call such a loop: limiting cycle. We shall also suppose that the y vs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001390_robot.1997.606894-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001390_robot.1997.606894-Figure3-1.png",
        "caption": "Figure 3: Illustration of collision-free interval [ATin, Ayax] due to a physical obstacle. Constraints due t o joint limits and self-collisions are also represented as an interval.",
        "texts": [
            " First we present a local algorithm (SEARCH) that computes a local minimum of the optimization problem, and then we present EXPLORE that spreads landmarks over the configuration space. 3 The Local Algorithm SEARCH Our approach exploits the serial kinematic structure of manipulator arms [GupSO, GZ95] to construct an efficient local algorithm to solve the optimization problem posed in the previous section. Let robot. We denote by A; = [ATifl,ATax] C R the collision-free interval of joint i at q (see Figure 3). The joint limits are naturally represented as an interval and the collision constraints are easily computed as an interval by simple computational geometric methods $ = ( q l , q2, .... qi , .... qn) be a free configuration of the 21t is relatively straightforward to show that d is indeed a metric. [LP87]. The intersection of these intervals then gives the desired interval Ai which determines the feasible range of motion for joint i . Formally, let C8 c CA,,.,, denote this feasible interval set for joint i , i",
            " It is clear that all valid Manhattan paths of order k can be represented by a vector 2 E but not all 2 E Rn*\u2018 represent a valid Manhattan Path, since Ai E y k could easily violate a kinematic constraint, either due to an obstacle or due to joint limit. The bouncing technique allows us to map an arbitrary Manhattan path into an admissible Manhattan path. The basic idea is to bounce 08 the obstacle and has been used in [BA+93, HFT941 (see Figure 5). Suppose a certain Ai leads to collision. As mentioned before, at the given configuration, a collisionfree interval [AT\u201d, Ay\u201c\u201d] can be easily obtained (as in [LP87]) such that every joint value within this interval is collision-free (see Figure 3). We can then map the original interval A; modulo the collision-free interval to within the collision-free interval [ATin, AT\u2018\u201c]. Physically speaking, it is as if the the robot lin& repeatedly bounces off the obstacles until the entire Ai is travelled. Obviously, this bouncing move is not executed by the robot, it is just a mapping from Ai \u20ac R to [AY\u201d, Ayus] . Note that the range of link ( i + 1) depends on the moves of link 1 .. .i, i.e., A$; and AT: are functions of Aj for j = 1,2, . . . , i. We can now generate a random Manhattan path b y randomly ing a random vector x E and then transform it into an admissible Manahttan path using the bouncing t echnz qu e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003956_tia.2005.863899-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003956_tia.2005.863899-Figure2-1.png",
        "caption": "Fig. 2. Rotor lamination of a synchronous machine.",
        "texts": [
            " The machine has a rotor with 24 damper bars. The damper bars facilitate the self-starting of the machine and also damp out the machine oscillations. The rotor lamination of the machine is shown in Fig. 1. The salient-pole synchronous motor under consideration is a three-phase 208-V 1800-r/min 60-Hz 2-kW four-pole machine having 36 stator slots. The stator has a three-phase double-layer lap winding with a resistance of 0.6 \u2126/phase. The machine has 20 damper bars. The rotor lamination of the machine is shown in Fig. 2. In order to model the machine, various stator inductances are to be computed using the WFA. Its stator has a three-phase single-layer concentric winding with 47 turns per coil. The turns function of the stator phase A winding of the synchRel is shown in Fig. 3. The turns functions of phase B and phase C will be similar to that of phase A but will be displaced by 60\u25e6 and 120\u25e6 (mechanical), respectively. The turns functions of phase A, phase B, and phase C of the synchRel can be expressed using Fourier series expansions as given in (1)\u2013(3) nA(\u03c6) = aos + \u221e\u2211 k=1,3,5,"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002188_rob.4620040203-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002188_rob.4620040203-Figure1-1.png",
        "caption": "Figure 1. Sketch of PUMA arm.",
        "texts": [],
        "surrounding_texts": [
            "The contribution from this research is the elimination of the modem control algorithm implementation restriction imposed by Jacobian computational complexity. By employing symbolic reduction techniques in conjunction with the separation of the resultant equations into on-line, temporary variables and off-line constants, efficient formulations of the Jacobian, inverse Jacobian, and inverse Jacobian multiplied by a vector have been developed. Tables I and I1 clearly illustrate the computational savings inherent in the utilization of our Jacobian algorithms. Those efficient algorithms are supporting real-time implementation of modem control algorithms on a PUMA manipulator. Although applied to a specific manipulator, the techniques employed in this study are valid for any robotic arm. The symbolic nature of these equations allows flexibility in the definition of the kinematic parameters. The only restriction is that the manipulator\u2019s homogeneous transformation matrices be identical in form to those shown in Appendix A. Further reduction of the efficient formulations must be conducted by significance analysis. To accomplish that task, knowledge of the importance of individual terms should be evaluated over a range of trajectories representative of worse-case robotic motion. This work has been partially supported by National Science Foundation Grant No. ECS8312179. Captain Leahy is attending RPI under the Air Force Institute of Technology\u2019s civilian institute program. APPENDIX A PUMA Model Paul.\u201d Si and Ci denote the sine and cosine of joint i, respectively. The A matrices denote the homogeneous transformation matrices as defined by c 1 0 -sl 0 0 c 1 0 0 0 0 1 Al = [ s1 0 -1 0 0 Leahy el al.: Efficient PUMA Manipulator 191 s2 c 2 0 A 2 = I 0 0 1 L O 0 0 s3 0 - c 3 A ~ = ) , 0 L o O 0 r c 4 o - s4 0 c 4 - 1 0 L O 0 0 1 1 \"I 1 A 2 C 2 a2+52 D2 1 A 3 C 3 a3*53 0 1 D4 192 A 5 = [ Y c 5 0 A.;[Y C6 0 0 0 1 0 - S6 C6 0 0 Journal of Robotic Systems-1 987 0 0 1 D6 0 0 0 1 \" I"
        ]
    },
    {
        "image_filename": "designv11_24_0001762_s0022-460x(88)80375-4-FigureI-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001762_s0022-460x(88)80375-4-FigureI-1.png",
        "caption": "Figure I. Radial springs attached to ring.",
        "texts": [],
        "surrounding_texts": [
            "The problem under consideration is a free floating non-axisymmetric ring with attached radial springs at arbitrary locations, as shown in Figure 1. A similar problem with only one radial spring attachment was formulated in a previous paper by the authors [23]. In this paper, the problem is extended by formulating it for the general case of L arbitrarily spaced radial spring attachments. The modal expansion and receptance methods are used to formulate the problem. It will be shown that effects appear that were either not found when studying a single spring attachment or could not be recognized in their general form."
        ]
    },
    {
        "image_filename": "designv11_24_0000813_bf00571701-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000813_bf00571701-Figure5-1.png",
        "caption": "Figure 5. Scheme of the mechanism in the propelling sequence.",
        "texts": [
            " The DYNAMIC MODELLING OF A FOUR-LEGGED ROBOT 427 two support legs are on the diagonal or on the lateral. The indices j and k denote the two other legs. The kinematic analysis gives the relation between the twist vector ts of the system S and the balanced angle 0: 5:Gs = 0 YGs = O ( - a S O - bCO) (33) z < = O ( a c o - bSO) From relation (33), we can derive the matrix T as follows: T = (0 - aSO - bCO aCO - bSO 1 0 0) T, (34) with a = YGs - Yo~+z and b = zas - Zoi+z. 4.4.4. Prope l l i ng S e q u e n c e The same analysis as in the balanced sequence, with respect to Figure 5, allows to establish the T matrix as follows: T = ( di+lC(Oi+ 1 + Os) di+lC(Oi+l + Os), 0 0, di+lS(Oi+l + Os) di+lS(Oi+l + Os), 0 0, (35) 1 O, 0 0 , 0 - l I C O s , 0 0 , O l l S C O s O 0 , 0 1, 0 0 ) T, with II = V/(Xi+2 - xi) 2 + (z i+ 2 - zi) 2. (36) 4.5. GENERAL EXPRESSIONS OF T f , T g AND T m The general expressions of the wrench vectors of friction, driving actions and forces due to the gravity are defined, for each robot's link, as follows: - f O i ' T i n = c m ' - - m i 9 \" 428 M. BENNANI AND E GIRl The movement sequences of a quadrupled robot in a walking gait can be represented by the closed and/or loop mechanisms"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002512_026635118700200301-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002512_026635118700200301-Figure4-1.png",
        "caption": "Fig. 4. The erected building shown in this illustration is resting on flat ground with the side walls contacting the ground continuously. Obviously, the addition of extra modules would just replicate this elemental building lengthwise. It is not necessary for the side walls to contact the ground continuously as it is also not necessary for the ground to be perfectly flat. The flexibility in the device allows it to adjust to differing ground distortions. However, if it is necessary for the side walls to touch the ground continuously then the geometry of the erected structure becomes far more constrained. Figure 4 illustrates the major shortcoming of the 90\u00b0 element. If the folded device is manufactured so that it can be readily transported, then the maximum dimension on the side of the square would be about 2\u00b74m (0\u00b7707L). With this limiting dimension the erected structure would be 4\u00b78 m",
        "texts": [
            " Thus for each pair ofmodules the increase is four regardless of the number of elements in the module and if there are m modules the total number of degrees of freedom is n + 5 4- 2(m - 2) (i.e. n + 2m + 2), provided m is even and the pairs of modules are of the form shown in Figs 2, 4, 6 and 8. . Having established the number of degrees of freedom in the linkage, it is then necessary to determine what constraints need to be made to the device to turn it into' a structure. Perhaps it is best to illustrate the constraints with reference to a particular structure (in this case the simple structure of Fig. 4). The basic linkage here has II degrees of freedom. By pinning three of the corners, nine degrees of freedom are eliminated so that only two constraints are needed at the last corner. Inevitably, one of these constraints would be that the corner was in contact with the ground, resulting in the need to specify the location. in one direction\u00b7 only on the ground. For each additional pair of modules there are four extra degrees of freedom and two extra nodes. If each of these nodes is held in contact with the ground then they also have only to be located in one direction on the ground",
            " When the building is collapsed the slack cables do not appear to be an undue problem. A third technique is illustrated in Fig. 12, where the brace takes both tension and compression. In this form ofcolumn structure it is only the end modules that behave mechanistically so that constraint is needed only on the extreme ends. The same is true for structures erected on the ground to make enclosed buildings. Only the two ends ofthe building need be provided with bulkheads, regardless of the number of modules. If two modules were joined on their opposite sides to that shown in Fig. 4 (i.e. the half-elements faced out instead of in) then there would be 13 degrees of freedom instead of 11. The additional two degrees of freedom correspond with the end shape becoming a four-bar mechanism instead of a three-link structure and the end must be braced accordingly. C. G. Foster, S. Krishnakumar Physically unfolding the device and erecting it on the ground is quite simple. Predicting, mathematically, where the nodes would be is quite another problem. For regular isosceles elements in a structure erected on flat ground the calculation of node positions can also be simple"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001711_s0009-2509(01)00026-4-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001711_s0009-2509(01)00026-4-Figure1-1.png",
        "caption": "Fig. 1. Experimental set-up.",
        "texts": [
            " In our experiments we measured the pro1les of internal static friction angle, velocity and void ratio. We also made an attempt to create a simple semiempirical model, based on the variation of the internal friction angle, trying to explain the experimental velocity pro1les in the quasi-static frictional zone of the !owing bed. Experiments were carried out on a rough chute whose inclination could be easily changed operating on two blocking handle grips; it was constituted by a !owing channel, a feeding hopper and a collector bin (Fig. 1). The channel was made up of a wooden bottom and of two sidewalls in Perspex, 0:045 m high. It was 1:1 m long and had a variable width between 0.030 and 0:085 m. The wooden surface was roughened gluing one layer of particles of the same kind of those used in the experiments. Such layer had to be renewed from time to time, because of wearing. The two parallel sidewalls were perpendicular to the bottom and made of transparent Perspex to allow the observation of the !ows. One of them was 1xed while the other, 1xed to four L-bolts screwed on the wooden bottom, could move changing the channel width"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003549_rissp.2003.1285572-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003549_rissp.2003.1285572-Figure1-1.png",
        "caption": "Fig. 1: Pushing Manipulation by a Humanoid Robot",
        "texts": [],
        "surrounding_texts": [
            "This paper discusses Jhe. manipulation of an object by using the whole body o j a human type robotic mechanism. To manipulate a big object placed on the floor, a human type robot pushes it.\u2019 For this problem, we extend the internal force in grasping by a multi-fingered hand to the whole body manipulation by a humanoid robot and introduce the \u201cwhole body internal fake\u201d. To exert the pushing force effectiuely onto the object, we obtain some conditions regardzng the whole body internal force. W e also obtain the region o j the foot position enabling a robot to push an object without causing the slip.\n1 Introduction When a human manipulates a large object, he/she will exert the force effectively\u2019onto the object by using the whole body. Since the structure of a humanoid robot is similar to that of a human, it is effective also for a humanoid robot if a humanoid robot manipulates a large object by using the whole body. In this paper, we call such kinds of manipulation as the \u201cwhole body manipulation\u201d, and obtain the conditions for a humanoid robot to perform the whole body manipulation effectively.\nPreviously, much research has been done on the manipulation of an object by a robotic hand as shown in Fig.l(a),(b). Fig.l(a) shows an example of the fingertip grasp by a robotic hand where the object is grasped only by the fingertip. Fig.l(b) shows an example of the enveloping grasp of an object. The manipulation under the enveloping style is sometimes called the \u201cwhole arm manipulation\u201d[8] since the object is grasped not . only by the fingertip but also by the inner-link and the palm. In these two styles of object manipulation, the\u2019object is grasped by the robotic hand where it is fix to the arm-tip or the environment. On the other hand, Fig.l(c) sh0ws.m example of the \u201cwhole body\nmanipulation\u201d where a big object placed on the floor is pushed by using the whole body of a humanoid robot. The whole body manipulation is different from the manipulation by a robotic hand since the robot is not k e d to the environment, and since the contact forces occur at the contact points without generating acceleration at the body. Corresponding to the internal force existing in the grasp by a robotic band, we call the contact force without generating acceleration at the body a8 the \u201cwhole body internal force\u201d. The object will slide on the surface of the floor if the humanoid robot can exert the whole body internal force onto the object effectively. On the other hand, since the robot is not fixed to the environment, the feet of the robot may cause slip and fall down.\nIn this paper, after showing the kinematics and the statics of a humanoid robot, we define and formulate the whole body internal force. Regarding the whole\n0-7803-7925-x/03/$17.00 2003 IEEE 190",
            "body internal force, we consider giving answers to the following questions: 1) Under what condition can a robot exert a large contact force onto the object? 2) If a robot cannot kxert a large contact force, how much contact force can the robot exert? 3) To exert the contact force onto the object effectively, where should the feet be placed on the floor? To show the effectiveness of our idea, some simulation results will be shown.\n2 Relevant Works Humanoid Robot: Hirai et al.[l], Kagami et al.[2], and Konno et al.[3] constructed a humanoid robot and realized some basic, motions. Inoue e t a1.W organized the HRP (Humanoid Robotics Project) and developed humanoid robots. Inoue et al.[5] discussed the manipulability of the arm of a humanoid robot. Lim et d.16) and Kajita et al.[7] discussed the walking motion of a humanoid robot. However, there has been 'no research. on humanoid robot where the hand exerts'a force onto the object and manipulates it.\nPreviously, there have been much research on the manipulation of an object by a robotic hand. Especially, Salisbury(81 proposed the concept of the \"whole-arm manipulation\". Aiyama et al.[9] proposed the graspless manipulation where a robot -hand manipulates an object without grasping firmly., Kaneko et al.[ lO] proposed the manipulation of an enveloped object. Yoshikawa et a1.[13, 141 analyzed the internal force in grasping an object by a robotic hand. Recently, some researchers research on the manipulation of an object not only by a robotic hand. Omata et al.[12] prw posed the \"whole quadriiped manipulation\" where a quadruped robot manipulates an object by using some of the legs. Kaneko et al.[ll] proposed the hugging walk where a quadruped robot envelopes an environment and walks. However, there has been research on neither the internal force existing in the humanoid robot nor the region of the internal force formed by the friction constraint.\n. , Manipulation: , .\n3 Model 3.1 Kinematics . . .\nFig2 shows a model of a humanoid robot where E R , C B , P E E R3, RB E 50(3), B p H i E R3 (i = 1,2) , BpLj E R3 ( j = 1,2) denote the reference coordinate system, the coordinate system fixed to the body, the position vector of the origin of Cg with respect to ER, the rotation matrix of C B with respect to -PE, the position vector of the hand with respect to 'Cg, the position vector of the foot with respect to Cg, respectively. pHi and pLj can be given by\n. .\n, .\nBHC (i = 1,2), 0 y ( j = 1,2), I S , and * X denote the joint displacement vectpr of the i th arm, that of the j t h leg, the 3 x 3 identity matrix, and the 3 x 3 skewsymmetric matrix equivalent to the vector product, respectively. 3.2 Statics\nin the humanoid robot is'giveu by , .'\nBy using eq.(3), the relationship of the force acting"
        ]
    },
    {
        "image_filename": "designv11_24_0001474_s0167-8922(08)70580-7-Figure6.10-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001474_s0167-8922(08)70580-7-Figure6.10-1.png",
        "caption": "FIGURE 6.10 Hybrid journal bearing; a) with slots as gas outlets, b) with holes as gas outlets.",
        "texts": [
            " The distinction between a true 'hybrid bearing' and the pressurized lubricant supply to a journal bearing is that in the latter case, the purpose of the extra supply is to supply cool lubricant into the hottest part of the bearing. An important difference between hybrid and hydrostatic bearings is the absence of recesses in the hybrid bearings. Recesses cause reduced hydrodynamic pressures in the loaded parts of the bearing which are where hydrostatic gas or liquid outlets are usually positioned. As discussed previously, lubricant supply outlets are usually located remote from the loaded part of the bearing for efficient hydrodynamic lubrication. An example of a hybrid journal bearing is shown in Figure 6.10. Where several lubricant outlets are used it is important to avoid interconnection of the supply lines. If the supply lines are connected then recirculating flow of lubricant will occur which reduces the hydrodynamic pressure. The basic parameters of these bearings such as pumping power and size are designed as for a hydrostatic bearing and any hydrodynamic effect which improves bearing performance is regarded as a bonus [21. Chapter 6 HYDROSTATIC LUBRICATION 333 6.7 Hydrostatic bearings are subject to vibrational instability particularly under variable loads or where a gas is used as the lubricant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003371_s00170-006-0833-7-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003371_s00170-006-0833-7-Figure4-1.png",
        "caption": "Fig. 4 Right view and isometric view of W",
        "texts": [],
        "surrounding_texts": [
            "rotation of \u03b2 about the Y1 axis and a rotation of 1 about the X2 axis, where Y1 is formed by Ya rotating about Xa by \u03b1 and X2 is formed by X1 rotating about Y1 by 1. Thus, T is expressed as below:\nRB m \u00bc c\u03b2 s\u03b2 s1 s\u03b2 c1 s\u03b1 s\u03b2 c\u03b1 c1 s\u03b1 c\u03b2 s1 c\u03b1 s1 s\u03b1 c\u03b2 c1 c\u03b1 s\u03b2 s\u03b1 c1\u00fe c\u03b1 c\u03b2 s1 s\u03b1 s1\u00fe c\u03b1 c\u03b2 c1\n2 4\n3 5\n\u00bc xl yl zl xm ym zm xn yn zn\n2 4\n3 5\n\u00f08\u00de where s\u03b1=sin \u03b1, c\u03b1=cos \u03b1, s\u03b2=sin \u03b2, c\u03b2=cos \u03b2, s1=sin 1\nand c1=cos 1. Comparing each of the items in Eq. 8, and from Eq. 6c, we obtain:\nxl \u00bc c\u03b2; xm \u00bc s\u03b1 s\u03b2; xn \u00bc c\u03b1 s\u03b2 yl \u00bc s1 s\u03b2; ym \u00bc c\u03b1 c1 s\u03b1 c\u03b2 s1; yn \u00bc s\u03b1 c1\u00fe c\u03b1 c\u03b2 s1 zl \u00bc c1 s\u03b2; zm \u00bc c\u03b1 s1 s\u03b1 c\u03b2 c1; zn \u00bc s\u03b1 s1\u00fe c\u03b1 c\u03b2 c1 Xo \u00bc E Yo\u00f0 \u00dexm xl Zoxn xl \u00bc E Yo\u00f0 \u00des\u03b1 tan \u03b2 \u00fe Zoc\u03b1 tan \u03b2\n\u00f09\u00de From Eqs. 7a\u20137e and 9, ri can be expressed by five pose\nparameters (\u03b1, \u03b2, 1, Yo, Zo).\n3.2 Velocity and Jacobian matrix\nIn solving the inverse velocity problem, the velocity of the active legs can be solved as below [2, 3]:\nve \u00bc Jvr or vrJ 1ve \u00f010a\u00de\nwhere vr is the input velocity vector of ri (i=1,..., 5), \u03bde is the effective velocity vector of the five pose parameters (\u03b1, \u03b2, 1, Yo, Zo) and J is the Jacobian matrix. Their matrices formulae are expressed as follows:\nvr1 vr2 vr3 vr4 vr5\u00f0 \u00deT\n\u00bc J 1 d\u03b1 dt d\u03b2 dt d1 dt dYo dt dZo dt\nT \u00f010b\u00de\nJ 1 \u00bc\n@r1 @\u03b1 @r1 @\u03b2 @r1 @1 @r1 @Yo @r1 @Zo @r2 @\u03b1 @r2 @\u03b2 @r2 @1 @r2 @Yo @r2 @Zo @r3 @\u03b1 @r3 @\u03b2 @r3 @1 @r3 @Yo @r3 @Zo @r4 @\u03b1 @r4 @\u03b2 @r4 @1 @r4 @Yo @r4 @Zo @r5 @\u03b1 @r5 @\u03b2 @r5 @1 @r5 @Yo @r5 @Zo 2 6666664 3 7777775\n\u00f010c\u00de\nEach expression of the items in J\u22121 are given in the Appendix to this paper.\nFrom Eqs. 7a\u20137e, 9 and 10b, each of the partial derivatives in the Jacobian matrix J can be derived.\n4 Reachable workspace\nThe workspace is a critical index for evaluating the characteristics of a parallel manipulator. A reachable workspace W of a parallel manipulator is defined as all poses that can be reached by the centre of the platform m.\nGenerally, a reachable workspace W is formed from the outline of a group of similar surfaces, which are cascaded from a lower boundary surface Sl to an upper boundary surface Su, as shown in Fig. 3. When giving the maximum extension rmax, the minimum extension rmin and the",
            "increment \u03b4r of the active legs ri (i=1,..., 5), W can be constructed. Since the 4SPS+SPR parallel machine tool exhibits plane symmetry in YZ in its structure, its reachable workspace W must be plane symmetric in plane PYZ. Thus, only some sub-workspaces are required to be constructed. Each of them can be constructed by using following procedures:\n1. Set Li=100 cm, li=80 cm, rmax=200 cm, rmin=150 cm, \u03b4r=5 cm and n1=(rmax\u2212rmin)/\u03b4r. 2. Set n1=(rmax\u2212rmin)/\u03b4r, r2=rmin+j\u03b4r, (j=0, 1,..., n1\u22121) and ri=rmax (j=3,..., n). 3. Set j=0 and increase r1 by \u03b4r at each increment step from rmin to rmax. 4. Solve the three position components (Xo, Yo, Zo) of m in {B} by using the automatic solving function of Solidworks and insert them into the simulation mechanism.\n5. Construct a spatial curve c0 by the passing through the XYZ command.\n6. Repeat steps 3\u20135 above, except setting j=1, 2,..., n1, respectively. Thus, the other spatial curves cj are constructed.\n7. Construct the first upper right boundary surface Su1 from n1 curves cj (j=0, 1,..., n1\u22121) by using the loft command.\n8. Similarly, construct three lower left surfaces (Sl1, Sl2, Sl3) by following the processes in Table 1. 9. Construct a composite lower surface Sl from the lower parts of (Sl1, Sl2, Sl3). 10. Construct three right side surfaces (Sf1, Sf2, Sf3), respectively, from the three sidelines of Su1 and the three sidelines of Sl, respectively, by using the loft command.\n11. Construct W1 from Su1, Sl and (Sf1, Sf2, Sf3). 12. Construct plane PYZ in YZ. After that, construct the\nwhole W from W1 by using the mirror command for plane symmetry, as shown in Figs. 3 and 4.\nWhen varying ri in the range from rmin to rmax, many parts of m are located in W. When interferences among ri, m and B occur, we vary some extensions of ri. Thus, a reasonable workspace without interference can be determined.\n5 Active/passive forces\nWhen ignoring the friction of all of the joints in the 4SPS+ SPR parallel manipulator, the working loads include the inertia force/torque due to acceleration, the damping force due to velocity, the gravity of m and the working force/torque.",
            "Generally, these working loads can be simplified as a wrench load (F, T) which is applied onto m at o and is variable with time. (F, T) and its components (FX, FY, FZ, TX, TY, TZ) are balanced by five active forces (Fa1, Fa2..., Fa5) and one passive force Ft. Each of Fai is exerted on and along ri and Ft is exerted on r3 at A3 (see Fig. 5). Generally, the directions of (FX, FY, FZ, TX, TY, TZ) are the same as that of (X, Y, Z) in {B}.\nDuring the movement of the parallel manipulator, the passive force Ft does not do any work. Let \u03bdr3 be a translation velocity along active leg r3. Then there must be Ft\u00b7vr3=0, i.e. Ft\u22a5r3.\nLet R be a unit vector of revolute joint R in r3 and let \u03c1\u00d7Ft be a torque of Ft about R. Since Ft does not do any work, there must be R\u00b7(\u03c1\u00d7Ft)=0. Thus, Ft must be parallel with the axis of revolute joint R, i.e. Ft//x.\nIn order to solve the active/passive forces (Fa1, Fa2..., Fa5, Ft), a set of force/torque balancing equations of the parallel manipulator is yielded as follows:\nX5 i\u00bc1 Fai ri ri \u00fe Ft\u03c4 \u00bc F Fa1e1 r1 r1 \u00fe Fa2e1 r2 r2 \u00fe Fa3e2 r3 r3\n\u00fe Fa4e3 r4 r4 \u00fe Fa5e3 r5 r5 \u00fe Ft\u03c1 \u03c4 \u00bc T\n\u00f011\u00de\nwhere ei=o B\u2212aiB (i=1, 2, 3), \u03c1=oB\u2212A3 B, t is a unit vector of F\u03c4 and t=x. From Eqs. 3\u20135, they are derived as below:\nr1 \u00bc 1\n4\naexl eyl \u00fe 2Xo 2Es2\u03b8\naexm eym \u00fe 2Yo \u00fe 2Ec2\u03b8\naexn eyn \u00fe 2Zo\n8>< >:\n9>= >;;\nr2 \u00bc 1\n4\naexl eyl \u00fe 2Xo 2Ec\u03b8\naexm eym \u00fe 2Yo 2Es\u03b8\naexn eyn \u00fe 2Zo\n8>< >:\n9>= >;;\nr3 \u00bc eyl \u00fe Xo eym \u00fe Yo E eyn \u00fe Zo\u00f0 \u00deT\nr4 \u00bc 1\n4\naexl eyl \u00fe 2Xo \u00fe 2Ec\u03b8\naexm eym \u00fe 2Yo 2Es\u03b8\naexn eyn \u00fe 2Zo\n8>< >:\n9>= >;;\nr5 \u00bc 1\n4\naexl eyl \u00fe 2Xo \u00fe 2Es2\u03b8\naexm eym \u00fe 2Yo \u00fe 2Ec2\u03b8\naexn eyn \u00fe 2Zo\n8>< >:\n9>= >;\ne1 \u00bc e\n2\naxl yl\naxm ym axn yn\n8>< >:\n9>= >;; e2 \u00bc e yl\nym yn\n8>< >: 9>= >;;\ne3 \u00bc e\n2 axl \u00fe yl axm \u00fe ym axn \u00fe yn 8>< >: 9>= >;\n\u03c1 \u00bc E Y0\u00f0 \u00des\u03b1 tan \u03b2 \u00fe Zoc\u03b1 tan \u03b2\nYo E\nZo\n8>< >:\n9>= >;;\n\u03c4 \u00bc x \u00bc xl xm xn 8>< >: 9>= >;\n\u00f012\u00de\nFrom Eq. 9, these vectors in Eq. 12 can be expressed by five pose parameters (\u03b1, \u03b2, 1, Yo, Zo).\nEquation 11 can be transformed into a single equation as follows:\nGf Fa1; Fa2 . . . ; Fa5; F\u03c4\u00f0 \u00deT \u00bc F T\u00f0 \u00deT \u00f013\u00de\nwhere Gf is defined as an active/passive force transformation matrix of dimension 6\u00d76. Its formula is expressed as below:\nGf \u00bc r1 r1\nr2 r2\nr3 r3\nr4 r4\nr5 r5\nx e1 r1\nr1 e1 r2 r2 e2 r3 r3 e3 r4 r4 e3 r5 r5 \u03c1 x 6 6\n\u00f014\u00de Thus, a formula for solving the active/passive forces\n(Fa1, Fa2..., Fa5, Ft) is expressed as below:\nFa1;Fa2; . . . ; Fa5; F\u03c4\u00f0 \u00deT \u00bc G 1 f F T\u00f0 \u00deT \u00f015\u00deFig. 5 Force situation of the 4SPS+SPR parallel manipulator"
        ]
    },
    {
        "image_filename": "designv11_24_0003165_j.aap.2006.04.023-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003165_j.aap.2006.04.023-Figure1-1.png",
        "caption": "Fig. 1. Forces acting on car braking downhill.",
        "texts": [
            " Furthermore, the golf car indusry and golf course designers should work together to establish maximum allowable incline slope for both golf cars and golf ar paths as well as recommended minimum path turn radii for arious incline slopes. It is difficult to quantify the effect of these recommendations n actual occurrence of golf car accidents, as this requires extenive accident data for cars with different brake configurations, hich is not available at this time. However, it stands to reaon that improved braking effectiveness and yaw stability has he potential to significantly reduce the occurrence of golf car ccidents on steep downhill slopes. ppendix A Description of mathematical symbols used in Fig. 1 and Eqs. 1)\u2013(3): downhill slope of driving surface total vehicle mass acceleration of gravity horizontal distance from front axle to loaded vehicle CG horizontal distance from rear axle to loaded vehicle CG height of loaded vehicle CG above ground F combined normal force on both front axle tires Y Y and Prevention 38 (2006) 1151\u20131156 R combined normal force on both rear axle tires F combined longitudinal friction force on both front axle tires R combined longitudinal friction force on both rear axle tires F coefficient of friction applied to each front tire R coefficient of friction applied to each rear tire 2x\u2032/dt2 vehicle acceleration downhill parallel to driving sur- face eferences llen, R"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003371_s00170-006-0833-7-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003371_s00170-006-0833-7-Figure3-1.png",
        "caption": "Fig. 3 Front view and top view of reachable workspace W",
        "texts": [
            " 7a\u20137e, 9 and 10b, each of the partial derivatives in the Jacobian matrix J can be derived. 4 Reachable workspace The workspace is a critical index for evaluating the characteristics of a parallel manipulator. A reachable workspace W of a parallel manipulator is defined as all poses that can be reached by the centre of the platform m. Generally, a reachable workspace W is formed from the outline of a group of similar surfaces, which are cascaded from a lower boundary surface Sl to an upper boundary surface Su, as shown in Fig. 3. When giving the maximum extension rmax, the minimum extension rmin and the increment \u03b4r of the active legs ri (i=1,..., 5), W can be constructed. Since the 4SPS+SPR parallel machine tool exhibits plane symmetry in YZ in its structure, its reachable workspace W must be plane symmetric in plane PYZ. Thus, only some sub-workspaces are required to be constructed. Each of them can be constructed by using following procedures: 1. Set Li=100 cm, li=80 cm, rmax=200 cm, rmin=150 cm, \u03b4r=5 cm and n1=(rmax\u2212rmin)/\u03b4r"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001914_rob.10048-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001914_rob.10048-Figure6-1.png",
        "caption": "Figure 6. The modified vector loop formulation.",
        "texts": [
            " The geometricmass center of the systemwith respect to the origin of the moving frame can be obtained from: rC \u2032 = 1 6 6\u2211 i=1 ri (10) Furthermore, the directions of the resultant force and the resultant moment about the mass center can be evaluated respectively as: uF = \u22116 i=1 Fi\u2225\u2225\u2225\u22116 i=1 Fi \u2225\u2225\u2225 (11) and uM = \u22116 i=1 r \u2032 i \u00d7 Fi\u2225\u2225\u2225\u22116 i=1 r \u2032 i \u00d7 Fi \u2225\u2225\u2225 (12) where r \u2032 i = ri\u2212rc\u2032 and \u2016\u2022\u2016 indicate theEuclideannorm of a vector. With these equations in mind, one can see that the configuration error can be reduced effectively by translating the moving platform along uF , and simultaneously rotating it aboutuM. Theproblemthen is to find the optimal amount of translation and rotation to minimize the objective function (8). As shown in Figure 6, after the translation and the rotation, the vector representation of the limbs becomes: Li = PC \u2032 + suF + [R(uM, \u03c6)]r \u2032 i \u2212 Bi (13) where, given PC \u2032 = PC + rC \u2032 , s is the distance of the translation, and [R(uM, \u03c6)] is the 3 \u00d7 3 spatial rotation matrix, in which \u03c6 is the rotation angle about the uM axis. By taking the square of the Euclidean norm of both sides of Eq. (13), and then substituting the half angle formulae cos\u03c6 = (1 \u2212 t2)/(1 + t2) and sin\u03c6 = 2t/(1+ t2), where t = tan(\u03c6/2), into the resulting equation, after combining and simplifying terms, one obtains: l2i = s2+A1t2+A2s2t2+A3st2+A4st+A5s+A6t+A7 1+ t2 (14) where Ai (i = 1 to 7) are constant coefficients which can be calculated from the current values of PC , uF , uM, Bi , and ri "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003090_iembs.2006.259233-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003090_iembs.2006.259233-Figure2-1.png",
        "caption": "Figure 2. 3D model of slave manipulators attached with the endoscope",
        "texts": [
            " OVERALL ROBOTIC SYSTEM Figure 1 shows the proposed system layout whereby the endoscopist work on the master console while gathering visual feedback from the endoscope. A computer console will interpret the readings from the master console that will in turn give instruction to the slave robotic system to perform the treatment to the patient. This system allows complicated treatment to be performed with the added benefit of easy and intuitive control for the endoscopist. III. THE SLAVE MANIPULATOR The 3D model of the intended slave manipulator can be seen in Fig 2. In order for the surgeon to perform the necessary dexterous actions, the slave manipulators should possess a high number of Degrees of Freedom (DOF). The emphasis of the 1-4244-0033-3/06/$20.00 \u00a92006 IEEE. 3850 project is to make the slave manipulator to be as intuitive to control as possible. As such, the DOF and joints of the slave manipulator are modeled after a simplified human arm as shown in Fig 3. Altogether there are 5 DOF for positioning of the slave and an extra DOF for manipulating the end effector and the axis or rotation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003205_020-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003205_020-Figure1-1.png",
        "caption": "Figure 1.",
        "texts": [
            " A discussion of the optimal shape of the cylinder is given. Consider a cylinder of length L, radius R and density p. We shall consider the attraction at any arbitrary point, but for the convenience of the derivation, a point P in the base plane of the cylinder is first considered. Take Cartesian coordinates with the x axis through point P. Let a be the radial distance of P from the centre line of the cylinder, so that the radial gravitational force due to the cylinder on the unit mass at the point P will be, (figure 1). On differentiating with respect to variable a and integrating with respect to z and x , we find FL1) 2Gp(-I1+ 1 2 ) ( 2 ) where I I and I2 are ) dy L + (L2 + R2+ a 2 + 2 a J R 2 - y2) ' I2 L + (L2 + R2+ a2 - 2 a J R ' - yi)''2 11 = jo In ( 1 R 2 + a 2 + 2 a J R 2 - y 2 2 R 2 + a 2 - 2 a J R 2 - y i In ( (3) (4) The radial Newtonian gravitational force 1593 Although there is only one variable in equation (3) , two variables were used in the following transformation ) \u2018 I 2 [ = 1 + l+- +L2 J i - y 2 / ~ I ( R\u2019L:a2 2aR 1 / 2 Thus tZ [ B 2 -A2 + 2 A ( 5 - 1 ) 2 - (6 - 1)4]\u2019 /2 5 d5 I1 = I,, - 12 [ B 2 -A2 + 2A(r , - 1)\u2019- (77 - 1 ) 4 ] 1 / 2 d77 +I,, 77 where and A = 1 + ( R 2 + a 2 ) / L 2 5 1 = l + ( A + B ) \u2019 / 2 t2= 1 +A\u2019/\u2019 t71 = 1 - ( A - B)\u2019/\u2019 B = 2Ra/L2 772 =l+A\u2019 / \u2019 ",
            " I 1 = j 1 + J ( A - B ) t L2 x { [ 1 + 2 R 2 + a 2 7 J 1 + [ ( R - a ) / L I 2 x ( J 1 + [ ( R + a) /LI2+-) R 2 + a 2 L ] K ( k ) 1 1-41 + [ ( R - a ) / L J 2 +2 - ( R +a)\u2018 J 1 + [ ( R - a ) / L ] Z , ( , ~ , r , 2 , k ) ] + I o L2 1594 A H Cook and Y T Chen where Io = { :R2\u20192a 5 rra Ja + [ ( a + R ) / L ] * - - d l + [ ( a - R ) / L ] * J 1 + [ (a + R ) / L ] Z + J l + [ ( a - R ) / L I 2 when a 3 R when a s R k = 1 - J 1 + [ ( a - R) /LI2 l + J l + [ ( a + R ) / L ] \u201d f f 2 = K ( k ) , E ( k ) , ll($.rr, k , k ) and I I ($rr , a2, k ) are the elliptical integrals of the first, Equation ( 9 ) is the formula for the point in the end plane of the cylinder but with the ( 1 1 ) where L is the length of the cylinder and [ is the distance of the point Q from the end plane of the cylinder as shown in figure 1 . In Heyl\u2019s experiment, the test mass was in the middle plane of the cylinder (see figure 2 ) so the attraction, according to equation ( 1 1 ) is ( 1 2 ) If ( < 0 in figure 1 , according to the superposition principle, equation ( 1 1 ) will become second and third kind respectively. superposition principle of gravitation the formula for an arbitrary point is F ~ / ~ G P = Cy( L - l, R, a 1 + Cy(l, R, a 1 FL2\u2019 = 2FL\u201d = 4GpCy(tL, R , a) . Fa/2Gp=Cy(L+IlI ,R, a ) - C y ( l l l , R , a ) . ( 1 3 ) The radial Newtonian gravitational force of any complex co-axial cylinders will not be difficult to obtain from the following sum Heyl measured the period of the torsional pendulum in the near position and far position from a pair of cylinders (see figure 2 ) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000348_1.3101835-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000348_1.3101835-Figure3-1.png",
        "caption": "Fig 3. Skin friction gage for hot, high-speed flows (from DeTurris, Schetz and Hellbaum, 1990).",
        "texts": [
            " Our own studies and those of others have shown this to be a very important matter. Fourth, flows of this type generally involve multiple shocks, and they almost always feature strong 3D patterns. At the same time, high-speed flows usually have higher wall shears, so the floating head can be made considerably smaller. A design successfully used in a Math 3 flow with an incoming air total temperature of 1667 K and hydrogen injection and burning (DeTurris, Schetz and Hellbaum (1990)) is shown in Fig. 3. The floating head is made of the same material and thickness as the surrounding wall to match the local thermal behavior, and the unit is thermally protected by water cooling around the housing. The liquid filling the housing now plays the I i 0.000 Fig 3. O Streamwise Axis / ~ O Cross-stream Axis / D [2 D O O i i i i i r 0 2 4 6 8 10 F o r c e ( g r a m s = N / 9 8 0 0 ) r I l I l 0.005 0.010 0 .0 ;5 0.020 Force (Ibs) 4. Sample calibration curve for the gage shown in Fig. Downloaded From: http://appliedmechanicsreviews.asmedigitalcollection.asme.org/ on 01/30/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use Appl Mech Rev vo150, no 11, part 2, November 1997 important additional role of an efficient heat transfer medium. The fins on the support arm are for the same purpose"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003775_1.2748448-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003775_1.2748448-Figure4-1.png",
        "caption": "Fig. 4 Relative location of pinion and gear",
        "texts": [
            " 3 a . We shall construct the pinion tooth surface hat has only one point of contact with the gear tooth surface at ny phase of engagement. To find the gear considering position e require that in the moment, when the surfaces are in contact at he considering gear tooth surface point, the instantaneous gear atio m21 is equal to its nominal value m21 0 2 = z 1 /z 2 15 hich equals to ratio of pinion tooth number to gear tooth number. e propose that P 2 is located at the point P of immovable space Fig. 4 that is defined by the polar angle 0 2 . We shall consider the process of engagement in an arbitrarily 52 / Vol. 129, SEPTEMBER 2007 om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 08/07/201 located and orientated in space immovable assembly system Oaxayaza Fig. 4 . We place gear and pinion pitch cone apexes at the origin Oa. Then we superpose z-axis of the gear and the pinion systems Oxyz with za-axis. After that we turn the pinion z-axis around the point Oa in plane xaza through an angle and turn the gear through an angle 0 2 about the gear axis of rotation. In distinction to the gear, the pinion teeth are not generated yet. On the termination of the above described process of transmission assembly we shall consider all the introduced coordinate systems as immovable. The angular velocities 1 , 2 of a pinion and a gear rotation about their axis are not arbitrary. The projection of absolute velocity of point P 1 and the projection of absolute velocity of point P 2 on common normal t to tooth surfaces at a point of tangency are to be equal 1 rp,t = 2 rp,t 16 where 1 = 1 e 1 , 2 = 2 e 2 . Here rp is a vector drawn from point Oa to point P, and e 1 , e 2 are the unit vectors directed along the gear axis of rotation Fig. 4 . We note that in relation 16 the gear tooth surface normal t is considered as the common normal. If the machine-tool settings are known, one can determine this normal and vector rp as functions of 0 2 by solving system 9 , applying of relations 10 , and transforming components of these vectors from gear system Oxyz to system Oaxayaza. Condition of gear and pinion tooth surface tangency in point P is not considered yet. Relation 16 with regard that m21= 2 / 1 and rp is the point P vector in system Oaxayaza with known components makes it possible to compute the left side of Eq. 15 . Equation 15 does not depend on pinion tooth surface. The equation is solved using a numerical technique. After that the spherical coordinates latitude p 1 and longitude 0 1 Fig. 4 of point P are determined as p 1 = arcos rp,e 1 Lp ; 0 1 = arcsin sin p 2 sin 0 2 sin p 1 17 4.2 Conditions of Tangency of Gear Tooth Surfaces. Conditions of tangency of pinion and gear surfaces at point P are presented in the form Transactions of the ASME 7 Terms of Use: http://www.asme.org/about-asme/terms-of-use U c b s f i i i f w i p E c b a a t m T a N n n p p p i t t d s t S t b T c J Downloaded Fr f1 U,i, A, E = t 1 ,u 2 = 0 f2 U,i, A, E = t 1 ,v 2 = 0 18 nit vectors u 1 , v 1 , t 1 and u 2 , v 2 , t 2 of pinion and gear oordinate systems are constructed identically using relations 8 \u2013 11 ",
            " 9 Instantaneous contact area \u201eto the top\u2026 and the distriution of maximal major principal tensile stress along the gear ooth 58 / Vol. 129, SEPTEMBER 2007 om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 08/07/201 Mk matrices of coordinate transformation, corresponding to rotation about axis k=x ,y ,z about angle P a point of tooth surface Fig. 2 P n n=1,2 considering point of pinion n=1 or gear n=2 tooth surface Fig. 3 R mean pitch radius R0 ,Rc average tool radius and tool point radius U radial distance b face width Fig. 3 e n unit vector directed along pinion n=1 or gear n=2 axis of rotation Fig. 4 i velocity ratio a cradle angular velocity over a blank angular velocity km coefficient of modified roll m21 1 gear ratio in phase of engagement 1 mn mean normal module q installment angle for tool Fig. 1 r position vector in a coordinate system rigidly connected with a blank t n coefficients of Taylor series expansions of pinion n=1 or gear 2 t-coordinate of tooth surface, determined in own coordinate system =u ,v , ; =u ,v t * 1 coefficients of Taylor series expansion of pinion tooth surface t-coordinate that are defined in gear coordinate system =u ,v , ; =u ,v u ,v , t unit vectors of coordinate system Puvt Fig",
            " 3 along a tooth line and along a pitch cone normal the function of machine-tool settings that describes a difference of current pinion tooth surface from desired one 1 , 2 the functions of machine-tool settings that define lack of coincidence of normals to gear and pinion tooth surfaces at considering point 3 the function of machine-tool settings that characterize difference of current and desired contact path directions matrix of transformation from pinion u 1 v 1 t 1 system to to gear u 2 v 2 t 2 system * matrix of transformation from pinion Oxyz- system to gear Oxyz-system shaft angle Fig. 4 tool pressure angle n , n desired gear pressure angle and spiral angle Fig. 2 n * , n * pressure angle and spiral angle, considered as functions of machine-tool settings , f pitch angle and root angle Fig. 3 p polar angle that define the point P Fig. 2 t distance between mating tooth surfaces along t 2 axis p depth of painter coating in the process of testing , polar angle and cone distance of a point of generating surface angle of contact path inclination Fig. 3 n angle of rotation of the pinion n=1 or the gear n=2 with respect to considering position in the process of meshing 0 n polar angle that define pinion n=1 or gear n =2 considering point Fig. 4 ournal of Mechanical Design om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 08/07/201 current cradle angle in the process of generation p cradle angle in the moment when a generating surface is tangent to it\u2019s envelope at the point P n angular velocities of a pinion n=1 and a gear n=2 References 1 Litvin, F. L., and Fuentes, A., 2004, Gear Geometry and Applied Theory, Cambridge University Press, Cambridge, UK, 800. 2 Argyris, J., Fuentes, A., and Litvin, F. L., 2002, \u201cComputerized Integrated Approach for Design and Stress Analysis of Spiral Bevel Gears,\u201d Comput"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003032_s1474-6670(17)55336-7-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003032_s1474-6670(17)55336-7-Figure1-1.png",
        "caption": "Fig . 1. I llus t rat i on of t he dr iv i ng - axis coordina t e sys t em.",
        "texts": [
            " The coordinate transformation from frame i-1 to i can be obtained by 4 steps: 1) translating b~ along xi-1' 2) rotating f3 i about xi-1' 3) translating di along zi' 4) rotating 8 i about zi' The two steps in the first or last pair can be exchanged. The representation with the homogeneous transformation matrix (Paul, 1981) is i-1 ~i = ~(bi, 0, 0) ~(~, Ei) ~(O, 0, di) ~(~, ei) o 0 bi 1 0 0 0 o cosEi -sinf3i 0 r1 000 1 0 1 00 o 0 1 di 0001 [ COSei -sin8i 0 0] cosei 0 0 010 DRIVING-AXIS COORDINATE SYSTll1 o 1 00 001 0 0001 According to motion phenomenon we set a body-fixed frame on every driving axis, i.e. a rotational axis for a revolute joint or a translational axis for a prismatic joint (Fig. 1). For two adjacent connected links the driving axis of the outer link is even the transmitting axis of the inner link. The z-direction of the frame is coincident with the driving axis (e.g. zi = qi)' The x-direction is the direction from the driving axis to the transmitting axis along the common normal of them, if they do not intersect each other. The origin is then at the intersecting point of the driving axis and the common normal (e.g. in link i-1, xi-1 is the common normal of the driving axis, zi_1' and the transmitting axiS, zi; 0i-1 is the origin)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002175_1.1515333-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002175_1.1515333-Figure3-1.png",
        "caption": "Fig. 3 Force analysis of rotating tine",
        "texts": [
            " Assuming that the tines do not interact, the overall force on the brush is the sum of the forces on the tines. When the brush is rotating on a flat plane then all the tines will experience the same forces, providing an equal effect on the brush. Therefore, ignoring inertial effects, an analysis of a single tine may be extrapolated to give the response of the complete brush under these conditions. Ignoring the weight of the tines, the deflection at any given tine is due to the vertical applied axial load Ft and the centrifugal forces Fc acting along the length of the tine ~Fig. 3!. Applying d\u2019Lamberts principle to the rotating tine, from Fig. 3 the free body diagram ~Fig. 4! may be drawn. The problem now becomes a 2-D pseudo-static cantilever beam problem. It is also expected that the brushes will be experiencing large deflections along the length of the tine. Hence from large scale deflection theory \u2018\u2018the bending moment in the bar is equal to the flexural rigidity times the curvature.\u2019\u2019 @8# or: du ds 5 M EI (1) Since the applied vertical load has a point contact it is straightforward to analyze. However, the effect of the centrifugal force is dependent on the tine deflection and the brush rotational speed v: q~s !5M tR~s !v2 (2) It follows that the instantaneous centrifugal force cannot be calculated without knowing the brush profile while the brush profile cannot be analyzed without knowing the applied forces. 676 \u00d5 Vol. 124, DECEMBER 2002 rom: http://dynamicsystems.asmedigitalcollection.asme.org/ on 08/16/201 Nevertheless, from Fig. 3 it is clear that the deflection of the tines of a rotating brush are independent of the friction between the brush and the surface. By definition @9# the friction acts along the line of the motion of the end of a given tine. But with the brush rotating flat on the test surface, and deflecting only in the weakest plane, under steady state conditions the end of the tines are going to follow a circle. Hence at any given point the friction is going to be acting at a tangent to the end of the tine. Friction is, however, directly related to the driving torque required to rotate the brush, where the torque acting on any one tine is: TB5RtmFt (3) From this it is clear that the torque is dependent on the load and the contact point of the tine, both of which are directly related to the deflection profile of the tine",
            " Tines R2 5 768 Tine Mount, f 5 26 deg Other materials constants were taken from referenced sources @12# for mild steel: Density, r 5 7850 kgm23 Youngs Modulus, E 5 207 GNm22 678 \u00d5 Vol. 124, DECEMBER 2002 rom: http://dynamicsystems.asmedigitalcollection.asme.org/ on 08/16/201 The following charts represent test results for a typical large diameter cutting brush made of hardened tempered steel tines deflected against test plates of oil lubricated steel and also motorway grade concrete. The theoretical results have been generated using referenced materials data and from measurements taken directly from sample tines. Brush penetration is defined by D in Fig. 3. Ft , the load required to deflect the brush, is the axial load only and is measured by a load cell connecting the brush to the linear drive. The torque is measured by a non-contact torque sensor mounted as close to the brush as possible. In Fig. 10 the practical results for the test brush loaded against an oil lubricated mild steel test plate are shown with a solid line. Theoretical results are superimposed over the chart ~dashed lines! to help in the interpretation. Additional tests have been undertaken on a concrete test surface ~Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002942_6.2004-5008-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002942_6.2004-5008-Figure2-1.png",
        "caption": "Figure 2: Schematic of NFTP.",
        "texts": [
            " In section 4, we describe a current flying test platform system under development and outline its simulation-based performance assessment and comparison with a similar vehicle not using momentum exchange devices. Section 5 provides conclusions. To derive the equations of motion for a generic NFTP system1, a Newton-Euler formulation is used, and in particular, the sequence of formulation and notation found in [7], and extended to multiple gimbaled spinning bodies with vane rotational motion for vector thrusting. Only a summary of the results are given here and the interested reader is referred to [8] for details. Figure 2 shows a schematic of the NFTP describing its main components. 1\u201cGeneric\u201d in the sense of a flying platform propelled by multiple ducted-fan and vane system and augmented with multiple wheel system R Rigid platform Fi i-th Fan: Propeller(Pi) + Motor(Mi) Ci i-th CMG: Wheel(Wi) + Gimbal(Gi) B Momentum wheel, centered at Ob Ob origin of platform fixed axes Oc c/m of system (S = R+ \u2211 i(Fi + Ci) +B) Ocb c/m of R OFi origin of i-th ducted fan subsystem axes OGi origin of i-th CMG frame Let \u03c9si a\u0302i, \u2126B z\u0302, and \u03b7\u0307ig\u0302i, denote the relative angular velocities of the ith fan, momentum wheel, and the gimbal system relative to platform, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000861_177424.177987-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000861_177424.177987-Figure5-1.png",
        "caption": "Figure 5: A reduced form",
        "texts": [
            " (If the supporting lines are parallel, we drop the centering requirement.) In the remainder of the elimination process, the disk translates along with the intersection of the supporting lines, acting like a finite-size vertex. Because the disk and its contents are infinitesimal, we are sure that no translating edge touches the disk unless it also touches the corresponding vertex in the original edge elimination process. The infinitesimal edge is hidden inside the disk and does not participate directly in the remainder of the elimination process. See Figure 5. When the edge elimination process terminates, the reduced form of the polygon consists of a triangle with some microstructure at its vertices. Each vertex is contained in a disk, and the three disks are disjoint. If we look inside a disk, we see two infinite edges\u2014the ones that cross the disk boundary\u2014and a single finite edge joining them. The vertices where the finite edge joins the infinite edges have microstructure themselves: they are contained inside smaller disks that are disjoint from each other and completely inside the surrounding disk; each smaller disk contains recursively similar structures"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002252_physreve.67.041715-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002252_physreve.67.041715-Figure5-1.png",
        "caption": "FIG. 5. The geometry of the p cell and its microphotographs: ~a! a simulated structure, ~b! at 2 V, ~c! at 4 V, ~d! at 6 V.",
        "texts": [
            " Defects will necessarily be associated with the transition between the topologically inequivalent splay and bend states. In addition, the patternedelectrode cell applies a nonuniform electric field to the director field, which will affect the nucleation of defects. 04171 Therefore, in order to improve the electro-optical characteristics, it is very important to model director configurations with defects in the patterned p cell. For the experimental observation, we prepared a twodimensional periodic patterned p cell for the experiment. Figure 5~a! shows the geometry of the p cell for the calculation. The LC material used here is ZLI-1565 where K11 is 14.4 pN, K22 is 6.9 pN, K33 is 10.7 pN, \u00ab i is 10.7, \u00ab' is 3.7, q0 is 0, and the cell gap is 10 mm. Figures 5~b!\u20135~d! show photographs of the cell. Here, crossed polarizers are used for the observation. Figure 5~b! shows the photograph when lower voltage that is less than the transition voltage is applied. The LC directors which are inside the electrode begin to tilt toward the z direction, so that we can recognize the variation of the retardation of the cell. As we apply the higher voltage, a defect S is observed. Figure 5~c! shows the generation of the defect in the p cell. If we apply higher voltage than Fig. 5~c!, we can observe the movement of the defect to the edge of the electrode. The movement direction is dependent on rubbing direction. Figure 5~d! shows the moved defect in the patterned p cell. In considering to proceed with the calculations, we expect from experimental observations that the spatial region where the order parameter varies from its bulk value will be quite 5-5 small, possibly of the order of molecular dimensions. This means that for the real system to be modeled accurately, we will need to have grid points in the vicinity of a defect spaced at approximate molecular dimensions. To be able to model a pixel that is 10 mm wide and in a cell that has a 10-mm cell gap would require '13106 grid points if a uniform grid spacing is used",
            " However, if we consider the cell thickness of our experimental cell, we are not able to consider grid points spaced as tightly as in Fig. 6~c!. Therefore we will reduce the values of A1 \u2013 A4 to be 0.01, the values found for A1 0 \u2013 A4 0. In this case the defect nucleation and motion are expected to be similar to those which would be observed, but the region of defect size will be much larger ~a factor of '100! than could actually occur. Figure 7 shows the change of the order parameter S in the patterned p cell of Fig. 5 as the applied voltage is changed. We assumed hard anchoring energy at the surface of the cell, so that the order parameter S at the surface is always higher than in the bulk of the cell. Figure 7~b! shows the variation of the order parameter S at 2 V. On the center of the electrode, a wall is formed. In Fig. 7~c!, we can confirm that a pair of defects is generated on the surface of the electrode. The order parameter S of those positions is reduced by around 0 and it implies that topologically inequivalent phase transition between splay and bend begins at the center point in the electrode. In terms of these phenomena, de Gennes predicted the transition of a reverse-tilt wall to a pair of disclination lines. Higher voltage makes the pair of defect move to the edge of the electrode like Figs. 7~d! and 7~e!. This movement is exactly coincident with the physical phenomenon in Fig. 5~c!. Figure 8 shows the calculated director configuration of the patterned p cell in Fig. 5. In this figure the length of the 04171 cylinders is proportional to the amplitude of S, and the orientation of the cylinders gives the director orientation. From the figures, we can understand the generation of the defect pair. If the anchoring energy was very low, the defect pair would be expected to form from the region of high elastic distortion in center of the cell @the outlined area in Fig. 8~a!#. After nucleation, the movement of the pair of defects toward opposite surfaces will lower the elastic energy of the cell"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003529_gt2004-53611-Figure9-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003529_gt2004-53611-Figure9-1.png",
        "caption": "Fig. 9 Equivalent foil structural stiffness model",
        "texts": [
            " The analytical procedure to determine the FB structural stiffness relies on the assembly of reaction forces produced by individual bumps to balance an external load. The bump reaction forces depend of its material properties and geometry; and on its local deflection (\u03b6) which depends on the rotor displacement (X), nominal clearance (Cnom) and assembly Downloaded From: http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ashx?u preload (r). The model regards the bumps as individual spring like elements, as shown in Figure 9, whose stiffnesses are calculated using Iordanoff\u2019s formula [6]. This reference details the model including the effects of dry friction effects. Appendix B presents the formula for prediction of the entire FB structural stiffness. In conducting the predictions, the bump pitch (p) is regarded as constant and the interaction between bumps is neglected. The FB structural stiffness model is sensitive to the bump dimensions, material parameters, attachment and disposition. The influence of these parameters was evaluated to assure the reliability of the analytical predictions to the present test results"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001914_rob.10048-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001914_rob.10048-Figure1-1.png",
        "caption": "Figure 1. Classification of fully parallel, linearly actuated platform manipulators: (a) S-type LAP, (b) H-type LAP.",
        "texts": [
            " It should, however, be pointed out that although theCCD-NRalgorithmcanbe systematically applied tovirtually all typesofmulti-loopmechanisms, it would become cumbersome when dealing with the fully parallel, linearly actuated, platformtype manipulators, such as the Stewart platform10 or theHexaglide.11 This is becausemost of thedependent joint variables to be adjusted in the CCD phase can be eliminated, and the computation of the Jacobian matrix in the NR phase can be largely simplified, due to the geometric characteristics of these manipulators. In general, the kinematic structure of the fully parallel, linearly actuated platform (LAP) manipulators can be classified into two types. Their schematic diagrams are shown in Figure 1. Both types consist of a moving platform, six limbs, and a base. The end- effector is attached rigidly to the moving platform, and the two ends of each limb are respectively connected to the moving platform and the base through ball-and-socket joint and Hooke type universal joint. For the general configuration, the locations of the joints at the platform and the base are not coplanar. As shown in Figure 1(a), the limb lengths of the first type can be varied to change the pose of the moving platform. This type represents the generalized structure of the Stewart platform, and hence it is referred to as the S-type LAP in this article. The limb lengths of the second type cannot be varied, but the lower end of each limb is attached to a slider that can be slid along a rail fixed on the base to change the configuration of the moving platform, as shown in Figure 1(b). This type resembles the generalized structure of the Hexaglide, and henceforth will be referred to as the H-type LAP. The direct kinematics problem is to find the possible configurations of the moving platform for given driving joint variables, such as the limb lengths of the S-type LAP or the absolute slider positions of the H-type LAP.A newnumericalmethod for solving this problem is developed in this article. Similar to the CCD-NR algorithm, the presentedmethod consists of two stages. In the first stage, the limbs are considered as linear springs, such that they will exert unbalanced forces on the moving platform if the kinematic loops are not closed correctly"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000771_0890-6955(93)90096-d-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000771_0890-6955(93)90096-d-Figure1-1.png",
        "caption": "FIG. 1. Machine set-up for hob relief grinding with a dished-type grinding wheel.",
        "texts": [
            " To maintain the precision possessed by the new hob, the relief grinding must ensure an unchanged profile along the active part of the hob teeth. This requirement can be achieved only by using the correct set-up of the relief grinding machine. In this study, the calculation of the optimal values for the setting angles of the grinding wheel axis is presented, which ensure an almost unchangeable profile along the active part of hob teeth. 2. THEORETICAL BACKGROUND The helical generator surface of the hob with circular axial profile (Fig. 1) is defined by the following equation: Worm Gear Manufacturing Hob 617 F rh\" cosO 1 '(\"h)(rh'O ) = / rh \"sinO i LZa+khOl (1) where: k h = rOh\" tgO,}Oh sin v = za = Zp- (qo -P\" cosy). rob + P o - rh For tooth flank AB, Zp = 1; for flank CD, Zp = - 1 . The cutting edge of the hob teeth is the intersection curve of the generator and helical tooth face surfaces. It is given by the equation: r(h~)(rh) = r h \u2022 COS~e r , . s in% Za W kh \" 4e 1 (2) where: kh \u2022 ~ h - - Z a - - Z a o ~ = Oe-O~o+~ Oe - ktf+kh Oeo = ktf+kh h ktf = roh- costgtOoh sin B = - - rob ~h = ~OhO--~0h ,=arc sin(r\u00b0 ",
            " The normal vector of the hob tooth flank is defined by the equation: n(h h) = k h \u2022 a s inO-c . (Pv\" s inO+b, cosO) 1 / --kh\" a- cosO+c \u2022 (pv- cosO-b \u2022 s in~)] / a.b J (4) where: doe a = 1--p~. drh b = rh+p\" (O-dAe) drh ktf+kh kh\" + tgv c - dza drh Zp- tgv 618 V. SIMON d~h _ reh sin7 drh ~ COS(T+~0h) \" The term Pv is the variable relief grinding parameter. 2.2. Grinding wheel profile for hob relief grinding The geometry and kinematics of the relief grinding set-up for the conical or dishedtype grinding wheel are given in Fig. 1, and for the pencil-type grinding wheel in Fig. 2. The setting angles are \"r and ~ for the conical or dished-type grinding wheel, while tilt angle, ,rp, is used in the case of the pencil-type grinding wheel. The relative motion of the hob to the grinding wheel consists of the helical motion (with angular velocity and axial velocity k h ~ ) , and their radial approach of velocity pt~. The calculation of the grinding wheel profile for hob relief grinding is based on two conditions. (1) The normal vector of the hob tooth flank at the point of the processed cutting edge must intersect the grinding wheel axis, This condition is expressed by the equation: c ",
            " ( s ) (2) The normal vector of the hob tooth flank at the same point must be perpendicular to the relative velocity vector of the grinding wheel to the hob. Mathematically, this is given by: (,,h) (h) = O. (6) v h \u2022 n h Worm Gear Manufacturing Hob 619 The velocity vector of the relative motion of the grinding wheel to the hob is defined by the following equation: r r~)2)-P~\" c\u00b0s6 \" v~ g'h) =o~. /--r~h~).+p~. sin6 L - -kh (7) COS0t r where px = p cos(8-ar )\" 2.2.1. The profile of the conical or dished-type grinding wheel. In the case of hob tooth-relief grinding by conical or dished-type grinding wheels (Fig. 1), the coordinate transformation from system Kh (attached to the hob) into systems K s (attached to the grinding wheel) is performed by the equation: rg = M~)rh (8) where: (h~ ) ~-- m l l m12 m13 m14 m21 m22 m23 m24 m31 m32 m33 m34 0 0 0 1 m n = cos~l, cos6-s in r , sinTi, sin6 m12 = --COS~q \u2022 sin6--sinx\" sin~l \u2022 COS6 m13 = COS'r. sinrl m14 = sin~. (kh\" 6\" cosx+h \u2022 s in ' r ) - rg~- (xM-p , , . 6)\" cosrl m21 = cost-sin~ m22 = c o s ' r , c o s 6 m23 = sinr m24 = kh\" 6\" s i n r - h , cosx m31 = - s i n ~ "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001817_6.2003-6512-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001817_6.2003-6512-Figure1-1.png",
        "caption": "Fig. 1 X-Cell 60 helicopter with sensors and avionics box",
        "texts": [
            " For simulation purposes and control design, we have used a full analytic nonlinear dynamic model of the helicopter,3 consisting of a six-degree-of-freedom, quaternion model augmented with simplified analytic models for the rotor forces, torque, and thrust, flapping dynamics, horizontal stabilizer and vertical tail forces and moments, fuselage drag, and actuator states. For actual flight tests, we use a instrumented X-Cell60 acrobatic helicopter, which is a popular platform among competition R/C pilots for its capability to perform aerobatic maneuvers. The research vehicle (Figure 1) is a clone of a vehicle developed by MIT.4 The custom avionics package includes an inertial measurement unit (IMU) with three gyroscopes and three accelerometers, a GPS receiver, a barometric altimeter and a triaxial magnetoresistive compass. Wireless communications and an on-board microprocessor with compact flash memory is included. In brief, the SDRE approach2 involves manipulating the vehicle dynamic equationsq rts jvuxwzy q r {Gr)| (1) into a pseudo-linear form (SD-parameterization), in which system matrices are explicit functions of the current state: q rts j u~} y q r |$q rv y q r | { r (2) A standard Riccati Equation can then be solved at each time step to design the state feedback control law on-line (a 50 Hz sampling rate is used in the flight experiments)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002117_rob.10031-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002117_rob.10031-Figure1-1.png",
        "caption": "Figure 1. A two-link underactuated elastic manipulator.",
        "texts": [
            " An underactuated joint operates with no direct input. The motion of the passive joint is associated with its adjacent joint link, which has a direct input via stiffness in the force domain. Hence, the position analysis requires the force and torque constraints. In addition to the kinematic constraint,which is used to obtain the displacement of amanipulator, a force constraint is introduced in the analysis while considering a smooth and slow motion. The two-link serial manipulator is modeled in Figure 1. The elastic actuated joint has angular displacement input \u03b8s1, with stiffness k1, and the output angular displacement, \u03b81, of the first link. The underactuated joint operates with a stiffness k2. The constraint equation of this elastic-joint manipulator is 3\u2211 i=1 GT i wi + GT PwP + \u03c4 = 0, (1) where,wi , i = 1, 2, arewrenchesofgravitational forces of links, w3 is a payload at the end-effector, and wP is an external active force. These can be expressed as wi = {0, \u2212mig, 0}T and wP = { fxP , fyP , \u03c4P}T",
            " Similarly, the scope for control increases when the values of lm2, l2, m2, and m3 increase. The trajectory of the end-effector can be obtained from the preceding analysis. Figure 2 illustrates an endeffector trajectory in a polar coordinate system when the external active force wP is zero. The values of the parameters used in the calculation are the same as that in the solution analysis in the previous section. In the polar map, the angle, \u03be , is the orientation of line OP that connects the origin to the end-effector point P in Figure 1. The distance between the origin and the end-effector is denoted by rp in the polar coordinate. Changing the stiffness, k2, of the passive joint, different trajectories of the end-effector can be produced, as shown in Figure 3. These demonstrate the trajectory characteristics of a two-link underactuated elastic-joint manipulator. When the stiffness ratio of the passive to active joints, k2/k1, is 0.15 or greater, the manipulator rotates continually in the range of 0\u223c 2\u03c0 , and a closed curve is obtained in Figure 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003266_1.2179462-Figure11-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003266_1.2179462-Figure11-1.png",
        "caption": "Fig. 11 The optimal solution \u201emargin against slip criteria\u2026",
        "texts": [
            "211\u2026 constraints, but also optimize the contact force distribution fol- MAY 2006, Vol. 128 / 571 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F lowing the margin against slip criteria with contact point priority. Expressing these foot contact forces with respect to the Cartesian X-Y-Z body coordinate frame, the final optimal force distribution is found as F\u0304C1 = \u2212 2.393,\u2212 2.336,1.827 F\u0304C2 = 1.997,\u2212 1.594,1.872 F\u0304C3 = 0.396,3.830,4.300 23 This final optimal force solution is shown to scale in Fig. 11. The margin against slip NCi at each contact point for the three feet contact case is defined as one minus the ratio of Ci * to Ci 572 / Vol. 128, MAY 2006 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/27/201 where Ci * is the friction cone angle when the first solution is found and Ci is the actual friction cone angle. This can also be expressed in terms of the coefficient of friction which is the tangent of the friction cone angle, and hence NCi = 1 \u2212 Ci * Ci = 1 \u2212 tan\u22121 Ci * tan\u22121 Ci 24 Using this expression, the margin against slip for each foot contact point is found as NC1 = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001914_rob.10048-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001914_rob.10048-Figure4-1.png",
        "caption": "Figure 4. Spring forces exerted on the moving platform.",
        "texts": [
            " Consequently, the configuration error of the moving platform can be defined as: E = 6\u2211 i=1 ( l2i \u2212 l\u22172i )2 (8) where l\u2217i denotes the given length of the ith limb. The problem now becomes finding the optimal configuration of themovingplatform, such that E isminimized. To efficiently solve this problem, the limbs are first imagined as linear springs, as shown in Figure 3. The undeformed lengths of the springs are defined as the given lengths of the limbs, and, hence, they will exert either compression or extension forces on the moving platform for incorrect configurations, as shown in Figure 4. These imaginary spring forces are defined by: Fi = (l\u2217i \u2212 li ) ui (9) where ui is a unit vector that indicates the current direction of the limb, pointing from the base to the moving platform. Secondly, the moving platform is considered as a system of six particles of unit mass connected by massless rigid rods, as shown in Figure 5. The geometricmass center of the systemwith respect to the origin of the moving frame can be obtained from: rC \u2032 = 1 6 6\u2211 i=1 ri (10) Furthermore, the directions of the resultant force and the resultant moment about the mass center can be evaluated respectively as: uF = \u22116 i=1 Fi\u2225\u2225\u2225\u22116 i=1 Fi \u2225\u2225\u2225 (11) and uM = \u22116 i=1 r \u2032 i \u00d7 Fi\u2225\u2225\u2225\u22116 i=1 r \u2032 i \u00d7 Fi \u2225\u2225\u2225 (12) where r \u2032 i = ri\u2212rc\u2032 and \u2016\u2022\u2016 indicate theEuclideannorm of a vector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003470_s00202-004-0258-y-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003470_s00202-004-0258-y-Figure1-1.png",
        "caption": "Fig. 1 A quarter of the cross-sectional geometry of the 15 kW cage induction motor",
        "texts": [
            " 3, 5, 6 and 11 yields the space vectors of cagecurrent components in the rotor reference frame i\u0302 r r;p 1 t\u00f0 \u00de \u00bc \u00f0G p 1\u00de xr w \u00f0pr c0 \u00de e j xr w spxs\u00f0 \u00det # r b0f g i\u0302 r r;p\u00fe1 t\u00f0 \u00de \u00bc G p\u00fe1 xr w pr c0 ej xr w\u00fespxs\u00f0 \u00det\u00fe# r b0f g \u00f012\u00de Here we can remark that the space vectors of current components have different frequencies compared to the whirling frequency. The spatial distribution of the critical rotor-cage currents is obtained by inserting the equations of 12 into Eq. 10 in Part 1 of this paper [7] ir;n \u00bc XQr N1 1 m\u00bc1 Re i\u0302 rr;me j 2pmn=Qr \u00bcRe i\u0302 rr;p 1e j 2p p 1\u00f0 \u00den=Qr \u00fe i\u0302 rr;p\u00fe1e j 2p p\u00fe1\u00f0 \u00den=Qr \u00f013\u00de 3 Numerical results 3.1 Example motor The developed calculation procedures were applied to a 15 kW four-pole cage induction motor. The main parameters of this motor are given in Table 1, and the cross-sectional geometry is shown in Fig. 1. In the numerical examples the motor was invariably supplied by the rated voltage (380 V) and rated frequency (50 Hz). Three different operating conditions were included into the analyses: rated load, sp=0.032; half load, sp=0.016; and no load, sp=0.0. 3.2 Impulse excitation In numerical examples we applied a displacement impulse of the type ps c t\u00f0 \u00de \u00bc ed 2 1 cos 2p t t1\u00f0 \u00de Dt ; t1\\t\\t1 \u00fe Dt 0 otherwise ( \u00f014\u00de where the superscript s refers to the stator reference frame, d is the radial air-gap length, is the relative pulse amplitude, t1 is the starting time of the pulse and Dt is the length of the pulse"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003471_tsmcb.2006.879015-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003471_tsmcb.2006.879015-Figure2-1.png",
        "caption": "Fig. 2. Teapot grasped by (a) four-finger hand and (b) five-finger hand.",
        "texts": [
            " , m, have been calculated offline in Step 3) so that only m multiplications of a 3 \u00d7 6 matrix by a vector are required here. Therefore, for solving the DFD problem, this algorithm is more efficient than the previous ones with polynomial [12] or quadratic [13]\u2013[15] complexities. Compared with [18] and [19], its online computation cost is not greatly reduced, but the computed contact forces are indeed optimal. V. NUMERICAL EXAMPLE Herein we demonstrate the efficiency of the proposed DFD algorithm using Matlab. The object to be manipulated is a teapot, as shown in Fig. 2. Assume that the dynamic external wrench is given by wext =   0.5 cos 2.4\u03c0t (2 + 0.5 sin 2.4\u03c0t) sin 0.4\u03c0t (2 + 0.5 sin 2.4\u03c0t) cos 0.4\u03c0t \u2212 5 cos (sin 1.2\u03c0t) sin(cos 0.4\u03c0t)) sin(sin 1.2\u03c0t) cos (sin 1.2\u03c0t) cos(cos 0.4\u03c0t))   . The external wrench is periodic and its period T = 5 s. Assign the sampling interval \u2206t = T/1000 = 5 ms. We grasp the teapot with a four-finger [Fig. 2(a)] and a five-finger [Fig. 2(b)] robot hand. Their contact positions, unit inward normals, and force upper bounds are as follows: Grasp (a) r1 =[0 0 \u221220]T n1 =[0 0 1]T r2 =[50 0 40]T n2 =[\u2212 \u221a 3/2 0 \u22121/2]T r3 =[\u221225 25 \u221a 3 40]T n3 =[ \u221a 3/4 \u22123/4 \u22121/2]T r4 =[\u221225 \u221225 \u221a 3 40]T n3 =[ \u221a 3/4 3/4 \u22121/2]T fU 1 =20 N fU i =10 N for i=2, 3, 4. Grasp (b) r1 = [0 0 \u2212 20]T n1 = [0 0 1]T r2 = [0 \u2212 50 \u2212 15]T n2 = [0 \u221a 2/2 \u221a 2/2]T r3 = [0 50 \u2212 15]T n3 = [0 \u2212 \u221a 2/2 \u221a 2/2]T r4 = [50 0 40]T n4 = [\u2212 \u221a 3/2 0 \u2212 1/2]T r5 = [\u221250 0 40]T n3 = [ \u221a 3/2 0 \u2212 1/2]T fU 1 =20 N fU 2 = fU 3 = 15 N fU 4 = fU 5 = 10 N"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001455_50006-1-Figure5.62-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001455_50006-1-Figure5.62-1.png",
        "caption": "FIGURE 5.62 Torque diagram with reference frame [30].",
        "texts": [
            " The constant K a is ~0Ms 2 K a = ~ ( N t - N;), where N t and N 1 are the anisotropy constants along thickness and length of the plate, respectively [33]. There is a shape-induced torque on M which is given by 0wa Ta(0) =-Vmag ~0 = - - W m a g K a sin(20), (5.328) where Vmag is the volume of the plate. The negative sign in Eq. (5.328) indicates that T, , (O) acts to oppose an increase in 0. That is, T, , (O) acts to align M with the easy axis. There is an equal and opposite torque -Ta(O) on the plate itself. This acts to rotate the plate towards M, away from the substrate (Fig. 5.62). We use Eq. (5.328) to determine the equilibrium rotation of the magnetization. However, to determine this we still need an expression for M. We obtain this by considering the components of H along the direction of M. Specifically, we have H ' = + where H~ and H~ are the applied and demagnetization field components parallel to M (Section 1.8). Let 7 denote the fixed angle between Hex t and the initial (unactivated) direction of the easy axis, and let ~b denote the equilibrium rotation of the easy axis (i.e., of the plate) (Fig. 5.62). The 464 CHAPTER 5 Electromechanical Devices angle c~ between M and Hex t is ~ = 7 - 0 - 0 . Therefore, H~ can be written as H~ = H e x t c o s ( ? - 0 - 4 ) . The component H~ is given by S~ = -NM(O)M, where NM(O) is the demagnetization factor that accounts for the rotation of M. Specifically, if M is at an angle 0 with respect to the easy axis then N2(O) = N 2 cos2(0) -Jr- N 2 sin2(0). Therefore, H~ = -x/N/2 cos2(0) + N 2 sin2(0)M. At this point, we have expressions for H~ and H~, but still no expression for M",
            " This gives H ~ 0 inside the plate, which implies that H~ = - H II d/ o r M = Hex , cos(? - 0 - q~) (5.329) NM(O ) We use Eq. (5.329) for M when the plate is below saturation. Above saturation we assume that M = Ms. Therefore, the magnetization can be written as ( Nex t cos(? -- 0 -- q~) Ms). (5.330) M = min \\V/~/2 c o s ~ ~ + N 2 sin2(0), We are finally ready to determine the equilibrium rotation angle of the plate. Equilibrium occurs when the magnetic and restoring torques are in balance. We consider the torque on both M and the plate (Fig. 5.62). The torque on M is where and TM(O, q5, M) = TH(O, q5, M) - Ta(O), TH = V m a g [ . l o M H e x t sin(7 - 0 - ~b) Ta(O) = V m a g K a sin(20). (5.331) (5.332) We use Eq. (5.330) for M in Eq. (5.331). The torque on the plate is T p l a t e ( 0 , ~b) = T a ( O ) - - Tin(d~)). In equilibrium, the net torque on both M and the plate is zero. This occurs when Tu(O, q5) = T,(O) (5.333) and T,(O) = Tm(q~). (5.334) Combining Eqs. (5.333) and (5.334) gives TH(O, (/) ,M)= T,(e)= Tm(q~). (5.335) The relation (5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003960_detc2005-84728-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003960_detc2005-84728-Figure5-1.png",
        "caption": "Fig. 5 Double pinion arrangement \u2013 orientation and coordinate frames",
        "texts": [
            " But this theoretical calculation is still extremely useful in highlighting the interactions between the gear meshes and bearings and comparing the single pinion arrangement to the double pinion arrangement. In the double pinion arrangement, there are two pinions in the path from the sun gear to the ring gear. The pinion that meshes with the sun gear will be designated as SP and the pinion that meshes with the ring gear will be designated RP. The included angles between the centers of the sun gear, SP, and RP are \u03b1, \u03b2, and \u03b3 as shown in Figure 5. Two reference frames will be defined \u2013 one for SP and one for RP. The XSP axis is aligned along the line joining the centers of the sun gear and SP and the XRP axis is aligned along the line joining the centers of the ring gear and RP. The ZSP and ZRP axes project out from the plane of the paper. The planes of action at the three meshes are also shown in the figure. As before, consider the mesh contact forces to be concentrated loads at the center of the facewidth. As in the single pinion arrangement, the radial separating forces go through the origin of the coordinate frames and cause no moments and the tangential forces cause equal and opposite moments about the Z axes and result in no net moment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002157_027836498900800302-Figure9-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002157_027836498900800302-Figure9-1.png",
        "caption": "Fig. 9. Some test workpieces.",
        "texts": [
            "comDownloaded from 42 tioning table joint values and velocities for a sequence of closely spaced discrete points. The user controls the definition of the desired weld path, positioning of the workpiece, specification of the welding sequence, and specification of interweld trajectories. To evaluate AUTOWELD, a six-degree-of-freedom robot similar to a Unimation PUMA, and a generic positioning table with three degrees of freedom were specified. A trial CAD seam definition was generated explicitly, and several workpiece geometries were modeled as shown in Fig. 9. The robot was represented by three clusters of four parts total. The positioning table was represented by a single part. The test workpieces ranged in complexity from 2 parts to 10 parts. There does not appear to be any significant difference in the interactive performance of AUTOWELD for these different cases. Table 1 shows a typical welding program generated by AUTOWELD. All required joint values are generated for both the robot and the positioning table. Note that the trajectory from the starting configuration to the first weld position is specified by three joint interpolated positions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002473_s0020-7225(03)00241-6-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002473_s0020-7225(03)00241-6-Figure2-1.png",
        "caption": "Fig. 2. Force\u2013displacement curve of the cylinder for m \u00bc 0:25.",
        "texts": [
            " (24) and (31) yields: k2 \u00bc k m 1 \u00f032a\u00de r11 \u00bc E ln\u00f0k1\u00de \u00f032b\u00de P EA \u00bc k 2m 1 ln\u00f0k1\u00de \u00f032c\u00de This completely coincides with Eqs. (26) for logarithmic strain. This is because the principal axes are fixed and R \u00bc I, so that D \u00bc \u00f0lnU_\u00de [4] as can be seen in (29). Therefore, from (27) and (32) the force\u2013displacement relation for n \u00bc 0 will take the form: P EA \u00bc 1 \u00fe D L 2m ln 1 \u00fe D L \u00f033\u00de The force\u2013displacement curves of the cylindrical element for different indices n, and for the rate constitutive model, are shown in Fig. 2 assuming ratio m \u00bc 0:25. As can be seen, for n > 1 the cylinder stiffens in tension and softens in compression. Therefore, in finite elastic deformation problems, the use of Eq. (6) for n > 1 may result in softening in compression zones which may not be physically acceptable. For n < 0 the element shows tensile softening and compressive stiffening. For n \u00bc 1 it shows a linear behaviour and acts like a Hook string which obeys the linear Hook s law in every range of deformation. Fig. 3 shows the relative volume change det\u00f0F\u00de \u00bc dv=dV for nP 0, where dV and dv are initial and current infinitesimal volumes of a material particle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002414_iros.2000.894667-Figure14-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002414_iros.2000.894667-Figure14-1.png",
        "caption": "Fig. 14: execution error",
        "texts": [
            " In the case of rotation, that is the same. Because this motion can perform the similar method of make-contact, we do not treat this motion. 0 . Fig. 13: maintaining to singular detaching 5.4 Execution error A not-aimed movement leads to an execution error. In short, these three transitions of DOFs are relative to an execution error. In particular, a detaching to maintaining transition is very important. We will introduce the method to detect error contact-relations. For example, consider the case as shown in Fig. 14. There are four vertex-face contacts. Each contact inequality corresponding to each contact is obtained. Several contacts can be removed if, and only if, the answer satisfying inequalities (5) is not empty. -587 - f m l . > O 1 corresponding to : f several contacts another fn, ! j = 0 6 6.1 Singular maintaining to detaching 15, this transition appears in a slide sub-skill. Making singular contact correctly is very difficult, but a small execution error does not disable to realize the transition of the contact relations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001359_s0020-7683(99)00190-0-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001359_s0020-7683(99)00190-0-Figure5-1.png",
        "caption": "Fig. 5. Multilayer shell: material con\u00aeguration B, initial con\u00aeguration B0, and current con\u00aeguration Bt:",
        "texts": [
            " (8) and (9) that the outward normal ` n ` naEa to the material lateral boundary surface ` S, which is de\u00aened in Eq. (9), is such that ` n 0 n, 8` 2Nnf0g: 11 That is, the outward normals to the material lateral boundary surfaces ` S are the same for all layers. In other words, the surfaces ` S are all parallel to each other, and orthogonal to the material centroidal surface A 0 A (see Figs. 3 and 4). Let the initial con\u00aeguration of the multilayer shell be denoted by B0 R3, and the current (spatial) con\u00aeguration denoted by Bt R3 (see Fig. 5). Let F0: B4B0 be the deformation map from material L. Vu-Quoc, I.K. Ebciog\u00c6lu / International Journal of Solids and Structures 37 (2000) 6705\u00b167376710 con\u00aeguration B to the initial con\u00aeguration B0, such that x0 F0 x 2 B0, where x 2 B: Let Ft: B4Bt be the deformation map from B to the current con\u00aeguration Bt, such that xt Ft x 2 Bt, where x 2 B: Further, we de\u00aene the deformation map F: B R 4R3, such that5 F0 F , 0 , Ft F , t : 12 The deformation map for the shell relative to the initial con\u00aeguration is denoted by wt: B04Bt (see Fig. 5), with wt Ft F\u00ff10 : 13 With ` Ft: ` B4R3 being the deformation map for layer `), we have Ft x ` Ft x , 8x 2 ` B, 14 and also 5 R is the set of non-negative real numbers. L. Vu-Quoc, I.K. Ebciog\u00c6lu / International Journal of Solids and Structures 37 (2000) 6705\u00b16737 6711 ` wt ` Ft ` F\u00ff10 : 15 Now let ` t: A R 4S 2 be the director \u00aeeld of layer `), where S 2 designates the sphere de\u00aened as S 2M t 2 R3jktk 1 : 16 With ` j: A R 4R3 being the deformation map of the centroidal surface of layer `), we can now de\u00aene the deformation map ` Ft in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003917_0278364905058242-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003917_0278364905058242-Figure2-1.png",
        "caption": "Fig. 2. (a) A three-limb robot in a planar tunnel. (b) The parametrization of its contact c-space.",
        "texts": [
            " During a three-limb posture the robot changes its internal geometry in preparation for the next limb lifting. The PCG algorithm is presented in the context of such three-limb robots, but the algorithm generalizes to robots having a larger number of limbs. The foothold positions are represented as points in contact configuration space (c-space), which is defined as follows. Let L be the total length of the tunnel walls, and let si \u2208 [0, L] be an arc-length parametrization of the position of the ith contact along the tunnel walls (Figure 2). Then, for a klimb mechanism contact c-space is the k-dimensional space (s1, . . . , sk) \u2208 [0, L]k. The use of contact c-space is common in the grasp planning literature. In particular, Nguyen (1988), Ponce and Faverjon (1995), and Ponce, Stam, and Faverjon (1993) introduced the notion of contact independent regions. Given a k-finger grasp of a planar object, a contact independent region is a k-dimensional cube aligned with the coordinate axes in contact c-space. This cube represents k segments along the object\u2019s boundary, such that any placement of the k contacts inside these segments generates an equilibrium grasp",
            " Fourthly, the kinematic structure of the robot is lumped into a single parameter called the robot radius, R. This parameter is the length of a fully stretched limb, measured from the center of the robot\u2019s central base. The algorithm uses this parameter to ensure that the selected footholds can be reached from the robot\u2019s central base. Recall now that contact c-space of a three-limb robot is the cube (s1, s2, s3) \u2208 [0, L]3, where L is total length of the tunnel walls and si \u2208 [0, L] is an arc-length parametrization of the ith contact (Figure 2). The feasible three-limb postures must form stable equilibria, be reachable, and satisfy the following gait feasibility condition. This condition requires that the three-limb posture will contain two distinct two-limb postures: one for entering the three-limb posture by establishing a new foothold, and one for leaving the three-limb posture by releasing another foothold. Note that the initial and target three-limb postures are required to contain one rather than two two-limb postures. We now consider the individual constraints",
            " By definition, an equilibrium posture is force closure if the mechanism can resist any perturbing wrench by suitable adjustment of its contact forces with the environment (Bicchi 2000). In general, an equilibrium posture in a planar environment is force closure if the contact forces of the unperturbed posture lie in the interior of the respective friction cones (Yoshikawa 1999). We now write the above conditions as inequalities in contact c-space. Let W1, . . . ,Wn denote the tunnel walls, and let I1, . . . , In be a partition of [0, L] into intervals that parametrize the individual walls by arc length. These intervals induce a partition of contact c-space into cubes (Figure 2). For instance, the cube Ii\u00d7Ij \u00d7Ik parametrizes the three-limb postures where limb 1 contacts the wall Wi , limb 2 contacts the wall Wj , and limb 3 contacts the wall Wk. The unit tangent and unit normal to the wall Wi are denoted t i and ni , where ni is pointing away from the wall. Using this notation, points along Wi are given by x(s) = x i + (s \u2212 si0)t i , where x i is the initial vertex of Wi , s \u2208 Ii , and si0 is the minimal value of s \u2208 Ii . Given a contact force f i , we write the force as f i = f t i t i + f n i ni , where f t i and f n i are its tangent and normal components"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001203_oca.4660140405-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001203_oca.4660140405-Figure2-1.png",
        "caption": "Figure 2. The initial turning circles of the pursuer and the boundary of the permissible set",
        "texts": [
            " It was shown\u201d that such a problem has a solution (even for \u2018point capture\u2019, Rf = 0) with finite final time (tr < a) if We assume that these conditions are satisfied and moreover that Ro > R f 2 0 (12) The objective of our analysis is to determine the sufficient condition to be satisfied by the non-dimensional parameter in order to guarantee that the optimal trajectory belongs to category (a) for arbitrary $0, Op0 and O,(t) subject to (4)\u2019 (6) and (8). ep 4 rp/RO (13) 3. ANALYSIS We select the co-ordinate system ( x , y ) so that the origin is at the initial point of the pursuer\u2019s trajectory and the direction of x is aligned with the pursuer\u2019s initial velocity vector pm, i.e. Op = 0 (see Figure 2). These are two circles with radius r, and centres 01 and 0 2 tangent to V, along which the pursuer can initiate a turn. If the terminal point of a time-optimal trajectory towards a fixed target is not inside these initial turning circles, then this trajectory obviously belongs to category (a) and it starts along the circle whose centre is nearer to the terminal point of the trajectory. The terminal point of the \u2018limit\u2019 trajectory is on one of the circles. If we denote Pf(xpf,ypr) as the terminal point of the pursuer\u2019s time-optimal trajectory, this (14) (15) is expressed by the inequalities 2 2 XSr + (Ypr - rp)\u2019 2 r p XXr + (Ypr + rp)2 2 r p Since for such an optimal trajectory OP(tf) = Wf) one can construct the boundary which limits the terminal point of the evader, Ef(Xef,Yef). (Note that Ef is considered as a fixed target.) This boundary consists of the circular arcs with their respective centres at 01 and 0 2 of radius (17) as shown in Figure 2. Therefore the point Ef(xer,Yef) is called \u2018permissible\u2019 if it satisfies the inequalities (18) (19) Let Se, be the set of permissible points Ef(xef ,Yef) and a&, be the boundary of this set (see Figure 2), determined by the circular arcs A I A z A ~ and A3&AI. Now we construct a circle of radius RO with its centre at O(0,O) as shown in Figure 3, denoted in the sequel as CR,, c Se,. This allows us to consider the evader\u2019s motion, starting at Eo(Ro cos $0, Ro sin $ 0 ) E Se,, to the boundary a&, and the respective motion of the pursuer in the interception. Owing to symmetry, it is sufficient to consider the upper part of a&,, determined by the circular arc A3&A1 and denoted in the sequel as a S f "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001764_bi00103a008-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001764_bi00103a008-Figure2-1.png",
        "caption": "FIGURE 2: Dependence of the second-order rate constant for the Fe( 11)-dependent reduction of rusticyanin upon the corresponding rate constant for the reduction of Co(dipic); in the presence of different anions. Values for the second-order rate constants were obtained from Table I. Anions: a, perchlorate; b, selenate; c, bromide; d, sulfate; e, a-ketoglutarate; f, pyruvate; g, isocitrate; h, malate; i, lactate; j, phosphate; k, chloride; 1, citrate; m, oxalacetate; and n, pyrophosphate. The line was determined by a linear regression analysis using all of the data points. The correlation coefficient was 0.83.",
        "texts": [
            " The values of the corresponding second-order rate constants for the Fe(11)-dependent reduction of Co(dipic); are tabulated in the third column of Table I. It was evident that the values of the second-order rate constants in the two sets of kinetic data were related; in general, ligation of the ferrous ion by a particular anion influenced the rates of reduction of both the protein copper center and the small, organocobalt compound in a similar manner. The similar tendencies between the two series of rate constants are illustrated in Figure 2, where the values of the second-order rate constants for the liganded Fe(I1)-dependent reduction of the rusticyanin are plotted versus the corresponding values for the reduction of the Co(dipic);. Although there is considerable scatter about the linear regression line drawn through the data points in Figure 2, the line nonetheless serves to emphasize that a rough correlation exists between the two sets of rate constants. There would be considerably less scatter among the remaining points if data points labeled 1 (citrate) and m (oxalacetate) were omitted from the linear regression calculation. Subsequent analysis of these and ad- 9446 Biochemistry, Vol. 30, No. 39, 1991 Blake I1 et al. ditional data (Figure 4) suggests that, indeed, there may be good reason to omit these two points. Oxidation by Liganded Fe(III)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002942_6.2004-5008-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002942_6.2004-5008-Figure3-1.png",
        "caption": "Figure 3: Reference frames for modeling loads produced by Fans, Vanes, and CMG.",
        "texts": [
            " Hence we do not include these terms in this paper but is addressed in [8]. The terms \u03c4s\u0302i and \u03c4g\u0302i denotes the internal torques on the i-th CMG wheel due to the wheel motor, the internal torques on the i-th CMG subsystem due to the gimbal motor, respectively. The variable \u03c4 Bz denotes the internal torque on the momen- tum wheel due to its motor, while \u03c4 Fi denotes net torque on the i-th fan due to a combination of external fan rotational drag and internal fan motor torque, including back EMF effects. Figure 3 shows a set of frames used to conveniently describe various loads produced by engine thrust, vane deflections, and fan rotational drag. 2.1.1 Net propulsive forces acting on OFi T\u2212\u2192i (\u03c9si , \u03b8i) = FT b C T Fi Ti(\u03c9si , \u03b8i), Ti \u2208 R3\u00d71 (17) where Ti(\u03c9si , \u03b8i) \u2248  cTxi cTyi cTzi  \u03c92 si +  cxi\u03b8i cyi\u03b8i \u2212czi\u03b8 2 i  \u03c92 si := ei(\u03b8i)\u03c9 2 si (18) 2.1.2 Net propulsive moments acting about OFi \u03c4\u2212\u2192i (\u03c9si , \u03b8i) = FT b C T Fi \u03c4i(\u03c9si , \u03b8i), \u03c4i \u2208 R3\u00d71 (19) where \u03c4i(\u03c9si , \u03b8i) \u2248  c\u03c4xi c\u03c4yi c\u03c4zi  \u03c92 si +  lxi lyi lzi  \u03b8i\u03c9 2 si := fi(\u03b8i)\u03c9 2 si (20) 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000259_(sici)1097-4687(199703)231:3<287::aid-jmor7>3.0.co;2-8-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000259_(sici)1097-4687(199703)231:3<287::aid-jmor7>3.0.co;2-8-Figure1-1.png",
        "caption": "Fig. 1. G. domesticus. Representation of skeletal elements by an open kinematic chain. The position of the head with respect to the body is defined by the distance d and the elevation b; the orientation of the head is indicated by g. The neck posture is characterized by the length of the bars and the angle ai between successive bars.",
        "texts": [
            " Each of the 15 cervical vertebrae is represented by a separate bar, except the atlas and axis, which are represented as a single bar. These two most rostral vertebrae are short and show hardly any dorsoventral flexion. The most rostral bar represents the head. The vertebrae are counted from rostral to caudal and are indicated by a \u2018\u2018V\u2019\u2019 followed by the appropriate number. Vertebrae caudal to V15 (notarium) show no flexion. A neck posture is defined by the length of the bars and the angles (ai) between successive bars (Fig. 1). The model uses as input the length of all bars and the position and orientation of the head with respect to the body. A simplex optimization procedure (see below) is used to optimize a cost function. The output of the model is a series of angles between the vertebrae. The length of each vertebra was determined from a radiogram of a dead chicken in lateral view. The length was taken as the distance between the centers of successive joints and includes the intervertebral disc. The length of the head was measured from the tip of the beak to the condylus occipitalis",
            " However, independentmeasurements on the same postures show that the position of the center of a joint is judged differently on separate occasions. This results in an overall measurement error of 64.0\u00b0. On most radiograms vertebrae 15\u201313 were masked by the wings, and angles could not be measured. However, the position of the tip of the notarium could be reconstructed from amarker on the bird\u2019s back and was taken as the base for a fixed coordinate frame with the abscissa parallel to the notarium. The position of the head with respect to the body was measured in polar coordinates (Fig. 1). One coordinate was measured as the distance (d) between the notarium and the cranial end of V2 1 1; the second coordinate was the angle (b) between this line and the notarium (x-axis). The orientation of the head was measured as the angle (g) between the notarium and the line through the occipital condyle and the upper beak. Postures were distributed among birds and the position of the headwas adjusted for small differences in the length of the vertebrae. The optimization procedure used for the simulations is the so-called complex method described by Bunday (\u201984)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002619_095440605x31481-Figure12-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002619_095440605x31481-Figure12-1.png",
        "caption": "Fig. 12 Tracing out the concave flank of a CC1-rack by a stylus point on a rotating head that is fed at an inclination to its plane, f \u00bc 208",
        "texts": [
            " It should be noted that, for any but the smallest values of b, the variation across the gear face of the cutting conditions in terms of the tool rake and side-clearance angles is quite adverse, rendering both the previous suggestions impractical. It is also noted that CC1-gears cannot be crowned \u2013 the radius R being the same throughout \u2013 nor could they be finish-ground. All the C-gears described hitherto are generated by tools that simulate a cutting rack whose pitch plane is fed tangentially to the gear pitch circle. Departure from this principle begins here, and CC2-gears will better be introduced after an alternative description of the tooth surface geometry of CC1-racks. Figure 12 shows the circular path of a stylus point (or a number of such) on a rotary head that moves at a velocity v cos f in a direction inclined to its plane by the pressure angle f. Simultaneously, a CC1-rack is made to move parallel to the stylushead plane at a velocity v. Thus the stylus point will be sweeping out, in a closely wound helical path, the oblique cylinder that makes the rack tooth surface of constant pressure angle f. The other component velocity, v sin f, is the rate at which the circular path descends the tooth flank"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003989_6.2005-6254-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003989_6.2005-6254-Figure3-1.png",
        "caption": "Figure 3. RLV aerodynamic surfaces configuration.",
        "texts": [
            " This model is based on the following assumptions6: \u2022 The forces induced by RCS are quite small compared to the aerodynamic forces acting on the vehicle, and thus are ignored in the translational dynamic simulations. \u2022 The dynamic response time for getting on the thrusters is also very small, around 40 ms, which could be neglected. 5. Aerodynamic Control Surfaces and EMA The X-38 type configuration has two sets of aerodynamic surfaces, namely two flaps and two rudders, independently driven by four Electro-Mechanical Actuators (EMA), as illustrated in Fig. 3. Unlike conventional aircrafts, the RLV is equipped with rudders and flaps only. However, by commanding their deflections either symmetrically or asymmetrically, these two sets of surfaces provide the same control authority as if conventional rudders, elevators, ailerons and speed brakes were used. Various constraints are applicable to the operation of aerodynamic control surfaces. The elevon and aileron controls are only used when the dynamic pressure is greater than 96 Pa. Moreover, the rudders must not be used with Mach numbers above 6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003586_11505532_10-Figure10.2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003586_11505532_10-Figure10.2-1.png",
        "caption": "Fig. 10.2. Reference vehicle at the distance d and angle \u03b3m from the leader vessel",
        "texts": [],
        "surrounding_texts": [
            "As a fist step in order to assure a safe replenishment operation, we design a reference position for the follower vessel at some distance from the leader. This reference position will be in the form of a reference vehicle with a kinematic model. We will in this section develop a general reference vehicle model for an arbitrary heading assignment, i.e. the heading angle of the reference vehicle \u03c8r can be different from the heading angle of the leader vessel \u03c8m, and in Sect. 10.2.5 for the particular case of parallel motion where the heading angles are equal; \u03c8r = \u03c8m. The kinematic model (10.5) of the leader vehicle Vm with the position/heading vector xm can be written as x\u0307m = J (xm) \u03bdm (10.12) and by using (10.7) takes the form 178 E. Kyrkjeb\u00f8 et al. x\u0307m = um cos\u03c8m \u2212 vm sin \u03c8m y\u0307m = um sin \u03c8m + vm cos\u03c8m (10.13) \u03c8\u0307m = rm Let d (= const) be the desired (required) distance between the leader and the follower vessel, and \u03b3m (= const) the angle between the xb-axis of the leader and the vector d, positive counterclockwise, as shown in Fig. 2. We can calculate the \u201dposition\u201d \u03c7 of the leader in the BODY m-frame1 of the leader \u03c7m m = JT (xm)xm (10.14) Superscripts denote the reference frames, and subscripts denote which vehicle position/heading vector that is described. We will use \u03c7 to denote position/heading in the BODY -frames with no immediate physical interpretation, and x as the position/heading of vehicles in the NED-frame. Thus, xm is the position vector of the leader vehicle m in the NED frame, while \u03c7m m is the position vector of the leader vehicle in its own BODY m frame. We also have that the position vector of the reference vehicle in the NED frame can be written as xr = J (xr) \u03c7r r (10.15) The position vector of the reference vehicle in the BODY m frame of the leader can be written as \u03c7m r = \u03c7m m + dm r (10.16) where 1 Note that the position of the vehicle in the body-frame does not have any immediate physical interpretation as the integral ! t 0 \u03bdbdt, but its mathematical representation is still valid. 10 A Virtual Vehicle Approach to Underway Replenishment 179 dm r =  d cos \u03b3m d sin \u03b3m \u03b1  (10.17) with the distance d and rotation \u03b1 separating the two frames. The angle \u03b1 is the desired difference in heading between the leader vessel and the reference vehicle, and defined in the BODY m-frame. Expressed in the NED frame, (10.16) becomes xr = J (xm) \u03c7m r = xm + J (xm)dm r (10.18) Taking the time derivative through J\u0307 (xm) = J (xm)S (rm), where S (rm) is the skew-symmetric matrix S (rm) =  0 \u2212rm 0 rm 0 0 0 0 0  (10.19) we get x\u0307r = x\u0307m + J (xm)S (rm)dm r + J (xm) d\u0307m r (10.20) In component form this is equivalent to x\u0307r = um cos\u03c8m \u2212 vm sin \u03c8m \u2212 drm cos \u03b3m sin\u03c8m \u2212 drm sin \u03b3m cos\u03c8m y\u0307r = um sin \u03c8m + vm cos\u03c8m + drm cos \u03b3m cos\u03c8m \u2212 drm sin \u03b3m sin \u03c8m (10.21) \u03c8\u0307r = rm + \u03b1\u0307 By investigating (10.21) more closely, we can rewrite this as x\u0307r = cos\u03c8m (um \u2212 drm sin \u03b3m)\u2212 sin \u03c8m (vm + drm cos \u03b3m) (10.22) = (um \u2212 drm sin \u03b3m) 2 + (vm + drm cos \u03b3m) 2 (cos\u03c8m cos\u03b1\u2212 sin\u03c8m sin \u03b1) where we have cos\u03b1 = um \u2212 drm sin \u03b3m (um \u2212 drm sin \u03b3m) 2 + (vm + drm cos \u03b3m) 2 (10.23) sin \u03b1 = vm \u2212 drm cos \u03b3m (um \u2212 drm sin \u03b3m)2 + (vm + drm cos \u03b3m)2 (10.24) Similarly, we can rewrite (10.21) as 180 E. Kyrkjeb\u00f8 et al. y\u0307r = sin \u03c8m (um \u2212 drm sin \u03b3m) + cos\u03c8m (vm + drm cos \u03b3m) (10.25) = (um \u2212 drm sin \u03b3m)2 + (vm + drm cos \u03b3m)2 (sin \u03c8m cos\u03b1 + cos\u03c8m sin \u03b1) and by using that tan \u03b1 = sin \u03b1 cos\u03b1 = um \u2212 drm sin \u03b3m vm + drm cos \u03b3m (10.26) we get \u03b1\u0307 = (u\u0307m\u2212dr\u0307m sin \u03b3m)(vm+drm cos \u03b3m)\u2212(um\u2212drm sin \u03b3m)(v\u0307m+dr\u0307m cos \u03b3m) (vm + drm cos \u03b3m) 2 cos2 \u03b1 (10.27) and thus the total system can be written as x\u0307r = (um \u2212 drm sin \u03b3m) 2 + (vm + drm cos \u03b3m) 2 cos (\u03c8m + \u03b1) y\u0307r = (um \u2212 drm sin \u03b3m) 2 + (vm + drm cos \u03b3m) 2 sin (\u03c8m + \u03b1) (10.28) \u03c8\u0307r = \u03c8\u0307m + \u03b1\u0307"
        ]
    },
    {
        "image_filename": "designv11_24_0002619_095440605x31481-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002619_095440605x31481-Figure6-1.png",
        "caption": "Fig. 6 Cutting geometry of a CV2-gear in a singleindexing cycle, the dashed lines are the mating tooth traces, R/m \u00bc f/m \u00bc 10",
        "texts": [
            " CV1-gears could be finish-ground by the methods explained later for CV2-gears, when adapted to produce the desired equal or slightly unequal tooth trace radii. This is a form of gears that is generated by one cutter head in a single-indexing cycle. The cutter head carries a set of nominally identical cutters, all at the same mean radius R, but they ought to be thinner than a tooth space and staggered for better chip removal. The cutters have outside- and insidecutting straight edges, inclined at +fm to the cutter-head axis (Fig. 6). The two sets of edges sweep out two coaxial, opposed conical frusta at different heights from their respective vertex, which generate the concave and the convex tooth flanks concurrently. The resulting tooth traces will be circular arcs with radii Rcav and Rvex that differ by a halfpitch. This geometry gives a transverse tooth space that widens and tooth thickness that decreases as the section shifts away from the midplane. The generating rack swept out by the cutters and a rack being cut are self-complementary only in the midplane, but not in three-dimensional space",
            ") The grinding wheel rim is bevelled in its axial section to a generating rack tooth shape, and it touches both flanks of a tooth space at a point each. The rest of the grinding surfaces gradually clear the flanks as the wheel cross-section in the pitch plane forms a crescent. The grinding wheel is made to oscillate about a \u2018vertical\u2019 axis located at a radius R from the middle of the tooth space to over-travel the gear facewidth, while generatingrolling motion is imparted to the gear. The inside and outside generatrices in the plane that contains the cone and the oscillating axes mimic the machining process of Fig. 6, yet in a serpentine route. This grinding method offers the advantage of not imposing bounds on the number of teeth; it could even be used to finish CV2-racks. (A flaring-cup milling cutter could be used to generate CV2-gears and racks according to the same method.) It is worthwhile to study the geometry of this method a little deeper. By completing the construction lines in Fig. 7 it can be shown that the crescent section is delimited by two ellipses of minimum radii of curvature (at their vertices) given by rcav,vex \u00bc k cosfm sin (60+ fm) w tan (60+ fm) (5) Proc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000852_s0022112098002596-Figure11-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000852_s0022112098002596-Figure11-1.png",
        "caption": "Figure 11. Schematic of the impulsive motion of a sphere near a wall in an inviscid irrotational flow.",
        "texts": [
            " This equation can be time-integrated through the impact time duration from t = 0 to t = \u03c4 to obtain u\u03c4 \u2212 u0 = \u2212 1 \u03c1f \u2207I, (4.2) where u0 and u\u03c4 are the particle velocities before and after the collision and I is the pressure impulse (as defined in equation (2.1)). If the flow is incompressible, then it follows that \u22072I = 0. (4.3) Thus the pressure generated by the impulsive motion of a body is governed by Laplace\u2019s equation, and resembles the velocity potential for the steady potential flow around that same body. Consider the domain shown in figure 11. A spherical particle, of diameter d, is positioned at a certain distance, b, away from a solid wall. The fluid is incompressible and is at rest for t 6 0. If at t = 0 the particle is accelerated instantaneously from rest to a velocity u\u03c4, the impulse pressure equation (4.3) can be solved using the following boundary conditions: at the wall, n \u00b7 \u2207I = 0; far away from the wall, I = 0 (n \u00b7 \u2207I = 0, could also be considered); on the surface of the particle, n \u00b7 \u2207I = \u03c1fu\u03c4 cos \u03b8. An approximate solution of the impulse produced by a sphere suddenly accelerated towards a wall can be obtained by superposing two doublets that are mirror images",
            " Normalizing by \u03c1fu\u03c4d leads to I\u0302w = I(x = 0, y = 0) \u03c1fu\u03c4d = 1 8 ( d b )2 . (5.1) The dashed line in figure 13 shows the impulse calculated from this expression. For simplicity, only the results for the 6 mm glass spheres are shown in this figure. Clearly, the model appears to predict the decay of the impulse with distance, and over-predicts slightly the magnitude of the impulse. In the experiment two particles collide. Therefore, a more appropriate model can be obtained, in an approximate solution, by the interaction of two pairs of doublets. As depicted in figure 11, the doublet modelling the second particle, the impact particle, is placed at x = b + d with strength \u03c1fu\u03c4, with its respective mirror image placed at x = \u2212(b+ d) with strength \u2212\u03c1fu\u03c4. Therefore, I = 1 2 \u03c1fu\u03c4(d/2)3 ( x+ b ((x+ b)2 + y2)3/2 \u2212 x+ b+ d ((x+ b+ d)2 + y2)3/2 \u2212 x\u2212 b ((x\u2212 b)2 + y2)3/2 + x\u2212 b\u2212 d ((x\u2212 b\u2212 d)2 + y2)3/2 ) . (5.2) Thus, the normalized impulse at the wall reduces to I\u0302w = 1 8 ( d b )2 ( 2b/d+ 1( b/d+ 1 )2 ) . (5.3) The dashed-dotted line in figure 13 shows the calculated impulse for the case of two doublets with their respective images"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002467_87.998019-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002467_87.998019-Figure1-1.png",
        "caption": "Fig. 1. The relative misalignment between the rotor and the stator in the sealing dam.",
        "texts": [
            " First contact is monitored from the dynamic behavior of the seal using eddy current proximity probes. These provide instantaneous information on proper or improper seal behavior. Then, a control strategy as well as control system are developed and physically implemented to keep both the clearance and the relative misalignment as small as possible in order to ensure noncontacting operation of the FMR mechanical face seal. II. INTERMITTENT FACE CONTACT A basic description and nomenclature of the FMR mechanical face seal are given in Fig. 1 (see [5] for details of this kinematical model). The sealing dam is the area between the slanted face of the rotor and the fixed stator (both are shown also in Fig. 2). To minimize wear one of these faces is usually made of a softer material, e.g., carbon\u2013graphite. During operation the faces lift off to a certain a centerline clearance, , while the softer material also distorts because of mechanical and thermal deformations, as represented by the coning angle, . Note that both , and are very small (of the order of a micron and 1063-6536/02$17.00 \u00a9 2002 IEEE mrad, respectively) and, hence, Fig. 1 is not shown to scale for these dimensional parameters. Fluid leakage due to the pressure drop across the seal occurs as fluid flows into the converging gap created by (in Fig. 1 flow occurs from the peripheral area toward the center). Ideally, seal faces are arranged perpendicular to the shaft and parallel to each other. As the name implies, there should be no face contact during the operation of the noncontacting mechanical face seal. However, in reality, during operation contact may occur due to large relative misalignment between the seal faces. The relative misalignment between seal faces, (see Fig. 1), is the result of manufacturing and assembly tolerances, machine deterioration, or from disturbances in the process operation, bent shafts, etc. Seal face contact, not only generates an impact force that is not easy to predict, it also increases the friction and wear of the faces. Heat generated by prolonged contact can also deform the seal faces and generate additional stress problems. Whether seal face contact will occur depends not only on the relative misalignment between the rotor and the stator, , but also on the designed seal clearance, , and the seal inner and outer radii, and (for consistency with previous publications [5]\u2013[15] an asterisk or, a lower-case letter indicates dimensional/nonnormalized variables). These can be grouped together into the normalized relative misalignment, , defined as [5]. Seal face contact could either occur at the inner radius or the outer radius, depending on the normalized coning angle, (now Fig. 1 is better scaled for the nondimensional parameters, where ). A properly de- signed seal, must have a coning angle, , greater than critical [5], [8]. (The critical coning angle , provides positive fluid film stiffness; where is the dimensionless inner radius of the seal, .) Should contact occur it would take place at the inner radius. In which case, the normalized relative misalignment, , can be used to determine contact occurrence. When contact occurs at the inner radius (1) and, therefore, nondimensionally (2) Thus, in order to avoid the possibility of contact between the seal faces both the design and operation should ensure at all times",
            " An eigenvalue stability analysis [5], [8] reveals that the FMR seal in the current test rig is dynamically stable up to shaft speeds of at least 1300 Hz and below a clearance of 10 m. These limits are extremely high, and out of the range of normal operation for most practical cases. The problem of contact that occurs here is the steady-state response to the stator misalignment (or initial conditions). A rotor that poorly tracks the stator and its own initial rotor misalignments, leads to a relative misalignment (see Fig. 1), large enough to cause contact. The purpose of the contact elimination strategy is to improve upon the rotor response and reduce such that noncontacting operator prevails. However, other factors, such as kinematics of the flexible support and its rotordynamic coefficients uncertainties, machine deterioration, transients in sealed pressure or shaft speed, or unexpected shaft vibration, affect the dynamic behavior of the seal and, hence, the relative position and misalignment between the rotor and the stator"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000244_s1388-2481(99)00068-5-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000244_s1388-2481(99)00068-5-Figure1-1.png",
        "caption": "Fig. 1. Simulated cyclic voltammograms (2nd cycle) of an electrochemically reversible system with the depolariser in the bulk of the solution being in its reduced and oxidised forms, respectively. Initial conditions: EstartsEl,csy500 mV, DoxsDreds10y5 cm2/s, scan rates0.1 V/s; simulations with the finite difference method according to [10].",
        "texts": [
            " Here, we communicate that information on the redox state of the depolariser can be very simply derived from cyclic voltammograms, as the entire voltammograms, although * Corresponding author. Tel.: q49-3834-864-450; fax: q49-3834-864451; e-mail: fscholz@mail.uni-greifswald.de fully identical in shape, are shifted along the current axis depending on the redox state. This can easily escape attention when zero current is not marked in the figures, as is, unfortunately, common practice. This feature of cyclic voltammetry has not yet been discussed in the literature [1\u20138]. Fig. 1 shows simulated cyclic voltammograms (second cycle; semi-infinite linear diffusion) of an electrochemically reversible system when the depolariser is present in the bulk of the solution either in its reduced or oxidised form. Clearly, the voltammograms are of identical shape, but their position with respect to zero current is shifted. In the case of the reduced form, the current at the positive potential limit exceeds the magnitude of the current at the negative potential limit. The function IsNil,aNyNil,cN will be larger than unity and vice versa for the solution of the oxidised form"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003883_1.2165233-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003883_1.2165233-Figure1-1.png",
        "caption": "Fig. 1 Two-degree-of-freedom model",
        "texts": [
            " Then typical properties of stick-slip limitcycles in the system are presented, with a special note on subcritical limit-cycles in the case of the kinetic coefficient of friction exceeding the static one. Consequently exemplary transition to a stick-slip limit cycle in a linearly stable, subcritical system configuration is shown and discussed. Finally a technique for determining the worst case amplification of the system\u2019s tangential velocity component is presented. Since we are to investigate effects of systems which are prone to mode-coupling instability, the simplest model to set up is a two-degree-of-freedom lumped mass model. A graphical interpretation of the model used is given in Fig. 1. The model may be thought of as a single point mass sliding over a conveyor belt moving with constant speed v. The mass is mainly held in position by two linear springs Kx and Kz parallel and normal to the belt surface. Note that Kz may be regarded as the physical contact stiffness between the objects in relative sliding motion. Moreover, there is another linear spring k oriented at an oblique angle of 45 deg relative to the normal direction leading to off-diagonal entries in the model\u2019s stiffness matrix"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001841_095440603321509711-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001841_095440603321509711-Figure7-1.png",
        "caption": "Fig. 7 Axisymmetric FE modelling of the bolt set with a circular washer",
        "texts": [
            " This would appear to be intuitively the correct situation. Washers are one of most extensively used components in mechanical, aeronautical, automotive and structural engineering. They usually play a very important role in fastener design, as shown in F ig. 7. The main purposes of a washer are to make the interconnection and contact between nut and joint components more stable, more reliable and more durable. For such purposes, it is desirable that the contacts between the nut, plate set and washer have as uniform a stress distribution as possible. Figure 7 shows the axisymmetric FE model for the bolt system, where the washer is placed between the nut and the plate set. Unlike the rivet head studied earlier, the washer involves two opposing contact interfaces. It would be bene cial to simultaneously improve the contact stress distribution for both interfaces during the shape design optimization. The entire washer region is set as the design domain (slightly shaded in Fig. 7), where re-meshing takes place during gap modi cation. Proc. Instn Mech. Engrs Vol. 217 Part C: J. Mechanical Engineering Science C10902 # IMechE 2003 at UNIV OF PITTSBURGH on March 16, 2015pic.sagepub.comDownloaded from Both the individual [equation (7)] and the uni ed design criteria [equation (8)] for the two design regions are applied to this example. D ifferent from the previous example, both criteria lead to the common uniform contact stress over these two regions. This is simply because of the equal but opposite contact design areas and an identical load level"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000332_s0094-114x(96)00076-6-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000332_s0094-114x(96)00076-6-Figure5-1.png",
        "caption": "Fig. 5.",
        "texts": [
            " On the other hand, where there exists the second order contact between E~ and Ecc, the striction points of Yq and Y, cc are coincident while the normal lines of El and Ecc at this point are collinear according to theorem 3 in Ref. [6]. Thus, the normal distance r0 between the line in moving body (or the generator of El, which is collinear with the ruling of Ecc) and the axis of Y, cc in the fixed reference system Of-idfkr is defined as the radius of Ecc and can be written as ro - the common normal of the line in the moving body and the axis of Ecc intersects with the line at point B and with the axis at point 0 B. We call the point B a striction point and define the point 0B as an axis point, see Fig. 5. Substituting equations (27)-(29) into the above equation and combining it with equation (39) or the second group expressions in equation (44), we have sin 0 + fl* cos to sin to _ B, ctg6 = fl* sin 2 tO r0 - 1 + [ f l * ( 1 - + I <q} 12p 1 -- l~ + llfll(1 -- 1~) + fl._] ~ (45) (ll fl~l)~* ,..1_ fl*(1 -- /~1) The above equations are defined as the Euler-Savary analogue of a line trajectory in spatial kinematics, its geometrical significance is shown in Fig. 5. According to Ref. [6], the sign of r0 (+ or - ) in the above equation indicates that the positions of the axis of the osculating constant axis ruled surface Ecc is located on the positive or negative direction of the normal vector ~l) of a line trajectory El at the striction point while the direction of ~1 is determined by equation (18). Now, the properties of the Euler-Savary analogue of a line trajectory in spatial motion are revealed in detail. Since the striction points of the line's trajectories are on a plane (N ml, Nm~x I) or (N \u00b0, N \u00b0 x "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000602_mssp.1997.0092-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000602_mssp.1997.0092-Figure7-1.png",
        "caption": "Figure 7. (a) Three-dimensional view of the four sensors measuring the shaft whirl orbit. (b) Planar view of the four sensors measuring the shaft whirl orbit indicating the undeflected position.",
        "texts": [
            " Here, we prefer a more systematic approach that allows us to solve for the wave amplitudes by using the spatial discrete Fourier transform (DFT). This approach is later generalised for the multi-wavelengths case. 3.1.2. Method II: a spatial approach for separating forward and backward whirls for shafts We can write three equations for the three unknowns (f1(t), f\u22121(t), C) (see Appendix D). Here we prefer to use the Fourier (spatial) transform in order to obtain the desired coefficients and for that purpose we use a hypothetical arrangement consisting of four sensors, as shown in Fig. 7. Separating the static part (x0, y0) for the dynamic part (f1(t), f2(t)) it can be observed that the following relationships hold for the various sensors: s1(t)= x0 + f1(t) s2(t)= y0(t)y0 + f2(t) s3(t)=\u2212x0 \u2212 f1(t) s4(t)=\u2212y0 \u2212 f2(t) (8) From equation (8) it can deduced that only two sensors are required, but for convenience we use all four sensors in the DFT formula, as follows (see also appendix D): pn (t)= s 3 k=0 sk (t) e\u2212i(pkn/4) (9) where k, n=1, 2, 3 and pn (t) is the term associated with the nth nodal diameter motion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000727_j.2168-9830.1999.tb00427.x-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000727_j.2168-9830.1999.tb00427.x-Figure2-1.png",
        "caption": "Figure 2. Dimensions of the conveyor belt system",
        "texts": [
            " Production lots dealt with shortage attributed to the varying heights of products produced during forging. This variance had a negative impact on the company\u2019s profits. The students\u2019 task was to build a model of a system that would automatically transport the products on a conveyor belt. Students had to design a height-sensing conveyor belt system that could recognize the height of the objects within three different ranges. The project called for the design of a model of a conveyor belt system with the dimensions given in figure 2. The system had to be designed in such a way that once an object (a block of less than 20 grams) was placed in a designated space the motor would start running. The conveyor belt was required to stop automatically once the block reached a certain designated place in the system. Three types of blocks would be placed on the belt: \u2022 Blocks which are less than 1\u201d high \u2022 Blocks which are between 1\u201d and 2\u201d high \u2022 Blocks which are more than 2\u201d high The conveyor belt had to have a security system detect the size of the block"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003251_j.comcom.2006.02.012-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003251_j.comcom.2006.02.012-Figure3-1.png",
        "caption": "Fig. 3. Challenges illustration.",
        "texts": [
            " \u2022 Applications, where the sensors and actors in a particular region address different types of events occurring at the same time. For these applications, the following associated challenges need to be addressed while addressing the hazards: \u2022 Parallel dependency among directives: Some applications may not require that all the directives for the event region to execute in an ordered fashion. Directives should be executed sequentially only based on the dependencies with the previous set of directives issued. Consider the case, where there are three sets of dependent directives for a particular event in the network (see Fig. 3(a)). Now, if the dependent sets of directives are completely independent across another set, then the hazard-free operation is only necessary within the individual sets (I1 fi I2 or I3 fi I5 in Fig. 3(a)). Further, if a particular directive (I6 in Fig. 3(a)) requires synchronization with respect to both sets, then that directive should be synchronized with respect to both sets. \u2022 Opportunistic execution of directives: Thus far, we have considered applications, where it is absolutely essential to address all the hazards while executing all the directives. In certain applications, while the relative ordering of directives is important, it may not be important to execute previously issued directives if they arrive outof-order. As an example, consider the case, where the sink sends directives I1 ",
            " Consider the case when the application does not require that all the directives be executed, but only requires that the relative ordering between directives be maintained, if at all a directive is to be executed. In this case, if directives I1 . . . I4 were executed sequentially, and directive I6 arrives before I5, then directive I6 is executed without waiting for directive I5. When directive I5 arrives at a later instance of time, it will be ignored to preserve relative ordering. \u2022 Merging of events: In certain applications, it is possible that two overlapping regions of the network experience an event at about the same time (see Fig. 3(b)). If the events are unrelated, then we must allow the directives for the two set of events to proceed independently. On the other hand, if the events are the same, the set of directives will be dependent across the regions and so the directives must be addressed to both event areas so that the overlapped regions are not acted upon twice. In the fire extinguisher example, this would correspond to two fire outbreaks in close-by regions, that eventually spreads and results in an overlap of event areas. If the intensity of the fire in both regions are similar, then it should be treated as a single event with the union of both areas. \u2022 Pruning of events: When an event that had occurred in a certain region has now decreased in size, then it is necessary that the directives addressed to this event are only executed in the current event region (see Fig. 3(c)). In the fire extinguisher example, if suppose there is a fire in a region and if the intensity of fire is maximum at the center of the region, it is possible that the fire is extinguished fully in the peripheral sub-regions of the event area, while the center is still in flames. In this case, any hazard among the directives issued is only applicable in the current event region. \u2022 Selective directives: Given the vast nature of a WSAN network, it is possible that various regions of the network experience different types of event that require a different set of tasks (see Fig. 3(d)). For example, in the fire extinguisher system, it is possible that a certain region may experience fire, while another nearby region, may be experiencing flooding caused by over reacting to the fire. In this case, the problem should be addressed in such a way that it is possible to issue separate set of directives for the different regions that are not related to each other. Even if the regions overlap, as long as the events are not related to one another, the directives for each event should be executed independently"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003856_s00170-004-2190-8-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003856_s00170-004-2190-8-Figure4-1.png",
        "caption": "Fig. 4. Radius-following device",
        "texts": [
            " The mathematical model of the tension control system shows that the system needs to be compensated in terms of the following three aspects: The radius change of the unwinding roller causes the change of the scroll moment, i.e. the change of F0 R(t) in Eq. 2, where R(t) is detected by a radius tracker. One end of the radiusfollowing arm touches the unwinding spindle, and its other end is connected to the rotating potentiometer via a gear magnifying structure, thus transforming a change in the spindle radius to a change in voltage, as shown in Fig. 4. To reduce the calculating error, the centric line of the following arm is, at the initial state (namely, when the spindle radius is at maximum), set to be tangent with the centric track of the roller, i.e. OB\u22a5AB, where OB is equivalent to arm length L . Based on the relationship between the chord-tangent angle and central angle, the following hold BOC = 2 ABC = \u03b8 sin (\u03b8/2) = BC/2 OB cos (\u03b8/2) = BD/BC BD \u2248 Rmax \u2212 R(t) OB = L trimmed as sin \u03b8 = Rmax \u2212 R(t) L or \u03b8 = arcsin\u22121 Rmax \u2212 R(t) L where Rmax is the maximum radius of spindle and L is the length of radius tracker arm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003996_tase.2005.846289-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003996_tase.2005.846289-Figure3-1.png",
        "caption": "Fig. 3. Cusp triangles in one facet. (a) Triangles in 3-D space and slicing. (b) Projection along direction (single facet). (c) Projection along the direction.",
        "texts": [
            " The staircase effect is always produced when the layer boundaries do not conform to the original model. In view of this, nonplanar LM has been studied to reduce the effect of staircase and the layered processing error [25]. In this paper, we present a different deposition method for this type of flat surface, i.e., the surface where is nearly 0 . The objective of this approach is to minimize the staircase effect through a multidirection deposition. B. Volumetric Error Analysis in the LM Process Consider the triangle shown in Fig. 3(a), which is one of the facets in the STL model. The model is sliced with thickness of along build direction , with the normal of that triangle being , and the angle between the build direction and the surface normal being . The projected view in the direction of reverse is shown in Fig. 3(c), and is the distance between the two sections measured in the plane of triangle; it is obvious that (4) Let be the length of the line resulting from the intersection between this triangle and the slicing planes. If is small enough, we can approximate the area of the cusp triangles by (5) Based on (3), the area of this cusp triangle is (6) Then the volumetric error caused by slicing in this triangle can be represented as (7) Substituting (4) and (5) into (7), we obtain (8) Then, the total volumetric error is (9) For the convenience of description, we define , and this factor is only related to the angle between the deposition direction and the normal of that facet"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003564_epepemc.2006.4778433-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003564_epepemc.2006.4778433-Figure6-1.png",
        "caption": "Fig. 6. Trajectory of IPM-C",
        "texts": [
            " The torque around the supporting point u is not used for this control, and so Zero Moment Point (ZMP) always stays at the supporting point of the inverted pendulum. ZMP is defined as the center of rotation of COG. It is one of the indexes for stability of walking motion [4]. In this research, z = Zc is selected as the constraint line and the biped robot is controlled so that the height of COG is constant. C. Inverted Pendulum Mode with Constant leg length (IPM-C) In IPM-C, COG trajectory is expressed as the motion of an inverted pendulum whose leg length is constant. This inverted pendulum model is shown in Fig. 6. The radius of the arc, which the inverted pendulum draws, is ra. ra equals to Zc. The initial condition is when COG is just above the supporting point of the support foot of IPMC. In this phase, COG moves on a circular orbit whose center is set at the supporting point. Hence, ZMP shifts from the supporting point of LIPM to the supporting point of IPM-C. Equation (10) is derived from the law of conservation of mechanical energy with COG angle \u03b8G = 0 as the initial condition. 1 2 Mr2 a\u03b8\u03072 G = Mgra(1 \u2212 cos \u03b8G) + 1 2 Mr2 a\u03b8\u03072 0 (10) \u03b8G means the angle between COG and the perpendicular line which goes along the supporting point",
            " The symbol \u02c6 means that the vector is expressed in the new coordinate system whose origin is at the supporting point of the new inverted pendulum. From (14), the angle \u03b8\u0302G between perpendicular line which goes along the new supporting point and COG is obtained. Therefore, COG trajectory is calculated as follows. \u03b2 is a parameter to change angular velocity of IPM-C, like \u03b1. x\u0302g = ra cos( \u222b \u03b2 \u02c6\u0307 \u03b8Gdt) (15) z\u0302g = ra sin( \u222b \u03b2 \u02c6\u0307 \u03b8Gdt) (16) The swing leg in IPM-C is controlled so that its ankle moves along the other arc whose radius is rb. It is also controlled so that the ankle position is \u03b8swing away from COG as shown in Fig. 6. The swing leg is set to the position with cubic polynomial in LIPM so that the position and velocity become continuous. The trajectory of the ankle of the swing leg is expressed as follows. xt and zt mean position of the ankle of the swing leg. The origin of the coordinates is at the supporting point of the linear inverted pendulum. xt = lstretch + rb cos( \u222b \u03b1\u03b8\u0307Gdt) (17) zt = rb sin( \u222b \u03b1\u03b8\u0307Gdt) (18) The swing leg touches the ground vertically since its movement is constrained on the arc. rb can be controlled by adjusting the proportion of LIPM to IPM-C"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002386_s0301-679x(01)00116-5-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002386_s0301-679x(01)00116-5-Figure4-1.png",
        "caption": "Fig. 4. Schematic geometry of arc type grooved aerostatic bearing (mm).",
        "texts": [
            " Nakamura [3] reported a theoretical analysis for rectangular thrust bearings with horizontal and vertical grooves. Boffey [4] presented the static characteristics of a single pad bearing under a uniform air gap condition. Chen et al. [5] analyze the static characteristics of the aerostatic bearings with X-shaped grooves by finite element method. This paper aims to clarify the behaviors of grooved aerostatic arc type bearings. The types of air bearings include four axial and circumference-grooves types as shown in Fig. 4. This study forms a numerical approach to the lubrication aspect of this type of bearings. In addition, we propose a computer program dealing with the nonsymmetrical complexity geometry of film gap clearance between the bearing and steel shaft guide, which is Nomenclature a area of the restrictor, cm2 A1\u20135 coefficient of the mass flow rate equation B1\u20135 coefficient of the mass flow rate equation CL stiffness, kg/\u00b5m C1\u20133 coefficient of the mass flow rate equation C0 the orifice discharge coefficient D0 feed hole diameter, mm Ds precision steel shaft guide diameter, mm FL load capacity, kg g acceleration of gravity, m/s2 Gw groove width, \u00b5m hi,j film gap of the bearing at land region, \u00b5m h0 film gap of the bearing at land region in equilibrium position, \u00b5m Hg groove depth,\u00b5m mi, j, i+1, j+1 mass flow of gas in or out the reference area,kg/s M the division number of bearing in horizontal Min mass flow of gas through feed hole,kg/s N the division number of bearing in vertical Pa ambient pressure, kg/cm2 Ps supply pressure, kg/cm2 Pr the recess pressure, kg/cm2 Pi,j pressure distribution of the bearing r radius of the bearing, mm R gas constant, m/K s1, s2 the reference distance T absolute temperature, K y1, y2 the reference distance a declination angle, \u00b0 g declination angle, \u00b0 d declination angle, \u00b0 the gas exponent of heat insulation m coefficient of viscosity, kg s/cm2 r density of gas, kg/m3 \u03c8 the coefficient of orifice outlet flow q angular coordinate in resistance network method, \u00b0 Fig",
            " The static performance of arc type aerostatic bearing for a linear guideway include the load capacity, stiffness, and flow rate of bearings. In the following section we introduce the related characteristics of the proposed aerostatic thrust bearings. Fig. 11 show the pressure distributions of the proposed bearing with grooves by RNM. It can be seen that there are four obvious pressure peaks around each source point. They are calculated with the pressure is 6 Kgf/cm2, and the orifice diameter, 0.2 mm. Other dimensions are shown in Fig. 4, the groove depth Hg is 30 \u00b5m, and the groove width Gw is 0.3 mm. As displays in Fig. 11 the pressure distributions around the feed holes is higher and the decrease in pressure from source point to ambition is slower. Besides pressure distribution in bearing, we can also obtained differential in proprieties such as load capacity, stiffness, and flow rate accompanied with different bearing clearances. Figs. 12 and 13 showed the effects of groove depth and width on the load capacity, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002960_tac.2004.825651-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002960_tac.2004.825651-Figure2-1.png",
        "caption": "Fig. 2. Schematic configuration of a neutrally buoyant multibody underwater vehicle with two proof mass actuators.",
        "texts": [
            " For the unbalanced case, it is shown in [39] that the equilibrium configuration set associated with a shape equilibrium is given by , where is an equilibrium attitude at . Applying Proposition 2, it can be shown that is a conserved quantity [9], [39]. This is consistent with the fact that the vertical component of the inertial angular momentum is conserved. 3) Neutrally Buoyant Multibody Underwater Vehicles: In this section, we consider a class of multibody underwater vehicles in an ideal fluid; a uniform gravitational field is assumed [20]. See Fig. 2 for a schematic configuration illustrating a base body and two proof masses. The base body of the vehicle can translate and rotate freely in three dimensional space according to Kirchoff\u2019s equations. The vehicle is assumed to be neutrally buoyant, but the center of gravity need not be coincident with the center of buoyancy. A base body coordinate frame is chosen with its origin at the center of buoyancy of the system. The configuration manifold is , where , represents the base body attitude, and represents the position of the center of buoyancy of the vehicle in the inertial frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003028_intlec.2005.335203-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003028_intlec.2005.335203-Figure3-1.png",
        "caption": "Fig. 3 dq reference frame.",
        "texts": [
            "3)UDC3 (4) US3 = (-X1-2 +2X3)UDC3 where XI, 22 and 23 represent the commutation command variables of each inverter arm and UDC represents the dc bus voltage of the inverter. From (4), one can model the three phase inverter in a dq reference frame according to (5): Usd = 23[IF COS(0)+\u00b1I2 sin(0)] U = 21[-F sin(0)+F2 cos(0)]sq 1 where, F1 = 2(2US -US2 -US3) r2 = J'2(uS2 u53)UO The phase 0 represents the reference frame position. On the other hand, as the inverter is controlled by current, one can model the dc bus by (7): dlvc =Xl isl + X2'S2 + k3iS3(7dIVC C (7)dt C 2.3 Induction Generator Modelling (3) As illustrated in Fig3, the three phase squirrel cage asynchronous machine model is established considering that de d axis, of the dq reference frame, is over the rotor flux vector, allowing the modelling induction generator by equations (8) to (13): di5d 1 ( 1 '-':SV -a dt Usd + lls,d+(o sq++ AVrd(8)dt GTL,S ars Crr) GtrM di I ( Ia' -cs __ Us- -+ Ijs +0CD)s + ~7Coriy (9) dt aL, sqyrarTSs am rr As it can be seen from Fig2, one can express: dVdM. 1 ==_isd-W-rddt Tr Tr 0 =-isq-((or))rd Tr (10) (11) (-'5) tr-,\\ =e -isqWvrdLr 0)r =npp0)m (13) In the previous equations iyrd, isd, isq represent, respectively, the rotor flux and current components in the stator"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001863_s0094-114x(02)00005-8-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001863_s0094-114x(02)00005-8-Figure1-1.png",
        "caption": "Fig. 1. Illustration of the Denavit\u2013Hartenberg convention.",
        "texts": [
            " If Fb is obtained by rotating Fa through an angle h about the axis described by a unit vector~n, then C\u0302\u00f0a;b\u00de can be expressed as the following exponential rotation matrix [6\u201310]: C\u0302\u00f0a;b\u00de \u00bc e~nh \u00bc I\u0302 cos h \u00fe ~n sin h \u00fe n nt\u00f01 cos h\u00de: \u00f02:1\u00de Here, I\u0302 is the identity matrix, n \u00bc n\u00f0a\u00de \u00bc n\u00f0b\u00de, and ~n is the cross-product matrix generated from n so that ~n v \u00bc n v. This matrix is generated as follows: n \u00bc n1 n2 n3 2 4 3 5 ! ~n \u00bc 0 n3 n2 n3 0 n1 n2 n1 0 2 4 3 5: \u00f02:2\u00de It can be shown that the cross-product matrices and the exponential rotation matrices have the following properties: The kinematic configuration of a 6-joint serial manipulator will be described here by using the DH (Denavit\u2013Hartenberg) convention as illustrated in Fig. 1. According to this convention, the unit basis vectors of the link frame Fk are defined as follows. 1. ~n2 \u00bc n nt I\u0302 ; ~n3 \u00bc ~n: \u00f02:3\u00de 2. ~n ~m \u00bc m nt \u00f0 mt n\u00deI\u0302: \u00f02:4\u00de 3. If u \u00bc ~n m; then ~u \u00bc ~n ~m ~m~n \u00bc m nt n mt: \u00f02:5\u00de 4. rt~n r \u00bc 0; rt~n2 r \u00bc \u00f0 nt r\u00de2 rt r 6\u00bc 0: \u00f02:6\u00de 5. \u00f0e~nh\u00de 1 \u00bc \u00f0e~nh\u00det \u00bc e ~nh: \u00f02:7\u00de 6. e~nhe~n/ \u00bc e~n/e~nh \u00bc e~n\u00f0h\u00fe/\u00de: \u00f02:8\u00de 7. e~nhe ~m/ 6\u00bc e ~m/e~nh 6\u00bc e\u00f0~nh\u00fe ~m/\u00de if m 6\u00bc n: \u00f02:9\u00de 8. e~nh n \u00bc n; nte~nh \u00bc nt: \u00f02:10\u00de 9. e~nh~n \u00bc ~ne~nh 6\u00bc ~n: \u00f02:11\u00de 10. Rotated axis property: If m \u00bc e~nh u, then ~m \u00bc e~nh~ue ~nh; \u00f02:12a\u00de e ~m/ \u00bc e~nhe~u/e ~nh: \u00f02:12b\u00de 11"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000742_bf00198774-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000742_bf00198774-Figure1-1.png",
        "caption": "Fig. 1. a Theoretically derived relation between kinetic energy Em and frequency f for a non-conservative, adiabatically transformed system; the slope represents the adiabatic invariant of action H, E t is the constant energy dissipated per cycle, and fn t is the interception of the relation with the f axis. b Theoretically derived relation between amplitude 0 and period 9 for the system satisfying the f-E., relation in a",
        "texts": [],
        "surrounding_texts": [
            "On the basis of considerations of physical systems exhibiting frequency changes, Kugler and Turvey (1987, Chaps. 10-12) have argued that the ability of a rhythmic movement unit to operate at many different frequencies is anchored in the reciprocal notions of adiabatic transformation and adiabatic invariant. The term adiabatic means \" to not go through\". In its original use it referred to processes in which heat, conceptualized as a substance, did not flow across a system's boundaries (Rankine 1854). The contemporary understanding of adiabatic is different, derived from the modern interpretations of heat and work as ways of transferring energy: A system undergoes an adiabatic transformation when there is no transfer of energy by heating. Usually an adiabatic change is defined as an infinitely slow change, for example, a piston that moves with negligible velocity and, thereby, negligible friction and energy transfer by heating, as it compresses the volume of a chambered gas and changes the frequency with which the gas molecules collide. Kugler and Turvey (1987) argued, however, that the classical rate limitation on adiabatic transformability need not apply when the forces producing the change in the system of interest are derived from an energy reservoir internal to the system. Under these latter conditions rapid transformations can be adiabatic. Kugler and Turvey (1987) also proposed that the term adiabatic applies even when there is dissipation of energy - contrary to the accepted definition - as long as the dissipation is independent of time. Biological systems derive forces from an internal reservoir. Mechanical forces are generated from chemical energy carried \"on-board\" in the tissues of the body. Consequently, according to Kugler and Turvey's hypothesis, biological systems and biological subsystems, such as rhythmic movement units, can be transformed (in principle) adiabatically. The special significance of an adiabatic transformation is that it leaves certain quantities invariant. These quantities are referred to as adiabatic invariants. The quantity action, which is the ratio of average cycle energy to frequency, is an adiabatic invariant. Ehrenfest (1959) referred to adiabatic invariants as \"semi-permanent quantities\" to highlight their hybrid nature; action, for example, is a conserved quantity (energy) in ratio with a variable of motion (frequency). As with constants in general, adiabatic invariants reduce the number of active degrees of f r e e d o m - given two variables linked by a constant, only the value of one of the variables needs to be specified. These semi-permanent quantities, if available biologically, suggest a potentially significant method by which rhythmic movement systems might achieve a reduction in the degrees of freedom to be regulated (Turvey 1990): They can take advantage of constants that arise within the rhythmic activity. Ehrenfest's (1959) original adiabatic hypothesis is that an invariant ratio exists between the oscillatory energy and frequency of a conservative periodic system during transformations that are conducted infinitely slowly. The hypothesis is depicted by a straight line in frequency-energy coordinates with a constant slope (the action) that intersects the origin. According to Kugler and Turvey (1987), if the frequency of a limb moved rhythmically by muscular con t rac t ions - a nonconservative oscillatory s y s t e m - changes via an adiabatic transformation, then the system should behave as in Fig. l a. That is, there should be a linear relation between average cycle energy (Em) and frequency ( f ) , with a constant slope (H) and a positive frequency intercept ( fn t ) and, therefore, a negative energy intercept (E,), where the subscripts m and t denote mechanical and thermal, respectively. The nonconservative adiabatic transformation of frequency is indexed by the constant E, interpreted as the amount of energy that is put into the cycle to offset the energy lost per cycle: changes in cycle frequency (a mechanical quantity) incur no changes in the amount of energy dissipated per cycle (a thermodynamic quantity). The adiabatic invariant is the constant proportionality H (the action) found betwen Em and f - f n t . That is, H = constant = (Em - O)/(f--fnt). (2) The kinematic character of a non-conservative adiabatic system is shown in Fig. lb. It comprises a nonmonotonic, nonlinear relation between amplitude (0) and period (z) over the range z = 0 and z = Tin t (the inverse of lint ) with a maximum value of 0 occuring at z* which is 1/2zi.t (or 2fnt). The z-O relation follows from (2) by writing Em as I/2(02/z2), where I is moment of inertia, and rearranging terms. Thus, 0 = +_ [2Hz2(f- fnt) / I] l /2 (3) Equations (2) and (3) together provide the patterns of relations among the major observables that are predicted by the adiabatic hypothesis of frequency change in biological rhythmic movement systems. From Fig. lb, ~* refers to that period of oscillation at which amplitude is maximal; z* is the rhythmic movement unit's resonant period. Referring to (1), although (o0 and g might be fixed, the composition of F can be variable, meaning that z* can be variable. Variations in z* will rise by virtue of the important fact that F has to be assembled each time from a microstructure of many different components operating at many length and time scales (Schmidt et al. 1991). The assembling and, therefore, the determination of z*, is a \"statistical mechanical\" affair in which the particular ensemble of microcomponents used to produce the macroscopic system is inconstant from one instance to the next. Consequently, each different assembly of F for a given dynamic dictated by co o and g means that the rhythmic movement unit will be characterized by a different r*. Inspection of Fig. lb suggests that if 0 is observed empirically to increase as z increases, then the rhythmic movement unit must be operating in the region in which z exceeds z*. In the plot of Em against f (Fig. la) this means that all data points lie to the right of 2f , t. In contrast, if 0 is observed to decrease as z increases, then the rhythmic movement unit must be operating in the region in which z is less than ~*. In the plot of Em against f (Fig. la) this means that all data points lie to the left of 2f.nt. 1.2 Testing the adiabatic hypothesis It is useful to introduce the phrase \"dynamic run\" (Jackson 1989) for an experimental situation in which an oscillator is observed behaving under fixed values of its parameters. The parameters are the aspects of the system that remain constant (e.g., mass, damping coefficient, stiffness coefficient, and so on) within a dynamic run and are variable only across dynamic runs. The evidence collected to date favoring an Ehrenfest relation has been obtained in a situation in which a biological oscillator is assembled at the outset of a trial and sustained for the duration of a trial (Kugler and Turvey 1987; Kugler et al. 1990). The changes in frequency and, therefore, the changes in the parameters responsible for f requency- occurred discretely across trials, that is, across dynamical runs, with the magnitudes of the changes dictated in largest part by the differences in the conditions imposed across trials. In comparison, locomotory activity (walking, running) is characterized by changes in frequency in which shifts to higher or lower frequency occur continuously, with the timings of the changes, and the sizes of the changes, determined by the locomoting animal. An ordinary bout of locomotory activity, therefore, is not truly a dynamical run. At best, it is a succession of connected dynamical runs. An experimental paradigm directed at evaluating the hypothesis of an Ehrenfest relation in rhythmic movement would do well to mimic the foregoing conditions of movement frequency modulation. In the present research we use a simple approximation to this ideal. A subject begins at a prescribed frequency and then over a given interval of time alters the frequency at will and continuously in either an increasing or decreasing direction. Of concern experimentally is the energetic and spatial changes in the rhythmic movement that accompany the frequency changes. Because of the fluidity of the rhythm and the spontaneity of the changes, analysis is at the level of the individual cycles (e.g., their amplitudes, their durations) and not at the level of mean states. 1.3 Expectations from the adiabatic hypothesis In the continuous-frequency-change task just decribed, the subject is required, at the outset of each trial, to assemble a rhythmic movement unit that oscillates at a frequency f specified by a metronome. Then the subject has to change f continuously in a specified direction (higher or lower, depending on the trial). What should be expected of this rhythmic activity? If the continuous changes in f conform to adiabatic transformations, as hypothesized, then the following outcomes should be observed. (1) The amplitudes 0 of the cycles and the periods z of the cycles will be related systematically. The expected systematic z -O relation need not be fixed, however. It need not be the same from subject to subject; and for a given subject, it need not be the same from trial to trial. As is evident from the z - 0 plot of Fig. lb, the nature of the relation (direct, inverse, direct and inverse) evident in any given trial depends on where the observed cycle durations lie with respect to the z* characterizing the oscillator assembled for that trial. (2) The relation between cycle E,, and cycle f should be positive linear (Era increases as f increases) with the f intercept (fnt) nonzero and positive or, synonymously, the Em intercept (E,) nonzero and negative. (The hypothesis of Kugler and Turvey (1987) predicts that Em can also be independent o f f . This alternative is restricted to conditions in which E,, is at or near the maximum possible. The present experiment was designed to keep the Em magnitudes comfortably below this upper bound. In consequence, the constant E,, of f mapping was not expected.) Predictions (1) and (2) were evaluated through an experiment using the procedure identified above."
        ]
    },
    {
        "image_filename": "designv11_24_0003809_detc2005-84681-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003809_detc2005-84681-Figure2-1.png",
        "caption": "Figure 2: Reference frames used",
        "texts": [
            " DYNAMIC MODELLING Here the emphasis is on modeling the rotating shaft (rotor). Dynamic effects due to high rotational speed and elastic deformations, such as gyroscopic coupling and spin softening, can have a significant influence on spindle behavior. Rotor motion is considered as the superposition of rigid and elastic body displacements. In order to introduce elastic displacements, 2 Copyright \u00a9 2005 by ASME erms of Use: http://www.asme.org/about-asme/terms-of-use Dow the finite element method is used. A special beam element (see figure 2a) is developed and gives a good compromise between precision and complexity. Mass and stiffness element matrices are expressed in a co-rotational frame. Lagrange equations and the additive properties of kinetic and elastic energy enable rotor dynamic equations to be obtained. As presented in figure 2b, a differential section, at initial position x and with thickness of dx , is considered. Reference and co-rotational frames are denoted respectively by ( )000 ,, zyOR = 0, x and ( )1111 ,,, zyxCR = . ( )aaaa zyGR ,,= x x, refers to the frame attached to the section at its center of mass . In the initial configuration coincides with the origin of frame . Finally, xG xG 1R ( )2222 ,,, zyxCR = [ zyxG x uuu=r is an intermediate frame. In a deformed configuration, the position of G is given by three translations, , in the co-rotational frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003044_978-1-4613-2359-4_4-Figure12-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003044_978-1-4613-2359-4_4-Figure12-1.png",
        "caption": "Figure 12. Schemes showing the application of enzymes to promote electrochemical reactions.",
        "texts": [
            " Thus, it can be seen that the study of the electrochemical behavior of protein macromolecules in the adsorbed state can provide highly important information on their redox transformations. It is necessary, however, to take into account the possibility of significant conformational restructuring of pro teins in the adsorbed state. To elucidate the role of conformational changes it is necessary to undertake investigations combining electrochemical and spectral methods. Several methods of using biocatalysts to accelerate electrochemical reac tions have already been developed.(99-100) Their schemes are shown in Figure The first method (Figure 12a, b) involves obtaining, in the course of an enzymatic reaction, intermediates (S*) whose electrochemical transformation on the electrode from a given material into the end product is realized at a lower overvoltage as compared to the initial substrate (sred). The enzyme is solubilized or fixed on the electrode. In this case the overall process is likely to be accelerated; however, it is obvious that not all of the free energy of the reaction sred -+ S + ne is used electrochemically. Nonetheless, this scheme has certain development prospects, since electrochemical transformations of the majority of organic substances proceed at high overvoltage. Another, more general, method involves electron exchange between the electrode and the active center of the enzyme where the substrate is activated and reacts (Figure 12c, d). In this caser the enzyme plays the typical role of an electrocatalyst and its effect corresponds to the notion of \"bioelectrocataly sis\". The central problem is effecting electron transport between the enzyme active center and the electrode. The solution of this problem can be approached by two radically different methods. In the first case (Figure 12c, e), electron transfer from the active center onto the electrode is effected by low-molecular weight carriers-mediators. According to the \"c\" scheme, all reaction components (substrate, mediator, and enzyme) are present in a solubilized state. The reaction takes place in the bulk solution, while the electron transport is effected by a low-molecular weight carrier. According to schemes \"d\" and \"e,\" one of the components, either the mediator or enzyme, is immobilized, but electron transfer is brought about by the mediator",
            " In order that a compound be used as a mediator, it must satisfy quite a number of requirements: 1) the interaction stage between the mediator and the enzyme active center must be fast (the mediator must be a \"specific\" substrate of the enzyme); 2) the normal oxidation-reduction potential of the mediator must be close to that of the reaction concerned; 3) the mediator should be subject to electrochemical oxidation (or reduction) on the electrode made from a given material under conditions close to reversible ones. By no means are all of the known mediators able to meet the above requirements. used in bioelectrocatalysis are given. BIOELECTROCATALYSIS 261 The second, or more accurately, the third method (Figure 12f) represents a radically different organization of electron transport-direct electron exchange between the enzyme active center and the electrode. This variant appears to be most alluring, since it enables us to eliminate the intermediate link associated with the mediator transfer of electrons from the enzyme onto the electrode, and to develop a heterogeneous system not different from conventional, electrocatalytically active electrodes. However, by no means in every case, as will be demonstrated further, is it possible to realize a reaction without the participation of a mediator"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001886_iecon.2000.972612-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001886_iecon.2000.972612-Figure7-1.png",
        "caption": "Fig. 7 Hand-eye system for automatic teaching",
        "texts": [
            " After judging the feasibil ity of this program through simulation, it is loaded down to robot controller and the robot is operated according to the taught program for test. 3 Coordinates calibration In teaching automation by image information, the taught location is represented in two coordinate systems. The first is image coordinate system through which the desired location is taught on image in OLP. The second is robot coordinate systems which is robot world coordinate system of the robot controller. In order to exactly transform image coordinates to robot coordinates, a calibration process should be performed [2], [6], [7]. Fig. 7 shows the configuration of the system to be calibrated. In this configuration, the soldering task is executed on the plane of workpiece which is parallel to the robot base plane. The world coordinates of 6-axis articulated robot are represented as x, y, z, a. ji. r. The x, y, Z represent the position of standard point of robot hand, and a, /1, r represent the orientation of hand [8]. The soldering is supposed to be executed only on one plane, thus calibration process is needed for two dimensional coordinates, x, y"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003687_bf01516929-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003687_bf01516929-Figure5-1.png",
        "caption": "Fig. 5. Buoyancy components",
        "texts": [
            "~ (372 __ ~iy) ~- k l 0 ~4 2 F \") y ( 31 5/i2,~ 1 ~I i ,~) 1 + lO ~---5-+ 2 Ii ~ Y \" Using the boundary conditions for P: L P = 0 at z = + _ 7 we find from eqs. [43], [57], and [58]: p _ q U R c 2 ( Z 2 - + L2) / fi,~ 18 h2,.~ 2 /i,~.~ \"] \u2022 ~3-~-~- + 2 /P 5 P J 9. Buoyancy and frictional force In determining the buoyancy, we disregard the region of enlarged clearance, for which eq. [60] yields a negative pressure. For an elastico-viscous liquid this leaves the interval 02 > 0 > 01, with 0 2 slightly larger than re. (In the Newtonian case, the regarded interval is 0 < 0 < n). The buoyancy components are accordingly (see fig. 5): L/2 02 We = - 2 R L ~ ~ ecosoaoaz, [61] 0 01 L/2 02 IVy = 2 R L ~ ~ PsinOdOdz. [62] 0 Ot The friction force acting on the bearing at y = 0, within the limits of the pressure wave, is given by\" L/2 02 F = 2R ~ ~ Sxy~y=o)dOdz. [63] 0 0~ Sxy = ~/u,y - q z(u,yx u + u,~y v + u,r= w). [64] At y = 0 all terms but the first vanish, and we [58] obtain\" U _ U Sxr = q---c-u,; = q--C--(tio.; + 26~.~). [65] [59] Differentiating [57] and substituting y = 0 , we obtain: 1 /~,x tT,~ = - - + 2 - - [66] h 2h 2 \" Comparative numerical values of the non[60] dimensional buoyancy I f = w c Z / q U L 3, and its components ifx, ifx and the coefficient of Table 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003861_msf.505-507.949-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003861_msf.505-507.949-Figure3-1.png",
        "caption": "Fig. 3. The circular arc tooth profile.",
        "texts": [
            " The transformation matrix from the crown gear rotatable coordinate system pS to internal bevel gear rotatable coordinate system 2S can be obtained and denoted as { } { } { } { } { } { } { } { }2 2 0 0 M M M M m p m p = , and the detail is given as, { } { } 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 cos cos sin sin sin cos sin sin sin cos sin cos 0 cos sin sin cos sin cos cos cos 0 M cos sin cos cos sin 0 0 0 0 1 c c c c c c p c c \u03d5 \u03d5 \u03d5 \u03b4 \u03d5 \u03d5 \u03d5 \u03d5 \u03b4 \u03d5 \u03d5 \u03b4 \u03d5 \u03b4 \u03d5 \u03d5 \u03b4 \u03d5 \u03d5 \u03b4 \u03d5 \u03d5 \u03b4 \u03d5 \u03b4 \u2212 \u2212 \u2212 + \u2212   \u2212 \u2212 =  \u2212 \u2212     . (5) From the above mentioned, to avoid the second undercutting in machining process, the double circular arc profile shown in Fig. 3 is proposed in nutation drive and the normal section of circular arc helical tooth profile in crown gear rotatable coordinate system pS is presented in Fig. 4. Here, \u03c1\u2032 is the polar radius of point nO at actual gear alignment curve of the tooth surface obtained by moving the common symmetry center gear alignment curve in the normal direction with equivalent distance. The amount of this movement is equal to the half width of tooth thickness or space width, the common symmetry center gear alignment curve is a loxodrome with equivalent helical angle \u03b2 and can be denoted as cote\u03b8 \u03b2\u22c5 ; \u03b8 is the rotating angle representing the tooth parameter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001923_robot.1998.677014-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001923_robot.1998.677014-Figure1-1.png",
        "caption": "Fig. 1 Definitions of feathering motion and lead-lag motion",
        "texts": [
            " The mechanism of locomotion of the aquatic animals can provide us with new sights on maneuverability and stabilization of underwater robots. is This paper focuses on biomimesis on maneuver performance of aquatic animals to create a new device for maneuvering of underwater robots. One of the authors developed an apparatus of pectoral fin motion for maneuver of underwater robots based on observation and experimental analysis of pectoral fin motion of Black Bass[2]. The work revealed (1) that the combination of feathering and lead-lag motion of a pair of pectoral fins on both sides of fish (see Fig. 1) dominantly generates the fish motions of forward swimming, backward swimming, hovering and turning, (2) that the apparatus making the feathering motion and the lead-lag motion of the pectoral fin generates thrust force in a certain range of phase difference between both motions., and (3) that the fish robot consisting of fish rigid body and a pair of the apparatus on both sides of the body can perform forward swimming, backward swimming, and turning. 0-7803-4300-~-5/98 $10.00 0 1998 IEEE 446 This paper focuses on (1) maneuver test in horizontal plane of the fish robot equipped with a pair of the apparatus of pectoral fin motion on both sides and (2) guidance and control of the fish robot in horizontal plane, i",
            " GUIDANCE AND CONTROL OF FISH ROBOT WITH A PAIR OF PECTORAL FINS IN HORIZONTAL PLANE We discuss in this section performance of guidance and control of the fish robot with a pair of the pectoral fins in horizontal plane for the docking with an underwater post in a water current. Using sinusoidal motion for the lead-lag motion and feathering motion, the output variables we handle for the motion control of the fish robot in the horizontal plane are phase differences on both sides between lead-lag motion and feathering motion, in total 5 . The input variables are X-axis component of the position, Y-axis component of the position and yaw angle. Because the motion of the fish robot is highly non-linear about the output variables, we use fuzzy control. shown in Fig. 1 1 and that in water currents in Fig. 13. In case without water currents, we use a fbzzy control law of straight forward swimming from point 0 to point A, from point A to point B and fromi point B to point C . In addition, we use a fizzy control law of turning at point C to guide the fish robot precisely to an underwater post at point C. We set the underwater post that has a hole with the diameter of 0.08 m \u20acor docking. In case with a water current of 0.025 d s , we use a fbzzy control law of straight forward swimming from point 0 to point B and from B to C , and f i zzy control law of turning around point B"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001625_0300-9084(89)90188-0-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001625_0300-9084(89)90188-0-Figure5-1.png",
        "caption": "Fig. 5. A plot of dissymmetry, factor value in the 420- and 495-nm bands.",
        "texts": [
            " From the mode of action of the activating cations on the absorban~'e and CD spectra, it can be seen that the torm of the holoenzymc with protonated nitrogen atom of \"internal\" aldimine is a catalytically active form: there is a linear correlation between the V value of fl-elimination and the content of the holoenzyme protonated form (Fig. 4). It has also, been found for E. coli tryptophanase that the holoenzyme with a protonated nitrogen atom in the \"'internal\" aldimine is a catalytically active form [14]. The increase level ef t~-proton labilisation under the action of monovalent cations in the enzyme-inhibitor complex of tyrosine phenol-lyase is also linearly correlated with the content of the protonated coenzyme form (Fig. 5). Therefore, the activating effect of monovalent cations on tyrosine phenol-lyase is most likely, mainly associated with the generation of the active (ketoenamin) enzyme form, which is not only capable of binding the substrates and inhibitors, but can also undergo further transformation (in particular, it can produce an intermediate quinonoid complex with the inhibitors). Apparently, the active form is created owing to conformational rearrangements of the protein. The existence of conformational rearrangements upon cation binding is indicated by a significant change in the dissymmetry ~,ctor value of the CD band for the protonated holoenzyme form and in the dissymmetry factor value of the CD band for the intermediate quinonoid complex of the enzyme with alav"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001108_1.1308033-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001108_1.1308033-Figure5-1.png",
        "caption": "Fig. 5 Experimental apparatus",
        "texts": [
            "asmedigitalcollection.asme.org/pdfaccess.ashx?url= Equation ~12! shows the modification of the web spacing with groove to the web spacing without groove, and it can be used for very small grooves. The applicable range of Eq. ~12! is limited to h0.0; that is Sg, L n heq (13) To confirm the effectiveness of two types of stationary guides, the web spacing is measured for ~a! hollow porous guide and ~b! circumferentially grooved guide, and the measured results are compared with the calculated results. Figure 5 shows the outline of experimental apparatus for measuring the web spacing. The audio-tape is used as the web, which is driven by the capstan motor pressed with nip roller ~4! and sent from the unwinding reel ~1! to the winding reel ~2!. The web velocity is controlled by the capstan motor ~3! to maintain the constant velocity, and the velocity is equal to the surface velocity of the shaft of capstan motor, which is calculated from the rotational speed of motor measured by the tachometer. The web tension is generated by the lever with the spring ~5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003426_1.2120780-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003426_1.2120780-Figure2-1.png",
        "caption": "Fig. 2 \u201ea\u2026 Variables utilized in the static force balance analysis; \u201eb\u2026 Scheme of the laser beam keyhole",
        "texts": [
            " Based on extensive experiments it has been found that to achieve reliable and repeatable droplet detachment, a laser pulse of high power and short duration time has to be applied after the molten pendant droplet formation process, as shown schematically in Fig. 3 8,16 . With the aim to provide an estimate of laser power pulse that causes detachment of a molten pendant droplet, the static force balance of a pendant droplet and heat balance at the onset of the keyhole are analyzed in the following. 2.2.1 Static Force Balance Analysis. A pendant droplet schematically shown in Fig. 2 a is subjected to a gravitational force Fg, surface tension force Fs, and drag due to the gas jet Fdg. Significance of particular terms can be estimated from the material properties, such as density and surface tension of nickel 17 , density and velocity of shielding argon gas, and coefficient of resistance. The surface tension force can be estimated by Fs = 2 rw 8 where represents the surface tension 1.778 N/m for nickel 1 and rw is the wire radius. For the case of this wire, the calculations reveal that the gravitational force and the gas jet force are, respectively, one and two orders of magnitude smaller than the surface tension force",
            " In the keyhole an additional vapor pressure pkh appears so that the pressure in the keyhole exceeds the ambient pressure pa and causes a force on the pendant droplet. Due to the symmetry of the process achieved by the application of three laser beams, the horizontal components of the keyhole pressure forces are theoretically in balance. To estimate the keyhole pressure force Fkh exerted on the droplet in a vertical direction, a keyhole of a depth equal to the wire radius rw is considered, as shown schematically in Fig. 2 b . The keyhole diameter is approximately determined by the diameter of the laser beam d b 20 . From these parameters, the force Fkh on the droplet caused by the developing keyhole is expressed as Fkh = pkhd brw 9 where pkh is the overpressure in the keyhole. In the cases considered in this paper, the force Fkh is three times larger since a triplet of laser beams is used in the experiments. If the keyhole pressure is set to pkh 104 Pa, as suggested in 21 , the estimated keyhole pressure force Fkh prevails in the resultant force on the droplet and it is sufficient to detach the droplet"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003821_iros.2006.282500-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003821_iros.2006.282500-Figure1-1.png",
        "caption": "Fig. 1. Example of a differential-drive mobile robot with relevant variables.",
        "texts": [
            " Another advantage of the proposed method is that it keeps the use of the linearity as in [2]. Finally, differently from most of the algorithms proposed in the literature, no predefined path is required; the mobile robot can then execute a generic path in order to estimate its odometric parameters. Experimental results on a Khepera II mobile robot, whose movement is registered by the use of a video-camera, are reported to validate the proposed approach. Let us consider a differential-drive mobile robot as sketched in Figure 1. The motion of the left and right wheels is characterized by the sole (scalar) axis angular velocities \u03c9L and \u03c9R, respectively; the rear castor wheel is passive. Let us consider a ground-fixed inertial reference frame \u03a3i. By defining as wheelbase the segment of length b connecting the two lateral wheels along their common axis, it is convenient to choose a vehicle-fixed frame \u03a3v such as: its origin is at the middle of the wheelbase, its x-axis points toward the front of the robot body and its y-axis points toward the left wheel, completing a right-hand frame",
            " Therefore, in the vehicle-fixed frame the vector v is completely characterized by its sole x-component denoted as v. By denoting as x and y the coordinates of the origin of \u03a3v expressed in the frame \u03a3i, and as \u03b8 the heading angle between the x-axis of \u03a3v and \u03a3i, the robot kinematic equations are written as \u23a7\u23a8 \u23a9 x\u0307 = v cos(\u03b8) y\u0307 = v sin(\u03b8) \u03b8\u0307 = \u03c9 . (1) Due to the kinematic characteristic of such a differentialdrive robot it can be recognized that the curvilinear abscissa s is easily related to the linear velocity: s\u0307 = v . (2) It can be recognized (see Figure 1) that the body-fixed components v and \u03c9 of the robot velocity are related to the angular velocity of the wheels by [ v \u03c9 ] = \u23a1 \u23a3 rR 2 rL 2 rR b \u2212 rL b \u23a4 \u23a6 [ \u03c9R \u03c9L ] = C [ \u03c9R \u03c9L ] , (3) in which rR and rL are the radiuses of the right and left wheel, respectively. In view of the equations above, it can be observed that: \u03c9 = c2,1\u03c9R + c2,2\u03c9L , (4) with c2,1 = rR/b (5) c2,2 = rL/b . (6) On the other hand, the time derivative of the curvilinear abscissa is related to the wheels\u2019 radii by s\u0307 = rR 2 \u03c9R + rL 2 \u03c9L "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001455_50006-1-Figure5.17-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001455_50006-1-Figure5.17-1.png",
        "caption": "FIGURE 5.17 Axial-field actuator with spring mechanism.",
        "texts": [
            " For example, they are routinely used for positioning read/wri te heads in computer disk drives. These actuators consist of pie-shaped magnets that are positioned above (and/or below) a coil that is free to rotate as shown in Fig. 5.16. When the coil is energized, it experiences a torque and rotates either clockwise or counterclockwise depending on the direction of current. A mechanical component such as a spring is often used to provide a restoring torque, and to fix the unenergized position of the coil (Fig. 5.17). Axial-field actuators can be designed and optimized prior to fabrication using lumped-parameter analysis [9, 10]. We develop a model for performing such analysis in the following example. EXAMPLE 5.9.1 Determine the equations of motion for the axial-field actuator shown in Fig. 5.16. Assume that the coil has n turns. SOLUTION 5.9.1 This device is a moving coil actuator and is governed by Eqs. (5.102), di(t) dco(t) dt = -L VS(t) - i(t)(R + Rr + [(~ x r) x Bext \" oil l [ i ( t ) f c [rx(dlxBext)] l:-ffTmech(0)] dt Ym oil dO(t) dt = ~o(t)",
            "197) into Eq. (5.188) and obtain di(t) 1 dt = L [Vs(t) - i(t)(R + Rcoi,) - nBext(R 2 - R2)(~(t)] dog(t) 1 dt Ym 2 R 2) if_ T m e c h ( 0 ) ] --[i(t)nBext(R - dO(t) dt = co(t). (5.198) These equations are solved subject to the initial conditions of Eq. (5.89). Finally, from Eq. (5.198) we see that the electrical constant K e equals the torque constant K, (see Eq. (5.100)). Specifically, K e - - K t = r/Bext(R 2 - R2). Calculations: We apply Eq. (5.198) to an actuator with the mechanical mechanism shown in Fig. 5.17. Here, the mechanical torque is supplied by the spring. To perform the analysis we need expressions for the coil inductance L and the mechanical restoring torque Zmech(0). Inductance: The inductance of the coil can be estimated by considering a short circular coil with a height h c equal to that of the actuator coil, and with a radius r c, R2 - R1 (5.199) r e = 2 \" To first order, the flux through the center of the coil (through each turn) is 9 2 ~~ (5.200) 9 (i) ~ (h 2 + (2rr Therefore, the flux linkage is A(i) = nq~(i). Recall that the inductance is dA(i) L = (5.201) di ' which gives L ~ ~~ (5.202) (h2c + ( 2 r c ) 2 ) 1/2\" This approximation is appropriate if the mean circumferential arc subtended by the coil is approximately equal to R 2 - R 1 , which is the case for many practical designs. However, if this is not the case the inductance can be determined empirically, or calculated using three-dimensional FEA. Mechanical Torque: The mechanical torque is provided by the spring mechanism shown in Fig. 5.17. The restoring force is F(Y) = k s ( Y - Yo) + Fo, where k S is the spring constant, Yo is the initial spring length, F o is the force 400 CHAPTER 5 Elect romechanical Devices when Y = Yo, and Y is the stretched length. The length Yo is defined by the angle ft. From geometry we have Y = J X 2 + D 2 - - 2XD cos(fl + 0). The restoring torque is given by Tmech(O) = DF(Y(O))cos(fi + 0). (5.203) Analysis: We substitute Eqs. (5.202) and (5.203) into Eq. (5.198) and perform the analysis. The applied voltage V s (t) is shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002064_3-540-36224-x_1-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002064_3-540-36224-x_1-Figure7-1.png",
        "caption": "Fig. 7. Parameterization of configurations of a truck towing two trailers.",
        "texts": [
            " The usual vector fields associated to this system, corresponding respectively to the linear velocity of the truck and to the steering angle time derivative are: Y1 =   cos(\u03b8) sin(\u03b8) sin \u03d50 l1 cos \u03d50 0 \u2212 l2 sin \u03d50+sin \u03d51l1 cos \u03d50+m1 cos \u03d51 sin \u03d50 cos \u03d50l1l2 sin \u03d51l3\u2212l2 cos \u03d51 sin \u03d52 l2l3 + m1 sin \u03d50(cos \u03d51l3\u2212sin \u03d51 sin \u03d52l2) l2l3l1 cos \u03d50   Y2 =   0 0 0 1 0 0   where configurations are parameterized by vector q = (x, y, \u03b8, \u03d50, \u03d51, \u03d52), (x, y) being the position of the middle point of the truck rear axis, \u03b8 the orientation of the truck, \u03d50, the steering angle, \u03d51 the orientation of the first trailer w.r.t. the truck and \u03d52 the orientation of the second trailer w.r.t. the first trailer (Figure 7). As for Hilare and its trailer the tangent linearized system of the above system produces matrices H\u22121(s) that grow exponentially and numerical troubles make the algorithm behave poorly when the interval of deformation becomes large. Once again the solution we propose is based on intuition and we only observed that this solution makes the algorithm behave much better, without any further proof. The idea of this solution is basically the same as for Hilare with trailer and consists in finding a combination of the control vector fields X1 = Y1 + \u03b1(q)Y2 X2 = Y2 such that matrix A(s) of the tangent linearized system (4) about integral curves of X1 has 0 as unique eigenvalue"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003304_0375-9601(81)90164-x-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003304_0375-9601(81)90164-x-Figure1-1.png",
        "caption": "Fig. 1. Calculated melt depthversus time and as a function of Fig. 3. Calculated surface temperature and melt depth versus laser energy density. time with and without taking evaporation effects into account.",
        "texts": [
            " temperature as a function oflaser energy density can The results of the calculation are given in figs. 1\u20143. indeed be well above the melting point of GaAs. ThereThe use of a ruby laser with wavelength 694.3 nm and fore, we have incorporated the effects of evaporation pulse of gaussian shape with FWHM of 20 ns has been in the calculations. From the saturated vapor pressure assumed. In the calculations .~z= 50 nm and z~thave of As at Tm, \u201cv = 0.9 atm, we obtained the saturated been taken according to condition (9). Fig. 1 gives the vapor density at other temperatures according to the thickness of melted GaAs as a function of time and relation n(T) P~/kT.The number of escaping As atlaser energy density. The figure shows that in order to oms may be estimated from n(T)\\/2kT/m t. We get anneal ion-implantation damage in GaAs for a layer of ~2 X 1014 cm\u20142 ns1 for the number of As atoms 200 nm thickness an energy density of 0.6\u20140.8 J/cm2 is needed, assuming melting and liquid phase epitaxy. Experimental data in refs. [14,15] indicate that an- GaAs E~0",
            " It is striking that due to evaporation the melt depth is References reduced by 50% and the melt duration decreases from 60 ns to 45 flS. [1] S.D. Ferris, H.J. Leamy and J.M. Poate, eds., Laser\u2014solid From figs. 2 and 3 it is clear that at laser energy interactions and laser processing (American Institute of densities above I J/cm2 the maximum surface temper- Physics, New York, 1979). ature increases very rapidly and the effect of evapora- [2] C.W. White and P.S. Peercy, eds., Laser and electron beam processing of materials (Academic Press, 1980). tion must become dramatic. From fig. 1 the melt dura- [31 D. Hoonhout, Thesis, Univ. of Amsterdam (1980). tion can be estimated to be 160 ns at 1 J/cm2. Then [4] Proc. MRS Symp. on Laser and electron-beam solid interthe number of evaporated As atoms becomes 3 actions and materials processing (Boston, MA, 1980), to X 1016 cm2. This is a lower limit because we have ig- be published. [5) S.U. Campisano et al., Solid State Electron. 21(1978)nored evaporation below themelting point, whereas 485. decomposition of GaAs is known to occuralready at [61 Y"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000017_s0043-1648(99)00148-9-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000017_s0043-1648(99)00148-9-Figure4-1.png",
        "caption": "Fig. 4. Typical temperature field in the EHD film.",
        "texts": [],
        "surrounding_texts": [
            "For the experiments described in this paper the reference oil Nr. 3 of the Forschungsvereinigung Antriebstech\u017d .nik FVA is used. For the required calculation of the viscosity at every node in relation to local temperature and pressure the following equation was used instead of the w xone published by FVA 12 : w x\u017d .DqE Br qqC5B py10 h sA exp q1q , p 8\u017e /qqC 2=10 24\u017d . Parameters A, B, C, D and E were calculated from the measured viscosity values provided by FVA and are as follows: As3.439P10y5 Pas, Bs1.138=103 8C, Cs 1.063=102 8C, Ds6.600=10y1, Esy9.570=10y3. \u017d .The reason for this substitution is that Eq. 24 correctly describes the viscosity as a decreasing function of temperaw xture, whereas the one given by FVA 12 gives an increasing viscosity with rising temperature, for temperatures higher than 1708C. The pressure viscosity exponent, required for the calculation of the dimensionless parameter \u017d .G, can be obtained from Eq. 24 : 1 A B w x\u017d .DqE Br qqCa s ln q 2q ,2000 8 \u017e /h qqC2=10 q , p0 25\u017d . Finally thermal conductivity at every grid point is calculated as function of the local temperature using the following equation: lsl ya q , where l s0.134 Wr m8C and\u017d .0 l 0 a s7.27=10y5 Wr m8C 2 26\u017d . \u017d .l"
        ]
    },
    {
        "image_filename": "designv11_24_0000161_ft9949000987-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000161_ft9949000987-Figure2-1.png",
        "caption": "Fig. 2 Catalytic waves due to the oxidation of glucose (0.12 mol I - \u2019 ) on a GC electrode modified by hydrogel (type 111) for different redox mediators: 1, 0.25 mmol 1-\u2019 hydroquinone; 2, 0.5 mmol 1-\u2019 [RU(NH~)~(PYZ)]*\u2019; 3, 0.5 mmol I-\u2019- NH,[FeCp,SO,] and 4, 0.5 mmol 1 - Fe(CN):-",
        "texts": [
            " 62%) containing soluble redox species show electrochemical and diffusion behaviour comparable to that of aqueous solutions. The enzyme, however, is present only in the hydrogel layer adjacent to the electrode surface. Dk = P i D , , where D, is the diffusion coefficient in aqueous solution and P i , the square of the partition coefficient for R between the hydrogel and the external electrolyte. Redox Enzyme Catalysis The catalytic waves for anaerobic enzymatic oxidation of Dglucose by GOx immobilized at electrodes, with different redox mediators in aqueous solutions, are shown in Fig. 2. In electrodes of types I1 and 111, the position and shape of the symmetric redox enzyme catalytic waves are the same as described for native GOx and redox mediator in solution, which has been shown elsewhere.16 These waves reflect the changes in surface concentration of the oxidized form of the redox couple. For electrodes of type I, with no BSA matrix, a very small catalytic current was observed as shown in Fig. 1 (dotted line), which can be attributed to the small enzyme loading in that case",
            " As for aerobic conditions a ping-pong mechanism is valid for glucose oxidase and a one-electron redox mediator, however, the intrinsic kinetic parameters differ from those for aerobic kinetics and depend strongly upon the nature and charge of the redox cofactor. The different values observed for the apparent Michaelis constant Kk = K d P , [kl/kcat in reaction (111)] for both redox mediators and oxygen are more difficult to rationalize since they would suggest that the value of k , depends on the nature of the redox cosubstrate. K, has been obtained from the ratio between the slope and the intercept of a plot of C;l i-, us. C; (Fig. 8). Inspection of the simulated concentration profiles in Fig. 7 for hydrogels and in Fig. 2(b) 3 of ref. 22 for soluble enzyme under conditions where eqn. (27) holds, indicates that there is a significant contribution of mass Pu bl is he d on 0 1 Ja nu ar y 19 94 . D ow nl oa de d by T em pl e U ni ve rs ity o n 31 /1 0/ 20 14 1 3: 03 :0 3. 994 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 at y = E , ~ where: transport of substrate which has not been taken into account in deriving eqn. (28). Internal diffusion of substrate could therefore be the source of the observed differences in the values of K s derived"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002398_robot.1991.131855-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002398_robot.1991.131855-Figure7-1.png",
        "caption": "Figure 7:Geometry of constrained motion experiment",
        "texts": [
            "2) where: J (9) *, J (q) E RmXn a q X A - vector of Lagrange multipliers, X E Rm. As in McClamroch and Wang (1988), using a nonlinear transformation the following closed-loop equations of motion are obtained (4.5a) E2 (x2) E; { e2 + G, e 2 + Gd e2 ] = 0 (4.5b) el = O (4.5c) - * x1-xf = 0 * x2-x2. d el e2 - where: As demonstrated in the paper by McClamroch and Wang (1988), the matrices G, and Gd are selected so that e2 + 0 and q + qd as t + 00. The geometry of the manipulator for the constrained motion experiment is shown in Figure 7. With this geometry, we define the constraint h c - tion in terms of joint coordinates as 5. Conclusion This paper has presented experimental results of two control laws applied to robotic manipulators. The discontinuous control law of Mills (1990a) was implemented and has been demonstrated experimentally to solve the complex problem of control of manipulators during the transition to and from contact motion. Stable transitions are seen during implementation of this control. Further, the control is Seen to have a number of highly desireable features which make this control attractive for use in industrial manufacturing settings"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002959_tmag.2005.846254-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002959_tmag.2005.846254-Figure2-1.png",
        "caption": "Fig. 2. Calculated p 1 harmonic of the flux density in time domain presented in complex plane.",
        "texts": [],
        "surrounding_texts": [
            "The impulse method has already shown to be a very efficient tool to calculate the electromagnetic forces created by the rotor eccentricity in induction motors [7]. The paper shows that the frequency response of the flux density harmonics can also be calculated by impulse excitation. The exception is that the frequencies of the response and excitation are not the same anymore. Similarly, the harmonics of the rotor currents, caused by rotor eccentricity, can be calculated by impulse method [12]. The strength of the impulse method is that by one simulation the studied variable is calculated for a wide whirling frequency range. The knowledge of the forces for a wide whirling frequency range is very important when the electromechanical interaction in the rotor dynamics is studied [13]. The behavior of the flux density or rotor and stator current harmonics explains well the behavior of the forces versus whirling frequency."
        ]
    },
    {
        "image_filename": "designv11_24_0003947_icma.2005.1626582-Figure15-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003947_icma.2005.1626582-Figure15-1.png",
        "caption": "Fig. 15. Control Method of Double Tube Catheter for Solid Organs",
        "texts": [
            " Figure 14 shows a curved double tube catheter. This curved double tube catheter is the most simple formation of CMT catheter, and it is considered that CMT catheters of this type are applicable to various medical treatments. Figure 14(a) shows Straight Outer Tube, and Figure 14(b) shows Curved Inner Tube. Figures 14(c) and (d) show the two states of the curved double tube catheter. As shown in Figure 14(c), the curved double tube catheter becomes almost straight in Stat 1 by the difference of the rigidity of tubes. Figure 15 shows the control method of the curved multitube system for solid organ. When this method is used for solid organ, the tissue of the solid organ does not destroyed. VII. VARIOUS APPLICATIONS OF CURVED MULTI-TUBE CATHETER We have started the joint studies with the laboratories in the graduate school of medicine of Osaka University in the fields of liver-paracentesis, venepuncture, and brain surgery. The curved multi-tube system can be applied to various fields of medical treatments as in the following"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002715_j.jcsr.2005.04.020-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002715_j.jcsr.2005.04.020-Figure3-1.png",
        "caption": "Fig. 3. Vertical dimension of the A\u2013A section for the hypar shaped space truss.",
        "texts": [],
        "surrounding_texts": [
            "The finite element method is used to predict the final space formation and post-tensioning forces of the space truss and to investigate the feasibility of the proposed post-tensioning method. The shape formation process induces large deformations, and then the analysis is highly performed with nonlinear analysis. In the finite element analysis herein, the closings of gaps for each of the bottom chords are simulated by the element shortening caused by a negative temperature load. For the analysis by the finite element method the top chords are modeled with beam elements, while the other members are modeled with rod elements. The numerical analysis was performed with MSC/NASTRAN. The shortenings of the diagonal bottom chords are simulated with uniform negative temperature loads proportional to the values of gaps chosen to form a hypar shape. The temperature load is divided into five load steps, and geometric nonlinear analysis is used to consider the large displacement effects in the shape formation analysis. On the basis of the results of the finite element analysis, the coordinates of every joint in the hypar space shape can be obtained. When the final space shape is determined, the post-tensioning forces and induced stresses can be found from current results of the finite element analysis. These results can be used to form the desired space shape with the predicted post-tensioning forces. And the nonlinear analysis was performed with the test model on the load frame for a shaped hypar space truss too."
        ]
    },
    {
        "image_filename": "designv11_24_0001914_rob.10048-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001914_rob.10048-Figure5-1.png",
        "caption": "Figure 5. Definition of the geometric mass center of the moving platform.",
        "texts": [
            " The undeformed lengths of the springs are defined as the given lengths of the limbs, and, hence, they will exert either compression or extension forces on the moving platform for incorrect configurations, as shown in Figure 4. These imaginary spring forces are defined by: Fi = (l\u2217i \u2212 li ) ui (9) where ui is a unit vector that indicates the current direction of the limb, pointing from the base to the moving platform. Secondly, the moving platform is considered as a system of six particles of unit mass connected by massless rigid rods, as shown in Figure 5. The geometricmass center of the systemwith respect to the origin of the moving frame can be obtained from: rC \u2032 = 1 6 6\u2211 i=1 ri (10) Furthermore, the directions of the resultant force and the resultant moment about the mass center can be evaluated respectively as: uF = \u22116 i=1 Fi\u2225\u2225\u2225\u22116 i=1 Fi \u2225\u2225\u2225 (11) and uM = \u22116 i=1 r \u2032 i \u00d7 Fi\u2225\u2225\u2225\u22116 i=1 r \u2032 i \u00d7 Fi \u2225\u2225\u2225 (12) where r \u2032 i = ri\u2212rc\u2032 and \u2016\u2022\u2016 indicate theEuclideannorm of a vector. With these equations in mind, one can see that the configuration error can be reduced effectively by translating the moving platform along uF , and simultaneously rotating it aboutuM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003210_j.robot.2005.09.013-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003210_j.robot.2005.09.013-Figure2-1.png",
        "caption": "Fig. 2. Three-joint robotic manipulator simulator model.",
        "texts": [
            " The a priori information needed for manipulator control analysis and manipulator design is a set of closed form differential equations describing the dynamic behavior of the manipulators. Various approaches are available for formulating the robot arm dynamics, such as Lagrange\u2013Euler, Newton\u2013Euler and Recursive Lagrange [12,13]. The configuration of the three-joint robotic manipulator model and its main dimensions can be seen in Fig. 1. The three-joint robotic manipulator model and the constitution of the (x, y, z) coordinates of the end point in the manipulator model are given in Fig. 2. The equations which were used for the calculation of the (x, y, z) coordinates in the manipulator model are given as (1)\u2013(3): x = (l1 + l2 cos \u03b82 + l3 sin(\u03b82 + \u03b83)) cos \u03b81 (1) y = (l1 + l2 cos \u03b82 + l3 sin(\u03b82 + \u03b83)) sin \u03b81 (2) z = l2 sin \u03b82 \u2212 l3 cos(\u03b82 + \u03b83) (3) where l1, l2, and l3 are the lengths of limb 1, limb 2, and limb 3 respectively and \u03b81, \u03b82, and \u03b83 are the angular positions of joint 1, joint 2, and joint 3 respectively. In this study, Lagrange\u2013Euler is used for dynamics modeling of the three-joint robotic manipulator",
            " The Lagrange\u2013Euler equation of motion is d dt ( \u2202L \u2202\u03b8\u0307i ) \u2212 \u2202L \u2202\u03b8i = \u03c4i (4) where \u03c4i is generalized torque applied to the system from joint i, L is the Lagrangian function (L = K \u2212 P; K : total kinetic energy of the manipulator; P: total potential energy of the manipulator), \u03b8i is the angular position of joint i , and \u03b8\u0307i is the first-order derivative of \u03b8i . The equations which were used for the calculation of the total kinetic energy of the manipulator are given as (5)\u2013(7): K = 3\u2211 i=1 Ki (5) Ki = \u222b dKi (6) dKi = 1 2 (x\u03072 i + y\u03072 i + z\u03072 i )dm (7) where dm is the mass of a constant point inside limb i and xi , yi , and zi are the coordinates of this point, as seen in Fig. 2. The equations which were used for the calculation of the total potential energy of the manipulator are given as (8)\u2013(11): P = 3\u2211 i=1 Pi (8) Pi = \u2212mi gr i 0 (9) r i 0 = Ai 0ri (10) ri = (xi , yi , zi , 1)T (11) where mi is the mass of limb i, g is the gravity vector, Ai 0 is the transition matrix. |g| = 9.8062 m/s2. The main parameters of the manipulator model can be seen in Table 1. The equations which were used for the calculation of the friction effects are given as (12) and (13): \u03c4s(t) = \u03c4viscous + \u03c4coulomb = V1\u03b8\u03071 V2\u03b8\u03072 V3\u03b8\u03073  + K1sgn(\u03b8\u03071) K2sgn(\u03b8\u03072) K3sgn(\u03b8\u03073)  (12) sgn(\u03b8\u0307i ) =  1 if \u03b8\u0307 > 0 0 if \u03b8\u0307 = 0 \u22121 if \u03b8\u0307 < 0 (13) where Vi and Ki are the air and surface friction effects"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000246_s0379-6779(98)00188-x-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000246_s0379-6779(98)00188-x-Figure5-1.png",
        "caption": "Fig. 5. CV of coated electrodes in an acetonitrile solution containing 0.1 y1 \u017d .M TEAPC with a scan rate of 50 mV s at different mole ratio; a \u017d . \u017d .n rn s50, b n rn s100, c PPyrPAAm electrode.AAm Py AAm Py",
        "texts": [
            "acetonitrile solution containing Py and AAm, curve c was obtained, which is regarded as a superposition of \u017d . \u017d . \u017d . \u017d .curve a on curve b . However, curves a and b do not \u017d .strictly add up to make curve c . It must be noted that in the case of using both monomers at the same time, the diffusion limiting current shifts to 1.60 V vs. SCE, indicating the inclusion of AAm to the PPy on the surface of the working electrode. For that reason, the CV of the coated electrodes were taken between 0.00 and 1.50 V in fresh y1 \u017d .electrolyte at a scan rate of 50 mV s Fig. 5 . The conductivity of resulting copolymer coated electrodes depending on the ratio of n rn used in the reactionAAm Py mixture show different characteristics. In the case of lower \u017d .AAm concentration n rn s50 the current obtainedAAm Py of 26.2 mA decreases to 3.0 mA in the case of n rnAAm Py s100 indicating the lower conductivity of the polymer coated electrode which was enriched in AAm. Decreasing current value by increasing AAm concentration in the reaction mixture supports the previous conclusion that more AAm was incorporated to the resulting polymer structure which decreases the conductivity of coated electrode obtained"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003316_cdc.2006.377782-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003316_cdc.2006.377782-Figure4-1.png",
        "caption": "Fig. 4. Earth-fixed and body-fixed reference frame for a ship.",
        "texts": [
            " The passivity framework is applied to obtain an extended class of feedback functions Fi that can address performance properties and increase robustness to disturbance and delays for a group of vessels. Some purposes of formation control for ships are underway replenishment operations, reduced drag forces, cooperative towing, etc. We consider a model of a fully actuated tugboat in three degrees of freedom where the surge mode is decoupled from the sway and yaw mode due to port/starboard symmetry \u2013 see Figure 4. The body-fixed equations of motion for vessel i = 1, . . . , r are given as (see [22] for details) \u03b7\u0307i = R\u03bdi (52a) Mi\u03bd\u0307i + Ci (\u03bdi) \u03bdi + Di (\u03bdi) \u03bdi = \u03c4i (52b) where \u03b7i = [xi, yi, \u03c8i] is the earth-fixed position vector, (xi, yi) is the position on the ocean surface and \u03c8i is the heading angle (yaw), and \u03bdi = [ui, vi, ri] is the body-fixed velocity vector. The model matrices Mi, Ci, and Di denote inertia, Coriolis plus centrifugal, and damping, respectively, while \u03c4i is a vector of generalized control forces and moments, and R is the rotation matrix between the body and the Earth coordinate frame, dependent on the heading angle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002617_1.1139544-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002617_1.1139544-Figure1-1.png",
        "caption": "FIG. 1. Richardson-Dushuman plots for various types of zeolite A. Jo is the saturation emission current density at vanishing electric field strength and is determined from Schottky-type plots. The slopes of the plots provide the ionic work functions.",
        "texts": [
            " Us ing this law the effective emitter area was determined. The evaluated emitting area was always - 20% smaller than the geometrical one. This fact suggested that the temperature was not so uniform as expected. The Schottky plot of the emission current yielded the saturation current density Jo at vanishing field strength. The Richardson-Dushman equa tion appears to be valid for this type of ion emitter, Jo =AT 2 exp( -\u00a2/kT) , where A is the emission area, T is the emitter temperature, \u00a2 is the ionic work function, and k is Boltzmann's constant. Figure 1 shows the plots of log(JoIT2) vs 1/T. The slope of Richardson-Dushman plot provides the work func tion of the ion emitter. Since the slopes for each ion species are different, it appears that the work function depends on ion species of the zeolite. The values of r/> for tested zeolites are summarized in Table I together with published data of TABLE I. Work functions of various alkali aluminosilicate emitters. All work functions (,p) are the results of the continuous emission experiments except those in Ref",
            " 5 We tried to transport relativistic electron beams (REB) with periodic permanent magnet (PPM) ficlds,6 and made a compact, axially movable Faraday cup to measure the tem poral behavior and the axial dependences of the REB. In this note we report the noise tests of the Faraday cup, The PPM had an inner diameter of 20 mm and an axial length of 105 mm. The head of the Faraday cup should, therefore, be smaner than the PPM in diameter, and the stroke of the cup be long enough to cover the axial length of the PPM. Figure 1 shows the cross-sectional view ofthe Far aday cup. Vacuum sealing was obtained with O-rings and a hermetically sealed SMA connector. As a load resistor a 50- ,um-thick, ll-mm-long stainless-steel pipe was argon arc welded at the ends of the cup. The shank was also made of stainless steel. The head had six 2-mm-diam holes on the outer conductor to evacuate the inside of the head. A Kap ton foil was inserted between the outer conductor and the stainless-steel resistor to inhibit charged particles from im pinging on the stainless-steel resistor directly. A carbon col lector was arranged coaxially with the 10ad resistor to reduce residual inductances. J The Faraday cup was turned to move axially, so we can know its displacement by the number of turns. The shank was tightly fixed to the REB generator with a lock nut to get good electrical connection between them. As seen in Fig. 1, the aperture was in direct contact with the PPM with springs to shunt the erroneous current caused 140 Rev. Sci. instrum. 58 (1), January 1987 0034-6748/87/010140-03$01,30 (0) 1986 American institute of Physics 140 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 146.189.194.69 On: Thu, 18 Dec 2014 18:47:02"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003307_elan.200503459-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003307_elan.200503459-Figure1-1.png",
        "caption": "Fig. 1. Cyclic voltammetric response recorded at a Pt microdisk 10 mm radius, in a 100 vol% ethanol solution containing 1 mM Cu2\u00fe and 0.1 M LiClO4; Einitial\u00bc\u00fe0.45 V, Einv\u00bc 0.3 V, v\u00bc 5 mV s 1.",
        "texts": [
            " A Methrom 605 pH-meter (Herisau, Switzerland) and a Crison microCM 2202 conductimeter (Barcelona, Spain) were employed for pH and conductivity measurements, respectively. Electroanalysis 18, 2006, No. 7, 633 \u2013 639 www.electroanalysis.wiley-vch.de J 2006 WILEY-VCH Verlag GmbH&Co. KGaA, Weinheim Preliminary, the cyclic voltammetric behavior of copper ions was investigated in synthetic ethanol-watermixtureswith an ethanol content ranging from 40 to 100 vol%, i.e. to include the volume % of alcohol present in most grappa samples. Figure 1 shows a typical CV response recorded at 5 mV s 1 with a Pt microdisk, in a 100 vol% ethanol solution spiked with 1 mM Cu2\u00feand containing 0.1 M LiClO4 as supporting electrolyte. The voltammogram displays the main features expected for the reduction of a metal ion to the metallic phase under nonplanar diffusion.During the forward scan, a main cathodic wave (II) and a prewave (I) are evident. On reversal of the scan direction, a nucleation loop typical for the growth of ametallic phase onto the solidmicroelectrode surface [31], and a stripping peak due to the oxidation of metallic copper are observed",
            " This prewave could be due to the formation of an intermediate Cu(I) species, partially stabilized by some Cl ions present as impurities in the solution (for example, leaching from the Ag/AgCl reference electrode). If an intermediate Cu\u00fe species is involved in the prewave (I), it therefore resulted the more stable, the higher was the ethanol content. The effect of Cu2\u00fe ions concentration (CCu) on the voltammograms recorded in various ethanol-water mixtures was investigated over the range 5 10 5 \u2013 5 10 3 M. The general voltammetric behavior observed was similar to that shown in Figure 1. However, for a given ethanol-water mixture, the wave (I) to wave (II) height ratio was the lower, the higherCCu, while the current loopon reversal of the scan, by keeping constant the reversal potential, was much less marked as CCu decreased. Also these results are congruent with both the formation of an intermediate transient species (i.e., the secondorderReaction 3), andwith a thinner copper film formed onto the electrode surface. From an analytical point of view, it must be noticed that in all the mixtures studied, the overall reduction limiting current, IL,c, (i",
            " The natural matrices are more complex than the synthetic hydro-alcoholic mixtures, and contain, among others, higher alcohols, esters, fatty acids and other organic substances [34, 35]. These may bind, to a different extent, the copper ions on either Cu(II) or Cu(I) oxidation states. To investigate on the effect of the organic matrix on the voltammetric behavior of Cu2\u00fe, the grappa samples were spiked with known and sufficiently high amounts of Cu2\u00fe ions, to overcome their natural content. The cyclic voltammograms thus recorded displayed a behavior similar to that reported in Figure 1. In the forward scan, however, the first wave was well developed, the nucleation loop on the backward scan was present only for the highest copper concentration (i.e., >0.5 mM) and occurred at more negative potential values. Nevertheless, in any case, a stripping peak was obtained on reversal of the scan, provided that a sufficient long time elapsed once the applied potential was over the plateau region of the second wave. An example of a typical response obtained for a raw grappa sample with an alcohol content of 73 vol% and spiked with 5 10 5 M Cu2\u00fe is shown in Figure 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003752_s0278-6125(06)80012-9-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003752_s0278-6125(06)80012-9-Figure7-1.png",
        "caption": "Figure 7 Improved Design",
        "texts": [
            " I have worked in groups many times in the past and I try to avoid working in groups with members that try to overcomplicate things. What usually happens is that a complicated design that cannot actually be made is created, and the rest of the group is stuck with the burden of how to fix the mess. In the end, the rest of the group is stuck with damage control.\" Eventually one student took the initiative to use a 3-D modeling program to capture the improved de- Journal of Mam<fdcturing Systems Vol. 24/No. 3 2005 sign (Figure 7). Three-dimensional modeling was used to help visualize the final product and to see how it would all fit together. The same student also machined the mold to be used for the manufacture of both the nose cone and the aft body section. At this point, the students not only seemed to be more satisfied with the class project, they also gained recognition from the aero professor and the consultant. What was accomplished during the first four weeks of the class was quite impressive. Leadership and Project Management Each of the main two groups had a group manager who was assigned by the instructor based on her assessment of students' group dynamics during brainstorming sessions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002472_robot.2002.1014811-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002472_robot.2002.1014811-Figure7-1.png",
        "caption": "Figure 7: Margin from falling down or turning over.",
        "texts": [
            "5 Margin from falling down When the humanoid robot is standing or walking, it may fall down by disturbances or other various reasons. Zero Moment Point (ZMP) is a well-known criterion to evaluate the stability of walking. Since we are focusing on static postures, Z M P is simply the projection of the center of gravity of the total system (CG) to the supporting ground. To evaluate the stability margin, we introduce the following index: where Nl denotes the current moment around the reference point and Nl,m, represents the maximum moment allowable around it. For example, if the robot is simply standing as shown in Figure 7(a), we set the reference point to the centroid of the foot. Letting d be the distance from the centroid to the current ZMP, Nl and Nl,\" are given by Nl = Mgd, (7) N1,max = Mgdmax, (8) where M denotes the total weight of the humanoid and g means the amount of acceleration of gravity. In addition, dm, means the maximum value of d, namely the distance between the centroid and the edge of the foot (either the toe or the heel). In case 1, the robot may fall down either forward or backward. We can take the worse value of Cm from these two possibilities. When the humanoid robot is grasping something fixed to the environment, we cannot use eqs.(7) and (8) anymore. For example, Figure 7(b) shows an extreme case where the humanoid is supporting itself by only its arm. In this case, we set the reference point to the pivot, and introduce a new index: where Na and Na,\" are given by (9) where n denotes the current moment applied to the robot hand, and nm, is the maximum moment that the hand can apply. The maximum moment nm, depends on the friction coefficient between the hand and the bar and how firmly the hand grips the bar. Figure 7(c) and (d) illustrate other situations where the robot supports itself by both its arm and leg. In these cases, we have to set the reference points at foot and hand, and the choose the worst one: Considering the turning-over around the grasping point, we can set Na and Na,\" as follows: (13) n if n < 0, 0 if n 2 0. Na = { Na,max = Md+nmax (14) where 1 denotes the distance between the center of gravity CG and the grasping (pivoting) point. Note that 1 should be horizontal distance when CG becomes higher than the grasping point to get a reasonable evaluation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000371_20.717855-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000371_20.717855-Figure3-1.png",
        "caption": "Fig. 3. Pole pitch region ofthe machine.",
        "texts": [
            " 2), and Ss,T is the submatrix of S(a) which describes the interconnections between the edges of potentials cp, and other edges of the band. It can be proved that if the rotor region is empty, i.e. V=VO, J=O, and subdivided into bands of regular elements, similar to the moving band, the torque calculated from (9) is exactly equal to zero, i.e. (9) gives a faultless result. This is the most advantageous property of the presented formula. IV. EXAMPLE Transients in a drive with a 4-pole permanent magnet motor are analysed. The pole pitch region of the machine is shown in Fig. 3. Permanent magnets are mounted on a cylindrical laminated rotor. The single-layer winding is composed of 4 multi-turn coils per phase. The coils are connected in series. The coil-end arrangement is shown diagrammatically in Figs. 3 and 4. The filamentary conductors presented in Fig. 3 lie in the centre of coils. Fig. 4 presents the position of coil ends in the region of all poles. The coil ends of each phase take both the position represented by the arc of radius rl and the position represented by the arc of radius r2. Thus, the phase windings are distributed symmetrically. However, the distributions in the region of each pole pair are different. Therefore, in the case of exact 3D analysis, the region of two pole pairs should be considered. The author proposes to apply a simplified model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002193_87-gt-110-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002193_87-gt-110-Figure1-1.png",
        "caption": "Fig. 1 Cross-section of RR 153 turbocharger",
        "texts": [
            " NOMENCLATURE bearing width, stiffness coefficients, damping coefficients, bearing diameter, [DF- -Re/X/ \"V(Re/ X /1 2 +am/X /1 2 I rotor speed, s-1 floating ring speed, s-1 specific load, N/m2 Sommerfeld number [So - \" 2 1 7/ \u2022 co -1 B CIK dIK 0 DF n nB So damping factor U 151( 71K f unbalance, mkg damping coefficients, dimensionless stiffness coefficients, dimensionless bearing or damper eccentricity, dimensionless Presented at the Gas Turbine Conference and Exhibition, Anaheim, California \u2014 May 31-June 4, 1987 Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use INTRODUCTION The market for small turbochargers, particularly for high speed diesel engines in the range of 600 - 2000 KW per turbocharger unit, has demanded improved overall efficiency as well as a higher flow capacity of the RR 153 turbocharger [1] shown in Fig. 1. It was assumed that this could be achieved by a redesign of the compressor and turbine stages without the need to alter the original rotor-bearing system. However, the selection of a mixed flow turbine for the new turbocharger - the RR 151 (see Fig. 2) - instead of a radial turbine as used in the RR 153, changed the vibration behavior of the rotating machinery drastically. The increased weight of the turbine due to a 40 % increase in flow capacity resulted in significantly higher rotor vibrations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001020_analsci.8.553-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001020_analsci.8.553-Figure4-1.png",
        "caption": "Fig. 4 K+ measurements of aqueous solutions with an ionselective membrane consisting of valinomycin, BBPA as the",
        "texts": [],
        "surrounding_texts": [
            "reference electrodes with a diffusion (convection) barrier as illustrated in Fig. 2, this phenomenon can be sup-\npressed. Thus, the measured potential remains constant during a measuring sequence as presented in Fig. 3 The quality of the membranes and their suitability foi serum assays were carefully evaluated. For sodiumn measurements, the optimized membrane consisted of hemisodium as the ligand, PVC as the matrix and BBPA as the plasticizer. The electrical asymmetry of thf membranes was well below 0.2 mV, the slope was 100\u00b1 1.1 % of the theoretical value, the standard deviation syx of the single values from the linear regression line of the calibration curve in the physiological range was about \u00b10.1 mV. The results of measurements in biological material were equally satisfying: 10 calibration-freE measurements of EMF values on serum samples withirr the physiological range coincided with the theoretical ones (see below) within 0.3 mV, the drift during thf serum measurements being 0.3 mV/ h and the asymmetry potential induced by proteins being below 0.1 mV. The membranes for potassium measurement consisting of valinomycin, PVC and BBPA showec similar properties. With these optimized membranes sera with patho. logical concentrations of sodium and potassium wen assayed. The reliability of the measurements was testec by making a comparison with independent methods especially with flame photometry, and to some extent with measurements utilizing sodium glass electrodes.\nIn the Nicolsky-Eisenman equation (1):20\nEMF[mV] = Eo slog aid KPot(aj)Z''Z' (1, J1\nwith\nEo=EDGE (2,\nand\n2.303RT S =\nziF =59 .2 mV/z1. (25\u00b0C) (3)\nEo is the standard cell potential and depends on E, a constant potential difference (depending on the reference electrodes and the temperature but not on the sample solution) and on ED, the liquid junction potential difference generated between the reference electrolyte and the sample solution. R is the gas constant (8.314 J K-1 mol-1), T the absolute temperature and F the Faraday constant (9.6487X104 C mol-1); zi, zj are the charge numbers of the primary ion I and the interfering ions J; ai, aj are the activities of the respective ions in the sample solution (moll-1); KP\u00b0t is the selectivity factor which describes the preference of the interfering ion J relative to the ion I by the ISE membrane. Ideally, all KP\u00b0t equal zero.\nThe results of measurements in aqueous solutions indicate that the membranes exhibit sufficient selectivity to make corrections for interfering ion obsolete. In addition, the slope of the ion-selective electrode is theoretical within the limits of our measurements. Since the applied membranes as well as the reference electrodes are electrically symmetric, Eo reduces to sample induced changes AED in the liquid junction\npotential ED (Eq. (2)). By utilizing the above described symmetric measuring cell with an electrolyte containing the ion I at an activity a1(r) (reference solution) in one compartment and the sample solution with an activity at(s) in the other, the cell EMF e.g. EMFx is obtained from Eqs. (1) to (3):21\nEMFx[mV] = ZED + s loga;(s)/ai(r). (4)\nWith the chosen reference solution and bridge electrolyte the change in the liquid junction potential DED due to a change from reference to sample solution is sufficiently sma11.15 By neglecting AED and rearranging Eq. (4) the following equation (5) is obtained:\nat(s) - a(r) '10EMFx/s (5)\nFor the following correlations (Figs. 5 - 10) the expressions 10EM>~x/s were plotted on the x-axis of a coordinate system. The activities of the measured ion a1(s) were arranged on the y-axis. In case of measurements of aqueous solutions, these activities were calculated using the Debye-HUckel formalism.22 For serum samples, the activities at(s) are based on values obtained by independently performed FAES measurements. All FAES values were corrected for a lipid/\nprotein volume effect of 7%. The single ion activity coefficients were calculated based on the FAES readings for the measured ion and a constant background identical to the reference electrolyte . solutions. The counter ions were supposed to be ClAccording to Eq. (5) the slope of the correlation lines",
            "ANALYTICAL SCIENCES AUGUST 1992, VOL. 8\nof the activities of the sample solution at(s) versus IOEMFx/s should equal ai(r). Using the Debye-Hi ckel formalism22 a(r) was calculated to be 104.5 mM and 3.13 mM for Na+ and K+ respectively. This is indeed the case for our ab initio measurements. For aqueous solutions the agreement between the fitted values and the theoretical values is very good. The slope of the correlation line for K+ measurements equals 3.14 mM and the one for Na+ measurements is 104.1 mM (see Figs. 4, 5 and Table 1). For sera in the normal concentration range (e.g. 3.5 -\n557\n5.1 mM K+, 136 -145 mM Na+) the a(r) values for K+ measurements is 3% too low, whereas for Na+ measurements they are 3% too high. Liquid junction errors, therefore, are not giving a systematic bias. For both electrolytes the standard deviation syx found is very similar to the one obtained when measuring aqueous solutions (K+, 0.02 mM versus 0.06 mM; Na+, 1.4 mM versus 1.2 mM; see Table 1 and Figs. 6 and 7). As far as sera in the pathological concentration range are concerned (e.g. 2.5 - 7.6 mM K+,115 -161 mM Nat, respectively) the K+ measurements are in very good agreement with the theoretical value (3.15 mM found\nplasticizer and PVC as the matrix. The diffusion barrier as presented in Fig. 2 was employed. The y-axis shows the activities a1(s) of the potassium reference solution values (of the following concentrations: 2.75, 3.25, 4.25, 5 and 5.75 mM K+, respectively), the x-axis indicates the expression 10EMFx/s.\n10EMFx/ s.",
            "558 ANALYTICAL SCIENCES AUGUST 1992, VOL. 8\ncompared to 3.13 mM expected, see Fig. 8). The Na+ values are still 3% too high, compared to the theoretical value (108 mM measured compared to 104.5 mM expected, see 4 mM. Deviations\nof the measured a;(r),"
        ]
    },
    {
        "image_filename": "designv11_24_0001028_hc.520030316-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001028_hc.520030316-Figure3-1.png",
        "caption": "FIGURE 3 Cyclic voltammograms for the l T F (A-D) / glucose oxidase / carbon paste electrodes (scan rate: 10 mWs) in pH 7.0 phosphate buffer (with 0.1 M KCI) solution with no glucose present (dashed line) and in the presence of 100 mM glucose (solid line): (a) mediator A, (b) mediator B, (c) mediator C, (d) mediator D.",
        "texts": [
            " In the constant potential experiments, the background current was allowed to decay to a constant value before samples of a stock glucose solution were added to the buffer solution. A constant background current was attained approximately 10-20 minutes after application of the potential. A C D B 0 1 I I I I I I -50 0 50 100 150 200 250 Applied Potentiol (mV vs. SCE) FIGURE 4 Steady-state current response to 31.5 mM glucose for the TTF (A-D) / glucose oxidase / carbon paste electrodes at several applied potentials. Each point is the mean result for three electrodes. The mediators are indicated next to each curve. 17.5 t 308 Lee et al. Figure 3 shows typical voltammetric results for carbon paste electrodes containing glucose oxidase and the TTF derivatives A-D as electron transfer mediators. With no glucose present, the voltammograms display anodic and cathodic waves due to the oxidation and reduction of the TTF and TTF+ species, respectively. Upon addition of glucose, the voltammetry changes dramatically, with a large increase in the oxidation current and no increase in the reduction current. The fact that the reduction current does not increase along with the oxidation current is indicative of the enzyme-dependent catalytic reduction of the TTF+ produced at oxidizing potential values",
            " Electrodes containing glucose oxidase and the other mediators in Figure 1 (mediators E-H) do not display these voltammetric characteristics upon addition of glucose. Their voltammetric peaks are too small to be measured, and there is no change upon addition of glucose, which indicates that they are not efficient electron transfer mediators. In addition, voltammograms made with carbon paste electrodes containing only glucose oxidase with no mediator do not display the catalytic behavior shown in Figure 3. This mediation is shown conclusively in stationary potential measurements using electrodes modified with both glucose oxidase and the TTF mediators. Figures 4 and 5 show the steady-state response to 3 1.5 mM glucose at several applied potentials for electrodes containing each of the electron transfer mediators. No response to glucose was observed in Arnperornetric Enzyme-Modified Electrodes 309 the absence of either the mediators or glucose oxidase. As expected from the cyclic voltammetry results above, sensors containing mediators A-D display much larger responses to glucose than those containing mediators E-H"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001108_1.1308033-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001108_1.1308033-Figure4-1.png",
        "caption": "Fig. 4 Concept of equivalent web spacing for circumferentially grooved guide",
        "texts": [
            "10, it is necessary to take into account the fluid inertia effects in the derivation of the modified Reynolds equation as has been done by Mu\u0308ftu\u0308 and Cole @18#. Solving numerically the simultaneous equations ~3! and ~8! with the same boundary and continuity conditions in Eqs. ~4! and ~5!, the numerical solutions of web spacing will be determined for prescribed parameters. Web Spacing Analysis for Circumferentially Grooved Guide. In order to take the effects of circumferential grooves into consideration in the web spacing analysis, a concept of equivalent web spacing heq , as shown in Fig. 4, is introduced. The averaged flow model for the Reynolds equation @13,14# can be used to determine the equivalent spacing heq . In that case, however, the equivalent spacing is given by the numerical solutions. For web transporting system designers, it is more convenient to obtain the closed form solution of equivalent spacing. So, in this paper, we have tried to obtain the closed form solution by applying a mass conservation equation as shown in the following. In Region II ~web wrapped region! in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000077_cp:19991029-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000077_cp:19991029-Figure2-1.png",
        "caption": "Figure 2: Simplified model for thefield oriented control of the drive",
        "texts": [
            " To evaluate the influence of the different faults on the machine, the currents are transformed to space vector representation as follows: Where 5' denotes the complex zone factor of the faulted phase and 5, stands for the magnitude of the zone factor for a symmetrical winding. The complex phasor represents the MMF in the air gap of the faulted machine due to the symmetrical values of i,, i2 and i,. This phasor & can be expressed as a superposition of the phasor is of the symmetrical machine and a phasor is,d which is the result of the asymmehy. Model ofthe Drive The machine is connected to a voltage source inverter and is operated with field oriented control under steady state operation. This control is based on a simplified model (fig.2) of the induction machine in order to save calculation time of the signal processor. In this simplified model 171, the total leakage flux will be associated with the stator. The rotor inductance consists only of a main inductance (1 - 0). X, . --U Therefore the stator current space phasor can be separated into two components. m e stator current component j z which is aligned with the rotor flux determines the magnitude of the rotor flux, with the current component perpendicular to the rotor flux is\" the instantaneous torque is adjusted"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003124_3-540-26415-9_80-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003124_3-540-26415-9_80-Figure2-1.png",
        "caption": "Fig. 2. Pitch-Pitch (PP) configuration, composed of two Y1 modules connected in the same orientation.",
        "texts": [
            " Y1 modules can be connected one to each other maintaining the same orientation, so that, they can only rotate on the pith axis. This connection is used for the construction of a chain of modules that rotates in the plane perpendicular to the ground, like in Cube worm-like robot. There is another kind of connection. One module can be rotated 90 in the roll axis and connected to another Y1 module. This configuration has pitch and yaw axis. This configuration is constructed attaching two Y1 modules as shown in Fig.2. Experiments show that this configuration can move on a straight line, backward and forward. Also, the velocity can be controlled. Therefore, this is the minimal possible configuration for locomotion, using this modules. Fig.3a shows the robot parameters. \u03d51 and \u03d52are the rotation angles of the modules 1 and 2 respectively. The locomotion is achieved by applying a sinusoidal function to the rotation angles: \u03d5i = Ai sin ( 2\u03c0 Ti t + \u03c6i ) (1) where i \u2208 {1, 2}. The values of the parameters: Ai, Ti and \u03c6i determines the properties of the movement"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002464_a:1021791817718-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002464_a:1021791817718-Figure2-1.png",
        "caption": "Figure 2. SOT modified with in-situ lubrication device. Top plate rotated upwards for better view.",
        "texts": [
            " Accelerated testing is achieved by limiting the amount of available lubricant. During the test, the lubricant is continuously consumed and eventually the lack of lubricant leads to an increase in the friction coefficient. Failure is defined as when the friction coefficient exceeds some predetermined value, normally 0.28, and the test is shutdown. In a standard test, the ball is lubricated with approximately 50 g before the test begins. Only the ball is lubricated. For the in-situ lubrication tests, the SOT was modified (figure 2) with a heater and collimator. The heater cup contained a drop of liquid Pennzane1 (Nye 2001A). When the friction began to rise above a steady-state value, the heater was turned on and lubricant evaporated. The heater cup consumed 15\u201330W of power during these evaporations. The collimator allowed the evaporant to reach only the wear track on the rotating upper plate and prevented its undesirable deposition elsewhere in the chamber. Once the proper evaporation temperature ( 250 C) of the heater cup was reached, the temperature was maintained until the friction coefficient dropped below the desired level"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003805_07313567908955358-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003805_07313567908955358-Figure8-1.png",
        "caption": "Fig. 8: Prevention of oscillations by control of w 2",
        "texts": [
            " i~ is increased to ~ - step function assumed -, w2 is put to a value to create the torque wanted. If w2 remains constant there will be oscillations as shown in Fig. 7 - in ~2(t) as well as in the torque T(t). If w2 is increased by 6w2 dur~ng 6t in such a way that the wanted steady state position of ~2 is almost reached during the first swing of the spiral - i.e. during 6t - and then 6w2 is put to zero the behaviour of ~2 and therefore of the torque shows very small or even no oscillations and is optimal as is illustrated in Fig. 8. Physically this can be explained as follows: at no load the angle between the axis of the current distribution and the peak of the rotating field is zero. Under load there has to be a phase angle $ between them while both rotate atv+w 2 =w l.Since the ref~rence frame is synchronously rotating 1 1 is always constant and JjJ2 is constant after it has reached an angle $ D ow nl oa de d by [ N an ya ng T ec hn ol og ic al U ni ve rs ity ] at 1 1: 54 1 0 Ju ne 2 01 6 44 D. NAUNIN lagging behind ~ (F ig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002619_095440605x31481-Figure17-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002619_095440605x31481-Figure17-1.png",
        "caption": "Fig. 17 Continuous generating kinematics of a CC5gear, R/m \u00bc f/m \u00bc 10, N \u00bc 20, f \u00bc 258, and q \u00bc 1",
        "texts": [
            " The double-eccentricity method adopted is the same as that of Waguri [29]. Similar to the conceptual development from CV1gears into CV5-gears, the outside- and inside-cutting tools of CC4-gears are alternately arranged on one cutter head that generates CC5-gears in one continuous-indexing process. The straight, parallel cutting edges of the two cutters are located at the same radius R. All the attributes of CC4-gears will be maintained, except that the tooth trace on the base cylinder will be a prolate trochoid, and mating gears have to be right- and left-hand. Figure 17 shows instantaneous relative positions of the two cutters relative to the gear blank. The cutter head and blank are depicted only in synchronized (indexing) rotations, which are related by v \u00bc 2pn/N. The generating-rolling motion components are considered momentarily stopped (the tangential feed rate v and a corresponding blank angular velocity increment 2v/mN cos f). The trochoidal path traced out by the outside finish-cutting point in the plane tangent to the base cylinder will be replicated by the next inside cutter\u2019s point after the base cylinder has moved through a circumferential distance equal to the tooth base space (not a half-pitch)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003625_1-84628-269-1_7-Figure7.4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003625_1-84628-269-1_7-Figure7.4-1.png",
        "caption": "Figure 7.4. Finite element model of the bearing support structure as shown in Figure 7.3",
        "texts": [
            " To establish a reference basis for sensor location comparison, numerical analysis using the finite element (FE) method is performed, based on the geometry of the bearing test bed I shown in Figure 7.3, as described below. Finite element modeling has been applied to the analysis of rotating machine dynamics and defect detection [7.14][7.15]. To investigate the effect of sensor location on signal strength in response to an impulsive input and subsequently, a total of six representative sensor locations, noted as S1 through S6, were identified, as illustrated in Figure 7.4. Selection of location S2\u2013S6 was based on common measurement practice and accessibility to the test bed, whereas S1 was selected based on the concept of \u201cembedded\u201d sensing [7.9][7.10][7.16]\u2013[7.21]. When setting up the FE model for the bearing, contact elements were used to reflect the interactions between the rollers and the bearing raceways. To model the bearing housing structure, the degree-of-freedom along the z-axis was constrained such that only responses in the x and y planes were considered"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003941_physreve.71.056611-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003941_physreve.71.056611-Figure1-1.png",
        "caption": "FIG. 1. Ellipsoid with semiaxes a1 ,a2 ,a3 sa1=a2,a3: prolate spheroid; a1=a2.a3: oblate spheroidd and electric permittivity \u00ab2 and conductivity s2 inside a host medium with permittivity \u00ab1 in the external electric field EW 0.",
        "texts": [
            " III we calculate the basic parameters required to determine the electric field and the electric current of a dielectric ellipsoid with permittivity \u00ab2 and conductivity s2 that is embedded into a host medium with permittivity \u00ab1 and conductivity s1. In Sec. IV we investigate stability of the orientation of particle in the external electric field. Let us consider an ellipsoidal particle with permittivity \u00ab2 and conductivity s2 embedded into a host medium with permittivity \u00ab1 and conductivity s1 in the external electric field with a strength EW 0 ssee Fig. 1d. In a conducting medium a potential component of an electric field EW =\u2212\u00b9W w is determined by the following system of equations: \u00b9W \u00b7 DW = rex, ]rex ]t + \u00b9W \u00b7 jW = 0, s1d where electrostatic induction DW and electric current density jW are determined by the following relations: DW = \u00ab0\u00abEW , jW = sEW , EW = \u2212 \u00b9W w . s2d Hereafter we assume that a particle is at rest. Formula s2d for an electrostatic induction implies that a characteristic time required to attain an equilibrium polarization is substantially smaller than other characteristic times in the problem",
            " Using the obtained results we investigate variation of the electric field during electric charge flow from the external source to the surface of the ellipsoid, variation of the electric charge g at the surface of the ellipsoid and dependence of the electric charge relaxation time upon the geometrical parameters of the ellipsoid. Consider an ellipsoidal inclusion with the half-lengths of the axes a1 ,a2 ,a3, permittivity \u00ab2 and electric conductivity s2 that is immersed instantaneously into a host medium with permittivity \u00ab1 and electric conductivity s1 in the external electric field EW 0 ssee Fig. 1d. The solution of an electrostatic problem is performed in a system of coordinates associated with an ellipsoid. In this system of coordinates the equation of a surface of the ellipsoid and the components of the electric field are determined by the following equations: u = o i=1 3 xi 2/ai 2 \u2212 1, EW = o i=1 3 EieWi, eWi = \u00b9W xi. s5d If before the insertion of an ellipsoidal particle, the electric field was homogeneous then electric potential w can be written in the following form: 056611-2 w = o i=1 3 wi = \u2212 o i=1 3 E0ixi\u201e1 + Fisj,td\u2026 , s6d where j sand coordinates h ,\u00a7 used belowd are the ellipsoidal coordinates determined through x1 ,x2 ,x3 by formulas presented in f17g sChap",
            " Equations s29d and s31d yield a formula for a torque acting at the ellipsoid for an arbitrary orientation of the external electric field and axes of the ellipsoid: MW = \u00ab0\u00ab1Vo i=1 3 o k=1 3 E0iE0k\u00abikmeWmS \u201e1 \u2212 Pistd\u2026k\u00ab 1 + f i\u00ab + Pistdks 1 + f is D , s32d where \u00abikm is a fully nonsymmetric unit tensor. Let us consider a spheroid with a coefficient of the depolarization n1=n2= 1 2 s1\u2212nd, n=n3, f1\u00ab= f2\u00ab, and f1s= f2s. In a case of a prolate in the direction of eW3 spheroid, n3,n1 ,n2, 056611-7 while for an oblate ellipsoid n3.n1 ,n2. The limiting cases of a cylinder sn3!n1 ,n2d and of a disk sn3@n1 ,n2d were considered earlier. Let us define angle u in the plane spanned by vectors EW 0 ,eW3 ssee Fig. 1d. The electric field EW 0 can be represented as follows: EW 0 = E0 cos ueW3 \u2212 E0 sin ueW1. s33d In the adopted coordinate system ssee Fig. 1d a total torque acting at the particle is directed along the eW2 axis, i.e., MW =MeW2. Using Eqs. s32d and s33d we arrive at the following formula for M: M = \u2212 \u00ab0\u00ab1VE0 2 sins2ud 2 Fk\u00abS1 \u2212 P3std 1 + f3\u00ab \u2212 1 \u2212 P1std 1 + f1\u00ab D + ksS P3 1 + f3s \u2212 P1 1 + f1s DG . s34d In a constant electric field at t=0, P3s0d=P1s0d and Ms0d = \u00ab0\u00ab1VE0 2 sins2ud 4 k\u00ab 2s3n \u2212 1d s1 + f1\u00abds1 + f3\u00abd . s35d Equation s35d recovers the known formula for a torque acting at the dielectric spheroid as a function of the angle between the axis of symmetry of the spheroid and the direction of the external electric field EW 0 ssee, e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000431_978-94-015-9064-8_40-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000431_978-94-015-9064-8_40-Figure1-1.png",
        "caption": "Figure 1. The n-bar mechanism (a) and the involved degrees of freedom (b).",
        "texts": [
            " This paper is structured as follows: Section 2 describes the closure equa tions used, Section 3 gives an introduction to interval methods, in Section 4, the basic steps of the algorithm are described and, in Section 5, three different examples are presented. The n-bar mechanism used here was first introduced in (Thomas, 1992) and is defined as a closed single-loop mechanism composed of n links -or bars-, each one being orthogonal to the next bar and having a rotational and a translational degree of freedom (Fig.1). The loop equation of the n-bar mechanism can be expressed as n IT T(di)R(<Pi)Z = I , (1) i=1 where T(di) is a translation along the x-axis, R(<Pi) a rotation around the x-axis and Z a rotation of 1r /2 around the z-axis. The n-bar mechanism is defined by the vector of rotations, \u00a2 ~ (<PI, <P2, ... , <Pn), and the vector of translations, d ~ (d1, d2,.\u00b7\u00b7 ,dn). Any single-loop kinematic chain can be described using an n-bar mech anism. We have been using it as an alternative to the Denavit-Hartenberg parameters to represent spatial mechanisms because of its simple struc ture, which leads to more regular closure equations than using the D-H parameters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003135_1.2389233-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003135_1.2389233-Figure8-1.png",
        "caption": "Fig. 8 Torque on driver pulley",
        "texts": [],
        "surrounding_texts": [
            "om: http://computationalnonlinear.asmedigitalcollection.asme.org/ on 01/ pulley deformation. The following equations describe the pulley deformation effects as introduced by the model in Fig. 3 = 0 + 2 sin \u2212 + 2 R tan = r tan 0 \u2212 tan \u2212 0 1 It is to be noted that although the amplitude of the variation in the pulley groove angle is small, it is not constant during shifting transients. Sferra et al. 17 proposed the following correlations for the variation and the center of the pulley wedge expansion, , Fig. 5 Free body diagram of driver band pack Transactions of the ASME 28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use s t a b f l t a f t d i r m J Downloaded Fr equently gives rise to variations in the band pack tensile force T , as illustrated in Fig. 5. As the belt traverses the pulley wraps, he compressive force Q between the elements builds up. In ddition to the normal and friction forces from the band pack, the elt element is also subjected to the normal and frictional forces rom the pulley, as depicted in Fig. 7. Since the belt slips along the ine AD refer to Fig. 4 , the friction force acts along this line and hus is composed of two components one in the axial direction nd the other in the rotational plane ABE . In addition to the orces acting on the belt, Figs. 6 and 7 highlight the forces and orques acting on the pulley. Similar free-body analysis can be one on a belt segment engaged with driven pulley under the nfluence of load torque, l. The constraint of inextensibility of the belt implies that the time ate of change of length of any infinitesimal element of belt s ust be zero, i.e., d dt s = 0 i . e. ournal of Computational and Nonlinear Dynamics om: http://computationalnonlinear.asmedigitalcollection.asme.org/ on 01/ d dt r cos = 0 3 Further simplification of 3 yields, r\u0307 r + \u0307 tan + 1 d dt = 0 4 Now, for an infinitesimal time step, introducing tangent approximation further reduces Eq. 4 as, r\u0307 r + \u0307 tan + 1 d dt = 0 r\u0307 r + \u0307 tan + \u0308 \u0307 = 0 5 Also, for an infinitesimal time step, tan r\u0307 r\u0307 6 Incorporating 6 into the final equation of 5 results into the following constraint equation for belt inextensibility: r\u0307 \u0307 + \u0307 + r\u0308 = 0. 7 Since the belt is treated as an inextensible strip, the total length of the belt refer to Fig. 9 must be constant. The constraint of constant belt length L can be mathematically expressed as dL dt = 0, where L = 0 rd cos + 0 r d cos + 2d cos = sin\u22121 r \u2212 r d 8 The constraint equation 8 kinematically couples the driver and driven systems to each other. Since the flexural effects of the metal belt are assumed to be negligible, it is reasonable to assume that the belt always exits and enters the pulley tangentially. Using this, the wrap angles can be found to be = \u2212 2 sin\u22121 r \u2212 r d = + 2 sin\u22121 r \u2212 r d 9 The relative velocity between a belt element and the pulley can be readily obtained as, v\u0304rel = r\u0307er + r se s = \u0307 \u2212 Also, tan = r s r\u0307 10 It is to be noted that the relative velocity, v\u0304rel, as given by Eq. 10 is not the actual sliding velocity of the belt element. It only rep- JANUARY 2007, Vol. 2 / 89 28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use r l s s p T o t I s d I t r p s e t t Q S n o M w f 9 Downloaded Fr esents the relative velocity between the belt element and the puley in the rotational plane ABE refer to Fig. 4 . Since the belt lides on the sliding plane refer to Fig. 4 , the actual or true liding relative velocity, vs, between the belt element and the ulley is, in fact, given by, vs = r\u0307 sec2 + tan2 , tan s = tan cos he absolute acceleration of the belt element, a\u0304, can be easily btained from the absolute velocity v\u0304 of the belt element, and is hus expressed as a\u0304 = dv\u0304 dt = r\u0308 \u2212 r\u03072 er + r\u0308 + 2r\u0307\u0307 e 11 n addition to the aforementioned assumptions, the following asumptions are also made in the analysis to aid the solution proceure: \u2022 Uniform pressure distribution dN /rd between the belt and the pulley; \u2022 Assume is negligible and \u0307 \u0307. t is reasonable to assume to be a small quantity as it implies hat the rate at which belt pitch radius changes is smaller than the ate at which belt traverses around the pulley. Moreover, it is lausible that the rate at which the slope angle changes is maller than the rate at which the angular position of the belt lement changes. Under all these assumptions, the following equations refer to he Appendix for detail describe the dynamic interactions beween the belt element and the driver pulley: Kinematics r\u0307 r\u0307 \u0308 = \u2212 r\u0307\u0307 r 12 Driver band pack T\u0307 = aF\u0307 \u2212 br\u0307r\u0308 T\u0307 \u2212 F\u0307 = b \u2212 rr\u0308\u0307 + r2\u03073 + r\u03072\u0307 13 Driver belt element \u02d9 \u2212 aF\u0307 + 2N\u0307 sin \u2212 b cos s sin \u2212 b cos s cos = er\u0307r\u0308 \u2212 Q\u0307 + F\u0307 \u2212 2N\u0307 sin \u2212 b cos s cos + b cos s sin = e \u2212 rr\u0308\u0307 + r2\u03073 + r\u03072\u0307 14 Driver pulley axial force Fz = N\u0307 \u0307 cos + b sin s 15 ince the driver pulley runs at a constant angular speed, the pulley ormal force N can be obtained by summing the torques acting n the driver pulley, thereby, yielding, N\u0307 = \u2212 in\u0307 2 br cos s sin 16 oreover, the constraint of the constant belt length, i.e., Eq. 8 , hich couples the driver to the driven system, reduces to the ollowing form: 0 / Vol. 2, JANUARY 2007 om: http://computationalnonlinear.asmedigitalcollection.asme.org/ on 01/ r\u0307 + r\u0307 = 0 17 Similar analysis of a belt element engaged with driven pulley under load torque conditions yields the equations for the driven system dynamics refer to the Appendix . The pulley flexibility causes the belt pitch radius to change refer to Fig. 3 , which is accounted for by introducing the following equations: = 0 + 2 sin \u2212 + 2 R tan = r tan 0 \u2212 tan \u2212 0 R\u0307 R = r\u0307 r \u2212 \u0307 sec2 \u2212 0 tan 0 \u2212 tan \u2212 0 \u2212 \u0307 sec2 tan \u0307 = \u0307 2 sin \u2212 + 2 + 2 \u0307 \u2212 \u0307 cos \u2212 + 2 18 The time rates of change of amplitude, , and of the center of wedge expansion, , can be obtained from Eq. 2 . There are 14 primary unknowns seven each for driver and driven in the CVT model, as R , ,T ,Q ,F ,N , . Since the driver pulley speed is maintained as a constant, the driver system has only six unknowns. Equations 12 \u2013 14 and 16 can be solved simultaneously to obtain the time histories of the six unknown driver system parameters. Later, appropriate modifications are introduced in the form of pulley bending equations to take flexural effects into account. Knowing the driver system parameters, the driven system solution procedure can be initiated using the constraint Eq. 17 . Almost all the models, except a few, mentioned in the literature use the classical Coulomb-Amonton friction law to model friction between the contacting surfaces of a CVT. The friction phenomenon described by this law is inherently discontinuous in nature. It is a common engineering practice to introduce a smoothening function to represent the set-valued friction law. However, certain friction-related phenomena like chaos, limit-cycles, hysteresis, etc., are neither easy to detect nor easy to explain on the basis of classical Coulomb-Amonton friction theory. It is also quite feasible to have a lubricated contact Stribeck-type friction characteristic in a belt CVT in order to reduce the losses due to wear and thermal effects. Since it is difficult to monitor friction experimentally during the running conditions of a complex nonlinear system e.g., a CVT , mathematical models of friction give insight into the different dynamic maneuvers that a system can undergo. With the aim to understand friction-related dynamics, two different mathematical models of friction were incorporated to describe friction between the belt element and the pulley. Figure 10 depicts the friction characteristics described by these mathematical models. The coefficient of friction between the belt element and the pulley is governed by the following relationship: Case 1: b = a + bo \u2212 a 1 \u2212 e\u2212 vs /b Case 2: b = bo 1 \u2212 e\u2212\u0304 vs 1 + fr \u2212 1 e\u2212\u0304 vs 19 The coefficient of friction mentioned in case 1 describes the classical Coulomb-Amonton friction law which aptly captures the dynamics associated with kinetic friction and is most commonly referenced in the literature. However, the coefficient of friction in case 2 is more detailed as it not only captures the dynamics associated with kinetic friction, but also captures the dynamics associated with stiction- and Stribeck-effects which are prominent under dry and lubricated contact conditions, respectively ."
        ]
    },
    {
        "image_filename": "designv11_24_0001060_0003-2670(92)85135-s-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001060_0003-2670(92)85135-s-Figure2-1.png",
        "caption": "Fig 2 Cathodic stripping voltammograms of Pt electrodes, electrochemically oxidized during 5 min in 1 M H 2 SO4 , and treated with HMDS 1 no HMDS treatment, 2 30 s HMDS, 3 5 min HMDS",
        "texts": [
            " method for on-wafer fabrication of free-chlorine sensors is described The sensor structure consists of a planar three-electrode electrochemical cell covered with a poly(hydroxyethyl methacrylate) hydrogel membrane This membrane is photohthographically patterned on-wafer In order to guarantee good adhesion of the membrane to the electrode surface a special oxidation step consisting of a treatment in an oxygen plasma followed by a silanization procedure has been developed The optimal operational polarization voltage of the integrated sensor for detection of hypochlorous acid was found to be 0 mV vs the on-chip Ag/AgCI reference electrode in a solution of 0 1 M KCI Sensors with membrane thicknesses of 10 and 50 \u00b5m are found to give linear calibration curves between 0 1 and 5 mg 1 -1 free chlorine, with sensitivities of 2 0 and 0 4 nA (mg respectively Keywords Sensors, Chlorine detection, Diffusion membrane, Silicon based sensor There is an increasing need for the determination and continuous on-line monitoring of residual water disinfectant Although several alternatives, like ozone, bromide, iodine or chlorine dioxide, exist for disinfecting purposes, none can compete with chlorine with respect to its effectiveness, easy applicability, presistence and low Correspondence to A van den Berg, Institute of Microtechnology, University of Neuchatel, Rue A -L Breguet 2, CH2000 Neuchatel (Switzerland) 0003-2670/92/$05 00 \u00a9 1992 - Elsevier Science Publishers B V All rights reserved cost [1] At the normal pH values of drinking water (pH 6 5-9), chlorine is present in the form of hypochlorous acid, HC1O, or its conjugated base, the CIO- anion [2] However, since the disinfecting reactivity of HCIO is about 10000 times higher than that of the CIO - anion [3,4], we will focus on the detection of hypochlorous acid Different methods exist to detect dissolved chlorine, most of them based on electrochemical principles A potentiometnc approach, as pro- 76 posed by Schlechtriemen and Sohege [5] for the detection of chlorine gas is less appropriate for on-line monitoring because of its logarithmic response, giving the sensor a large dynamic range but a relatively low precision Detectors based on amperometnc detection respond linearly to concentration variations, and are thus more promising In this case, use is made of the strong oxidative nature of the hypochlorous acid, which enables its electrochemical reduction at a relatively anodic potential thus excluding interference of other oxidants like dissolved oxygen Conventional analyzers often use rotating disk electrodes that provide sufficient sensitivity and selectivity, but are rather bulky systems that are not easily introduced on a large scale for on-line monitoring [6] The same holds for FIA-based systems that use iodometric [7,8] or direct amperometric detection [9] A macroscopic membrane-covered amperometric detector fabricated by conventional techniques with good sensing properties has been described by Ben-Yaakov [10], but this approach lacks the possibility of easy mass-fabrication Finally, an alternative optical detection as recently proposed by Piraud et al [11] for the moment does not attain the required detection limit of about 0 01 mg 1 - I and the measurement system cannot be easily miniaturised The sensor we present here is based on a Clark-type device It uses a planar three-electrode electrochemical cell covered with a thin hydrogel membrane to detect the hypochlorous acid The distinctive feature of our approach is that the entire sensing element is realized on silicon with standard IC-fabrication techniques, implying that the sensing element can be easily and reproducibly mass-produced Thin-film platinum working- and counter-electrodes, and a partially chloridized silver reference electrode were used The latter can be used as a reference electrode since the Cl - concentration in drinking water is fairly constant The electrode reactions taking place at the working electrode (WE) and counter electrode (CE) are respectively WE(cathode) HC1O + 2e ) OH- + Cl - CE(anode) 211 20 0 02+ 4H++ 4e A van den Berg et al / Anal Chim Acta 269 (1992) 75-82 To prevent the convective effects such as stirring from influencing the mass flow to the working electrode, we used a diffusion limiting membrane (DLM) to define a stagnant surface layer m which diffusion is the only process determining the mass transfer and thus the measured current Under potentiostatic operation at a properly chosen working potential, the measured current is proportional to the amount of reduced free chlorine Recently, we have proposed the use of a poly(hydroxyethyl methacrylate) (polyHEMA) hydrogel layer as DLM for the detection of hydrogen peroxide and oxygen [12] This membrane has the advantage that it can be photolithographically polymerized and patterned enabling the fabrication of the complete cell with IC-compatible methods With this technology, polyHEMA layer thicknesses of between 10 and 100 \u00b5m can be realized In this way an optimal trade-off between a high sensor current and a rapid response on one hand (thin membrane) and a signal insensitive to stirring on the other hand (thick membrane) can be chosen Special attention has been paid to the adhesion of the polyHEMA membrane It is known that chemical pretreatment of oxide surfaces such as SI02 and A1203 with methacrylic functional silane strongly improves the adhesion [13] However, such a treatment can not be directly applied to the surface of a platinum electrode Therefore we investigated methods to oxidize and subsequently functionalize a platinum electrode, with the extra requirement that the method should be applicable on-wafer EXPERIMENTAL Basic device fabrication The basic structure consists of a three-elec- trode cell realized on a silicon wafer The working- and counter-electrodes consist of a 1500 A 0 thick Pt layer on top of a 500A thick Ti adhesion layer The reference electrode is made by chemical chloridisation of a 1 \u00b5m thick Ag layer Further details of the fabrication of the device are given in [14] A van den Berg et al / Anal Chun Acta 269 (1992) 75-82 Instrumentation and methods Cyclic voltammetry measurements were per- formed using a PAR 273 potentiostat For all cyclic voltammetric measurements a solution of 1 M H2SO4 and a scan rate of 100 mV s-i were used, except for the determination of the interference of oxygen reduction relative to the hypochlorous acid reduction, where a solution of 0 1 M KCl with 0 01 M phosphate buffer (pH 5 8) and a scan rate of 10 mV s -i were used For potentiostatic measurements a potentiostat built in-house was used The plasma oxidation of the platinum electrodes was carried out using an oxygen plasma in an Alcatel GIR 300 plasma etch machine Measurements of polyHEMA membrane thicknesses were carried out with an Alphastep 200 step height profiler Visual inspections after the measurements confirmed that the scan of the stylus did not cause any damage to the membranes Electrode surface modification Electrochemical oxidation of the platinum electrode surface was carried out by polarizing the electrodes in 1 M H 2SO4 at +25 V vs SCE during 5 min Chemical oxidation was carried out in 0 25 M (NH 4)2 S 20 8 , 0 5 M HCIO, or 1 M HNO3 Plasma oxidation was carried out in an oxygen plasma at a frequency of 13 5 MHz, a pressure of 0 1 mbar, and using a power of 100 W Silanization of the electrode surface was carried out by dipping the electrodes in hexamethyldisilazane (HMDS) (Fluka) Subsequently, the electrodes were blown dry in nitrogen Functionalization of the surface with methacrylic groups was performed by treating the electrodes for 1 min with a solution of 10% (trimethoxysilyl)propyl methacrylate (TMSM) (Aldrich) and 0 5% H20 in toluene at 60\u00b0C Membrane deposition The monomer mixture consisting of 57 5 wt % hydroxyethyl methacrylate (HEMA) (Fluka), 38 wt % ethyleneglycol (EG) (Merck), 1 wt % dimethoxyphenylacetophenone (DMAP) (Aldrich), 2 5 wt % polyvinylpyrrolidone K90 (PVP) (Aldrich) and 1 wt % tetraethyleneglycol 77 dimethacrylate (TEGDM) (Fluka) was placed by pipette on the wafer in an amount corresponding to the required membrane thickness A Mylar sheet was then pressed onto the mixture which was allowed to spread out over the wafer until the required coverage of the wafer was obtained Then the monomer mixture was selectively photopolymenzed with UV light Exposure times of 30 s to 3 min were used This was followed by development in ethanol The sensors were preconditioned in 0 1 M KCl prior to measurement RESULTS AND DISCUSSION Surface modification of the electrodes In the fabrication process of the completed cell with hydrogel membrane, a crucial element concerning the durability is the membrane adhesion to the electrode surface In order to be able to apply the frequently used method of surface silanization, the surface of the platinum electrodes must first be oxidized A well-known standard method to do this is electrochemical oxidation [15] The formation of oxide (mono)layers at the electrode surface can be monitored by reducing the oxide in a cathodic scan starting at high anodic potential In Fig 1 stripping voltammo- 78 grams of platinum, untreated and electrochemically oxidized for 1 s, 3 min and 5 min, respectively, are shown In this figure, two different cathodic waves can be clearly distinguished one corresponding to a quickly formed, and easily reduced oxide (reduction potential about +400 mV vs SCE), and a second wave corresponding to an oxide form that is only formed after a few minutes of polarization at + 2 5 V vs SCE, and reduced at approximately -50 mV vs SCE The presence of these two waves is in good correspondence with the results reported in [14], where they were attributed to two different forms of platinum oxide We will also designate the two waves as A and B for the more anodic and more cathodic waves, respectively, in accord with the nomenclature used in [15] In order to see which one of the two oxides is necessary for the silanization, we performed a simple silanization reaction with HMDS which is comparable to the somewhat more elaborate reaction with TMSM Such a reaction should passivate the formed oxide, and disable its electrochemical reduction In Fig 2 the effects of the silanization on the appearance of both oxide peaks is shown From the three curves representing untreated oxide, oxide treated in HMDS for A tan den Berg et al / Anal Chem Acta 269 (1992) 75-82 30 s, and oxide treated in HMDS for 5 min, two conclusions can be drawn The first and most important conclusion is that the oxide represented by wave A does not react with HMDS The second conclusion is that wave B reacts only relatively slowly with HMDS, and that it takes about 5 min to obtain a fully silanized oxide From the above results it can be concluded that in order to be able to silanize the electrode surface, the formation of platinum oxide of type B is necessary Since electrochemical oxidation is not easily applicable on whole wafers, we investigated other chemical treatments that could provide the platinum type B oxide Unfortunately, treatments with oxidants such as nitric acid, and ammonium peroxodisulfate did not result in the appearance of the type B oxide The only treatment which did give both oxide waves was a treatment in oxygen plasma, as shown in Fig 3 From this figure it can be concluded that a 5-min treatment of the platinum electrode in an oxygen plasma results in similar A- and B-type oxide waves as obtained with the electrochemical oxidation Membrane deposition The deposition of the polyHEMA hydrogel membranes was carried out as described in the A van den Berg et al / Anal Chtm Acta 269 (1992) 75-82 experimental part Some difficulties were encountered when we tried to wash away the unpolymerized regions from the wafer in the development step Therefore we had to modify the mask in such a way that only every second basic electrode was covered with the polyHEMA membrane A SEM micrograph of a part of a wafer covered with membranes is shown in Fig 4 From this figure, it can be concluded that a satisfactory lateral resolution of some tens of microns is obtained, which is largely sufficient for our purpose The homogeneity of the membrane thickness over the wafer was investigated by step-height measurements On 32 evenly distributed membranes over the wafer a mean thickness of 618 \u00b5m was found with a standard deviation of 7 3 \u00b5m An important part of the thickness variation was caused by a continuous varying thickness of the membranes over the wafer If closely located membranes were considered, typical standard deviations of 3-4 \u00b5m were found Sensor characterization A first characterization of the electrodes was carried out to determine the optimal polarization potential for the detection of free chlorine Therefore, cyclic voltammograms were taken of the bare platinum electrodes in background electrolyte under nitrogen and with added sodium hypochlorite A background electrolyte a solution of 0 1 M KCI with 0 01 M potassium dihydrogen- phosphate (pH 5 8) was taken to ensure that all the free chlorine was present as hypochlorous acid In order to examine the interference of oxygen, a third cyclic voltammogram was recorded in background electrolyte and ambient air, as shown in Fig 5 From the cyclic voltammogram of the reduction of hypochlorous acid (at E < + 700 mV vs SCE) and of oxygen reduction (E < + 300 mV vs SCE), a polarization potential \"window\" between + 300 and + 400 mV vs SCE can be determined where the hypochlorous acid reduction is relatively potential independent, and there is no oxygen reduction interference It must be remarked here that the finally desired detection limit for free chlorine is in the micromolar range, whereas the figure shown is obtained with a concentration of 1 mM hypochlorous acid The above mentioned conclusions were verified with potentiostatic measurements carried out with mounted and encapsulated three-electrode devices covered with a polyHEMA membrane of approximately 10 \u00b5m thickness In Fig 6, the sensor current as a function of the free chlorine concentration at three different polarization potentials is measured At the most cathodic potential (- 100 mV vs on-chip reference electrode) an offset current due to oxygen reduction is found At 0 mV this offset current is largely suppressed, whereas the same sensitivity to free chlorine is 79 80 A van den Berg et al / Anal Chum Acta 269 (1992) 75-82 2 1 "
        ],
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        "original_path": "designv11-24/openalex_figure/designv11_24_0003775_1.2748448-Figure3-1.png",
        "caption": "Fig. 3 Parameters of synthesis: \u201ea\u2026 considering point location and \u201eb\u2026 inclination of contact path and major axis of contact ellipse",
        "texts": [
            " 4 Determination of Pinion Machine-Tool Settings on the Basis of Prescribed Conditions of Synthesis The next problem is synthesis of a pinion tooth side surface that is in localized contact with the above-constructed gear tooth surface. The pinion tooth surface is generated by means of a single side method. The following tool parameters, point radius Rc and pressure angle , are known. The synthesis is reduced to interactive selection of the following synthesis parameters: \u2014 displacements r and v of a considering point P 2 with respect to gear tooth surface mean point M 2 Fig. 3 a along a tooth line and along a pitch cone normal. The mean point is located in pitch cone generatrix at a mean cone distance Lm. We shall construct a pinion tooth surface SEPTEMBER 2007, Vol. 129 / 951 7 Terms of Use: http://www.asme.org/about-asme/terms-of-use W c w v i i T s c e c n \u201c t p c T o t c i t a w t r w W 9 Downloaded Fr that provides a contact pattern with center at the point P 2 . The two spherical coordinates of a considering point, distance Lp and altitude p 2 , are the single valued functions of displacements r and v; \u2014 acute angle between axis v of system Puvt and tangent to the contact path at point P 2 Fig. 3 b ; \u2014 desired relative length p=a /b of major contact ellipse Fig. 3 b and depth p of the painter coating or tool point radius Rc; \u2014 coefficient km of the modified roll. e propose that the relation of the blank turn angle with the radle turn angle in the process of generation is = 1 i0 \u2212 + km \u2212 p 2 2 12 here i0 is ratio of a cradle angular velocity to a blank angular elocity in the cradle position = p. Litvin 1 showed that localized contact of gear and pinion teeth s possible in case the transmission error function 2 1 = 2 \u2212 1 z 1 z 2 13 s negative and close to parabolic function 2 1 2 1 2 2 2 = d2 2 d 1 2 1 =0 0 14 he angles 1 and 2 are counted off the gear and pinion poition, then a selected pair of teeth touch each other at the gear onsidering point P 2 ",
            " In the case of modified roll application, generation of the pinion ooth surface that provides the required transmission error 14 is ossible even if a tool of a small diameter is used. We shall propose that pinion tooth surface meets the following onditions 1 : \u2014 gear tooth surface and pinion tooth surface have a common normal in gear considering point P 2 at some gear position; \u2014 in the moment of contact in considering point P 2 the instantaneous gear ratio is equal to its nominal value z 1 /z 2 ; \u2014 desired inclination of a contact path Fig. 3 b ; \u2014 desired major axis of a contact ellipse with center in the considering point Fig. 3 b . he goal of the algorithms that are described in Secs. 4.1\u20134.5 is to bserve the above-mentioned requirements. 4.1 Algorithm for Determination of the Considering Posiion and the Pinion Tooth Surface Considering Point P\u201e1\u2026. The onsidering point P 2 in the gear tooth surface was selected as it s shown in Fig. 3 a . We shall construct the pinion tooth surface hat has only one point of contact with the gear tooth surface at ny phase of engagement. To find the gear considering position e require that in the moment, when the surfaces are in contact at he considering gear tooth surface point, the instantaneous gear atio m21 is equal to its nominal value m21 0 2 = z 1 /z 2 15 hich equals to ratio of pinion tooth number to gear tooth number. e propose that P 2 is located at the point P of immovable space Fig",
            " The relations between increments U, i, A, and E f variables U, i, A, and E are the following: 1 = 1 U U + 1 i i + 1 A A + 1 E E = 0 2 = 2 U U + 2 i i + 2 A A + 2 E E = 0 29 here 1 and 2 are the increments of functions 1, and 2 aused by increments U, i, A, and E of the arguments. We onsider the variables U, i as independent. Increments of all other ariables are determined using 29 as functions of increments U, i. 54 / Vol. 129, SEPTEMBER 2007 om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 08/07/201 4.5 Observation of the Condition Imposed on Length of Contact Ellipse Major Axis. Either a desired relative length p =a /b of major contact ellipse Fig. 3 b and depth p of painter coating, or tool point radius Rc may be considered as conditions of synthesis. In the case of assigned values of p and p, the required tool point radius Rc of the gear tool is searched automatically by solving the equation p ,Rc = p with respect to Rc. For evaluation of p ,Rc at a given Rc the algorithms of Secs. 4.1 and 4.4 are used. If , are the principal axes of quadratic form 20 , the distance t is defined by the relation t= tmin 2 + tmax 2; the major axis of a contact ellipse is presented as a = p / tmin",
            "org/about-asme/terms-of-use N F b t 9 Downloaded Fr 4 The computer program of synthesis is developed that is based on the described technique. Recommendations on the selection of proper synthesis parameters are presented. An example of transmission synthesis and analysis is considered. omenclature A Corrected soft mounting distance A0 soft mounting distance in case a pitch cone apex is located in machine center Le ,Lm external cone distance and mean cone distance Lp distance from pitch cone apex to a point P Fig. 3 ig. 9 Instantaneous contact area \u201eto the top\u2026 and the distriution of maximal major principal tensile stress along the gear ooth 58 / Vol. 129, SEPTEMBER 2007 om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 08/07/201 Mk matrices of coordinate transformation, corresponding to rotation about axis k=x ,y ,z about angle P a point of tooth surface Fig. 2 P n n=1,2 considering point of pinion n=1 or gear n=2 tooth surface Fig. 3 R mean pitch radius R0 ,Rc average tool radius and tool point radius U radial distance b face width Fig. 3 e n unit vector directed along pinion n=1 or gear n=2 axis of rotation Fig. 4 i velocity ratio a cradle angular velocity over a blank angular velocity km coefficient of modified roll m21 1 gear ratio in phase of engagement 1 mn mean normal module q installment angle for tool Fig. 1 r position vector in a coordinate system rigidly connected with a blank t n coefficients of Taylor series expansions of pinion n=1 or gear 2 t-coordinate of tooth surface, determined in own coordinate system =u ,v , ; =u ,v t * 1 coefficients of Taylor series expansion of pinion tooth surface t-coordinate that are defined in gear coordinate system =u ,v , ; =u ,v u ,v , t unit vectors of coordinate system Puvt Fig",
            " 2 uk ,vk coordinates of a point of maximal surface approach u\u0303k , v\u0303k projections of contact point nonmaterial point absolute velocity on coordinate axis u and v of the immovable system xg ,yg ,zg unit vectors of coordinate system Pxgygzg Fig. 2 z n number of teeth of pinion n=1 or gear n=2 machine root angle Fig. 1 A machine center to back Fig. 1 B sliding base Fig. 1 E blank offset Fig. 1 v , r displacements of the a considering point P 2 with respect to gear tooth surface mean point s-section in the vicinity of fillet surface Transactions of the ASME 7 Terms of Use: http://www.asme.org/about-asme/terms-of-use J Downloaded Fr M 2 Fig. 3 along a tooth line and along a pitch cone normal the function of machine-tool settings that describes a difference of current pinion tooth surface from desired one 1 , 2 the functions of machine-tool settings that define lack of coincidence of normals to gear and pinion tooth surfaces at considering point 3 the function of machine-tool settings that characterize difference of current and desired contact path directions matrix of transformation from pinion u 1 v 1 t 1 system to to gear u 2 v 2 t 2 system * matrix of transformation from pinion Oxyz- system to gear Oxyz-system shaft angle Fig. 4 tool pressure angle n , n desired gear pressure angle and spiral angle Fig. 2 n * , n * pressure angle and spiral angle, considered as functions of machine-tool settings , f pitch angle and root angle Fig. 3 p polar angle that define the point P Fig. 2 t distance between mating tooth surfaces along t 2 axis p depth of painter coating in the process of testing , polar angle and cone distance of a point of generating surface angle of contact path inclination Fig. 3 n angle of rotation of the pinion n=1 or the gear n=2 with respect to considering position in the process of meshing 0 n polar angle that define pinion n=1 or gear n =2 considering point Fig. 4 ournal of Mechanical Design om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 08/07/201 current cradle angle in the process of generation p cradle angle in the moment when a generating surface is tangent to it\u2019s envelope at the point P n angular velocities of a pinion n=1 and a gear n=2 References 1 Litvin, F"
        ],
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    },
    {
        "image_filename": "designv11_24_0003999_j.bios.2006.06.002-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003999_j.bios.2006.06.002-Figure3-1.png",
        "caption": "Fig. 3. Schematic diagram of the air-tight cell coupled with an oxygen optical transducer. (1) Aluminium cell body with magnetic stirrer (1\u20131); (2) Teflon gasket; ( ) and (",
        "texts": [
            " / Biosensors and Bioelectronics 22 (2007) 1337\u20131344 3 m e a a a e ( 7 a t m m m u a f c e T C u E A S S C 3) integrated cell cover with glass cover (3\u20131), oxygen-sensitive particles (3\u20132 4\u20132); (5) hood with fastener hook (5\u20131). .2. Biocatalytic action of different enzyme immobilised ethods In order to compare the biocatalytic activity of various nzyme immobilisation methods, enzymatic reactions were rranged to take place in a laboratory-made aluminium biorector (2.0 \u00d7 2.0 \u00d7 3.0 mL) coupled with an oxygen transducer s illustrated in Fig. 3. With this sealed bioreactor, four nzyme immobilisation methods were tested: AOx and HRP 1) deposited on silica gel particles, (2) entrapped within the 00\u20131000 m spongiform, (3) 300\u2013500 m spongiform (Wu nd Choi, 2004) and (4) our current immobilisation architec- s a r able 1 omparison of the bioreaction rates of 20.0 mM methanol in n-hexane catalysed wit nder stir operationa nzymes immobilisation format Particle size ( m) dsorbed on silica gel 50b pongiform formatc 700\u20131000 pongiform formatc 300\u2013500 urrent format 300\u2013500 a Time taken to reach the relative signal change, Rs = 1"
        ],
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    },
    {
        "image_filename": "designv11_24_0003624_acc.1995.532385-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003624_acc.1995.532385-Figure3-1.png",
        "caption": "Fig. 3: Graphical prediction of limit cycle.",
        "texts": [
            " The linear subsystem of Figure 2 is given by 1 s2 + [1,2]s + [0.25,1] G(jo,q) = and the characteristic equation is = O 1 '+ [0'41sz + [1,2]s + [0.25,1] i.e. s2 + [ 1,2]s + [0.25,5] = 0 Hence, the Kharitonov polynomials of the system are K, (s)=sZ+s+0.25 K2 (s) =s2+ 2 s + 5 K3 (s) = s2 + s + 5 K, (s) = s2 + 2 s + 0.25 All four Kharitonov polynomials are second order with positive coefficients and are therefore stable. Hence the system is robustly stable by Theorem 3. The frequency response of G(j w, q) and the describing function N(A, k) are plotted in Figure 3. The figure shows that the describing function plot does not intersect with the value sets of G(j w, 4). Hence, the system is asymptotically stable as concluded using Theorem 3. Conclusion Combining Kharitonov stability theorems with describing function analysis yields a new powerful tool for the prediction of limit cycles in uncertain systems with a separable nonlinearity. The results are applicable in cases where the uncertainty is in the linear subsystem, in the nonlinearity, or both. Two new Kharitonov theorems were derived"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002138_03321640310482869-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002138_03321640310482869-Figure3-1.png",
        "caption": "Figure 3. The cross-sectional geometry of the 15 kW motor",
        "texts": [],
        "surrounding_texts": [
            "Two machines, 15 and 37 kW four-pole cage induction motors were chosen for test motors to study the spatial linearity of the electromagnetic forces. The quarters of the cross-sectional geometry of the motors are shown in Figures 3 and 4 and the main parameters of the motors are presented in Table I. The main difference between these motors is that the 15 kW motor has open and the 37 kW motor has closed rotor slots. The values of the varied parameters in the analysis were the following: the used voltages were 100, 250 V and the rated voltage (380 V for 15 kW motor and 400 V for 37 kW motor). The used values for the slip were s \u00bc 0; 1.6 and 3.2 percent for 15 kW motor and s \u00bc 0 and 1.6 percent for the 37 kW motor. The frequency response functions (FRF) were calculated using a displacement pulse with amplitudes 10, 20, 30 and 40 percent of the air gap. COMPEL 22,4 868 At first, the 15 kW motor, which has open rotor slots was studied. Figure 5 shows the FRF of the radial component and Figure 6 the FRF of the tangential component of the force. The voltage was 100 V and the slip s \u00bc 0 for all the used displacement pulses. The radial component of the FRF grows slightly when the amplitude of the displacement pulse increases. In Figure 5, the upper most curve is calculated by a 40 percent displacement pulse and the lowest is calculated by a 10 percent pulse. The radial component of FRF by the 40 percent displacement pulse is on an average about 18 percent larger than the corresponding response calculated Figure 4. The cross-sectional geometry of the 37 kW motor Parameter (kW) 15 37 Number of poles 4 4 Number of phases 3 3 Number of parallel paths 1 1 Outer diameter of stator (mm) 235 310 Core length (mm) 195 249 Inter diameter of stator (mm) 145 200 Airgap length (mm) 0.45 0.8 Number of stator slots 36 48 Number of rotor slots 34 40 Connection Delta Star Rated voltage (V) 380 400 Rated frequency (Hz) 50 50 Rated current (A) 28 69 Rated power (kW) 15 37 Table I. The main parameters of the test motors An unbalanced magnetic pull 869 by the 10 percent pulse. Anyway, the difference in the FRF is less than 10 percent for the pulses of 20 and 30 percent. The tangential component of the FRF seems to be independent of the amplitude of the pulse in this case. All the four responses in Figure 6 are almost equal, the maximum difference between them is less than 2 percent of the amplitudes. At voltage level 100 V, the maximum value of flux density is 0.69 T, so there are no saturation effects. At 250 V voltage, the maximum flux density is 1.32 T and the saturation slightly affects the magnetic field. Instead, at 380 V voltage, the motor is strongly saturated \u00f0b\u0302 \u00bc 2:04 T\u00de: Figures 7 and 8 show the FRF Figure 5. The radial components of the FRF function of the forces at U \u00bc 100 V, s \u00bc 0 percent for the 15 kW motor. The curves represent all the displacement pulses COMPEL 22,4 870 at rated operating point U \u00bc 380 V and s \u00bc 3:2 percent for all the used displacement pulses. The frequency response functions presented in Figures (5)-(8) have a typical shape for the four pole cage induction motors. The behavior of the FRF as a function of the pulse amplitude is the same for all the calculated voltage levels. To study the spatial linearity more precisely, the electromagnetic forces are calculated from the FRF at the whirling frequency of about 10 Hz. The behavior of the forces as a function of the displacement is similar at reduced voltage levels, so the results are presented only at the 250 V voltage level. The radial Figure 7. The radial components of the FRF of the forces at U \u00bc 380 V, s \u00bc 3.2 percent for the 15 kW motor An unbalanced magnetic pull 871 and tangential component of the forces are presented as a function of the relative displacement in Figure 9 at 250 V and in Figure 10 at 380 V voltage for slip values s \u00bc 0; 1.6 and 3.2 percent. According to the results presented in Figures 9 and 10, the tangential component of the force is almost a linear function of the rotor displacement and it is independent of the slip. However, near to synchronous speed, the tangential component of the force depends strongly on the slip, but it is still a linear function of the rotor displacement. The slip has a visible effect on Figure 9. The forces as a function of relative displacement at 250 V and whirling frequency 10 Hz for the 15 kW motor COMPEL 22,4 872 the radial components of the forces. The radial component of the force follows the analytical theory well in the reduced voltages 100 and 250 V. Table II shows the average difference of absolute value of the total force at whirling frequency range 0-50 Hz as a function of displacement pulse compared with the total force calculated by 10 percent displacement pulse. The difference is calculated by calculating the difference of the absolute value for each of the studied whirling frequencies and taking the average of the differences at valid frequency range. The total forces are calculated by varying the values of the voltage and slip. According to Table II, the frequency response of the forces is almost the same for 10 and 20 percent rotor displacements. We can assume that the spatial linearity is valid for smaller than 10 percent displacements. Actually, Table II shows the error, which results when using the assumption of spatial linearity, at different values of relative rotor displacement for different operating characteristics of the motor. After the analysis of the 15 kW motor, the spatial linearity is studied for the 37 kW motor. Figure 11 shows the FRF of the radial component and Figure 12 the FRF of the tangential component of the force at 400 V voltage in no load condition (s \u00bc 0 percent) for all the used displacement pulses. Figure 11 shows the nonlinear behavior of the forces at this operating point and used displacements. The smallest pulse gives the largest radial component of the FRF. The exception is the synchronous speed, at which no equalizing currents are induced into the rotor cage and the FRF is independent of the pulse. The closed rotor slots can explain the nonlinear behavior. The eccentricity harmonics in equation (8) open the rotor slots magnetically and the damping currents start to flow in the rotor cage when the amplitude of the displacement increases. The tangential components of the FRF (Figure 12) are almost equal s \u00bc 0 percent s \u00bc 1.6 percent s \u00bc 3.2 percent"
        ]
    },
    {
        "image_filename": "designv11_24_0003262_ac00232a013-Figure6-1.png",
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        "caption": "Figure 6. The peak height vs. the applied phase angle in flow conditions, f = 10 Hz. For further conditions see Figure 4.",
        "texts": [
            " Again the dependence of the peak height upon the applied amplitude was measured at two frequencies (see Figure 5). In contrast to the behavior in the batch experiment there is a difference in response for the two 1364 ANALYTICAL CHEMISTRY, VOL. 53, NO. 9, AUGUST 1981 frequencies used. But equally, the peak height increases linearly with the amplitude up to 15 mV, while up to 35 mV there is a favorable gain in signal. In the measurement of the peak height as a function of the adjusted phase angle the difference between batch and flow conditions is striking. In Figure 6 a vectorial representation of the total, capacitive and faradaic currents is given. Especially the relation for the capacitive current differs greatly with that under nonflow conditions. Probably a phase angle shift due to the geometry and construction of the cell could be held responsible for this phenomenon. However, a phase angle of Oo still offers the best distinction of the faradaic component of the total current from the capacitive current. Performance as Detector for HPLC. For the measurement of the linearity of response, sensitivity, and detection limit an actual chromatographic system was adapted"
        ],
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    },
    {
        "image_filename": "designv11_24_0001780_1.1628451-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001780_1.1628451-Figure2-1.png",
        "caption": "FIG. 2. The two angles uX and uY between the resultant force F and its three components Fx ,Fy ,Fz .",
        "texts": [
            "37 The time series of the resultant ground reaction force exerted on the force platform was recorded as the athlete tried to regain balance following the perturbation. For the purposes of the present study the time series of the three forces FX ,FY ,FZ are converted into time series of the two angles uX and uY , with uX being the angle of the resultant force F from the vertical in x anteroposterior direction, and uY being the angle of the resultant force F from the vertical in the y mediolateral direction, see Fig. 2. We present a plot of the time series of the angles uX and uY ~see Fig. 3! and also of the two angles plotted against each other ~Fig. 4!. One of the main features of these graphs is the presence of oscillations; the more unstable the body the larger the oscillation. It should be noted, however, that large oscillations can be considered to be stable under certain constraints ~see Bardy et al.27!. We make the claim that the large scale oscillations seen in Figs. 3 and 4 are due to the motion of the center of gravity of the body as it is perturbed to an unstable state ~i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002326_dac-34138-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002326_dac-34138-Figure7-1.png",
        "caption": "Figure 7 Non-uniform layer building process",
        "texts": [
            " For one non-uniform layer, the distance between the upper slice and lower slice varies from point to point. Due to the difficulty of the deposition thickness control, currently the laser deposition process can only build the layer with uniform thickness. In order to build a non-uniform layer, a uniform (thickness) layer is deposited and then the machining process is carried on to craft the shape of a non- 44 aded From: http://proceedings.asmedigitalcollection.asme.org/ on 01/28/2016 Terms o uniform layer, shown in Figure 7. For a non-uniform layer, the only geometry information is upper slice and lower slice [10]. The geometry of uniform layer for deposition has to be generated first and in this paper it is also called nominal layer or slice. Since the deposition shape is defined by two slices and the lower slice (bottom slice) is the substrate for the current layer, the task for finding the geometry of the uniform layer is to find a nominal upper slice. Upper slice generation (geometry generation) The two slices forming the geometry of the non-uniform layer consist of a set of loops with a number of edges [10]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000602_mssp.1997.0092-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000602_mssp.1997.0092-Figure6-1.png",
        "caption": "Figure 6. One nodal diameter motion of a shaft with a rigid disc.",
        "texts": [
            " Rotating shafts with flexible discs Flexible discs exhibit a spatial vibratory response having more than a single nodal xdiametral component. At a constant radial position r= r0, one can express the spatial displacement at any angular location by superposition of wave functions [8]: Cn (r0) einu and C\u2212n (r0) e\u2212inu (3a) where r0 and u measure the radial and angular locations on the disc respectively and n represents the number of nodal diameters on the disc. In the disc co-ordinate system, a pictorial representation of the first nine possible wave functions (i.e., n=1, 2, . . . , 9) is shown in Fig. 6, for a specific radial location r= r0. Since we are dealing with a rotating structure, the combinations of all the mentioned patterns (wave functions) can be time-varying, so that a stationary sensor located at (r0, u) in a polar co-ordinate system will measure a time-varying superposition of the spatial forms: su (t)= s a n=0 pn (t) einu + p\u2212n (t) e\u2212inu (4) Here pn (t) (p\u2212n (t)) are the time-varying forward (backward) n-nodal diameter related amplitudes. su (t) is the signal measured by a sensor located at an angle u"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002006_978-3-662-09769-4-Figure8.4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002006_978-3-662-09769-4-Figure8.4-1.png",
        "caption": "Figure 8.4: Geometry of the mechanism",
        "texts": [
            " The drive wheel is driven by an engine which exerts a torque MD on the mechanism. 8.2.1 Notations The model equations of the mechanism will be derived on the assumption that the vehicle does not move while the wheels rotate around the axles (a vehicle which is mounted on a test stand). Let Ci (i = 1, ... , 6) be the centers of mass of the bodies, and consider Pi as the reference points which are fixed on the bodies. Subsequently, Pi will be identified with Ci for i = 1, ... , 6. The mutual contact points of the wheels are called Q1 , ..\u2022 , Q5 (Figure 8.4). Let \u00b7- ( T T T) T llll36 P .- P1 , P2 , \u00b7 \u00b7 \u00b7 , P6 E l\u00df (8.35a) be the vector of the Cartesian coordinates of the mechanism with and R ._ ( R R R )T rP;O .- xp,o, Yp,o, zp,o ' (8.35b) M D to rq ue o f th e en gi ne (5 ) cr ow n w he el (a ) T ec hn ic al d ra w in g (b ) Sc he m at ic d ra w in g F ig ur e 8. 3: D ra w in g o f th e di ff er en ti al g ea r w ~ n M 2 = M A 2- M B2 \"'\" <0 O l ?\" w '\"C :I ~ \u00a7.: 8 ~ ::s - \u00a7 u; \u00b7 ~ \"'1 ~ ::s - ~ .... e:. .... o3 : 0. . c:r 0 0. . (;) \" fJ J 8.2 Differential gear (two rot",
            "39j) and finally, (8.39k) The assaciated constraint velocity equation is ( 0 , -Wz3 , Wy3 ) ( 0) Wz3 , 0 , -Wx3 \u00b7 0 -Wy3 , Wx3 , 0 1 ar (8.391) and finally, tagether with (8.39k), 93bv = Wy3 \u00b7 CaS 'ljJ3 + Wx3 \u00b7 Sill 'I/J3 = ih = 0. (8.39m) Constraint between the bodies 3 and 5: The matrix (8.35g) pravides, tagether with 03 = 0, the matrix (8.40a) Camparing this matrix with the matrix (8.39g), pravides the constraint po sition equation 98 = 'P3 - '/)5 = 0. (8.40b) This is easily seen by direct inspectian af Figure 8.4. The canstraint velacity equatian, assaciated with (8.40b), is (8.40c) The kinematic DE (8.35f) pravides, far i = 3 and tagether with ARL3 (8.39g), and ( 1, 0 ' 0 ) H31 = 0, c 'P3, -s 'P3 0 ' s 'P3 ' c 'P3 far 03 = 0, (8.41a) 504 8. Spatial mechanisms with several rigid bodies the relation ( Wx3) Wy3 Wz3 A L3R H-1( ) (. e\u00b7 .i. )T = . 3 113 . C{J3, 3, 'f/3 ( ) T ( ) c 7/J3 , -s 7/J3 , 0 1 , 0 , 0 = c 'P3 \u00b7 s 7/J3 , c 'P3 \u00b7 c 7/J3 , -s 'P3 \u00b7 0 , c~s 'P3 , - sin cp3 s 'P3 \u00b7 s 7/J3 , s 'P3 \u00b7 c 7/J3 , c 'P3 0 , sm 'P3 , cos cp3 (8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003904_13506501jet91-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003904_13506501jet91-Figure6-1.png",
        "caption": "Fig. 6 Evolution of pressure, normal deformation of the lip, and thickness for roughness model (nz \u00bc 8, nx \u00bc 1) and for 5000 r/min: (a) Newtonian fluid, and (b) Gecim fluid",
        "texts": [
            " One notices two trays corresponding to a Newtonian behaviour and between theme; a shear thinning behaviour function of the shear rate and the k parameter. Smaller k parameter leads to the larger effect of shear thinning. Results have been generated for typical data with the base parameters shown in Table 1. The roughness model of the lip is defined by equation (4). The calculated characteristics are the film thickness field, the pressure field, the power loss, and the leakage. In order to illustrate the results, Fig. 6 shows the evolution of thickness and pressure fields and the lip distortion for one rotational frequency along two circumferential periods. Figure 6 shows that whatever the examined characteristic and the fluid may be, the geometric distributions are slightly modified. These representations do not really permit to measure the differences between Newtonian and non-Newtonian behaviours. To point out this difference in behaviours, it is necessary to analyse every characteristic in a detailed way. Figure 7 shows the evolution of the minimal and average thickness, according to the rotational frequency, in the case of the Newtonian and Gecim fluids"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003784_s11044-006-9030-6-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003784_s11044-006-9030-6-Figure3-1.png",
        "caption": "Fig. 3 Lumped mass model of aircraft-cable system",
        "texts": [
            " A variety of mathematical representations of the cable have been used, such as single link models [15], continuous inextensible models [29], lumped mass inextensible models [8], continuous extensible models [30], lumped mass extensible models [31], and so on [32, 33]. Lumped mass models generally provide a very good compromise between efficiency and accuracy and have the advantage that they are easy to formulate [34]. To model the cable dynamics, taking into consideration deployment/retrieval, a lumped parameter representation has been selected. The cable is represented by a series of point masses connected via viscoelastic springs. The model is illustrated in Figure 3. Although this type of model neglects the rotational inertia of each cable segment, it has been shown to accurately reflect the dynamics of towed cable systems over a range of operating conditions [35, 36]. Consider the motion of the jth mass. The position vector of the jth mass in the inertial frame (assumed to be attached to a flat Earth) is given by r j = ( x + q2( j\u22121)+1 ) i + ( h + q2( j\u22121)+2 ) j, (26) where (q2( j\u22121)+1, q2( j\u22121)+2) are the coordinates of the jth mass relative to the aircraft center of mass"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003768_j.mechmachtheory.2005.10.010-Figure9-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003768_j.mechmachtheory.2005.10.010-Figure9-1.png",
        "caption": "Fig. 9. The sun-worm axial section of conical roller enveloping.",
        "texts": [
            "5 mm. The contact curve is a circle on the surface of the spherical roller and is also called u curve. The sun-worm tooth profile is determined by Eq. (7). By substituting Eqs. (1), (14) and (16) into Eq. (7) with u 2 [ 4,4], i21 \u00bc 1 8 , b = 10 , q = 8 mm, a0 = 119 mm, r2 = 62.5 mm and the length of the sun-worm with l = 90 mm, the tooth profile of the sun-worm generated by the enveloping movement of the conical roller can be obtained and the axial section of the sun-worm tooth profile is shown in Fig. 9. The axial tooth profile is a straight line. By substituting Eqs. (1), (21) and (23) into Eq. (7) with u 2 [ 4,4], i21 \u00bc 1 8 , q = 8 mm, a0 = 119 mm, r2 = 62.5 mm and the length of the sun-worm with l = 90 mm, the tooth profile of the sun-worm generated by the enveloping movement of the cylindrical roller can be obtained. The axial section of the sun-worm tooth profile is shown in Fig. 10. The axial tooth profile is a straight line. The sun-worm tooth profile generated by the enveloping movement of the spherical roller can be obtained by substituting Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000634_s0301-679x(00)00027-x-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000634_s0301-679x(00)00027-x-Figure1-1.png",
        "caption": "Fig. 1. Four bearing misalignment rig.",
        "texts": [
            " This rig should be able to introduce a wide range of lateral alignment changes and be so instrumented and dimensioned as to enable theoretically predicted lateral alignment effects on bearing reaction forces, on unbalance response and on stability to be experimentally * Corresponding author. Tel.: +61-2-9385-4093; fax: +61-2-9663- 1222. E-mail address: e.hahn@unsw.edu.au (E.J. Hahn). 0301-679X/00/$ - see front matter  2000 Elsevier Science Ltd. All rights reserved. PII: S0301- 67 9X( 00 )0 0027-X evaluated. This paper describes the rig and its salient features, presents predictions for the natural frequencies, mode shapes and stability pertaining to the rig, and illustrates some predicted effects of lateral alignment changes on the rig vibration behaviour. The rig is shown in Fig. 1. The rotor consists of two identical shafts rigidly coupled together and connected at one end via a flexible coupling to a 1 kW motor which has a variable speed range from 0 to 4500 rpm. Each individual shaft has a disc, midway between two hydrodynamic bearing supports where balance masses can be applied. Each bearing consists of a circumferentially grooved self-aligning hydrodynamic journal bearing with the housing supported on an \u2018L\u2019-shaped pedestal which form load cells for measuring lateral reaction forces in the horizontal and vertical directions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003936_13506501jet75-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003936_13506501jet75-Figure4-1.png",
        "caption": "Fig. 4 Arrangement of spraying water",
        "texts": [
            " The reason for using the ECB is that it can apply braking torque to the rail disc gradually and continuously, that is, it can precisely control the slip ratio in the microslip region. In the experiments with the twin-disc rolling contact machine for wet conditions, water stored in a highpressure (200 kPa) tank was sprayed from a nozzle onto the contact zone between the two discs to simulate the rainy situation. The rate of water flow was about 400 ml/min. The high-pressure tank was used here because it could make water flow surely inside the contact zone of the two discs. Lack of water might influence the value of the adhesion coefficient. Figure 4 gives a schematic of the water spraying system adopted in the experiments. In this study, water at two different temperatures, approximate to 5 (termed cold water) and 50 8C (termed hot water), was arranged in the experiments for considering the real rail temperature in the summer and winter. Before the experiments, water was stored (the necessary temperature 5 or 50 8C) into the tank and then sprayed during the experiments. The actual temperature of water in the experiment was measured by using a thermometer that was set up on the tip of the nozzle of spraying water"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003641_tmag.2006.879067-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003641_tmag.2006.879067-Figure1-1.png",
        "caption": "Fig. 1. Machine cross section.",
        "texts": [
            " These techniques rely on a good mesh, which is one that exhibits geometrical symmetry in terms of the air gap, poles, and slots; automatic mesh generators now address this [4]. The air gap should also be multilayer and ideally, as rotation takes place, the shape of the elements should stay constant. Alternatively, an early paper [5] addresses a technique which uses the change in stored energy to calculate the torque, and this method is addressed in this paper. An example machine is used to test the method (Fig. 1) using PC-FEA. This is a brushless permanent-magnet six-pole threephase machine. Two half-magnet pitches are modeled giving the minimum periodicity. In the paper, some of the results are compared to other methods already implemented in PC-FEA and tests conducted under different loadings. This machine is a known servo alternating current machine and its parameters are given in Table I. The stator teeth are shown in Fig. 1 and it can be seen that the tooth tips are split to reduce the cogging torque; the actual machine has one stator slot skew; however, here we will assume zero skew to produce cogging torque. Digital Object Identifier 10.1109/TMAG.2006.879067 While intuitively, it may seem reasonable to reduce the step angle, many methods rely on differences in stored energy or 0018-9464/$20.00 \u00a9 2006 IEEE coenergy, and these differences become small at small step angle so that numerical errors occur. Maxwell stress analysis is very prone to numerical error and [2] and [3] report on filtering methods to combat this"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000493_06)15:3<137::aid-bio576>3.0.co;2-j-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000493_06)15:3<137::aid-bio576>3.0.co;2-j-Figure1-1.png",
        "caption": "Figure 1. Design of the flow cell reactor and the flow cell holder for the chemiluminescence monitor.",
        "texts": [
            " For assaying the activity of HRP, absorbance at 505 nm was measured by addition of the phenol and 4-aminoantipyrine solution (3 mL) and H2O2 (97 mmol/L; 100 mL) to the HRP immobilized supports (30 mg). The activity of the immobilized HRP was determined as delta A 505/10 min/100 mg beads. The \u00afow cell reactor. The flow cell reactor was made by packing HRP-immobilized supports into a flow cell (Teflon tube; 6 cm 0.96 mm i.d.), using an aspirator, and plugging the two ends of the column with quartz wool. The flow cell reactor was set into the cell holder of the chemiluminometer and located in front of the photomultiplier (Fig. 1). System for micro-\u00afow injection\u00b1chemiluminescence. The micro-flow injection\u2013chemiluminescence (Fl\u2013CL) system for determination of H2O2 consisted of two pumps for high performance liquid chromatography Copyright  2000 John Wiley & Sons, Ltd. Luminescence 2000;15:137\u2013142 138 ORIGINAL RESEARCH O. Nozaki and H. Kawamoto (HPLC: PU-980, Jasco, Tokyo, Japan), a degasser (DG 980-50, Jasco), an autosampler (AS-950, Jasco), a chemiluminometer with a flow cell (825-CL, Jasco) and a data processor (LCSS-905, Jasco) (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003882_s0007-8506(07)60477-6-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003882_s0007-8506(07)60477-6-Figure8-1.png",
        "caption": "Figure 8: Corridor, limited by tangential planes in a gap between two teeth.",
        "texts": [
            " Typically for bevel gears, this gap gets wider towards the tooth tip and the back of the reference cone (a) Situation in wider gap, deeper dipped ball. (b) Situation in narrower gap, less dipped ball. edatum: Datum gap width e: Actual gap width dT: pitch diameter r dip: Radius of the ball probe centre position, where a simultaneous contact at both flanks occurs Thus, one could imagine the corridor as a conical slit, where the probe ball is rolling through. Consequently, the corridor centre line in Figure 8 (b) indicates all theoretically possible positions of centre points of the ball probe. This model reflects the reality only in a limited region around the pitch points. Within this region, the intersection point between sampling cone and centre line of corridor gives the virtual probe ball centre of direct runout measurement (see also Figure 1 (a)). (a) Gap with two pitch points. (b) Schematic detail A from (a). For a better estimation of the situation inside a gap, standard geometry elements with one, two or more curvatures offer better geometric models"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001788_bf02459024-Figure10-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001788_bf02459024-Figure10-1.png",
        "caption": "Fig. 10. - The arcs Q--)P and Q'--)P' are congruent: they can be obtained from each other by a y-parallel translation. The arcs P--, Q and P\"--. Q\" are congruent: they can be obtained from each other by a y-parallel translation. The arcs P\"--)Q\" and P\"---, Q\" are symmetric with respect to the origin O.",
        "texts": [
            " Clearly this is certainly verified for the first-order descending reversal curves because of the very way in which the functions ~(a, b) and f (a) were determined. It is easy to verify that property A implies that the minor loops are closed and, after being closed, have no more influence on the subsequent evolution. Moreover, from properties A and B it follows that the reversal curves issued from points having the same reversal input are congruent in the geometrical sense, i.e. they can be deduced from each other by a y-parallel translation (see fig. 10). This property allows one to reduce the higher-order arcs to the first- order ones. Let us recall that from the symmetry property with respect to the origin it follows that the first-order ascending reversal curves can be espressed by the first-order descending reversal curves: Y(Xo'=Xs, Xl,X2) = -y (xo = - x s , - x l , - x e ) , -xs<~x~ <~x2<~x~. Hence, the output y(xo = - x s , \u20221, ..., x,a, X) of the actual HT at the generic input-sequence Xo = - x~, x l , . . . , x~ , x can be written only as a function of its first-order descending reversal curves (25) y ( X o = - X ~ , xl, "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000062_3.26486-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000062_3.26486-Figure5-1.png",
        "caption": "Fig. 5 Computational grid.",
        "texts": [
            " The use of a wrap-around grid would have resulted in large and rapid variations of the metric terms, which could have severely degraded the quality of the solution.8'9 The zonal approach allowed the accurate modeling of the wrap-around fin projectile's geometry while retaining a smooth, continuous D ow nl oa de d by C L A R K SO N U N IV E R SI T Y o n O ct ob er 9 , 2 01 3 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .2 64 86 Pressure Contours for Mach 2,5, \u2022 Alpha =.0 computational mesh. A cut-away view of the computational grid can be seen in Fig. 5. The grid was designed for viscous computation. It was highly clustered near the body and fin surfaces. The total number of points used for the computation was 951,888. The dimensions for each of the seven zones were as follows: (20 X 80 X 32), (20 X 80 X 32), (130 X 80 X 32), (130 X 80 X 32), (20 X 80 X 18), (96 X 80 X 18), (36 X 26 X 48). As stated earlier, these seven zones were configured to model one-fourth of the wrap-around fin projectile. An algebraic grid generator, developed at BRL, was used to build the computational mesh"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000976_robot.1993.292009-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000976_robot.1993.292009-Figure1-1.png",
        "caption": "Figure 1: contour and surface following task.",
        "texts": [
            " Surface identification is a more complex threedimensional problem, because at each contact point a tangent plane (or a normal vector in the space) has to be identified. For simple surfaces, a spatial discretization of the surface can be devised, selecting a number of curves on it that are the intersections with a family of parallel virtual planes. One subtask for the robot arm consists in remaining in the specified plane, following the intersection curve at a given tangential velocity. The problem of following and identifying a single curve is very close t o the contour following problem, as fig. 1 suggests. As a consequence henceforth we concentrate mostly on the twedimensional problem of contour following and identification. Define a reference frame OS fixed with the robot base and a moving task frame tS as in fig. 1, having the z-axis tangent to the object contour and the y-axis normal to it. The implementation of our control scheme, described briefly in a section below, requires the knowledge of the orthonormal matrix ORt that rotates vectors from OS to tS. The columns of ORt are the unit vectors zt , yt and zt expressed in OS coordinates. The partial knowledge required on the environment is summarized in the knowledge of zt, that in our set-up is parallel to X O . The bidimensional identification problem is limited to estimate zt and yt using position and force measures"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003996_tase.2005.846289-Figure13-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003996_tase.2005.846289-Figure13-1.png",
        "caption": "Fig. 13. Volume decomposition.",
        "texts": [
            " Otherwise, when the deposition directions are not perpendicular to each other, some special processing steps are needed to avoid the problem of staircase interaction: in Qian and Dutta\u2019s work [28], feature interaction volume (FIV) (shown in Fig. 12) was used to act as a bridge between different features, and the refined feature volumes (RFVs) are then obtained by subtracting the FIV from different feature volumes. The computation of FIV and RFV is quite complicated, while in the proposed orthogonal LM system there is no staircase interaction by nature or the FIV is degenerated into the interface plane. Shown in Fig. 13 is the result of volume decomposition for the part in Fig. 9, the interface between the flat volume and the rest of the part is a horizontal plane, hence the computation is significantly simplified in this condition. The processing techniques for slicing and path generation in the conventional LM process planning can also be applied in this method. The only difference is that the slicing will be in the horizontal direction for the flat volume. As shown in Fig. 14, the part was separated into two parts: the flat volume and the steep volume"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003426_1.2120780-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003426_1.2120780-Figure5-1.png",
        "caption": "Fig. 5 \u201ea\u2026 Position of a laser beam before application of a laser pulse; hs is displacement of the wire during the laser pulse duration time. \u201eb\u2026 A proper position of the laser beam with respect to the pendant droplet before the application of detach-",
        "texts": [
            " In the pendant droplet formation experiments, the following demands have to be fulfilled: 1 uniform heating and melting of the wire, 2 influencing the droplet size, 3 compensation of upward droplet displacement caused by surface tension, and 4 a proper positioning of the droplet before the application of the detachment pulse. The foregoing demands are satisfied by the following: First, uniform heating is assured by proper selection of the laser pulse power form P t and velocity profile v t . These two quantities are strongly coupled, and one is selected regarding the other. Second, the droplet volume Vd is influenced by the total displacement of the wire, including starting vertical shift hw and displacement of the wire during the laser pulse duration time hs Fig. 5 a . In the experiments, the starting vertical shift hw is varied from 0.3 to 1 mm with regard to the displacement hs and desired droplet volume Vd. Third, displacement of the molten droplet neck out of the laser beam focus spot, which is a consequence of the surface tension force, is compensated for by the wire movement. Fourth, the proper position of the droplet before the application of 310 / Vol. 128, FEBRUARY 2006 rom: http://manufacturingscience.asmedigitalcollection.asme.org/ on 01/2 the detachment pulse, shown in Fig. 5 b , is achieved by the wire displacement, either during or after the pendant droplet formation pulse. Because of the importance of proper wire positioning and movement, special attention was paid to determination of the velocity profile v t . It was chosen based on the following reasoning: at the beginning of the laser pulse, the wire is cool and needs intensive heating which implies low velocity. When the temperature of the wire surface increases, heat conduction to the cooler interior of the wire increases, and hence velocity has to be increased to maintain uniform heating of the wire. After the pendant droplet is formed, it has to be correctly positioned on the droplet neck before the detachment portion Pd of the laser pulse is applied Fig. 5 b . On the basis of the foregoing reasoning, a triangular form of velocity profile v t was selected for the nickel wire, as shown in Fig. 6. Acceleration of the wire and its maximal velocity were set to 10 m/s2 and 6.6 m/min, respectively, in the case of the nickel wire. In order to investigate the influence of the laser pulse on the formation of a nickel pendant droplet, preliminary experiments were conducted. Pulses of different duration tp and power Pp were applied and analyzed with respect to the images of the final state of the process after solidification"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000718_s0020-7403(99)00013-2-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000718_s0020-7403(99)00013-2-Figure3-1.png",
        "caption": "Fig. 3. Relationship of coordinate systems of shaper, spur opinion and face-gear.",
        "texts": [
            " A su$cient condition for singularity of & 2 can be represented by *2 1 #*2 2 #*2 3 \"F(u s , h s , u s )\"0. (18) A simple way to avoid singularity and undercutting of the face-gear surface, & 2 , is to solve [1,6] f (u s , h s , u s )\"0, F(u s , h s , u s )\"0. (19) With the relation of r s \"r s (u s , h s ) given in Eq. (1), simultaneous Eq. (19) can be solved to determine a line \u00b8 1 which de\"nes the undercutting limit on the generating surface. Similarly, the undercutting limit line on the generated face-gear can also be derived by transformation from coordinate system S s to S 2 . In Fig. 3, The location of the tooth pointing is at the point I. Point P in the \"gure is the pitch point. The maximum radius \u00b8 2 which will limit the tooth length to avoid pointing on the face-gear can be determined by \u00b8 2 \"r ps (1/tan c s !1/tan c)#a g /tan c#*1, (20) where *1\" r ps tan c s A cos a 0 !cos a cos a B. (21) c s and a g denote half-pitch cone angle of the shaper and addendum of the face-gear, respectively, and a is the instant pressure angle during generation. 5.2. Undercutting and pointing of the face-gear meshing with spur pinion During the spur pinion meshes with the face-gear, the mathematical de\"nition of singularity of & 2 are same as Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000718_s0020-7403(99)00013-2-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000718_s0020-7403(99)00013-2-Figure1-1.png",
        "caption": "Fig. 1. Face-gear generation process.",
        "texts": [
            " Finally, the conditions of undercutting and pointing for a face-gear drive were all identi\"ed in meshing with and without assembly error along the direction of the axis of face-gear and misalignment of angular displacement between axes of spur pinion and face-gear. Several numerical examples were also presented. ( 1999 Elsevier Science Ltd. All rights reserved. Keywords: Face-gear; Tooth contact analysis; Kinematic error; Undercutting; Pointing 1. Introduction Face-gears have been widely used in low-power transmission applications. An important application of a face-gear drive is in a helicopter transmission [1,6] as shown in Fig. 1. It uses the idea of the split torque that appears to be signi\"cant where a spur pinion drives two face-gears to provide an accurate division of power. This mechanism greatly reduces the size and cost compared to conventional design. 0020-7403/00/$ - see front matter ( 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 0 - 7 4 0 3 ( 9 9 ) 0 0 0 1 3 - 2 Nomenclature a g addendum of the face-gear D shortest distance between the axes of x a and z f in coordinate systems of S a and S f KE kinematic error L ij transformation matrices which transform the vectors from coordinate system S j to S i \u00b8 1 inner radius of face-gear out of undercutting in the generation process \u00b8@ 1 inner radius of face-gear out of undercutting during meshing of the face-gear drive \u00b8 2 outer radius of face-gear free of pointing in the generation process \u00b8@ 2 outer radius of face-gear free of pointing during meshing of the face-gear drive m ij gear ratio of N j to N i M ij homogeneous transformation matrices which transform the vectors from coordinate system S j to S i N i number of teeth of shaper, spur pinion and face-gear for i\"s, 1, 2 n(i) f unit normal of the spur pinion and face-gear tooth surfaces represented in the coordinate system S f (i\"1, 2) R(i) f position vectors of the spur pinion and face-gear tooth surfaces represented in the coordinate system S f (i\"1, 2) r as addendum circle radius of the shaper r b1 base circle radius of the spur pinion r bs base circle radius of the shaper r p1 pitch circle radius of the spur pinion r ps pitch circle radius of the shaper r i position vectors of the shaper, spur pinion and face-gear for i\"s, 1, 2 S i coordinate system S (i\"1, 2, a, b, c, f, m, s, t) u 1 Gaussian coordinate of & 1 u s Gaussian coordinate of & s v(s2) s sliding velocity between shaper and face-gear a instant pressure angle in the generation process a 0 pressure angle of the shaper *E shortest distance between the spur pinion and the face-gear axes *c angular misalignment of the face-gear *p assembly error along the axis of the face-gear u i rotational angle of shaper, spur pinion and face-gear for i\"s, 1, 2 h 1 Gaussian coordinate of & 1 h 0 the width of spur pinion teeth on the base circle h os the width of shaper teeth on the base circle h s Gaussian coordinate of & s c half-shaft angle of face-gear c f half-cone angle of face-gear including angular misalignment c m half-cone angle of face-gear & i tooth surface of spur pinion, face-gear and shaper (i\"1, 2, s) u i rotational speed of shaper, spur pinion and face-gear (i\"s, 1, 2) x(i) s rotation speed of shaper, spur pinion and face-gear (i\"s, 1, 2) in coordinate system S s Until now, there were few research activities about manufacture and design of face-gear drive",
            " Numerical analysis is performed for contact path and transmission errors induced by assembly errors along axis of face-gear direction and by misalignment of the crossed and angular displacements between axes of face-gear and spur pinion. (4) Undercutting and pointing. While designing a face-gear, it is important to avoid pointing and undercutting of the face-gear. E!ects of pressure angle and tooth number of the shaper on undercutting and pointing of the face-gear are studied. (5) Numerical results and discussion. (6) Conclusion. The analysis is limited to the case of face-gear drives with the intersecting axes. 2. Generation process of the face-gear The generation process of a face-gear by a shaper is illustrated in Fig. 1. The face-gear and the shaper rotate about their own axes with angular velocities u 2 and u s , respectively. Both axes intersect at the point O m . Coordinate systems S s (x s , y s , z s ), S 2 (x 2 , y 2 , z 2 ) and S m (x m , y m , z m ), are, respectively, \"xed on the shaper, face-gear, and the frame of cutting machine. The face-gear tooth surface, & 2 , is determined as the envelope to the family of shaper surface, & s , represented in coordinate system S s . The shaper surface, & s , and its position vector, r s , are related by [4,6] r s (u s ,h s )\"C r bs [sin(h os #h s )"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003456_ijmic.2006.008643-Figure10-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003456_ijmic.2006.008643-Figure10-1.png",
        "caption": "Figure 10 Rigid formation mode for a team of three robots",
        "texts": [
            " Following results can be used to illustrate the efficiency of the design procedure. The results based on a group of three robots were generated in SRI International\u2019s simulation environment SRIsim, operating on Linux machines. Each robot is a separately running C++ program that interacts with the simulation environment through a TCP-connection. To test the effect of communication, it made three SRIsim running in various PCs, which was different from most of multirobot simulations. The formation mode for the three-robot case comes in l \u03d5\u2212 law, which is shown in Figure 10. In Figure 11, R0 is leader, R1 is follower1 and R2 is follower2. To match the actual field in laboratory, the initial attitude of R0 was assigned as 2.363 m, 1.553 m, 90\u00b0, R1\u2019s was 1.571 m, 0.773 m, 90\u00b0 and R2\u2019s was 3.151 m, 0.773 m, 90\u00b0. Formation maintaining and changing are the basic functions in formation control system. The implementation of the design with these examples is illustrated as follows. The initial formation mode of robot teams is shown in Figure 11. The control goal was to maintain the formation shape while the team was moving",
            " The description of encoder localisation error can be referred in Cheng and Wang (2003). The fluctuations in 01l and 02l come from the response time of PWM motor in robot. The set iv and i\u03c9 value may not be accurately arrived in small motion cycles. However, the formation had been well shaped after 3-m motion, and l was stable in 50 sec. These demonstrate the design also feasible in real environment. To test fault-tolerance of the design system, consider the rigid formation management for the three robots shown in Figure 10. This is a system of three non-holonomic mobile robots. R0 is leader, while R1 and R2 are followers. Figure 15 shows the whole process of leader R0\u2019s machine failure detection and corresponding faulttolerance formation control. The initial attitude of R0 was 0.700 m, 1.000 m, 900, the R1\u2019s was \u22120.054 m, 0.325 m, 900 and the R2\u2019s was 1.467 m, 0.404 m, 900. Step 1 was the 4-m normal running process of three-robots in triangle formation, 0v = 50 mm/s, 01\u03d5 = 1200, 02\u03d5 = 2400 and 01 02l l= = 1.0 m. Now, the leader R0 stopped accidentally owing to machine failure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002199_bf02903529-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002199_bf02903529-Figure1-1.png",
        "caption": "Figure 1 Major hardware modifications to the Concept II rowing ergometer. See the text for a description of items A\u2013F.",
        "texts": [
            " 6 A sampling rate of at least 30 Hz, in order to generate a stick figure that moves at least as smoothly as a 24 Hz motion picture, but provides at least 20 sample points for a power profile if the rower is rowing at 30 strokes per minute and has a slide ratio of 2:1. 68 Sports Engineering (2003) 6, 67\u201379 \u00a9 2003 isea 7 The capability to save data and replay it at a later date and at a user-selected speed (i.e. to slow down the replay rate for more thorough analysis). The real-time biomechanical feedback system was constructed using the following components: 1 Concept II Model C Rowing Ergometer (Concept2, Inc. Morrisville, VT, USA), modified as follows (also see Figure 1): A A 10-turn linear potentiometer (Bourns Model # 3540S-1-503, 50 k\u2126 resistance) mounted at the flywheel hub via a miniature plastic chain sprocket assembly (Serv-o-Link Corporation, Fort Worth, TX), and calibrated to measure handle chain length from the flywheel hub to the handle centre. B A linear-position measuring transducer (McMaster-Carr catalogue # LX-PA-50, Santa Fe Springs, CA) mounted on the seat track between the foot stretchers, with the retractable wire end mounted to a modified ergometer handle, fitted with a custom handle radial bearing made of polyvinyl chloride (PVC) piping, and calibrated to measure distance from a wire guide installed just above the transducer to the handle centre",
            " Errors were evaluated both by direct measurements and by three-dimensional video analysis. Following calibration and setup of the system, joint and handle positions were determined using both a tape measure (i.e. direct measurements) and the RowTrainer system for three different rowers sitting statically at both the catch and finish positions. The differences in x and y locations measured directly and calculated using the RowTrainer system were determined (the x-axis was directed parallel to the floor in the direction of pull and the y-axis was directed vertically upward, see Figure 1). Additionally, static and dynamic system errors were evaluated by comparing joint centre locations determined by three-dimensional video analysis (Motion Analysis Corporation, Santa Rosa, CA) with those determined by the RowTrainer program. Reflective markers were placed over a rower\u2019s ankle, knee, hip, shoulder, and elbow joints, as well as on the handle. The rower rowed on the ergometer while video data were recorded along with RowTrainer data. A transistor-to-transistor logic (TTL) signal generated by the motion analysis system was collected by the RowTrainer program to time-match data from the two systems"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002619_095440605x31481-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002619_095440605x31481-Figure1-1.png",
        "caption": "Fig. 1 Curved tooth gear",
        "texts": [
            "eywords: curved-tooth gears, concavo-convex teeth, arcuate teeth, tooth trace inclination The prefix abbreviation \u2018C\u2019 is being suggested herein for collectively designating curved-tooth gears. These are parallel-axis gears that have tooth traces in the form of circular arcs or closely similar curves. Other names given to the teeth include lengthwise or longitudinally curved, concavo-convex, circular, curvilinear, arched, arcuate, and round. The general appearance of a C-gear is shown in Fig. 1. C-gears and their machining methods have attracted the interest of engineers over the past 90 years or so; since the pioneers Bo\u0308ttcher [1, 2], Wingqvist [3\u20135], Schurr [6], Farnum [7], Williams [8], and Lewis [9, 10] filed patent applications thereon in the teen years of the last century. Since then, C-gears and their manufacturing methods have been invented and reinvented several times. This was quite often made without reference to, and presumably without knowledge of previous disclosures; at those times information traffic was not nearly like it is nowadays"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003524_j.ijmecsci.2005.10.006-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003524_j.ijmecsci.2005.10.006-Figure2-1.png",
        "caption": "Fig. 2. Global and local loads at the contact.",
        "texts": [
            " \u00f014\u00de Due to the symmetry of the hysteresis loop the total tangential load in the reloading phase (with index r) can be obtained from Eq. (14) as follows: Tr\u00f0D;D \u00de \u00bc Tu\u00f0 D;D \u00de. (15) The formulas derived above are valid for normal contacts only. Dependence on the contact inclination angles can be incorporated using analysis to follow. We first focus on a single contact formed by ith asperity with the flat surface. It is assumed that the contact is inclined angle yi to the horizontal line as shown in Fig. 2. With introduction of yi, loads Ni and Ti acting at the contact are not anymore normal and tangent to the contact line (we will call these loads global). Instead, new local normal and shear loads, N0i and T0i, are introduced that are related to the original ones according to the following rule: T0i \u00bc Ti cos yi; N0i \u00bc Ni cos yi. (16) Similar relations are valid for the local and global displacements d0i, D0i and d0, D0. In the limiting case of yi \u00bc 0 the contact becomes normal with the maximal loss of energy, and in the case of yi \u00bc p=2 the contact is tangent with no slip developing and no loss of energy due to friction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001632_j.1460-2687.2000.00055.x-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001632_j.1460-2687.2000.00055.x-Figure2-1.png",
        "caption": "Figure 2 Analytical model. (a) Ball. (b) Club head.",
        "texts": [
            " The magnitude of the release velocity of the ball after impact, mb, is calculated for every impact point and the ratio between mh and mb is calculated as ai mb i=mh i 1; . . . ; n ; 1 where n is the number of impact points and ai is the meet ratio. The maximum value of the meet ratio is set at amax. The area where the meet ratio decreases less than 1.0% compared to amax, is de\u00aened as the uniform restitution area. The ball and the club head are modelled using a \u00aenite element method. The two-piece ball, with a diameter of 44 mm and weight of 43 g, shown in Fig. 2(a), is modelled using 840 tetrahedron elements with elastic property. The titanium driver head, whose loft angle is 11\u00b0, weight approximately 195 g and radius of curvature of the face shape approximately 370 mm, is modelled using 324 hexahedron elements with elastic property. Figure 2(b) shows a side view of the club head. The mesh pattern shown in Fig. 2(b) is designed to show the relatively accurate \u00aerst vibration mode shape, as the \u00aerst mode dominates the deformation. Table 1 shows the material data. Seven kinds of club head, with different locations of the centre of gravity and different moments of inertia, were made by changing the distribution of the mass as follows: the head model was divided into 14 parts and the thickness of the Table 1 Material data Material Young's Modulus E (N m)2) Poisson's Ratio m Density q (kg m)3) Butadien rubber 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002006_978-3-662-09769-4-Figure3.1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002006_978-3-662-09769-4-Figure3.1-1.png",
        "caption": "Figure 3.1: Drawing of a planar aircraft",
        "texts": [
            " Then a torque M which is generated by the force F may be written in the form and, tagether with r = XL \u00b7 exL + YL eyL and F = F{; \u00b7 exL + F{; \u00b7 eyL as the restrictions of L L 0 r = x \u00b7 exL + y eyL + \u00b7 ezL and F = F{;. exL + F{;eyL + 0. ezL to the x-y plane, in the form or as the component equation (3.1a) (3.1b) (3.lc) (3.1d) ML := ML = pL . XL - FL . YL = pR. XR- pR. YR = MR =\u00b7 MR Z y X y X z\u2022\" (3.le) 32 3. Planar models of an unconstrained rigid body 3.1 Planar airplane model (two tr. DOFs, one rot. DOF) Consider the drawing of the planar airplane of Figure 3.1, with a rigid body of the mass m, the center of mass C and the moment of inertia J~z with respect to C, and represented in the body fixed frame L with the origin P. The following forces act on the airplane: Fw as the weight of the aircraft, F ae as the aerodynamic resistance in the horizontal direction, F L as the lift force acting at the point CL ( center of lift), Fe as the force of the massless elevator at the point Ce, Fa as the force of the engine, and MD as the aerodynamic damping moment. Let 'T/x := X~p be the distance from P to C, \u00dfx := x~LP the distance from P to CL, Ox := x~"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002006_978-3-662-09769-4-Figure8.5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002006_978-3-662-09769-4-Figure8.5-1.png",
        "caption": "Figure 8.5: Reference points and frames",
        "texts": [
            "_ ( R R R )T rP;O .- xp,o, Yp,o, zp,o ' (8.35b) M D to rq ue o f th e en gi ne (5 ) cr ow n w he el (a ) T ec hn ic al d ra w in g (b ) Sc he m at ic d ra w in g F ig ur e 8. 3: D ra w in g o f th e di ff er en ti al g ea r w ~ n M 2 = M A 2- M B2 \"'\" <0 O l ?\" w '\"C :I ~ \u00a7.: 8 ~ ::s - \u00a7 u; \u00b7 ~ \"'1 ~ ::s - ~ .... e:. .... o3 : 0. . c:r 0 0. . (;) \" fJ J 8.2 Differential gear (two rot. DOFs) 497 (8.35c) and (/Ji, ei, 'lj;i as the Bryant angles of the body i with respect to the inertial frame R (Figure 8.5). The velocity vector of the mechanism is ( T T T)T llll36 v = v 1 , v 2 , ... , v 6 E m. (8.35d) with _ (( \u00b7 R )T ( Li )T) T Vi- TpiQ ' WLiR ' (8.35e) (8.35f) ( C i2 \u00b7C i3, C il \u00b7S i3 + S i1 \u00b7S i2 \u00b7C i3, S il \u00b7S i3 - C il \u00b7S i2 \u00b7C i3) A LiR __ -C i2 \u00b7S i3 , C il \u00b7C i3- S il \u00b7S i2 \u00b7S i3, S il \u00b7C i3 + C il \u00b7S i2 \u00b7S i3 , Si2 , -Sil\"Ci2 , Cil\"Ci2 (8.35g) ( cpi) ~: ' 498 8. Spatial mechanisms with several rigid bodies with (8.35h) c ij := cos ai.i , s i.i := sin ai.i for a;1 = Cf!i , CYi2 = 8; , ai3 = '1/Ji- The kinematic DEs of the mechanism are p = T(p) \u00b7 v, (8.35i) with and 8.2 Differential gear (two rot. DOFs) 499 8.2.2 Constraint equations Body 1 (Left-hand side wheel): This body is attached to the base by a revolute joint at the point P1 = C1, and with ex,R = ex,L, = ex, as the rotation axis (Figure 8.5). The constraint position equations of this joint are: R R R ( R R R )T 0 9la = Tp,o- C1 = Tp,o- Clx' clY' clz = 3 with the constant vector and the associated constraint velocity equation and \u00b7R 0 9lav = Tp,o = 3, with the constraint velocity equation and with ( 1, 0 ' 0 ) A RL, = 0 , c~s 'Pl , - sin 'Pl . 0 , sm 'Pl , cos 'Pl (8.36a) (8.36b) (8.36c) (8.36d) (8.36e) (8.36f) The kinematic DE (8.35f) of this body provides, together with i = 1, with the constraint velocity equation (8.36e), and (8.36g) the kinematic DE ( 1, 0 ' 0 ) (1, 0 ' 0 ) 0 , c~s 'Pl , sin 'PI \u00b7 0 , c~s 'Pl , - sin cp 1 \u00b7 0 , - sm 'Pl , cos 'Pl 0, sm 'Pl , cos 'Pl (8.36h) 500 8. Spatial mechanisms with several rigid bodies Body 2 (Right-hand side wheel): This body is attached to the base by a revolute joint at the point P2 = C2 with \u20acxL 2 = \u20acxL 1 = \u20acx1 aS the rotation axis (Figure 8.5). The associated constraint position equation is: (8.37a) with the constant vector (8.37b) and the constraint velocity equation (8.37c) and (8.37d) with the constraint velocity equation (8.37e) and ( 1, 0 ' 0 ) A RL2 = 0 , c~s <p2 , - sin (/)2 . 0 , sm 'P2 , cos 'P2 (8.37f) The kinematic DE (8.35f) provides, for i = 2 and in analogy with (8.36h), the relation (8.37g) Body 5 (Crown wheel}: The crown wheel is attached to the base by a revolute joint with the rotation axis exLs = exL 1 = ex1 \u2022 The common-point constraint equations of this joint are derived from the vector loop equation (8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003745_03043790600567860-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003745_03043790600567860-Figure4-1.png",
        "caption": "Figure 4. Student project \u2013 design of camera.",
        "texts": [
            " Models can then be provided within a matter of hours making them available to the student for evaluation at there next project, lab, or tutorial session. Prior to the establishment of the RD&M Centre this \u2018rich\u2019 feedback would have been extremely expensive and would not have been achievable within the constraints of educational timetables. The following example provides illustration of the know-how and judgement that students are able to acquire when exposed to a learning environment that incorporates access to Rapid Design and Manufacture technologies. The design of a camera (figure 4) provides a good example of how RD&M technologies combine with Virtual Prototyping to permit a student to develop design ideas to a more complete level than was economically possible in the past. The images illustrate the development of the camera design from a CAD model through to a rapid prototype part and onto a presentation model. This particular project was undertaken by a fourth-year Master of Engineering student of the Product Design Engineering degree programme, taught jointly by the University of Glasgow and the Glasgow School of Art"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000690_jors.1994.3-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000690_jors.1994.3-Figure2-1.png",
        "caption": "FIG. 2. Speed (log scale) versus slope.",
        "texts": [
            " From those 12 readings, the highest and lowest were excluded and the remaining ten averaged. For any setting, two averages were found in the morning and two in the afternoon, from which were derived the grand averages given in Table 1. The data given here relate to two subjects, the first a recreational runner and the second a long distance elite fell runner, whose anthropometric data are summarized in Table 2. Correspondence: J. M. Norman, Sheffield University Management School, PO Box 598, Crookesmoor Building, Conduit Road, Sheffield S/0 IFL, UK 2S Figure 2 shows speed (on a logarithmic scale) against slope. A visual inspection suggests that although there may be some curvature, especially with high heart rates, the data may be reasonably described by the formula (1) where, for a constant workrate, V0 is the speed sustainable over a long period on the level, () is the slope, measured in radians, c is a constant (2.8 in the case of subjects A and B), V is the speed sustainable over a long period, running up a gradient 0. It is stressed that this is a tentative relationship obtained over a limited range of slopes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002680_s09-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002680_s09-Figure5-1.png",
        "caption": "Figure 5. Single admission hydroinertia radial gas bearing.",
        "texts": [
            "1 mm of bearing clearance, the load capacity becomes almost constant and bearing stiffness k becomes almost 0. S229 In contrast, when the bearing clearance becomes small, for example, h < 0.03 mm in figure 4, the viscous effect of gas flow in the bearing clearance becomes predominant and the bearing acts as a conventional hydrostatics gas bearing. As a result, the gas flow rate becomes smaller and the bearing stiffness becomes much higher. A single admission radial bearing with inherent orifice shown in figure 5 is chosen as an analytical model of hydroinertia radial bearings. Its radial clearance, the diameter of the supply holes and the number are relatively large compared with the bearing dimension. In the case of radial bearings, it is difficult to determine the breaking position of the shock wave to the flow from each supply hole by simple calculations. Then, radial bearings are replaced approximately with appropriate hypothetical circular thrust bearings of the same number as the supply holes shown in figure 6",
            " Figure 9 shows the schematic configuration of the trial micro spinner test rig. The diameter of the spinner (\u00a91 of figure 9) is 4 mm and is driven by an impulse turbine (\u00a92 ) of the same diameter fitted at the end of the spinner. Two radial bearings (\u00a93 ) and a thrust bearing (\u00a94 ) set at the end surface of the spinner opposite to the turbine support the spinner. Rotational speed is measured by an optical sensor (\u00a95 ) and vibration by an eddy current type displacement meter (\u00a96 ). The radial bearings are of the same type as shown in figure 5 and their dimensions are almost the same as shown in figure 8. The spinner is made of stainless steel (Japanese standard SUS420) and the radial bearings are made of ceramics (zirconium). Figure 10 shows the 3D display of the shaft vibration spectrum. The horizontal axis shows the frequency from 0 to 50 kHz and the diagonal axis shows the rotational speed from 10 to 20 krps. Two vibrations are observed, one is synchronous to the rotational speed (shown by (A) in figure 10) and the other is at the low frequency of about 1 kHz (shown by (B))"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001020_analsci.8.553-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001020_analsci.8.553-Figure7-1.png",
        "caption": "Fig. 7 Na+ measurements of sera in the normal concentration range (136-145 mM Na+) (see also Fig. 5).",
        "texts": [],
        "surrounding_texts": [
            "ANALYTICAL SCIENCES AUGUST 1992, VOL. 8\nof the activities of the sample solution at(s) versus IOEMFx/s should equal ai(r). Using the Debye-Hi ckel formalism22 a(r) was calculated to be 104.5 mM and 3.13 mM for Na+ and K+ respectively. This is indeed the case for our ab initio measurements. For aqueous solutions the agreement between the fitted values and the theoretical values is very good. The slope of the correlation line for K+ measurements equals 3.14 mM and the one for Na+ measurements is 104.1 mM (see Figs. 4, 5 and Table 1). For sera in the normal concentration range (e.g. 3.5 -\n557\n5.1 mM K+, 136 -145 mM Na+) the a(r) values for K+ measurements is 3% too low, whereas for Na+ measurements they are 3% too high. Liquid junction errors, therefore, are not giving a systematic bias. For both electrolytes the standard deviation syx found is very similar to the one obtained when measuring aqueous solutions (K+, 0.02 mM versus 0.06 mM; Na+, 1.4 mM versus 1.2 mM; see Table 1 and Figs. 6 and 7). As far as sera in the pathological concentration range are concerned (e.g. 2.5 - 7.6 mM K+,115 -161 mM Nat, respectively) the K+ measurements are in very good agreement with the theoretical value (3.15 mM found\nplasticizer and PVC as the matrix. The diffusion barrier as presented in Fig. 2 was employed. The y-axis shows the activities a1(s) of the potassium reference solution values (of the following concentrations: 2.75, 3.25, 4.25, 5 and 5.75 mM K+, respectively), the x-axis indicates the expression 10EMFx/s.\n10EMFx/ s.",
            "558 ANALYTICAL SCIENCES AUGUST 1992, VOL. 8\ncompared to 3.13 mM expected, see Fig. 8). The Na+ values are still 3% too high, compared to the theoretical value (108 mM measured compared to 104.5 mM expected, see 4 mM. Deviations\nof the measured a;(r),",
            "ANALYTICAL SCIENCES AUGUST 1992, VOL. 8\ntheoretical values, are only found when measuring serum samples, not aqueous solutions. They may therefore be explained by uncertainties in the calibration of FAES, by uncertainties in the protein/ lipid volume effect of 7%, by unusual liquid junction potentials of the reference electrodes in contact with serum samples or by uncertainties due to the Debye-HUckel formalism, which perfectly describes aqueous systems, but not necessarily serum samples. The increase in the standard deviation for assays of sera in the pathological concentration range as compared to those in the normal concentration range (4.0 versus 1.4) is not due to measuring errors but most\nprobably to biological phenomena like protein or bicarbonate binding.23,24 This hypothesis is supposed by similar results obtained by independently performed measurements with a sodium glass electrode (111.2 mM= a;(r), syX=4.3 mM). As the results clearly show, a correction for changes in the liquid junction potential AED using the Henderson formalism15 is obsolete (see also Table 1). Thus, not only assays without any previous sensor calibration have become accessible, but in addition they need much less assumptions on calculations. Therefore, the described measurements could easily be performed in a doctor's office. Nevertheless, the most challenging action supported by the symmetric ion-selective assembly will be the standardization of ion activities in reference materials.25 The efforts of official centers in Japan, USA and Europe aim at defining primary standards for ion-selective measurements. Uncertainties in ion activity evaluations were mainly attributed to the influence of proteins on the liquid junction potential and were shown to be attributable to membrane asymmetries induced by the biological sample. The presented procedure allows to evaluate, quantify and eliminate different sources of errors and is thus suitable for the determination of ion activities ab initio.\nThis work was partly supported by the Swiss National\nScience Foundation and by Ciba-Corning Diagnostic Corp.\nReferences\n1. U. Oesch, D. Ammann and W. Simon, Clin. Chem., 32, 1448 (1986). 2. N. Fogh-Andersen, T. F. Christiansen, L. Komarmy and 0. Siggaard-Andersen, Clin. Chem., 24,1545 (1978). 3. U. Oesch, D. Ammann and W. Simon, in \"Methodology\nand Clinical Applications of Ion Selective Electrodes\", ed. A. H. J. Maas, F. B. T. J. Boink, N.-E. L. Saris, R. Sprokholt\nand P. D. Wimberley, p. 273, Interprint A/ S, Copenhagen, 1986. 4. H. W. Buhler, G. G. Rumpf, L. F. J. Durselen, U. E. Spichiger and W. Simon, \"Calibration free measurements with ISEs in clinical chemistry: the benefit of symmetrical\n559\ncells\", ed. A. H. J. Maas et al., p. 315, Elinkwijk, Utrecht, 1989.\n5. J. Koryta (ed.), \"Medical and Biological Applications of Electrochemical Devices\", John Wiley and Sons, Chichester, New York, Brisbane, Toronto, 1980. 6. M. Kessler, L. C. Clark, D. W. LUbber, I. A. Silver and\nW. Simon (ed.), \"Ion and Enzyme Electrodes in Biology and Medicine\", Urban & Schwarzenberg, Munchen, Berlin, Wien,1976. 7. J. D. Czaban, Anal. Chem., 57, 345A (1985). 8. P. Nabet, Analysis, 15, 379 (1987). 9. M. Rouilly, B. Rusterholz, U. E. Spichiger and W. Simon, Clin. Chem., 36, 466 (1990). 10. E. Wang, Diss. ETH Zurich, No. 9035, 1989. 11. K. Cammann, \"Das Arbeiten mit Ionenselektiven Elek-\ntroden\", 2nd ed., Springer-Verlag, Berlin, Heidelberg, New York, 1977. 12. R. G. Bates, \"Determination of pH. Theory and Practice\", 2nd ed., p. 73, Wiley, New York, London, Sydney,\nToronto, 1973. 13. J. A. Illingworth, Biochem. J., 195, 259 (1981). 14. A. K. Covington, P. D. Whalley and W. Davison, Anal. Chim. Acta,169, 221 (1985). 15. R. Dohner, D. Wegmann, W. E. Morf and W. Simon, Anal. Chem., 58, 2585 (1986). 16. L. F. J. Durselen, D. Wegmann, K. May, U. Oesch and\nW. Simon, Anal. Chem., 60,1455 (1988). 17. C. G. Fraser, \"Interpretation of Clinical Chemistry Labo-\nratory Data\", p. 124, Blackwell Scientific Publications, Oxford, 1986. 18. J. G. Batsakis, R. N. Barnett, R. K. Gilbert, G. F. Grannis and T. Peters, \"Analytical Goals in Clinical Chemistry, College of American Pathologists (CAP)\", CAP Conference, Aspen 1976. In Proceedings of the Aspen Conference on Analytical Goals in Clinical Chemistry, ed. F. R. Elevitch, College of American Pathologists, Vol. 3, 1976, p. 1. 19. D. P. Brezinski, Analyst [London], 108, 425 (1983). 20. G. G. Guilbault, R. A. Durst, M. S. Frant, H. Freiser, E. H. Hansen, T. S. Light, E. Pungor, G. Rechnitz, N. M.\nRice, T. J. Rohm, W. Simon and J. D. R. Thomas, Pure Appl. Chem., 48,127 (1976). 21. G. G. Rumpf, L. F. J. Durselen, H. W. Buhler and W. Simon, \"Opportunities and limitations in the use of ISEs in clinical chemistry: Assays without calibration?\" in \"Contemporary Electroanalytical Chemistry\"\n, ed. A. Ivaska et al., p. 305, Plenum, New York, 1990.\n22. P. C. Meier, Anal. Chim. Acta, 36, 363 (1982). 23. R. L. Coleman and C. C. Young, Clin. Chem., 28, 1936\n(1982). 24. H. G. J. Worth, Analyst [London], 113, 373 (1988). 25. U. E. Spichiger and G. Rumpf, \"What Do Ion Sensors Really Measure?\", in Proceedings of the 13th International Symposium of IFCC/JSCC-WGSE on Methodology and Clinical Applications of Blood Gases, pH,\nElectrolytes and Sensor Technology, October 6 - 9, 1991, Hakone, Japan, Vol. 13.\n(Received March 30, 1992) (Accepted May 18, 1992)"
        ]
    },
    {
        "image_filename": "designv11_24_0003441_tmag.2006.880222-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003441_tmag.2006.880222-Figure1-1.png",
        "caption": "Fig. 1. Flux density plot of the 6/4 DSPM with phases A and C excited with 360 A/pole with appropriate polarity, for the unaligned position of Phase-A.",
        "texts": [
            " In an SRM, nonuniform air gap can create different static torque profiles for different phases of the motor [2]. In this paper, using two-dimensional (2-D) finite element (FE) analyses, an attempt is made to predict the effects of air gap nonuniformities on the performance of a three-phase 6/4 DSPM. The dimensions of the three-phase 6/4 DSPM motor given in literature [3] are used to develop the FE models. Extensive Digital Object Identifier 10.1109/TMAG.2006.880222 FE analyses are carried out to generate and analyze the required data. Fig. 1 gives the flux density plot of the analyzed 6/4 DSPM motor in completely unaligned position w.r.t. Phase-A. Fig. 2 shows the permanent magnet (PM) torque of the motor for one complete electrical cycle, when the phases are unexcited. 0018-9464/$20.00 \u00a9 2006 IEEE The relative eccentricity between the stator and rotor axes occurs when the center points of these do not coincide. Because of this, the air gap at some point will be the smallest and at the diametrically opposite point, the biggest. The relative eccentricity is given by % (1) where \u201c \u201d is the radial air gap and \u201c \u201d is the eccentricity in the direction of shift"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000690_jors.1994.3-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000690_jors.1994.3-Figure3-1.png",
        "caption": "FIG. 3. Speed as the crow flies (log scale) versus slope.",
        "texts": [
            " A direct application of Equation (2) does much better, with 10 minutes a mile and 6, 7 and 9 minutes for 1000 ft of ascent for 0 = 0.1, 0.2 and 0.3 respectively (calculations are shown in Table 3). This is a partial justification for the use of the revised Naismith rules on the steep slopes of the Bob Graham round, particularly when the rules are applied separately on short segments of the route 2 \u2022 Formula (1) has the virtue of parsimony: it also gives quite a good fit to the data. A comparable fit is given by (5) as shown in Figure 3, where k has the value 3.5. If VcosO is interpreted as, say, Y, the speed as the crow flies, then (5) may be written (6) which is exactly comparable with (1). The implications for workrate and for Naismith's rule are unchanged, but there is a.slight change to the calculation of the optimal slope for uphill running, in that t is now a minimum when sin20 =~ For c = 2.8 and k = 3.5, the difference in slope is about 3\u00b0 (20\u00b0 and 17\u00b0 respectively). There seems little point in trying to decide which of (1) and (6) is a more appropriate model, on the basis of which better fits the data"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001334_robot.1996.509228-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001334_robot.1996.509228-Figure2-1.png",
        "caption": "Figure 2: \\ Planar wheel driven mobile vehicle",
        "texts": [
            " Finally, in section 4 we present solme issues for further research. 2 Problem Statement and Analysis Consider a wheeled mobile robot in a geometric environmenl, similar to this depicted in figure (1). The purpose j13 to lead the vehicle from the initial configuration to the final one by avoiding obstacles and obeying the nonholonomic coni3traints. 2.1 Mathematical Probilem Statement It has been shown in [PK95] that the equations describing the motion of the frame attached to point R of the rear wheel axis (fig. 2) a.re given by x = v *cos 8 ~ = v .s in0 8 = w where (2, y) defines its position, 6 its orientation, U its translational velocity and w its rotational velocity. Let us represent by W c IR2 the workspace, by B,, i = 1 , 2 , . . . the obstacles arid A(q) the robot at a configuration q = [z y 61 . s E [O,s,], parameterized by its length s , and : T We seek a path z(s),y(s) 0-7803-2988-4/96 $4.00 0 1996 IEEE 3389 a) connecting the starting and destination points, b) satisfying the nonholonomic constraints, written now as dx ds - = cos e dY - = sin0 ds (4) ( 5 ) since v = $ I and c) satisfying the collision avoidance constraints with the environment, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001108_1.1308033-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001108_1.1308033-Figure1-1.png",
        "caption": "Fig. 1 Example of web transporting system",
        "texts": [
            " From the calculated and measured results obtained, the effectiveness of two types of guides on the web spacing is clarified. Finally, based on the assumptions of Gaussian distributions of asperities, the simple relations to predict the friction coefficient between web and guide surfaces are formulated, and the variation of friction coefficient with velocity is shown for various values of web tension. @DOI: 10.1115/1.1308033# In the manufacturing fields of plastic sheet, paper, magnetic tape, thin metal plate, photographic film etc., the web transporting systems supported by guides and rollers, as shown in Fig. 1, are used often. In such systems, the moving web brings the surrounding air into the gap between web and guide or web and roller, and then the web is lifted slightly by the film pressure generated due to viscosity of entrained air @1#. Therefore, it is of cardinal importance to control the web spacing suitably according to the objective of guide and roller systems. For example, when the guide or roller is used as a turn bar in the commercial web offset press or used as a dryer in the coating process of web, it is sometimes necessary to maintain sufficient web spacing for avoiding the web defects due to surface roughness and stain"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002855_3.8549-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002855_3.8549-Figure1-1.png",
        "caption": "Fig. 1 Physical model of rotor blade.",
        "texts": [
            " Although general rotor trim may involve four or five control variables and many degrees-of-freedom, the rotor studied here includes only three control variables and two degrees-of-freedom. Nevertheless, the fundamental elements of control are present, and the method studied is easily extended to general problems of trim. The physical model used here consists of a single section of a slender, rigid, inelastic blade, which is hinged in the torsional and out-of-plane directions at the center of rotation with restraints Ke and Kp (Fig. 1). The blade is assumed to flap with angle /3, and to pitch with angle 6. The flapping spring is restrained at the root end at a precone angle /3pc, but the torsional spring is attached to a base point which is given a time-varying pitch schedule Br. The purpose of trim is to find the pitch schedule that will give a desired flight condition. The equations of motion for the model in Fig. 1 are derived in Ref. 7. They take the nondimensional form (1) (2) where Fp is the nondimensional section lift, Me the nondimensional section pitching moment, (3pc the precone angle, and 6r the prescribed root pitch (written in terms of pilot control settings). (3) Although a simple static stall is included in Ref. 7, here we treat only the unstalled case. Quasisteady aerodynamics without the apparent mass terms gives the following blade loads.8 (4) (5) where p and X are the nondimensional horizonal and vertical components of wind speed, and e2 is a ratio of inertias"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001679_095965180321700606-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001679_095965180321700606-Figure4-1.png",
        "caption": "Fig. 4 Back-up bearing support device: A, hard support; B, exible support; C, ball bearing inner constraint device",
        "texts": [
            " Two smaller contact journals, which serve as the contact partners with the back-up bearings, are mounted on the outboards of two AMBs. The rotor is driven by a speedvariable d.c. motor through a exible coupling. The two AMBs supporting the rotor are the same size. The whole set-up has a security cover, which is not shown in Fig. 3. The back-up bearings are single-pair normal ball bearings, which may be mounted on either a hard support device or a exible support device with a changeable support sti ness above 2.0\u00d7105 N/m, as shown in Fig. 4. These support devices are also the cover of the AMB on the outboard side. Another inner race constraint device, also shown in Fig. 4, which could constrain the rotation of the inner race of the back-up bearing through several small screws, may be attached to the hard or exible support device. With this constraint device the back-up bearing may be changed conveniently to a solid bush. The controller for the AMBs is a DSPACE-based controller with a PID type algorithm. The controller is at UNIV CALIFORNIA SANTA BARBARA on August 31, 2015pii.sagepub.comDownloaded from specially programmed so that both or either of the two AMBs may be selected for de-energizing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002427_20.104551-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002427_20.104551-Figure1-1.png",
        "caption": "Fig. 1. Coordinate system for deriving the ooundary conditions near an impervious surface.",
        "texts": [
            " Boundary conditions at an impervious surface Calculation of the right hand side of equation (2) requires values of concentration for the four surrounding meshes. For a mesh at the wire surface, however, there are only three meshes available and hence the value of &/a7 cannot be determined using equation (2). It is noted that whilst concentration is represented by a continuous parameter, it is actually a density and therefore a finite volume must be used to determine the particle concentration. Fig. 1 shows a rectangular parallelepiped FQRSTUVW with an impervious face PQRS. Considering the flow across face TUVW it is easy to show that the time rate of particle concentration for an impervious surface in the radial direction is given as (aC/a7),. = (1/6rn)(W%,) - (l/6r,)(Grc) (5a) and similarly for an impervious surface in the azimuthal direction. (ac /ado = (i/(r,6e))(ac/LM)-(l/(rn60))(Goc) . (5b) 0018-9464/90/0900-1867$01.00 0 1990 IEEE 1868 RESULTS A number of simulations have been performed to model the capture of manganese pyrophosphate (Mn,P,0,"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000336_7.381920-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000336_7.381920-Figure1-1.png",
        "caption": "Fig. 1. Aircraft force vectors.",
        "texts": [
            " Section IV is devoted to illustrating the analysis and synthesis techniques applied to the F-15 aircraft, and evaluating the performance of the designed pitch pointing control system. Finally, some conclusions are made in Section V. In studying the dynamics of aircraft, its principal axes are commonly chosen to represent the body axes (x,y,z). The airplane orientation in space is given by the Euler angles \u00c1 (roll), \u03bc (pitch), and \u00c3 (yaw or azimuth). Furthermore, the conventional forces acting on an aircraft in flight (see Fig. 1) are thrust, drag, lift, and gravity. For a point mass model of the aircraft, the equations of motion are given by [14], m _Va = Tcos\u00ae\u00a1D\u00a1mg sin\u00b0 (1) mVa _\u00b0 = T sin\u00ae+L\u00a1mg cos\u00b0 (2) _h= Va sin\u00b0 (3) _x= Va cos\u00b0 (4) _m=\u00a1 _w (5) where Va is the true airspeed, m is the mass of the aircraft, T is the thrust, D is the drag, L is the lift, g is the gravitational constant, \u00ae is the angle of attack, \u00b0 is the flight path angle, \u03bc is the pitch angle, _h is the rate of climb, x is the horizontal component of airspeed, _w is the fuel flow rate, Vw is the longitudinal component of the wind"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002700_j.adhoc.2005.01.003-Figure14-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002700_j.adhoc.2005.01.003-Figure14-1.png",
        "caption": "Fig. 14. Data link header initiated for each of the vertex neighbors.",
        "texts": [
            ") The sensor marked with sE, for example, is the sensor elected by si to be the representative of the edge neighbor E. The value a denotes the clockwise angle between the directed segment (si, sE) and the N vector (dotted line that crosses the center of the E polygon) denoting the direction of the N neighbor of polygon E. The value (x,y) denotes the location of SE on the coordinate system origined in the center of the polygon E, in which the N and E vectors are the positive axes matching the y and x axes. Fig. 14 shows the data-link header initiated for the vertex neighboring representatives sNE, sSE, sSW and sNW. Assuming a message is sent from polygon representative s1 to its neighboring representative s2 with data-link header hx,y,ai, we describe algorithms for constructing an updated data-link headers hx 0,y 0,a 0i for each of the neighboring polygons representatives of s2. Given a data link header hx,y,ai, a representative sD, the algorithms that appear in Figs. 15\u201322 describe how to construct an updated data link headers for each of the neighboring polygon representatives"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000041_1.1392031-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000041_1.1392031-Figure1-1.png",
        "caption": "Figure 1. Traditional flow\u2013through electrode configuration.",
        "texts": [
            " Extrapolation indicates that optimal performance in the 5 cm electrode can be achieved with fewer than 100 sections, a design that is feasible to construct with modern microfabrication technology. \u00a9 1999 The Electrochemical Society. S0013-4651(98)08-021-5. All rights reserved. Manuscript submitted August 6, 1998; revised manuscript received April 3, 1999. Industrial\u2013scale electrochemical processes require the use of reactors with a large electroactive surface area per unit volume, and porous electrode systems with flowing electrolytes can be used to satisfy this requirement. Figure 1 shows a traditional flow\u2013through design for an electrosynthesis reactor of this type. The working electrode is a porous bed through which the electrolyte solution flows prior to arrival at the counter electrode, located downstream in this work, although upstream counter electrode placement is also possible and may be preferable for certain applications.1 The problem of potential control in reactors of this type is due to the ohmic drop in the electrolyte solution in the current\u2013flow direction, which results in a natural tendency for current density to be concentrated in the portion of the porous electrode nearest the counter electrode"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001381_1.1287239-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001381_1.1287239-Figure5-1.png",
        "caption": "Fig. 5 Rotor angular misalignment orbit for different clearances \u201e6 mm, 3 mm, and 1 mm\u2026 \u201esmall stator and initial rotor misalignments gs\u00c4gri\u00c40.5 mrad\u2026",
        "texts": [
            " The feasibility of contact elimination through clearance adjustment is now experimentally investigated. The proximity probe measurements are used as feedback to calculate the clearance. The experiments are conducted at 344.8 kPa water pressure and 28 Hz ~176 rad/s! shaft speed, i.e., well within the range investigated in Fig. 2. The coning angle is set to 1 mrad, roughly twice as large as the largest critical value and sufficiently close to the optimal value of 0.5 mrad for minimum effort control ~see above!. Two sets of experiments are presented. Fig. 3 to Fig. 5 show the results for experiments with small stator initial rotor misalignments, both of 0.5 mrad, and Fig. 6 to Fig. 8 for experi- JULY 2000, Vol. 122 \u00d5 481 shx?url=/data/journals/jetpez/26797/ on 03/09/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F mental results with large stator and initial rotor misalignments, both of 1.5 mrad. Other experiments for mixed misalignments @21# show similar behavior. The desired clearance is stepwise set to 6 mm, 5 mm, 4 mm, 3 mm, 2 mm, and 1 mm, and held constant by a PI controller @13#, to investigate one at a time the clearance effect on seal face contact",
            " Figures 5 and 8 show the rotor angular misalignment orbit for the desired clearances of 6 mm, 3 mm, and 1 mm. ~The results of 5 mm, 4 mm, and 2 mm, are similar and were omitted for clarity.! Two circles are drawn in Figures 5 and 8 through orbit data obtained for the 6 mm clearance and for the 1 mm clearance ~no circle is drawn through the 3 mm data because it is very similar to the 1 mm case!. It is readily seen that the deviation of the data from a perfect circle in the 6 mm case is far bigger than that of the 1 mm cases. An odd shape cluster of data points in the 6 mm case of Fig. 5 ~the blackened area shown at the top of the postulated circles!, denotes part of the 6 mm orbit which clearly does not belong to the circle. Indeed, the orbit shape becomes more circular as the clearance Journal of Engineering for Gas Turbines and Power rom: http://gasturbinespower.asmedigitalcollection.asme.org/pdfaccess.a decreases, which is another indication of noncontacting operation @12#. Therefore, the absence of high harmonics in the PSD plot for these data and the more circular orbits obtained for decreased clearance both show that contact can indeed be eliminated by such clearance adjustment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001864_bf02327567-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001864_bf02327567-Figure7-1.png",
        "caption": "Fig. 7--Definitions of symbols and coordinates used in describing the Hertzian contact",
        "texts": [
            " The Cartesian components of the stresses at point 2Z +a p ( s ) ( x - s)~ds ~,= = - - - ~ I _ . {(x-s)~+z~}~ - 2 +a q ( s ) ( x - s ) 3 d s 7- I_,, {(x_s)~+z~}~ 2Z 3 t +a p ( s ) d s ~ , , = _ _ _ ~ _ ~ { ( x _ s ) ~ + z ~ } ~ - IF q(s)(x- s)ds 2Z 2 +a p ( s ) ( x - s ) tds q ( s ) ( x - s)eds (5) where the local pressures p and q are given in terms of the local normal contact forces P and tangential contact force Q by p ( s ) = 2___s (a ~ _ s , ) , , , , . / ra 2 q(s) = 2(2 (a 2_s=),,2 , x a 2 (6) Q =fP The coordinates (x ,z , s ) are defined in Fig. 7. The contact dimension a was measured from an enlargement of the fringe pattern. With this quantity known the integrals in eq (5) could be evaluated in terms of the unknown local forces P and Q. The results of this integration were substituted into eq (4) to give (A,P+B,Q)} + (CtP+ D,Q)] = (~f %2 \" 2h \" (7) where A, , BI, C, and D, are constants determined from the integration of eq (5), and the subscript j indicates the point selected at position (xs, Zs) with a fringe order Ns. The equation contains the unknown forces P and Q associated with the asperity contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003437_tac.2005.851431-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003437_tac.2005.851431-Figure5-1.png",
        "caption": "Fig. 5. Rotor body, arm, and pivot.",
        "texts": [
            " To form a cascade-limiter from the result of either method, the following approach may be used. Procedure 5.1 (Implementation as a Cascade-Limiter): 1) Implement both inner and outer loop compensators in observer form. 2) Insert a saturation element and constant reference filter between the inner and outer loop. 3) Decompose the outer loop output weight (where is of the form and contains the integral action) and pull through to the input of the inner loop (see Fig. 4). 4) Apply an antiwindup scheme, such as [17]. B. Design Example: Quanser Helicopter The Quanser Helicopter2 (Fig. 5) consists of a helicopter body, with fore and aft mounted fans and the freedom to pitch about a coupling to a supporting arm at its midpoint. The arm is connected to a stand so as to allow the helicopter body to move in elevation and travel. The objective is to design a cascade-limiter for the pitchtravel loop such that the rig will track demands in travel subject to maintaining the rotor pitch within specified bounds. This ensures the rotor body is maintained near the horizontal position, as in Fig. 5, and enables the design to be conducted for a linear approximation to the equations of motion. 2The experimental rig, power supplies and interface are commercially available from Quanser Consulting, Inc. In this instance, controller designs were implemented on a Pentium III 550-MHz CPU running WinCon 3.1 under a MS Windows NT operating system. The linearized equations in pitch , elevation and travel are, respectively, taken as where are moment arms, inertias, and the torque required to maintain equilibrium"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003687_bf01516929-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003687_bf01516929-Figure4-1.png",
        "caption": "Fig. 4. Short journal bearing",
        "texts": [
            " [23] we solve g\u00a2 an example of a periodical shear rate. / exy = );o cos ~ot. The solution according to the Maxwell equation [18] gives the maximum shear stress tSxyl and 7, the phase lag between the stress and the shear rate Sxy = ISxy[ cos(~ot - q'), where 2qyo ISx~L - ]/1 + V2(.O 2 and [27] Ltion ~d [28] . . . . [29] tan 7, = zoo. [29a] Fig. 3. Mohr's Circle flow. The latter being comparatively weak, q5 is small: { c ~ u / c 3 X ) = o ( C ) . [33] = o \\ Ou/ay / C = R 1 - R , the mean clearance of the bearing (see fig. 4). The angular velocity f2.~y of the principal axes is: f2~r = d~b [34] \u2022 d r The angle ~b varies over the transit time, and eqs. [21] and [34] yield: (cv 135] e, ,= In eq. [15] the product f2i~S'~j transforms the shear stresses into tensile stresses and its contribution in the flow equation, compared with that of its antecedent (OS'~flc~x~)v.~, is of the order of C2/R 2. Given a journal bearing with L ~ R (see fig. 4). Since Dubois\" (21) solution for an infinitely short bearing with a Newtonian liquid is a good approximation to conventional reality, his assumptions are reproduced here, except that the lubricant is elastico-viscous. Conventionally, C = O(10-3), [36] we also assume: L --R-- = O(10- ' ) [37] with O(10 -2 ) neglected with respect to unity throughout. The x,y, z dimensions are of the order of R, C and L respectively. In the con- tinuity equation, the gradients - ~ , -~- and (?-7- are all of the same order: ~3u ~"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003271_s10595-005-0099-z-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003271_s10595-005-0099-z-Figure1-1.png",
        "caption": "Fig. 1. Schematic representation of experimental setup: ( 1 ) He\u2013Ne laser, ( 2 ) mirror, ( 3 ) microobjective, ( 4 ) collimating lens, ( 5 ) working cell, ( 6 ) photographic camera, ( 7 ) video camera, and ( 8 ) additional light source.",
        "texts": [
            " 3 2005 THE STUDY OF THE EXTRACTION OF SURFACE-ACTIVE COMPONENT 319 faces. To avoid the saturation of water with alcohol, we installed an additional reservoir with water at the top of a cell. Initial diameter D 0 of cylindrical droplets placed in a cell with a syringe varied from 2 to 15 mm. The main series of experiments was carried out at ambient temperature T = (21.0 \u00b1 0.5)\u00b0\u00eb . To study the flows and concentration fields of surfactant, we used a setup consisted of Fizeau interferometer [9] and video camera with additional light source (Fig. 1). The interferograms of concentration distribution were recorded in both transmitted and reflected light. The passage form one interference fringe to another (isolines of refractive index) corresponded to the changes in alcohol concentration in water and chlorobenzene by 0.27 and 0.10%, respectively. Additional light source was used to increase the image contrast during video recording of the flows (with simultaneous shuttering of laser light). Flows and concentration fields inside and outside the dissolving droplets were visualized and studied in the course of experiments"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001837_095441003770887359-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001837_095441003770887359-Figure3-1.png",
        "caption": "Fig. 3 Forward-swept wing vehicle",
        "texts": [
            " The increased measurement noise ampli cation is attributable to the higher error derivatives that must appear in the de nition of the sliding mode when any actuator model is included in the design; i.e. the relative order increases by the order of the actuator model considered at the design stage. The aircraft model to be employed describes the longitudinal dynamics of a forward-swept wing aeroelastic vehicle as developed in reference [15]. The model of reference [15] is extended here to include thrust effects. Figure 3 shows the general vehicle con\u00aeguration. Proc. Instn Mech. Engrs Vol. 217 Part G: J. Aerospace Engineering G04702 # IMechE 2003 at Virginia Tech on March 14, 2015pig.sagepub.comDownloaded from The linearized vehicle dynamics are given below for a \u00afight condition of steady, wings-level \u00afight at sea level at a trim airspeed of 1000 ft/s. US customary units rather than SI units are employed to agree with the model description of reference [15]. The state vector in the model is de\u00aened as x\u2026t\u2020 \u02c6 \u2030a\u2026t\u2020, a\u2026t\u2020, y\u2026t\u2020, q\u2026t\u2020, Z1\u2026t\u2020, _Z1\u2026t\u2020\u0160T \u202612\u2020 where a\u2026t\u2020 \u02c6 airspeed deviation from the trim (ft/s) a\u2026t\u2020 \u02c6 angle attack deviation from the trim (rad) y\u2026t\u2020 \u02c6 pitch attitude deviation from the trim (rad) q\u2026t\u2020 \u02c6 _y\u2026t\u2020 \u02c6 pitch rate (rad/s) Z1\u2026t\u2020 \u02c6 generalized coordinate for the wing bending mode The control variables are de\u00aened as ua\u2026t\u2020 \u02c6 \u2030dc\u2026t\u2020, dt\u2026t\u2020, df\u2026t\u2020\u0160T \u202613\u2020 where dc\u2026t\u2020 \u02c6 canard deflection (rad) (positive leading edge up) dt\u2026t\u2020 \u02c6 thrust change (lbf) df\u2026t\u2020 \u02c6 flaperon deflection (rad) (positive trailing edge down) The vehicle model for two different centre of gravity (c"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000847_70.833184-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000847_70.833184-Figure6-1.png",
        "caption": "Fig. 6. Worst-case and best-case configurations of the RRC K-1207i for reducing the effect of joint-five error on the L-shaped object under the constraint of end-effector position/orientation given by (37). In the worst case, the line passing through the axis of the fifth joint lies far from all points on the object, and in the best case, the line passing through the axis of the fifth joint actually passes through the object. The motion of the object for these two configurations after a 0.1 rad error is shown at the bottom of Fig. 7.",
        "texts": [
            " For this example, errors for all points of the object are considered equally important so is assigned to a constant, m . Additionally, Euclidean distance is chosen as a rudimentary measure to focus on the final effect of the error [i.e., is given by (3)]. The end frame is constrained to a pose given by the following homogeneous transformation matrix relative to the base frame: (37) Under these conditions, the gradient-projection technique [25], [26] was used to find the worst-case and best-case configurations for tolerating a joint-five failure. These are shown in Fig. 6. The potential error in the L-shaped object caused by an error in joint five is greatly reduced by reconfiguring. In fact, for the best-case configuration of Fig. 6 is two orders of magnitude less than that of the worst case. Fig. 7 shows the errors in the object caused by a 0.1-rad error in joints two through five using best and worst-case configurations. The improvement, using the best configuration, for the joint two and joint five failures is especially substantial, but improvement is evident in all cases. If a calibration-type failure was experienced in one of these joints, reconfiguring might allow a task to be completed that would otherwise be impossible"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002387_robot.1997.619348-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002387_robot.1997.619348-Figure8-1.png",
        "caption": "Figure 8: The DII robot and the object",
        "texts": [
            "[400, 4001 N/m. Also in Fig. 7 (b) the error ey ( t ) between the measured trajectory X and the ideal end-effector trajectory Xu computed from (15),(16) are shown. The sampling time is 2.6 ms. The step response of the end-effector changes depending on BL1), and the control errors are quite small. Then, the response of the arm for an object close to the second joint is examined. The virtual circles are set at the second joint anld the end-effector with radius T ( ~ ) = 0.3 m and d2) = 0.1 m as shown in Fig. 8. The initial posture O(0) = [-0.56,1.45, -1.43IT rad is used as the equilibrium one. The object is located at the position with a distance 0.2 m apart from the initial end-effector position in the direction of y axis at t = 0 s and is removed at t = 2 E . Figures 9 and 10 show the results under Q = 0 and (L = 1 see(l4) , respective- and (b) the joint displacements. The joint impedance in (7) are chosen as M3 = diag. [0.02, 0.02, 0.021 kgm', BJ = diag. [0.9, 0.9, 0.91 Nm/(rad/s), Ii, = cliag. [2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001519_roman.2001.981940-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001519_roman.2001.981940-Figure5-1.png",
        "caption": "Figure 5: Directions of the elementary dynamic grasps",
        "texts": [
            "ed ca,p or screwing a hold in a nnt,, siiriple operation like P i c k d Race are not longer adcquate. Therefor neiv operations like Dynamic Grasps need to be inclnded in t,he PbD system. 6.1 Dynamic Grasps Wit11 Dy?ioinic Grasps ne denote operations like screw-, insert etc. which all have in common that finger joint,s are changed during a object is grasp (i.e. t,lie force sensors provide non zero d n e s ) . In onr first approach wc distinguish thrw clcmcntary Dynamic Grasps: Screw This operation describes rotations around the zaxes (see figure 5) which is performed when screwing a bold. Twist When opening a twisted cap a Twist Grasp can be performed. It denot,es t,he romtion around t,he x-axes referred in fignre 5. . Insert Other than the upper two dynamic grasps, the Insert Grasp specifies a t,ranslatoric move along the z-axes like shown in figure 5. These three elementary dynamic grasps lead to warious characteristics like number of finger which where involved in the grasp (i.e. form 2 t o 5) and t,he direction in which the rotation or translation was performed. On the another hand elementary dynamic grasps can be combined to an complex grasp. For esample during a screw operation a translatoric component i.c. a inser? operotion can be performed. Next section gives a brief overview about SV.M;s, before the result,s are presented in t,he last"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002124_bf03181623-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002124_bf03181623-Figure6-1.png",
        "caption": "Fig. 6. Geometry of the spark tracing method (Top view).",
        "texts": [
            " For the case of test balls B and C with seams and dimples, respectively, the critical Reynolds number is even lower than that of test ball A. Comparing test balls B and C, the critical Reynolds number is lower and the minimum drag coefficient is higher for test ball C. Figure 5 shows the drag coefficients of test balls A, B, and C at different ball angles. From the figures, it can be seen that the drag coefficients in the critical region are dependent on the ball angle . Drag coefficient increases as increases from = 0\u00b0, and becomes maximum at about 40\u00b0, followed by a gradual decrease. 3.2 Spark tracing method Figure 6 shows the geometry of the spark tracing method set-up. The photographs taken using this method are shown in Fig. 7 (a)~(c) for test ball A and in Fig. 8 (a)~(c) for test ball C corresponding respectively to Re =0.5\u00d7105, 0.9\u00d7105, and 1.4\u00d7105. From these figures, the drag coefficients of test balls A and C at Re =0.5\u00d7105 are found to be in the subcritical region. So, the positions of the separation points in Figs. 7 (a) and 8 (a) are almost equal at =\u00b185\u00b0, and the wake region formed downstream of the ball are virtually identical"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002680_s09-Figure13-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002680_s09-Figure13-1.png",
        "caption": "Figure 13. Bearing test rig for the micro gas turbine.",
        "texts": [
            " From the calculation results of load capacity, for \u03b5 < 0.1, k is given as k = 22.57 kN m\u22121 at the supply pressure ps = 150 kPa(G) and k = 34.75 kN \u00b5m\u22121 at ps = 300 kPa(G). The measured spinner mass is 2mw = 1.071 g and the calculated resonance frequency is N1 = 1033 Hz for ps = 150 kPa(G) and N1 = 1281 Hz for ps = 300 kPa(G). These values agree well with the measured resonance frequency shown in figure 12. Because of their high-speed stability, hydroinertia gas bearings are applied to a micro gas turbine. Figure 13 shows a bearing test rig for the micro gas turbine. A compressor impeller is replaced by a 10 mm diameter dummy wheel with equivalent moment. The diameter of the turbine is 10 mm and the shaft diameter is 4 mm. Two hydroinertia radial gas bearings support the shaft and a double action thrust ring hydroinertia gas bearing of 10 mm diameter is set at the center of the shaft and controls the axial position. For facility of assembly and to keep the dynamic balance of the shaft, the bearings are cut into two half cylindrical shapes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002680_s09-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002680_s09-Figure7-1.png",
        "caption": "Figure 7. Developed surface of the radial bearing and a hypothetical circular thrust bearing.",
        "texts": [
            " A single admission radial bearing with inherent orifice shown in figure 5 is chosen as an analytical model of hydroinertia radial bearings. Its radial clearance, the diameter of the supply holes and the number are relatively large compared with the bearing dimension. In the case of radial bearings, it is difficult to determine the breaking position of the shock wave to the flow from each supply hole by simple calculations. Then, radial bearings are replaced approximately with appropriate hypothetical circular thrust bearings of the same number as the supply holes shown in figure 6. Figure 7 shows the relation between a developed surface of the radial bearing covered by one supply hole and a hypothetical circular thrust bearing. In the radial bearing, gas from a supply hole flows radially to the circumference, the radius xt of which is equal to the outlet width of the radial bearing, and then flows uniformly in constant cross-sectional area. The radius R0 of the hypothetical circular thrust bearing is taken as the mean value of the streamline length li supposed in the radial bearing and is calculated by the following equations: R0 = 1 nk + 1 nk\u2211 i=0 li (12) li = La \u2212 La i cos( \u03b8 i) {(1 \u2212 sin( \u03b8 i)} + Lb (13) where La = \u03c0D/2n, Lb = L/2, D is the bearing diameter, L is the bearing length, n is the number of the supply holes, nk is the number of partitions and \u03b8 = \u03c0/nk "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001423_s0005-1098(99)00222-8-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001423_s0005-1098(99)00222-8-Figure2-1.png",
        "caption": "Fig. 2. (a) Switching of the H = gain scheduled controller set. (b) critical-point switching and hysteresis switching.",
        "texts": [
            " The switching scheme is described as the following three steps. First, we select a number of distinct and \"xed values, i.e., hM i 3!, for 14i4a. Second, we construct KK i at each hM i 3ShM which provides e\"e i . Third, if C i overlaps its neighbors, i.e., C i~1 and C i`1 su$ciently large, then the switched controller is determined to be KK i for h3C i . Otherwise, we rede\"ne ShM and C i , and repeat the above procedure. Then, we guarantee the internal stability in each circle C i for 14i4a as shown in Fig. 2(a). Remark 1. We note that the switching scheme of H = gain scheduled controller set is a 3-tuple M(hM i , KK i , e i )N where hM i is a selected point of scheduling variable h, KK i is an associated controller, and e i is a stability margin. In other words, for given hM i there exists a corresponding equilibrium point x(hM i ) and an associative controller KK i with e i such that lim t?= DDx!x(h)DD\"0 for h3C i L!h . In many cases, it takes in\"nite time for the state variable to reach its equilibrium point at each switching mode",
            " Thus, if the minimum holding time \u00b9 i,i`1 is determined from b i JM i /k i e~(Ni @2Mi )Ti,i`1\" b i`1 , then DDzdj (t)DD(DDzdi (toi )DD/bi max k|Mi,i`1NMbk JM k /k k N, t5to i , j3Mi, i#1N, for DDzdi (toi )DD(b i . h Remark 2. Note that \u00b9 i`1,i is also de\"ned similarly by interchanging the index i and i#1 in (8). Thus, global minimum holding time which is a minimally required holding time so as to achieve stable switching for all controllers, is determined by max(max 1yi:aM\u00b9i,i`1 N, max 1yi:aM\u00b9i`1,i N). In order to satisfy a switching condition, there are two switching policies for two overlapping controller, i.e., the critical-point switching and the hysteresis switching as shown in Fig. 2(b). The critical switching makes KK i switch to KK i`1 at a critical value of c i,i`1 3Rm whereas the hysteresis switching has no critical switching point but shows hysteresis property. We denote the Euclidean norm of the trigger margin associated with h between KK i and KK i`1 by H i,i`1 in Fig. 2(b). Then, we note that KK i should always cross over the required region H i,i`1 so as to switch to KK i`1 , and vice versa. Let S\"MI 0 , I 1 ,2, I j , I j`1 ,2N is a sequence of indices such that the switched controller is K k at t\"to k , k3S with the initially switched controller K I0 at t\"to I0 , as t goes on. Theorem 1. Suppose that AK ci (z(h), h)) is Hurwitz for every h3C i , 14i4a. Then there exists a xnite constant dK such that DDhQ (t)DD(dK , t5to I0 and for DDzdI0 (toI0 )DD(b I0 , the closedloop system (6) is stable in the sense of Lyapunov for every switching sequence"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003710_j.jsv.2006.04.008-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003710_j.jsv.2006.04.008-Figure2-1.png",
        "caption": "Fig. 2. Rigid rotor model.",
        "texts": [
            " Using coordinate transformation the non-dimensional stiffness and damping coefficients along the x and y directions can be obtained from K\u0304xx K\u0304xy K\u0304yx K\u0304yy \" # \u00bc cos f0 sin f0 sin f0 cos f0 \" # K\u0304 ee K\u0304 ef K\u0304fe K\u0304ff \" # cos f0 sin f0 sin f0 cos f0 \" # , (13) B\u0304xx B\u0304xy B\u0304yx B\u0304yy \" # \u00bc cos f0 sin f0 sin f0 cos f0 \" # B\u0304ee B\u0304ef B\u0304fe B\u0304ff \" # cos f0 sin f0 sin f0 cos f0 \" # . (14) where fo is the steady-state attitude angle. ARTICLE IN PRESS C.H. Chen et al. / Journal of Sound and Vibration 297 (2006) 635\u2013648640 2.4. Stability threshold of rigid rotor\u2013 hybrid bearing system In the fixed reference coordinates (Ob, x, y) a rigid rotor is supported horizontally by two identical hybrid journal bearings. The rotor is assumed to consist of a massless shaft and a single, centered mass m without unbalance mass as illustrated in Fig. 2. When the journal is operating in its steady state at the conditions of a given load capacity W, lubricant viscosity m, supply pressure Ps and shaft speed o, for a small disturbance in film pressure the non-dimensional perturbation equations of center motion of the rigid rotor with whirl frequency op about the equilibrium position can be expressed by Ml2 d2x\u0304 dt2 \u00bc 2F\u0304x \u00bc 2\u00f0K\u0304xxx\u0304\u00fe K\u0304xyy\u0304\u00fe lB\u0304xx _\u0304x\u00fe lB\u0304xy _\u0304y\u00de, (15) Ml2 d2y\u0304 dt2 \u00bc 2F\u0304 y \u00bc 2\u00f0K\u0304yxx\u0304\u00fe K\u0304yyy\u0304\u00fe lB\u0304yx _\u0304x\u00fe lB\u0304yy _\u0304y\u00de, (16) where M \u00bc mco2=PsLD is mass parameter, l \u00bc op=o is whirl ratio, and components of bearing force, along with the stiffness and damping coefficients, are determined by integration of static and dynamic pressures, respectively, as mentioned above"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002472_robot.2002.1014811-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002472_robot.2002.1014811-Figure2-1.png",
        "caption": "Figure 2: Humanoid robot model.",
        "texts": [
            " Actually, we could refer to the previous works on grasp analysis and grasp optimization. However, our target system is unique in a sense that we must consider different contact types at the same time. As the first step towards developing a system that can evaluate dynamic motion sequences, only static posture is evaluated in this paper, assuming stationary postures or quasi-static motions. Numerical examples show the validity of the proposed evaluation method. Based on the proposed evaluation, an example of optimizing a motion sequence is also shown. 2 RobotModel Figure 2 illustrates the kinematic configuration of the humanoid robot that will be used in this paper for posture evaluation, This is a simplified model of the humanoid research platform (HRP-1 equivalent to HONDA\u2019s P3) developed in the first half phase of the H R P project. To simplify the problem, we will set the following assumptions: 0 All of links including the torso, arms, and legs are rigid bodies. 0 Each arm has seven degrees of freedom (DOF) (three for shoulder, one for elbow, and three for wrist), whereas each leg has six DOF (two for hip, one for knee, and two for ankle)",
            " When the hand is gripping a bar, grip or any other cylindrical object fixed to the environment, the hand can exert force and moment to any direction within the joint torque limitation and the static friction limitation. 0 The bottom shape of the foot is flat and rectangular as shown in Figure 3@). Reaction forces from the environment can be summarized to four force vectors at the vertices of the foot. The foot slips when none of these forces is within the friction cones. 0 Motions are quasi-static and dynamics is not considered. As shown in Figure 2, a body coordinate frame Cg is attached to the center of gravity of the main body (torso). For notational convention, we assign a number to each limb, i.e., i = 1,2,3,4 for left arm, right arm, left leg, and right leg, respectively. We also assign a number to each joint from the body base to the limb end. For example, the 4th joint of the 1st limb means the elbow joint of the left arm and the 6th joint of the 4th limb is the last joint of the right ankle. Instead of the joint number, a special subscript \u2018h\u2019 is assigned to the hand joint of each ann to make a distinction from other joints"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000041_1.1392031-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000041_1.1392031-Figure5-1.png",
        "caption": "Figure 5. Scale drawing of the electrochemical cell: (A) packed beds of glass beads, (B) independent current feeders, (C) reference electrodes, and (D) multisectioned electrode.",
        "texts": [
            "0298 m/s (or to an average superficial linear velocity of roughly 0.01 m/s). The electrolyte solution flows vertically through the porous electrode. Above the cell, a 2 L cylindrical reservoir contains the counter electrode (B), which consists of a stainless steel grid (provided by Gantois, St Di\u00e9, France) of very large surface area in order to limit the current density on the cathode. Each graphite slice is connected to an independent current generator (C), with a common electrical ground at the counter electrode. Electrochemical cell.\u2014Figure 5 presents a scale drawing of the electrochemical cell. The external body of the cell is made of Altuglass (PMMA, polymethyl methacrylate polymer), and metallic parts have been avoided within the cell to eliminate the risk of possible corrosion. The system as constructed consists of the following specific parts: (i) Two packed beds (A) of 3 mm diam glass beads for flow distribution above and below the porous electrode. (ii) Ten independent current feeders (B), made of graphite and arranged in a spiral progression around the electrode to facilitate external electrical connection. (In Fig. 5, a cross\u2013sectional view, only two of the ten feeders are visible.) (iii) Two reference electrodes (C), one situated above and one below the porous electrode. (iv) The multisectioned porous electrode itself (D), consisting of the ten porous graphite slices. Each current feeder is connected to an independent current generator, and the current applied to each section can be set automatically. The potential differences between each working\u2013electrode slice and the counter electrode, as well as the potential differences between the reference electrodes and the counter electrode, are recorded continuously with a computerized data-acquisition system (Testpoint\u00ae on a Pentium\u00ae 75 processor)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001083_ip-cta:19960302-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001083_ip-cta:19960302-Figure1-1.png",
        "caption": "Fig. 1 Spacecruft attitude angle,,",
        "texts": [],
        "surrounding_texts": [
            "To prevent the control discontinuities, sgn(s) function in eqn. 7 is replaced by a unit saturation function sat(s), where sat(s) = [sat(sl), . . . , sat(s,)]'\nsat(s,) = (16) 1 if s j > E S , / E if sj < ) E / i -1 if sj < --E 1 j = 1;. . . ,m\nand E is the selected boundary layer thickness, common to all sliding hypersurfaces. An apparent effect of this substitution on the process described is that the attractivity condition (eqn. 6) can no longer be supported within the boundary layer with the gain selection of eqn. 14. So the s dynamics may behave contrary to this condition within the boundary. However, as soon as the boundary limit is reached the attractivity condition is reinforced. This can be seen very easily because on and beyond the boundary limits the sat(s) and sgn(s) functions are identical. Thus, in these zones the smoothing substitution does not alter the dynamics. The use of saturation function in the control provides us the desirable control smoothness characteristic (as stressed earlier). In return, the behaviour of s dynamics within the boundary layer manifests the influence of the perturbations, not the dictate of the attractivity condition. We focus on this aspect next. Within the boundary layer, s dynamics exhibits the form of\nSi(1tAAA-l ) PI+ -K s = AbtAAA-' (yr'-b-a) (17) ( : )\nEqn. 17 is obtained by substituting eqns. 15 and 16 into eqn. 9. It represents a low-pass filter behaviour against the perturbations. The respective break frequencies are expressed by the eigenvalues of\nR = (I + AAAp1) ( PI + -K 1 ) (18)\nTo attenuate the perturbations in the wide band, these break frequencies should be designed as high as possible following Elmali and Olgac [5]. However, there must be an upperbound to these break frequencies. This bound is introduced mainly by the capacity of loop closure speed, i.e. 6,,,. Depending on the form and magnitudes of the perturbations, the s dynamics of eqn. 17 may sprint beyond the boundary E before the next control action kicks in. This frequency upperbound CO,,, is a very complex and case-dependent selection.\nThe desired lowpass filter characteristics, as discussed, can be achieved by selecting\nUsing matrix norm properties\nI w m a x\nwith k,,, = max(kj), j = 1, ..., m is obtained. Thus, with the assumption of\n/ I AA 11511 A l l + l l LMA-l I / < 1 (21)\n218\na variable boundary layer thickness is obtained as 2 k n a z\nE =\nw m a x - 2P (22) w,,, - 2P > 0\nThis completes the steps taken in SMC for the output trajectory tracking operation. Having enforced the boundary lsjl 5 E, we use the definition of the sliding hypersurface (eqn. 4) to assess that the steady state tracking errors are bounded with\nj = 1,. . . ,m ( 2 3 )\nwhere h ... L-1 are the real poles of eqn. 4.\n4 estimation\nThe conventional form of SMC methodology presents a fundamental problem. The upperbounds of the perturbations Af and AG may not be known. If and when they are known, the selection of control gains of eqn. 14 is so conservative that they may push the practical limits of the control actuators. This conservativity may not even be necessary. In fact, very often the dreadful worst scenario for the perturbations does not happen to be the case. But the conservative SMC control still tries to fight against it.\nFrom this point of view, we pursue a control structure which estimates the effects of the perturbations at each control step instead of using their worst or maximum levels: sliding mode control with perturbation estimation (SMCPE) [5]. The starting procedure is in parallel to the 'time delayed control' concept of Youcef-Toumi [9]. The effects of the perturbations on the dynamics of eqn. 2 are combined as\nSliding mode control with perturbation\nQ ( ( : q ) n c t u a l (24)\nQ(<, q ) e s t i m a t e d = calculated - v(t - 6) (25)\nv(t) v(t - 6) (26)\nA b + AAApl(v - b) = - v Note that Y(f),clu,l can be estimated by ,p The 7th derivatives are numerically calculated. The assumption of\nis made for eqn. 25 which is reasonable if v(t) does not manifest discontinuities. Also 6 should be small, suggesting high-speed loop closure to be available. Following the similar steps of Elmali and Olgac [5] and the explanation of Section 3 , a synthetic input is proposed as v = -Ps - K Sgn(s) + Y$) - 0 - * ( E , 7 ) e s t i n a t e d (27) Note that the major distinction here is that the perturbation upperbounds are not provided. That is, sup]'!? (t),ctuall is not known. The synthetic input of eqn. 27 yields an s dynamics of\nS = - P s - K s g n ( s ) + ~ ( ~ , 7 ) , , t 2 L a l - ~ ( ~ , r l ) e s t i m a t e d (28 ) Again, the question is to find the diagonal gain matrix K which assures the attractivity condition (eqn. 6). Y(t)acru,l is not known in eqn. 28, but an assumption\nI @ ( < > 7 ) a c t u a l - @ ( E , v l e s t z m a t e d l 5 ~ l Q ( t ; 7 ) e s t i m a t e d I\nP > O\ncan be made. Then the attractivity condition is satisfied by assigning\n(29)\n[k l , . . . , km.1' = C L I Q ( E , q ) e s i m a t e d I (30)\nIEE Proc.-Control Theory Appl.. Vol. 143, No. 3, May 1996",
            "The claim is that these k, values are much smaller than those of eqn. 14. Notice the important difference that instead of bounding the present perturbations (like Af and AG) we bound much smaller quantity 'I' which really is a reflection of the measurement errors. The overall control takes the form U = AP1[-Ps-K sgn(s)-cr+yt) -b-'Pestzrnate,j] (31)\nThe smoothing substitution of sat(\u00a7) in place of sgn(s) is made in parallel to Section 3 with no effect on the s dynamics outside the boundary layer. That is, attractivity still holds when lsli 2 E,. We study the s dynamics within the boundary layer, next:\nwhere K = diag(k,/&,), j = 1, ..., m. Eqn. 32 is also a low-pass filter against the perturbation estimation errors this time. To subdue the effects of the wideband oscillations in the perturbations, we select the break frequencies of eqn. 32 as high as possible, say a,,. This can be achieved by selecting the boundary layers as\ns + (PI + E)s = *(<, 77)actual - *I(<, 7 ) e s t z m a t e d ( 3 2 )\n( 3 3 )\n5 Example\nThe control strategy developed is applied to the attitude control problem of a spacecraft. Typical dynamics and associated characteristics are taken from Singh and Iyer [lo]. If the spacecraft is on a circular orbit in an inverse square gravitational field, and the attitude of the space vehicle has no effect on the orbit (Fig. l), the equations of motion are\n(34)\nwhere x = (eT, oT)'is the state vector, U = (T I , T2, T3)' is the control torque vector and Td is the external disturbance vector. a = (a1, az, c ~ ~ ) ~ is the instantaneous angular velocity vector with respect to the fixed inertial space, ci, si represent cos(0,), sin(0,), respectively. 0 = (0,, e,, are ordered roll, pitch and yaw angles about the body fixed co-ordinates and it is taken as the output vector. a. is the orbital angular speed, Ii, i = 1, 2, 3 are the moments of inertia about the body fixed principal axes. The objective of this control strategy is to track Y d = ( O l d , 02d, in the presence of model-\nling uncertainties and external disturbances. It is selected as\nY d = [1 - e--0.353t (sin 0.353t + cos 0.353t)lr ( 3 5 ) where r = [180, 45, 9OlT deg. The values in this variation correspond to a damping ratio of 0.707 and a natural frequency of 0.5 (Fig. 2).\ntime,s Desired trujectories to be followed Fig. 2\nThe modelling uncertainties appear in the form of I, + AI,, i = 1, 2, 3. The numerical values of the inertia for this simulation are I = (874.6, 888.2, 97.6)T kgm2. The variations in the inertia are taken as\n{ ;:} = 0.5[1 + sin(0.l)tI { ::::} (36)\nwhere v1 = 0.4, v2 = 0.5, v3 = 0.6. The external disturbances are generated by a harmonic time function as\nAI3\nTdl = 150sin\nG(x) =\nIEE Proc -Control Theory Appl., Vol. 143, No. 3, May 1996 219",
            "0 0 0\n(WQW1 - 3w,\"c3<1) + 150 ( W I W 2 - 3w&C2) + y\nc2 c2 c2\nOn these dynamics, SMC and SMCPE control strategies are performed separately. For the integrations a fourth-order Runge-Kutta algorithm with a time step of 2.5ms is used. The control loop-closure period is taken as IOms. For both control strategies, the following common selections are made. The poles of the error dynamics of eqn. 4 are cj,l = 10rad/s, , j = 1, 2. The break frequency of the s dynamics a,,,, lOOradls and the proportionality gain P = loradis. Initial conditions are taken as = 0. The following results are presented.\n0 2 4 6 8 1 0 1 2 1 4 tirne,s\nFig.3 Control torques,for SMC\n-1: 0 2 4 6 8 1 0 1 2 1 4\ntime,s Fig.4 s dynamicsfor SMC\nThe corresponding plots for SMCPE strategy are shown in Figs. 6-8. The comparison of Figs. 3 and 6 reveals an astonishing similarity. This implies that in gross values both routines (i.e. SMC and SMCPE) concur on the control torques. However, a closer look at the nuances between SMC and SMCPE torques points out an interesting detail (Fig. 9): minute differences in control for the level o f perturbation at hand can yield a few orders of magnitude improvements in tracking errors. Figs. 5 and 8 compare very favourably for SMCPE, which settles the tracking errors at 0.0023 deg. while SMC can only achieve 0.17deg. This means an improvement of approximately two orders of magnitude. One should keep in mind that the tracking error of 0.17 deg. occurs over a desired motion in the range of 180\". Therefore substantial improvement in this error level only requires extremely fine control torque variations as happened to be the case in hand.\ntirne,s\ntime,s Fig.5 Trucking errors for SMC\nFigs. 3-5 reflect the control torques, the s dynamics and the tracking errors, respectively, for the SMC case.\n280\nThe torques (Figs. 3 and 6) show no chatter which is a direct result of the smoothing operation via the boundary layer concept. For the SMC case, s dynamics within the boundary layer is dictated according to\nIEE ProcControl Theory Appl.. Vol. 143, No. 3, May I996"
        ]
    },
    {
        "image_filename": "designv11_24_0002815_bf01896173-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002815_bf01896173-Figure1-1.png",
        "caption": "Fig. 1.",
        "texts": [],
        "surrounding_texts": [
            "This paper is a continuation of [I]. In this paper we investigate the distribution of steady motions of the liquid-filledcavity body, decide the stability of each steady motion and find out the corresponding regions of stability and instability. Besides, the behaviour of disturbed motion is analysed qualitatively.\nI. The Fundamental Formulas\nFor convenience' sake, some fundamental formulas and conclusions in [i] concern-\ning the following discussion are rewritten as follows(The No. of each formula is the\nsa~ne as that in [i]).\ni. The disturbed kinetic energy function\nI - z\n( o )\nwhere\nY P\ndisturbed angular velocity of cavity body inertia tensor of cavity body density of liquid disturbed velocity of liquid\no---volume of liquid\nIt is obvious that\nT~O (I.1)\n2. The disturbed potential energy function\nU = a s ~ + b9 ~ + 2c (g3s - - 1) (3 ,20}\nwhere\nr z,o r~ ! a= (C,+C2--A,--A~), b= ~ . (C,+C2--~--B~), c=~-(M,ah~+M~oh2)\n2 z\n(3.Z7)\nIn the above",
            "A,, A=; B,, B=, C1, C=\ncavity body\nM,, M,, h,, h2\nmain moment of inertia of the liquid and that of\nmass of the liquid and of the cavity body distance along Ox~ from the origin 0 to the centerof gravity of the liquid and of the cavity body\n@--- acceleration of gravity r o angular velocity of rotational coordinate system OX~X=X, ro-\ntating about O~ s , it is a constant and represents a steady motion of the liquid-filled-cavity body\n@,3, gz3. G,,-- direction cosine of Ox~ in the fixed coordinate system Ox~x~x~\nthey satisfy\ng~+gh +gL =I (4.t)\nGeometrically, (4.1) represents a unit sphere and /_/ is the definition given to function on the unit sphere. In the discussion below, we designate this sphere as\nK , and call the part of g~,~0 the upper semisphere, g,s<0 the lower semis-\nphere and g88=0 the equator of K 9\nLet\n,-q---qy--. g.,=\",/ 1--g~ cos0, g=,=J J--g,s sm~ (4.2)\nIt is evident that (4.1) can be satisfied identically, substituting (4.2) into (3. 20) we have U = (1 --g~,) ~ (1 +g3s) [ (a--b)cos=e+b] --2c} (4.3;\nFrom this we get\naU ag3~ - = -2~33[ (a--b)cosZS\u00a7 b] +2c (4.5)\naU a0 = - (1 - o ] , ) ( a - b) sln2e (4 . S)\nPutting U=0 we obtain the equation for U,0, (the zero value of U ) as follows:\nting\n2c g~'= (a_b)cosZO+b 1, g ~ ' = l (1.2)\nU ) can be o b t a i n e d by p u t - The equation for U,m, (the extreme value curve of\n~u ----0 in the form\ng~T' c ----%--b) cosZS-t.b (4.6)\nOU ~ 3~ Let 7=0, we have @=0,--,2 ='--2-~' and"
        ]
    },
    {
        "image_filename": "designv11_24_0000809_1.2826964-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000809_1.2826964-Figure3-1.png",
        "caption": "Fig. 3 A typical secondary linl(",
        "texts": [
            " The first secondary link in a mechani cal transmission line contains only one output gear since the other end is attached to a motor drive shaft. All the other second ary links contain two gears, one input gear and one output gear. Sometimes, the two gears on a secondary link can be combined into a single gear, but it still meshes with two other gears in a mechanical transmission line. For the manipulator shown in Fig. 1, there are two mechanical transmission lines: (5 - 1) and (3 - 4 - 2). The input gear on the secondary link 4 meshes with the gear mounted on Hnk 3 and the output gear meshes with the gear mounted on link 2. Figure 3 shows a typical secondary linky carried by a primary link i. Assume that each of the input and output gears meshes with a gear mounted on ttie secondary links j - I and ; -I- 1, respectively. Also, let a primary link k be the carrier of the gear pair [j - 1,;'] and a primary link ^ -f 1 be the carrier of the gear pair [j,j + 1]. Note that the input and output gears on a secondary link may have two distinct carriers. Typically, a pri mary link which carries a secondary link j is the carrier of the gear pair [j - 1, j] or gear pair [j, j + 1]",
            ",, f,,, and n,,,, are computed from the balance equa tions of the previous primary link. For the end-effector, these four vectors represent the end-effector output force and moment. The left-hand sides of Eqs. (15) and (16) contain all the un known force and moment vectors: f;,,-,, n,,,-! and gj.,,. For robotic mechanisms with pseudo-triangular structure, f,,,-i, n,,;_i and g\u0302 ., constitute six scalar unknowns. Hence, they can be solved one link at a time. Dynamics of the Secondary Links. Referring to Fig. 3, the force and moment balance equations for a secondary link j can be written as: Journal of Mechanical Design and (rj\u201e - r,.,) X g,_,,; + (r,-,,. - r^J X f,-. = Nf - (r,\u201e - r,.,) X g,.,,, (20) where Ff and Nf are the inertia force and moment for link j and can be computed similarly by Eqs. (17-18) . The vector gj,j+\\ in the right-hand sides of Eqs. (19) and (20) are computed from the balance equations of the higher level links. The left-hand sides of Eqs. (19) and (20) contain all the unknown force and moment vectors: fy,,, %,, and g/ i "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000103_0029-8018(94)00025-3-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000103_0029-8018(94)00025-3-Figure1-1.png",
        "caption": "Fig. 1. Notation for pitch and heave modes.",
        "texts": [
            " The controller is required to maintain a constant depth and pitch angle below the mean sea level with measurements which are, however, a function of instantaneous sea surface. The controller should also prevent saturation of the hydroplane angles at their physical limits. Also, large pitch angles are not desired, since they may induce the propellers or the bow of the ship to rise out of the water. 2. VEHICLE AND SEA MODELS 2.1. Vehicle dynamics The notation for the pitch and heave modes is given in Fig. 1. Assuming h(t) and 0(t) are small, the linear equations of motion along the z-axis and y-axis can be written as follows: ' 1, _ _ Z~BU 2 r = ZwU w(t) + - - (Z'o + m') UO(t) + ZbL O(t) + - - gB(t) Lm~ m 3 m; m;L Z~sUZ aS(t) + 2 2 + m ; ~ p-fL3m~m ~ Z . . . . (t) + We(t) COS0 COS, pL3m;, (1) (t( t) M\" M'~U M~U M;BU 2 = LF22 r + - ~ 2 w(t) + L i f e O(t) + ~ 2 2 8B(t) M;s U2 2mg(zG - zR) O(t) + M . . . . (t) (2) + a s ( t ) + p c s i P ' 2 where IX =/by - M~, m' = 2m/pL 3, m~ = m' - Z ' , and We(t) = Me(t) 9 g",
            "12 \u2022 10 -3 U28S( t ) - 1.08 \u2022 1 0 - 2 (ZB -- zG)O(t) - 2.2 \u2022 lO-9Mwave(t) (3) + 3.06 \u2022 lO-6Zwave(t) + 9.8 \u2022 lO-SMe( t ) and Q(t) = 4.0 \u2022 10 -5 Uw(t ) - 9.15 \u2022 10 -3 U Q ( t ) + 6.78 \u2022 10 -6 U2~B( t ) - 3.07 \u2022 10 - s U 2 ~S(t) - 2.65 x 10 -3 (zB - zc ) 0(t) - 7.14 \u2022 10 -8 Me(t) (4) + 5.42 \u2022 10 -1~ . . . . (t) - 2.20 \u2022 -9 Z . . . . ( t ) , where Q(t ) = 0(t). These two equations represent the linearized equations of motion in the vertical plane. However , they do not contain the depth as a state variable. From Fig. 1, for a constant depth Ho h( t ) = w( t ) cos0(t) - U(t) sin0(t) . (5) For a constant forward speed and small angles of pitch Adapt ive controller design for submersibles 597 h( t ) = w( t ) - UO(t) . (6) From Equations (3), (4), (6) and the definition of Q(t ) , we can write the state variable representation of vessel dynamics: 2v(t) = Avx~( t ) + B~u(t) + Fd( t ) (7) where x~(t) : [w(t), Q(t ) , O(t), h(t)] r, u(t) : [~B(t), ~S(t) , Me(t)] r and (8) d(t) = [Z . . . . ( t) , M . . . . (t)] r . In order to make the measurement proportional to depth error, the ordered depth Ho is extracted from the measurements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002386_s0301-679x(01)00116-5-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002386_s0301-679x(01)00116-5-Figure3-1.png",
        "caption": "Fig. 3. Arc type aerostatic bearing and the guideway.",
        "texts": [
            ": +886-4-7232105-7294; fax: +886-4- 7211097. E-mail address: chenmf@cc.ncue.edu.tw (M.F. Chen). 0301-679X/01/$ - see front matter  2002 Elsevier Science Ltd. All rights reserved. PII: S0301- 67 9X( 01 )0 0116-5 ear slide guideways 7 as the main guide, two arc type aerostatic linear guideways 8 as auxiliary guide, ball screws, linear scalars, and servo motors. The proposed new type mixed guideway system not only can reduce the friction force, but may increase the dynamic behavior of the linear guideway system. As shown in Fig. 3, the structure of the arc type aerostatic linear guideway system consists of two arc type aerostatic bearings and a precision steel shaft as guideway. This work analyzes a compound restrictor arc type gas bearing with axial and circumference shallow grooves machined on the bearing surface, along which the supplied gas flows. Kogure et al. made the first analysis on horizontal grooves of a rectangular gas bearing by the resistance network method (RNM) [2]. Nakamura [3] reported a theoretical analysis for rectangular thrust bearings with horizontal and vertical grooves"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002006_978-3-662-09769-4-Figure7.3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002006_978-3-662-09769-4-Figure7.3-1.png",
        "caption": "Figure 7.3: Spatial rigid body which is attached to the base by a revolute joint",
        "texts": [
            " Spatial modelsofarigid body under constrained motion These expressions provide the model equation of the mechanism: (7.47a) with (7.47b) (7.47c) (7.47d) (7.47e) and (7.47f) The symbolic expressions for j v (p,nJ, together with the matrix M ind (p,nJ and the vectors q0,nd(P,nd) and f,nd(P,nd' v,nd), have been computed using the algebra manipulation program MACSYMA. These expressions provide the model equations (7.33a). 7.2 Rigid body attached to the base by a revolute joint ( one rot. DOF) Consider the rigid body with the mass m 1 and the center of mass C1 (Figure 7.3). It is attached to the base by means of a revolute joint with the rotation axis through the points P 1 and Q1 . The point P 1 is fixed on the body and serves as a reference point in the subsequent model equations. It is located in the origin of a local frame L 1 on the body. Despite the fact that this system can be considered as a planar mechanism (see the Equations 4.67a and 4.67b of Section 4.3.1.3 of [1]), it will be modeled in the framework of the DAEs of a spatial mechanism (see the Equations 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000181_1.2787261-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000181_1.2787261-Figure5-1.png",
        "caption": "Fig. 5 T w o - r o d s sys tem",
        "texts": [
            " 6 T w o - r o d s s y s t e m - - t h e rotat ion 0~, \"\u00b0 as a funct ion of t ime: A - - \"Accurate, \" B - -Baumgar te , P - - P r e s e n t m e t h o d six degrees-of-freedom. The components of the cross-sectional moments of inertia of the rods are uniform and identical to those of the single rod of subsection 3.2. The mass per unit length of each rod is 0.113 kg, while its length is 0.254 m. The flexibility in the joints--about the x, y, and z-axes--is identical to the appropriate flexibility in the example of a single rod in Subsection 3.2. The system is loaded again by a compressive axial concentrated force P~(t) (see Fig. 5) at the tip of the second rod, in the same manner as in the single rod example. Similar to the single rod case, a very small lateral disturbance force, in the zdirection, is also applied. Its influence is negligible. 120 / Vol. 64, MARCH 1997 Transactions of the ASME Downloaded From: http://appliedmechanics.asmedigitalcollection.asme.org/ on 01/30/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use The exact response of the system includes two degreesof-freedom--0~ and 0~. Again three methods are used: accurate approach where two exact equations are integrated numerically and exact expression for the constraint force is used, the Baumgarte method and the present method"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003809_detc2005-84681-Figure9-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003809_detc2005-84681-Figure9-1.png",
        "caption": "Figure 9: Test configuration and results after tool holder node optimization.",
        "texts": [
            " Characterization of the complete spindle unit The modal parameters of the complete spindle result from a combination of the results presented above. The validation of shaft mode shapes is not experimentally feasible since the entire shaft-bearing system is totally enclosed inside the spindle housing. Identification of bending modes is again very complex because of inter-mode couplings and high damping rates. Study of the FRF curve delivered by the accelerometer placed on the tool holder tip (see figure 9) shows the evolution of rotating entity modes on the preloaded rolling bearing. The identification is of type SDOF rather than MDOF; thus there is no discrepancy between FRF and optimization is facilitated. This measurement makes it possible to validate the six-by-six mathematical rigidity matrix model for each rolling bearing [8]. Comparing the experimental and numerical results makes identification of guide parameters (such as stiffness, rear guide ball bush damping and bearing damping) feasible"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003814_12.601652-Figure12-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003814_12.601652-Figure12-1.png",
        "caption": "Figure 12. Two Primary Dimensions of Unit Cell Tool paths.",
        "texts": [
            " Aluminum has a much higher thermal expansion coefficient, but forms brittle intermetallics with many of the other materials. Invar has a very low CTE of course, but has problems with cracking during DMD processing. Chromium is the only material that remains. It is miscible in excess of 40 percent by weight at 1300 oC with nickel, and has a CTE that is less than half of nickel. Therefore it was chosen for the low- expansion phase of the structure, and nickel was chosen for the highexpansion phase. Fig. 12 shows two of the key dimensions of the unit cell tool paths labeled. These two dimensions are the spacing between the nickel and chromium tool paths around the perimeter of the cell itself, and the spacing between the chromium tool Figure 11. Contraction Mechanism of Negative CTE Structure. Table 2. Coefficients of Thermal Expansion, DMD Materials Material Coefficient of Thermal Expansion (10-6 cm/cm *C) Invar 1.54 Chromium 6.0 1020 Steel 12.0 Nickel 13.0 Copper 16.6 Aluminum 25.0 Table 3. Descriptions of Five Tool Paths Tool Number Path Design Chromium Intra- Tool Path Spacing (in) ChromiumNickel Spacing (in) 1 1 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001886_iecon.2000.972612-Figure9-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001886_iecon.2000.972612-Figure9-1.png",
        "caption": "Fig. 9 (a) Orientation for soldering (b) Orientation for image capture",
        "texts": [
            " First step is to find two dimensional transformation between image coordinates and robot coordinates. Second is to find the tip position of soldering iron on the base of image coordinates . 3.1 Transformation algorithm In order to find the displacement of image coordinates according to that of robot coordinates, /Image 2 -\ufffd------.., 1 Xc __ -1- __ _ 1 1 Yc I I I I 1 .----i\ufffd 1 ------1-- I I \\.., - -\ufffd------- 'Image 3 -'Pallet XR \ufffd_ - -- \ufffd- Feature ! Point Image 1 the tip position should be calibrated. The orientation of hand for soldering is ftxed as shown in Fig. 9(a) and Fig. 9(b) shows that for taking a photograph. The second step of calibration process is to find the image coordinates of the tip in the orientation of soldering. When the robot at the position, XRS, YRS locates the tip of soldering iron at some place on the pallet in soldering orientation, the contact point is marked. The marked point is shown at the position, XCmllrk' YCmllrk in the image which captured by camera of robot hand, when the robot position is x Rmark' Y Rmark' The image coordinates, Xes. Yes of the tip, are calculated by eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001533_robot.1989.100101-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001533_robot.1989.100101-Figure1-1.png",
        "caption": "Figure 1: Finger forces.",
        "texts": [],
        "surrounding_texts": [
            "1 Introduction In this paper we consider the manipulation of objects using multifinger robot hands. In such manipulations it is important to analyze the distribution of forces among the gripping fingers. Because knowledge of coeficients of friction is only approximate it is desirable to find the finger forces which hold the object in equilibrium (or overcome an external force) while requiring the smallest coeficient of friction. (We assume a Coulomb friction model for the surface contacts.) That is, we seek finger forces for which the maximum of the angles Bi ( i = 1 , 2 , 3 ) between each of them and the corresponding inward pointing normal is smallest.\nWe will prove here that, except for some separately treated special cases, the optimal equilibrium forces in the sense just described have the property that the Bi\u2019s are all equal in absolute value. We also provide a procedure for computing these equilibrium forces, which reduces the (nonlinear) optimization problem to a generalized eigenvalue problem (which is easily solved). We then extend our results to the case when the coefficients of friction at the contact points are different and to the three dimensional case.\nOur analysis is independent of the kinematic configuration of the fingers provided they can exert arbitrary forces within the friction cones. In particular, our results can be applied to sucli diverse multifinger manipulators as the Utah/MIT hand [ 5 ] , the Salisbury hand [lo], and NYU\u2019s Four Finger Manipulator [2].\nIn Section 2 we give a more precise formulation of the\nproblem and introduce some notation. In Section 3 we compare our approach to others in the literature. In Sections 4 and 5 we state our result on the geometric properties of the optimal equilibrium forces. In Section 6 we describe a procedure for finding those equilibrium forces. In Section 7 we present the generalizations. Because of limitations of space proofs will appear elsewhere.\n2 Notation and definitions We will assume throughout that we have three fingers and that the contact points between fingers and object are fixed. Moreover the contacts will be modeled as hard point contacts with friction. This means that each finger can transmit any force to the object through the contact (as long as it is within the cone of friction) but it can not transmit any torque. The relationship between the finger forces Fi ( i = 1 , 2 , 3 ) and the resulting force and torque on the object f, T can be described as follows (see Figure l),\ne F i = j , e F i x ri = r (1) i=l i= l\nwhere ri is the position vector of the contact point pi relative to the center of torque Q. In the planar case the\ntorque r can be identified with a one dimensional quantity. Equation 1 can be rewritten as\nG F = [ f ]\n936 CH2750-8/89/0000/0936$01 .OO 0 1989 IEEE\n_ _ _ ~ ~ _ _ _ ~ . - -",
            "where G is a 3 x G matrix in the 2-dimensional case (a 6 x 9 matrix in the 3-dimensional case), and F = (FF, FT, F r ) T . Given an object force/torque pair (1, T ) to solve for the finger forces we use the pseudoinverse G+ = @(GGT)-l to get\nF = G + [ ! ] + e (3)\nwhere e is an arbitrary vector in the right null space of G (NULL(G)). Since G has full rank, NULL(G) has dimension 3. That is, there are tliree independent parameters in the choice of the forces Fi.\nWe need to specify the vector e. This vector could be thought of as a vector of equilibrium forces. In particular the resulting torque should be zero. Therefore, except for the case when all forces are parallel, all three lines of action must intersect at the same point p. The point p accounts for two of the parameters in the choice of the Fib, the third parameter being the norm of e (which represents the strength of the grip). The set of solutions resulting in parallel forces Fi can be parametrized using only two parameters (a unit vector and a magnitude). Remark 2.1 If the Fi\u2019s are nonzero equilibrium finger forces (i.e. correspond to f = 0 and 7 = 0 in (3)) and two of them are parallel then all three are parallel.\nWe will return to the case of parallel forces later. Now, we look at the problem of finding e from the point of view of finding p which minimizes Omax = maxi lOi(p)I, where Oi(p) is the angle that p - pi (and hence Fi) makes with the normal ni to the object. To be more precise, Oi(p) is the smaller angle between ni and the line through p and pi. Notice that I tan(O,,,)I is the smallest coefficient of friction necessary to achieve the given grasp.\nThe problem is one of minimizing the function maxlOi(p)I of two variables (the coordinates of p) over a region of the plane. However, because of geometric considerations which will be explained in Section 4 the search for a minimum can be restricted to a finite set, thus yielding a finite algorithm to find the optimal p. The several points p where the minimum might occur will be listed in Theorem 4.1. Each case will need to be treated separately. One of the cases, however, merits special attention. That is when the minimum will be attained at a point p for which lOi(p)I = O for i = 1,2,3. To find such a minimum p we restate the problem as one of solving a generalized eigenvalue problem.\nThis method was implemented on NYU\u2019s Four Finger Manipulator. Experimental results can be found in [2,3].\nWe will need the following definitions. Given a set S, the interior of S, denoted S, is the set of all points p of S for which there is a disk (or a ball in the 3 - 0 case) centered at p and completely contained in S. The closure of S, denoted 3, is the set of points p for which every disk (ball) centered at p intersects S. The boundary of S, denoted as, is the set of those points of 3 which are not in S. 0 0\n3 Comparison to other methods Kerr and Rotli [7] consider the general problem of selection of the internal forces (called equilibrium forces here) in both 2 and 3 dimensions. They simplify the problem into a linear programming one by approximating the 3-dimensional cones by piecewise linear pyramids. They combine all the constraints coming from friction cones and joint torque limits into a set of linear inequalities. These determine a constraint polygon in m dimensional space (where m depends on the number of fingers and joints). They then choose a point which is furthest away from the boundary of this constraint polygon as the optimal internal forces. IIowever, no geometric interpretation of the resulting finger forces is given.\nSchwartz and Sharir [ll] developed an algorithm for finding the finger forces, which generalizes to an arbitrary number of fingers in the plane. They study feasibility regions in force/torque space and present a compjerity analysis of the algorithm. The approach is used to find optimal finger forces which overcome an arbitrary external generalized force on the object (and not simply equilibrium forces). Their method does not extend to 3-dimensions and does not provide an easy geometric interpretation of the finger forces.\nThe closest related work is that of Ji and Roth [GI. Using purely geometric reasonings they derive conditions for the internal forces to minimize the dependence on contact friction. They only consider some generic geometric arrangements of the object normals at the contact points. By using a combination of topological and algebraic tools, instead of purely geometric ones, we are able to consider all possible configurations for the object normals and include in the analysis the possibility of parallel finger forces. Furthermore, our approach easily extends to the case of three dimensions and variable coefficients of friction.\nAn approach to optimal grasping which takes into account the task to be performed was presented in [9].\nIn a related paper, Yoshikawa and Nagai [12], studied the problem of decomposing the fingertip forces into their grasping and manipulating components. This led them to the study of the regions of the plane where a possible concurrency point p (as mentioned in the previous section) might lie. An analysis of grasping and manipulating ability of a given multifinger hand was also presented in [8].\n4 Geometric Analysis We first examine the case of nonparallel forces. We write &(p) = ang(p - pi, ni), and ci(p) = tan(Oi(p)). We will also assume that ci(pi) = 0. Now, for a > 0, define the (two sided) cones (Figure 2)\nIci((*.) = { q : ICi(q)l 5 tan(a)).\nThat is, I&((*.) is the set of all points q for which the angle between q - pi and either ni or -ni is less than or equal"
        ]
    },
    {
        "image_filename": "designv11_24_0000371_20.717855-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000371_20.717855-Figure1-1.png",
        "caption": "Fig. 1 Conductors associated with the edges of 9-edge prism",
        "texts": [
            " Then, taking the Stokes' theorem into account, the sums of edge value of T are expressed by the face values of ampere turn density. For the p - th edge the obtained expression represents the p-th element of vector Ni,,,. This expression can be written as follows T [41, [51. where Nus is the element of the p-th row and the u-th column of matrix N, and iw, is the current of the u-th winding. Nus can be considered as the number of conductors of the u-th winding associated with the p-th edge. Here, the formulas for 9-edge regular prisms are discussed. If the p-th edge is described by vector QIQ,, such as is presented in Fig. 1, then the element NUB can be expressed as follows (3) where K=6 for the edges parrallel to axis z, K=12 for the edges that lie on the xpplane (see - Fig. 1); N+u,p,q ( q = i j ) are the numbers of filamentary conductors of the u-th winding which penetrate through the faces of common node Qq (q= i j ) , except the faces with edge Q 2 1 ; the subscript + denotes the conductors with the current directed inside the elements with edge Q,Q,, and the number of conductors with the currents directed fiom inside the elements is denoted by subscript -. The presented method of matrix N formulation leads to a Nu,, =. (N+u,p,1 - N-u,p,l + N - U J I J - N+U,P,J) K > 0018-9464/98$10"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000539_bf00239872-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000539_bf00239872-Figure3-1.png",
        "caption": "Fig. 3. Musculo-skeletal model of the elbow flexor muscle. IO =l=0.18 d; O, angular position; w, angular velocity; B I=A=l .17d ; where IO is the distance of the flexor muscle insertion point from the centre of rotation (I), d is the distance between styloid apophysis and epithrochlea-epicondyle axis, BI is the distance of the flexor muscle insertion on the humerus from the centre of rotation",
        "texts": [
            " F(x, v) = M(x, v) (9) dsin/3 V(x) = wd sin/3 (10) where M(x, v) is the muscle (or external) torque at a given muscle length (x), d the lever arm, ~o the angular velocity and/3 the angle between the force and the lever arm. To obtain d and /3, images of the ankle in the angular position during the isometric test were made by X-ray computerized tomography technique (DRH, Siemens Medical, Erlangen, Germany). For the elbow architecture, the musculo-skeletal model consisted of a classical link segment (Pertuzon and Bouisset 1971; Fig. 3), so that the relationships between muscle length (x), angular position (0) and velocity velocity (w) of muscle shortening (V) and anthropometric data were derived. F(x, v) - M(x, v) (11) /sina where /=0.18d, A=1.17d, x=VA2+12+2Alsina, and sin a = A/x. In these equations, I is the distance of the flexor muscle insertion point from the centre of rotation, d the distance between styloid apophysis and epithrochlea-epicondyle axis, A the distance of the flexor muscle insertion on the humerus from the centre of rotation, a the angle of the muscle action line with the forearm, F(x, v) the concentric force, and M(x, v) the concentric torque"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000170_s0263574700019147-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000170_s0263574700019147-Figure1-1.png",
        "caption": "Fig. 1. Multiple robots coordinating to manipulate one object.",
        "texts": [
            "125 228 Genetic algorithms The organisation of the paper is as follows. In section two, the problem of the trajectory planning of multiple coordinate robots is formulated. The optimisation method based on GA is proposed in section three. Then, a case study of trajectory planning for two coordinating robots is presented in section four and finally conclusions are drawn in section five. 2. PROBLEM FORMULATION 2.1 Dynamic Model of the Coordinating System Consider n robots manipulating one object, as shown in Figure 1, each robot having nt (n,==6) degrees of freedom. One of the robots (master) holds the object firmly, while the other robots (slaves) can move their position along the border of the object. All the contacts between slave robots and the object are supposed to be point contacts. Let Fo be the world reference frame. FE is the object-fixed frame, with its origin at the mass center of the object. Fei is the end-effector frame of the ith robot, with its origin located at the contact point. The dynamic equations for each robot in Fo can be expressed as follows: A(<7,)<7, + c,(qh q,) + JfF, = x, (i = 1, 2 , ",
            ";) e R\"1*\"1 is the ith robot inertia matrix Ci(qh qi) e R\"' is the vector including coriolis, centripetal and gravity forces Ji e R6*\"' is the Jacobian matrix of ith robot ft e R6 is the force vector exerted by the ith robot on the object x, e R\"' is the vector of ith robot's joint torques The dynamic equations of the object in Fo are given by: ME(p)p+cE(p,p) = F (2) where p, p, p e R6 are the vectors of the object posture (position and orientation), velocity and acceleration respectively ME e R6x6 is the object inertia matrix CE(p, p) e R6 is the vector of centripetal and gravity forces of the object F is the vector of the resultant force exerted onto the object by the end-effectors of the robot, and is given by: (3) In equation (3), JE e Rbxb is the Jacobian matrix of the object. 7},,- E /?6*6 is the force-moment transformation matrix from Fei to F\u00a3.18 2.2 Kinematic relationship of the coordinate system From Figure 1, the homogeneous transformation between Fo, FE and Fci are as follows.19 (1 = 1 , 2 , . . . , / ! ) (4) where T\u00b0E is the transformation matrix from Fo to FE, given by R3x3 0 Px Py Pz \"i\" (5) #3,3 = Rot (z, pez) Rot (y, Pey) Rot (je, Pex) (6) Px, Py, Pz are the position of the origin of FE in Fo and Pex, Pay, Pez a r e tr*e angles of axes between FE and Fo Tj is the transformation matrix from Fo to Fei T'E is the transformation matrix from Fei to FE. It is dependent on the position of ith robot's end-effector and has the following form: (7) (^3x3), is the rotational matrix from Fci to FE, which has the same form as equation (6) rei is the vector of the origin of Fei in FE"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000887_aic.690381205-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000887_aic.690381205-Figure1-1.png",
        "caption": "Figure 1. Geometric sketch of the slow motion of multiple spheres.",
        "texts": [
            " For the simple case of movement of two spheres, our numerical calculations for the droplet interactions show excellent agreement with the exact solutions for the axisymmetric case obtained by using the bipolar coordinate system (Haber et al., 1973) and with the asymptotic solutions derived by Geigenmuller and Mazur (1986) or Hetsroni and Haber (1978). The complete collocation results for the hydrodynamic interactions between pairs of droplets are also employed to evaluate the average settling velocity in a bounded suspension of small droplets. Analysis for Multiple Droplets We consider the slow motion of N fluid droplets in an unbounded, immiscible fluid in an arbitrary three-dimensional configuration as shown in Figure 1. The droplets are assumed to be small enough so that interfacial tension maintains their spherical shape. It is also assumed that there is no coalescence and Marangoni stresses are not important. For convenience, the rectangular coordinate system ( x , y , z ) is established such that the center of the first sphere is at the origin. The position of the center of droplet i is represented by coordinates (b , , ci, Vol. 38, No. 12 AIChE Journal di), and we have set bl = cI = dl = 0. The droplets may be formed from different fluids and have unequal radii",
            " The unknown coefficients Pjn, Sjn, ain and yln are to be determined using the boundary conditions at the droplet interfaces. Application of Eqs. A3 to Eqs. A4 leads to the components of fluid velocities _v and 3: m 1898 December 1992 Vol. 38, No. 12 AIChE Journal first multipole contributes to the drag force exerted on the droplet. +2p2\" (\")' Appendix B: Formulation for the Slow Motion of Multiple Rigid Spheres P,* *(r,, p,) = r;\"-'[ (2n + l)(n + l)G;,!iz ( P , ) For the three-dimensional motion of N rigid spheres in an immense, quiescent fluid as illustrated in Figure 1, only the flow field of the surrounding fluid phase needs to be considered. The boundary conditions for the fluid velocity at the particle surfaces are 1 -2(n+ I)P,~,,(P,) +; ( P I ) ] @lob) S,*(r,, p,) = r;\" ( 1 - pjY2[2nP. (P,) + 2nG; ( P , ) - 4 ~ 2 ' ~ - 1 (14 2(n- 1) 2(n - 2) +- p i ( p j ) - m p2P' j n - l ( PI .)] (AlOc) n instead of Eqs. 3a to 3c, for i = I , 2, . . . , or N. Here, 8 is the angular velocity of sphere i and can be written as Ql& + Q,ye, + Q,&. Applying Eq. B1 to Eq. 10a and employing the truncation procedure to result in Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003258_detc2005-84712-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003258_detc2005-84712-Figure1-1.png",
        "caption": "Figure 1. Planar 4-bar mechanism with links of unequal length.",
        "texts": [
            " That is, the computational complexity encountered for the determination of Gro\u0308bner bases may possess severe problems for multi-loop mechanisms. This section summarizes results for selected examples that exhibit special phenomena. For standard examples like Bricard or Bennett mechanisms (paradox, overconstrained) the well-known results are obtained, and are not shown here. Due to the equivalence of the three models, the kinematic tangent cone is given only for model I. Details are omitted for brevity. Figure 1 shows a planar four bar mechanism with L > 0 in its reference configuration with representing point q = 0. I. Kinematic tangent cone to V : The parameter space is V4 := T4. The filtration of D(1) in q0 = 0 terminates with D(2) (0) , se (2), \u03ba = 2. It is K2 q0 V ( IK ) = Cq0 V ( IK ) . The first and second order cones are K1 q0 V ( IK ) = {( \u2212s \u2212 ( 1 + \u221a 2 ) t, \u221a 2t, s, t ) ; s, t \u2208 R } K2 q0 V ( IK ) = C\u2032 q0 |V ( IK ) \u222a C\u2032\u2032 q0 V ( IK ) with C\u2032 q0 V ( IK ) = {(\u2212u, 0, u, 0) ; u \u2208 R} C\u2032\u2032 q0 V ( IK ) = {( u, 2 (\u221a 2 \u2212 2 ) u, u, 2 ( 1 \u2212 \u221a 2 ) u ) ; u \u2208 R } "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003882_s0007-8506(07)60477-6-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003882_s0007-8506(07)60477-6-Figure5-1.png",
        "caption": "Figure 5: Positions of the sampling points of a probe ball, for direct runout measurement, compared with the positions of the pitch sampling points",
        "texts": [
            " The pitch of a bevel gear is defined in [5],[6] as the arc length between all consecutive left or right flanks of one gear, measured at the pitch diameter d in a distance R from the apex of the reference cone. This measurement position is equal to that of the runout. Therefore, CMM manufacturers tend to save measurement time by using the points obtained during the pitch measurement to evaluate the runout. Thus, measuring strategy described in section 2.1 loses its importance. Figure 4 shows the principle of pitch measurements, where both probe movements sample pitch points at all left and right flanks, respectively. Figure 5 illustrates the difference between the sampling points obtained by pitch measurement and the direct runout measurements of a spiral bevel gear. For the latter method, the contact points of the ball probe with the left and the right flanks are on different z-positions, whereas the pitch points are on the same z-level. For helical cylindrical gears, this fact is less critical, because the involute flank form is mathematically well defined as a continuous surface. Thus, it is possible to determine exactly the positions of the probing ball centres",
            " Figure 6 (b) is extended by the ball probes for a direct runout measurement, where all centre points lie on a circle with the diameter dpb-mean. The relationships between the pitch sampling points, the contact and centre points of the ball probe are equal in each gap. Figure 6 (c) presents the same situation as in (b) but with an additional eccentricity fe in clamping. Now the relative positions of pitch points, contact points and centre points are no longer equally or evenly distributed. Moreover, the zpositions of all drawn points are different (see Figure 5). As a consequence, a mathematical solution for the runout evaluation has to be able to determine the 3D positions of the (virtual) ball probe centre points out of the (measured) pitch points. Every bevel gear evaluation software, sold by CMM manufacturers, includes its own method for calculating the theoretical entering depths of ball probes, based on measured pitch points. Some of them imply the determination of eccentricity from runout results. Neither the implemented algorithms nor comparisons of measurement results carried out with different CMMs have been published, as yet"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003917_0278364905058242-Figure12-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003917_0278364905058242-Figure12-1.png",
        "caption": "Fig. 12. The tunnel environment used in the simulations, and the sequence of footholds generated by the PCG algorithm.",
        "texts": [
            " The proof, which appears in Appendix A, realizes the path computed by the algorithm as a rectilinear path in contact c-space having one segment per edge of the subcube graph. Optimality of the resulting path follows from the fact that all paths associated with a three\u2013two\u2013three gait naturally embed in the subcube graph. Finally, note that the subcube graph is a fixed data structure for a given tunnel environment. Each new start and target need only be connected to the existing graph which is then searched for the optimal path. This section contains results of running the PCG algorithm on a simulated tunnel depicted in Figure 12. The tunnel consists of six walls whose lengths are marked in the figure. All length units are centimeters. The figure also shows a three-limb robot at its start and target positions. The robot\u2019s reachability radius is R = 60 cm. The coefficient of friction is \u00b5 = 0.5, a value that corresponds to rubber coated footpads contacting walls made of metal or perspex. Note that the simple tunnel already contains significant geometric features. The two walls at the tunnel\u2019s bottom form a closing cone. The tunnel next turns leftward and becomes two parallel walls. Finally, the two walls at the tunnel\u2019s top form an opening cone. These geometric features are significant, since the robot must use friction effects in order to traverse such features. The walls are parametrized by path length in counterclockwise order (Figure 12). Thus s = 0 and s = 270 correspond to the bottom and top of the tunnel\u2019s right side, while s = 270 and s = 540 correspond to the top and bottom of the tunnel\u2019s left side. Using this parametrization, contact c-space is the cube [0, 540]\u00d7[0, 540]\u00d7[0, 540] depicted in Figure 8. The center point of contact c-space at (270, 270, 270) represents three-limb postures where the three footpads touch the upper point of either side of the tunnel. Topologically, one ought to put a cube-shaped puncture at the center of contact c-space, since the top points on the left and right sides of the tunnel are physically distinct",
            " The algorithm next partitions each maximal cube along the separating planes of the other maximal cubes. The partitioning of the maximal cubes generated 230, 900 subcubes in contact c-space (the resulting subcubes are not shown). The algorithm next constructs the subcube graph, assigns unit edge weights, and searches the graph for the shortest path from the start to target postures. The result of computing the shortest path using Dijkstra\u2019s algorithm is shown in Figure 11. Each segment in the figure is an edge of the subcube graph representing one limb lift-and-reposition step. Figure 12 shows the same path in physical space, where each foothold is marked by its index in the sequence of steps taken by the robot. Let us denote the sequence of three-limb postures by (i1, i2, i3), where ij is the foothold position of limb j at the ith stage. Then the path computed by the algorithm consists of the three-limb postures: S = (1, 2, 3) \u2192 (4, 2, 3) \u2192 (4, 5, 3) \u2192 (4, 5, 6) \u2192 (7, 5, 6) \u2192 (7, 8, 6) \u2192 (7, 8, 9) \u2192 (7, 10, 9) \u2192 (11, 10, 9) \u2192 (11, 10, 12) \u2192 (13, 10, 12) \u2192 (13, 14, 12) \u2192 (13, 14, 15) \u2192 (16, 14, 15) \u2192 (16, 17, 15) \u2192 (16, 17, 18) \u2192 (19, 17, 18) \u2192 (19, 20, 18) \u2192 (19, 20, 21) \u2192 (22, 20, 21) \u2192 (22, 20, 23) \u2192 (22, 24, 23) \u2192 (25, 24, 23) \u2192 (25, 24, 26) \u2192 (25, 27, 26) \u2192 (28, 27, 26) \u2192 (28, 27, 29) \u2192 T = (30, 27, 29)",
            " This sequence describes a three\u2013two\u2013three gait pattern, where successive three-limb postures are interspersed by a two-limb posture that allows motion of a limb between the two three-limb postures. Note that the path generated by the algorithm is minimal in terms of the number of steps relative to the cube approximation of the feasible three-limb postures (Figure 10). Note, too, that the short edge along the s3-axis in Figure 11 corresponds to the transition (7, 8, 6) \u2192 (7, 8, 9). This edge takes the robot around the corner between the walls W5 and W6 in Figure 12. The difficulty in accomplishing this maneuver can be appreciated by inspecting the narrow overlap between the planar cells I5 \u00d7 I1 and I6 \u00d7 I1 in Figure 7. Some remarks on the algorithm\u2019s run time. The PCG algorithm took about 78 h to run this example, using Mathematica\u2019s native code on a 1.7 GHz Pentium with 512 MB RAM. The subcube graph for this example contains 230, 900 nodes, and most of the run time was spent on searching the graph using Dijkstra\u2019s algorithm, which took 117, 500 iterations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001141_s1359-6454(01)00438-4-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001141_s1359-6454(01)00438-4-Figure8-1.png",
        "caption": "Fig. 8. Schematic illustration of the laser surface annealing process. (a) Symmetrical geometric model; (b) the half of (a) for FEM simulations.",
        "texts": [
            " Their results are in very good agreement with the value obtained in the present research. Furthermore, the equation for the line in Fig. 7 was regressed to Eq. (24). The pre-exponential coefficient of the reaction constant k, k0, was deduced to be 4.98\u00d71013. ln[ ln(1 Xv)] 31.54 2.25 ln q (24) This equation was used in the simulation to calculate the volume fraction of the \u03b3 phase from the thermal histories of any point on the LSA processed surface. The LSA process is schematically illustrated in Fig. 8(a). Since the beads were much thinner compared with the total plate, the geometrical model of the heat transfer process was treated as being symmetrical around the plane \u2018I\u2019 formed by the laser beam\u2019s centerline and the scanning direction of the laser beam. Therefore, for simplification, only half of the geometrical model was selected as the FEM thermal simulation model, as illustrated in Fig. 8(b). Thus, it is rational to treat \u2018abcd\u2019, the cross face of the symmetrical plane \u2018I\u2019, and the physical sample as being heat insulated. It is essential to ensure there is no surface melting in the LSA processes; therefore, there is no need to consider the effects from the melting process, i.e. no latent heat is included in the calculation. It is also reasonable to neglect the heat loss by surface radiation when no melting occurs. Thus, the energy equilibrium equation in this process can be given as Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002984_cdc.2004.1429394-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002984_cdc.2004.1429394-Figure1-1.png",
        "caption": "Fig. 1. Aerodynamic forces and moment acting on the glider.",
        "texts": [
            " Since we investigate steady motions in this paper, we consider a rigid body with uniformly distributed mass, fixed wings and tail and fix any other masses at the center of gravity (CG). For the underwater glider, this makes the center of buoyancy coincident with the CG. For the purpose of exposition, we further assume (in the case of an underwater glider only) that the longitudinal section is circular. The extension of our results to the more general ellipsoidal case will appear in a future work. A schematic of the vehicle is shown in Fig. 1. We fix a frame on the body with e1 as shown defining the body 1-axis. The body 2-axis is defined by e2 which points into the page and e3 lies along the body 3-axis in the plane, perpendicular to e1 with direction defined by the right hand rule. In general the mass of the vehicle plus the added mass in the body-1 direction m1 differs from the mass plus added mass in the body-3 direction m3. With the circular section assumption, m1 = m3. We also define m0 to be the \u201cheaviness\u201d of the glider, i.e",
            ", the mass of the glider minus the mass of the displaced fluid. In the case of a vehicle in the air, added mass and buoyancy are negligible so that m1 = m3 = m0 = m, where m is the mass of the vehicle. We also let J2 be the moment of inertia (plus added moment of inertia if in the water) about the axis in the e2 direction passing through the CG of the glider. The pitch angle is \u03b8, the glide path angle is \u03c6 and the angle of attack is \u03b1; \u03b8 = \u03c6 + \u03b1. We model lift L and drag D forces, and an aerodynamic moment M as shown in Fig. 1. The forces depend on \u03b1 and longitudinal speed V of the glider: L = (KL0 + KL\u03b1) V 2, D = ( KD0 + KD\u03b12 ) V 2. The moment is a function of \u03b1, V and the pitch rate of the glider \u21262: M = (KM0 + KM\u03b1 + Kq\u21262)V 2. The coefficients of lift, drag and moment depend on the shape of the glider and the design of its wings and tail. They can be estimated using empirical relations, and fine tuned by system identification [13]. We note that Kq, which represents aerodynamic pitch damping, was not included in [11]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002466_iros.1993.583931-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002466_iros.1993.583931-Figure2-1.png",
        "caption": "Fig. 2 Sensor construction for two robots",
        "texts": [
            "1 For tlie stay-robot, thrcc oiniii-directional photodctcctors are prepared aiid are attached with a supportcr to the top of tlic robot. Note that these photodctcctors shape thc vcrtices of an equilateral triaiiglc in a horizontal plane. On tlic othcr hand, a lascr beam gciicrator 011 a rotation stage is attached to the move-robot. This rotation stage rotatcs thc laser bcaiii to a fixccl direction in tlie sainc liorizoiital plaiic as tlic pliotodctcctors of tlic stayrobot, at a fiscd aiigular spced. Figure 2 shows tlic top view of t,hc two robots. Tlic t,lirec pliotodctcctors of t,lic stay-robot gciicratc pulscs Sensor construction for two robots after bcing hit by tlie laser beam from tlie inovc-robot. Tlie stay-robot first approxiiiiatcly deteriniiics tlie direction in which tlic niovc-robot cxists by chcclting tlie ordcr of tlicse pulses. Then, it deteriniiics the relative-vector to tlic movcrobot using the time intervals betwcen each pair of pulscs. The principle of this process is shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003767_sice.2006.314829-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003767_sice.2006.314829-Figure4-1.png",
        "caption": "Fig. 4 Motion forms of starfish robot",
        "texts": [
            "1 Reward database Simulation In this study, the robot legs consist of four motors. Each leg can form three patterns by positioning the leg at three angles. Therefore, this robot has 81 (=34) motion forms and 6561 (=34 x 34) patterns are available for selection between the one-step transitions from some state to the next state; this is why this study attempted to reduce the motion patterns as far as possible in order to avoid the explosion of the number of combinations. Motion forms of 81 kinds in this starfish robot are shown in Fig. 4 and the ID numbers are assigned to each motion form for the convenience of creating the database during the simulation. Hence, we used an offline learning simulator based on the reward database in order to avoid the training for longterm learning and the mechanical fatigue of the robot due to the learning process. First, it is necessary to obtain the reward database in order to execute the learning simulation. Therefore, we measured the moved distance in the x and y direction and the rotated angle by using the two PSD sensors while the robot is moving for all the motion patterns"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001875_02ye0277-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001875_02ye0277-Figure2-1.png",
        "caption": "Fig. 2. Error vector chain. B } is denoted by Ci. The",
        "texts": [],
        "surrounding_texts": [
            "category is referred to as the self or autonomous calibration[5,11,12,15], which implements the identification by minimizing the residuals between the measured and computed values of the active and/or redundant joint sensors. It has been observed, however, that only a partial set of the parameters is identifiable due to the unknown information between the base frame in which the self-calibration is carried out and the calibration frame in which the pose accuracy is evaluated. Therefore, external measuring device is needed to determine the relationship between these two frames. In principle, the effects of the geometric errors on the pose accuracy of 6-DOF PKM systems can completely be compensated by software. However, as for the PKMs with DOF fewer than six, this is no longer true since the pose error has six components in terms of both translation and orientation. The difficulty also comes from the fact that the number of parameters in an ideal kinematic model is different from that in the model where the geometrical errors affecting the uncompensatable pose error are considered. Based upon our previous work[16,17], the kinematic calibration problem of a 3-DOF translational PKM with parallelogram struts is investigated in this paper. An approach to the geometric parameter error identification is proposed using the pose error in terms of the \u201cflatness\u201d, \u201cstraightness\u201d and \u201corientation\u201d measurements. The error compensation strategy is proposed which is particularly suitable for the PKM systems with translational moving capabilities. Experiment was carried out to verify the effectiveness of the proposed approach and the results show that the accuracy can be significantly improved.\n1 Error modeling[16,17]\n1.1 System description and error source tracking The object under consideration is a 3-DOF\nThe reference frame {O} is placed on the surface of the worktable with O being the intersection of the x y plane and the axial symmetric axis of the workspace. In the kinematic chain, {Bthi\nBi} is placed on the column such that BiB is",
            "located in the x y plane, the zBi axis is along the way\u2019s direction, pointing to the middle point Ci of two joints on the carriage, and the xBi axis is normal to the interface of the way and the carriage. The nominal position of and its error\nare given by b iB\n0 and bi. The orientation error of the column is given by Bi. Note that b0, bi and\nBi are referenced to an intermediate coordinate system {Oi} by rotating {O} about the z axis an angle 6 2 ( 1) 3i i (i = 1~3). Similarly, {Ci} is placed on the carriage with the yCi axis passing through the centers of two joints. The nominal distance and the error from BBi to Ci are given by qi0 and qi. The latter represents the\nhome error of the carriage. The orientation error of {Ci} relative to {Bi\nnominal distance between two joint centers is given by e, while its error is given by Ci which is equally shared by the two sides. On the other hand, {O } is placed on the platform with O being\nlocated on the axis of the spindle that serves as the z axis. The x axis is parallel to the bottom of\nthe platform. The nominal position of O is given by r0, while the pose errors of {O } relative to {O} are given by r and . An additional {Ai} is also placed on the platform with Ai being located at the middle point of two joints associated with the ith kinematic chain and the yAi axis passing through the centers of two joints. The nominal position of Ai and its error relative to O are given by a0 and ai. The orientation error of {Ai} is given by Ai. Note that a0, ai and Ai are referenced to an intermediate coordinate system iO by rotating {O } about the z axis by i. Just as\nin {Ci}, the distance error between two joint centers is denoted by ai. Moreover, the vector pointing from Cij to Aij can be linearly represented by the sum of three terms the nominal component lwi, its deviations and ij il w ijl w in terms of amplitude and direction. Here l is the\nnominal strut length, wi is the nominal unit vector and is the length error of the jth strut in the\nith kinematic chain.\nijl\n1.2 Error mapping function The first order approximation of the position error of O can be expressed by[16]\n0 3 2 2\n0 2\nsgn( ) 2 2\n2sgn( ) ,\ni i i Bi i i ij i\ni\nq j e e l\ne j\nr R e e e e w w\nR a e\nijl\n(1)",
            "i = 1 3, j = 1 2.\nwhere 3 ,i i i ia ,i Bi Ci Ai q e b e i ie c ia and E3 is a 3\u00d73 unit matrix.\n1 1 sgn( ) , 1 2 j j j T 2 0 1 0 , e T\n3 0 0 1 , e cos sin 0 sin cos 0 .\n0 0\ni i\ni i i\n1\nR\nNote that iC ( iA ) is placed in such a way that it allows the length error between two joint\ncenters to be equally shared by each side. This arrangement allows r in eq. (1) to be eliminated by a simple subtraction of two equations associated with two struts in a kinematic chain. Consequently, the orientation mapping function can be formulated by , J (2)\nwhere 1 , J A B\nT1 2 1 2 2 2 3 2 3 ,d A R e w R e w R e w\nTT 2 2diag , 1 ,i i i i i i id B B B w R e R e w R\nT TT T T T 1 2 3 , i i i il e\n1i\n.\n2i il l l represents the relative length error of two struts in the ith kinematic chain. Similarly, it is possible to achieve the position error mapping function by simple addition of two equations associated with two struts in the ith kinematic chain.\n,r rr r r rr r r r r J J J J J\n(3)\nwhere\n1 1\nT 1 2 3\nTT 0 3\nT 1 0 3 2 0 2 3 0 3\nT TT T T T 1 2 3\n, ,\n,\ndiag , 1 ,\n,\n, ,\nrr r\ni i i i i i i i\nr r r r ri i i i\nq\nl\ne\nJ C D J C EJ\nC w w w\nD D D w R R e w R\nE R a w R a w R a w\n1 2 2i i il l l is the mean value of the length errors of the two parallel struts in the ith ki-\nnematic chain. It can be shown that the projection of onto 2iy e 2i i R e w is zero. Thus, J should be modi-\nfied by eliminating the column associated with .iy Similarly, the projection of Biz 3i R e onto\nis zero and thereby the column of Jii weR 3 rr associated with Biz should also be eliminated."
        ]
    },
    {
        "image_filename": "designv11_24_0001934_robot.1992.220116-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001934_robot.1992.220116-Figure4-1.png",
        "caption": "Figure 4: Stability region defined by S = { p l , p z , w }",
        "texts": [
            " Let P be the set consisting of the vertices of A and of the points of the circles with a vertical (i.e. parallel to the y-axis) tangent. From each point p of P, we extend a vertical line segment (called a wall) until it hits the circles immediately above and below p . These walls decompose Id1 into trapezoids which are bounded by at most two walls and two circular arcs. M , we call stability region defined by S the following subset of the Euclidean plane: can be decompose d into trapezoi d s with no overcost. For any S qs) := CH(S) n (n qP)). (3) P E S Figure 4 shows the stability region defined by a subset of three sites. Definition 1 Let 3 be the union of the stability regions associated to all the subsets of M : 3:= U R(T). (4) T ~ M 3 is trivially the set of configurations which are feasible and stable. In other words, the free space of the robot. 3 is a region of the plane limited by circular edges supported by circles D(q) ( q E M ) and by linear edges supported by lines qq' ( q , q' E M ) . Figure 5 shows an example of the free space 7 for a small set of points"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003246_j.jsv.2005.04.019-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003246_j.jsv.2005.04.019-Figure1-1.png",
        "caption": "Fig. 1. Sketch of the decomposition of the fluid force in journal bearing.",
        "texts": [
            " It is shown that this derivation is simple and consistent with the commonly used formulae for the linearized stiffness and damping coefficients. What is more important is that the physical meaning of this derivation is clearer and simpler. r 2005 Elsevier Ltd. All rights reserved. 1. Introduction The existing definitions of the linearized stiffness and damping coefficients in polar coordinates are derived from the Taylor series expansions of the radial component fe and tangential component ff of the fluid force f (Fig. 1) and neglecting higher than first order terms. There are two commonly used approaches for arriving at definitions of these coefficients (see Section 2). However, they lead to inconsistencies in the final expressions for the stiffness and damping coefficients. Especially, when applied to infinitely short bearings, the inconsistencies become so obvious. This paper presents a more general and straightforward derivation of bearing stiffness and damping coefficients in polar coordinates. The final expressions for the stiffness and damping coefficients are consistent with those in both Refs",
            " Nomenclature bij damping coefficients of fluid film bearing, N s/m, \u00f0i; j \u00bc ;f\u00de (i is the direction of the force, j is the direction of the speed) b\u0304ij \u00f0C=R\u00de3 mL bij \u00f0i; j \u00bc ;f\u00de C radial clearance, m fe radial component of the fluid force, N ff tangential component of the fluid force, N kij stiffness coefficients of fluid film bear- ing, N/m, \u00f0i; j \u00bc ;f\u00de (i is the direction of the force, j is the direction of the displacement) k\u0304ij \u00f0C=R\u00de3 moL kij \u00f0i; j \u00bc ;f\u00de L bearing length, m Ob center of the journal bearing Oj center of the journal R journal radius, m t time, s x the coordinate in the horizontal direction y the coordinate in the vertical direction m lubricant viscosity, Pa s o running speed of the rotor, rad/s e eccentricity ratio f attitude angle 2. Existing inconsistencies between two kinds of existing definitions Fig. 1 shows the sketch of the decomposition of the fluid force in journal bearing. In Fig. 1, Ob is the center of the bearing; Ojs is the steady-state equilibrium position of the journal center; Oj is the dynamic position of the journal center; e and f are the eccentricity ratio and attitude angle of the journal center, respectively; subscript s represents the steady-state equilibrium position; C is the radial clearance; fe and ff are the radial and tangential components of the fluid forces f in journal bearing; x and y are the coordinates in the horizontal direction and vertical direction, respectively; ee and ef are the unit vectors in radial and tangential directions, respectively. Referring to Fig. 1, the fluid force f is f \u00bc f e \u00fe f fef \u00bc e ef h i f f f \" # . (1) The two commonly used definitions mentioned in Section 1 are both based on the same Taylor series expansions of the radial component and tangential component of the fluid force f separately while neglecting higher than first-order terms as follows [1\u20133]. f \u00bc \u00f0f \u00des \u00fe qf q qf qf qf q_ qf q _f D Df D_ D _f 2 66664 3 77775, f f \u00bc \u00f0f f\u00des \u00fe @f f @ @f f @f @f f @_ @f f @ _f D Df D_ D _f 2 66664 3 77775. The above equations can be written in the following form: f \u00f0f \u00des f f \u00f0f f\u00des ",
            " Direct deduction of the stiffness and damping coefficients One of the approaches in the existing literature arrives at the definition of the stiffness coefficients (kij) and damping coefficients (bij) from the Taylor series expansions\u2014Eq. (2)\u2014 directly [3]: f \u00f0f \u00des f f \u00f0f f\u00des ! \u00bc k k f kf kff \" # CD C Df ! b b f bf bff \" # CD_ C D _f ! , (3) where k k f kf kff \" # \u00bc qf Cq qf C qf qf f Cq qf f C qf 2 6664 3 7775 and b b f bf bff \" # \u00bc qf Cq_ qf C q _f qf f Cq_ qf f C q _f 2 6664 3 7775. (4) 2.2. Transformation approach for deriving the stiffness and damping coefficients From Fig. 1, the following transformation is used [1,2]: f 0 f 0f ! \u00bc cosDf sinDf sinDf cosDf ! f f f ! , (5) where f 0 is the component of the fluid force f in the same direction as the fluid force component f \u00f0 \u00des at the steady-state equilibrium position, and f 0f is the component of the fluid force f in the same direction as the fluid force component ff s at the steady-state equilibrium position. For a small perturbation, Df 1, so that cos Df 1, sin Df \u00bc Df. Using these two approximations, Eq. (5) can be rewriten as f 0 f 0f "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000971_cec.2000.870275-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000971_cec.2000.870275-Figure2-1.png",
        "caption": "Figure 2: Airframe axes",
        "texts": [
            " It describes a 5 DOF model in parametric format with severe cross-coupling and non-linear behaviour. This study has considered the reduced problem of a 4 DOF controller for the pitch and yaw planes without roll coupling. The angular and translational equations of motion of the missile airframe are given by: 1 1 2 Q = ZI;'pVoSd(-dCmqq + C m w W + VoCmgq) 1 2m 1 1 ZIG1pVoSd( z G T r + CnVw + V~C,CC) w = -PVo~(~zwW + v o c z g 4 + u q (1) + = 'Pvos(c,uv + VOC,CC) - ur (2) 2m where the axes(z, y, z), rates(r, q) and velocities (w, tu) are defined in (Figure 2). Equations (1,2) describe the dynamics of the body rates and velocities under the influence of external forces (e.g. Czw) and moments (e.g. Cmq), acting on the frame. These forces and moments, derived from wind tunnel measurements, are non-linear functions of Mach number, longitudinal and lateral velocities, control surface deflection, aerodynamic roll angle, and body rates. The aerodynamic coefficients: Cy,, C v ~ , zcp. and Cn, are presented by polynomials shown in Table 1. These polynomials are fitted to the set of curves taken from look-up tables for different flight conditions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000695_7.366334-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000695_7.366334-Figure2-1.png",
        "caption": "Fig. 2. Definition of tracking error for CLOS guidance law.",
        "texts": [
            " Then we have 264 x\u0308my\u0308m z\u0308m 375= 264c\u03bcmc\u00c3m \u00a1s\u00c1mcs\u03bcmc\u00c3m\u00a1 c\u00c1mcs\u00c3m \u00a1c\u00c1mcs\u03bcmc\u00c3m+ s\u00c1mcs\u00c3m c\u03bcms\u00c3m \u00a1s\u00c1mcs\u03bcms\u00c3m+ c\u00c1mcc\u00c3m \u00a1c\u00c1mcs\u03bcms\u00c3m\u00a1 s\u00c1mcc\u00c3m s\u03bcm s\u00c1mcc\u03bcm c\u00c1mcc\u03bcm 375 264 axayc azc 375\u00a1 26400 g 375 \u00a2 =TIM 264 axayc azc 375\u00a1 26400 g 375 (1) where \u03bcm and \u00c3m are pitch angle and yaw angle of the missile, respectively, and \u00c1mc is the roll angle command of the missile. The notations c\u03bcm, s\u03bcm, etc. stand for sin\u03bcm, cos\u03bcm, etc. We consider the same tracking error as defined in [1] as follows \" e1 e2 # = \" \u00a1s\u00bet c\u00bet 0 \u00a1s\u00b0tc\u00bet \u00a1s\u00b0ts\u00bet c\u00b0t #26664 xm ym zm 37775 \u00a2 =D(t) 26664 xm ym zm 37775 : (2) REMARK 1 As shown in Fig. 2, (Rp,e1,e2) represent the coordinates of the missile in the LOS frame, and they are related to (xm,ym,zm) through two rotations 492 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 31, NO. 1 JANUARY 1995 as follows264Rpe1 e2 375= 264 c\u00b0t 0 s\u00b0t 0 1 0 \u00a1s\u00b0t 0 c\u00b0t 375 264 c\u00bet s\u00bet 0 \u00a1s\u00bet c\u00bet 0 0 0 1 375 264xmym zm 375 = 264 c\u00b0tc\u00bet c\u00b0ts\u00bet s\u00b0t \u00a1s\u00bet c\u00bet 0 \u00a1s\u00b0tc\u00bet \u00a1s\u00b0ts\u00bet c\u00b0t 375 264xmym zm 375 \u00a2 =Tlos 264xmym zm 375 : Therefore the D(t) matrix consists of the second and third rows of the rotational matrix Tlos"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003970_0021-9797(79)90240-6-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003970_0021-9797(79)90240-6-Figure2-1.png",
        "caption": "FIG. 2. Stationary state of a cylindrical particle at a fluid interface; symbols are explained in the text.",
        "texts": [
            " 2, September 1979 free energy terms are also made dimensionless by using LRT23 as the energy unit. These free energy terms are marked by primes. The variable shape parameters are 0, ~b, and H. 0 is the instantaneous contact angle, the angle q5 determines the position of the three phase line on the cylinder, and H is the dimensionless elevation of the cylinder, H = h/R [3] (see also Figs. 1 and 2). The chosen shape variables are not independent. By expressing the capillary elevation Z0 (Z0 < 0 in Fig. 2) f rom the Laplace equation of capillarity (for a cylindrical meniscus) we obtain 2 O+q5 H - cos~h = - - c o s - - [4] C 1/~ 2 For simplicity we will retain all three variables 0, ~b, and H in the expression for AF. The reference state (where AF = 0) is chosen at 0 = 7r, ~b = 0, H = 1. These values imply the configuration in which the cylinder is above and just touching an undisturbed plane fluid interface. The overall change of the free energy from a reference state to any other state may be subdivided in three terms (1) as: AF = AF~ + AFz + AF3 [5] where AFI: is due to changes of the interfacial areas 13 and 12; AF2: is due to changes of the interfacial area 23, caused by the capillary deformation of the interface and the geometry of the shell; AF3: is due to the work done against gravity",
            " Work must be done against gravity to move the fluid phases from their position at the reference state to that at some other configuration. The set of formulas for AF3 given in (2, 3) can be simplified by considering a different subdivision of this free energy term: AF~ = AF31 + AF32 + AF~ The terms AF31 and AFz2 represent the free energy change associated with the displacement of fluid 2 by fluid 3. The term AFzl is associated with the volume 2 x (BQPB) \u00d7 L and AFz2 with the remaining volume 2 \u00d7 (BPTSB) \u00d7 L (see Fig. 2). The term AF,3 represents the free energy change associated with the displacement of fluid 3 by the cylinder. The combined analytical expression for AF~ is 4 l _ _ } A F t - 3C 1/2 [2 + c o s ( 0 + 6)] sin 0+2 q5 1 + C[H 2 s i n 6 - H(6 + \u00bd sin 26) + sin q5 - \u00bd sin 3 ~b] + CD~(H - 1). [9] It is noted that the free energy terms AF~ and AF~ do not depend on the homogeneity or heterogeneity of the surface. Therefore, these terms are equivalent to those derived for a homogeneous cylindrical surface at an interface (2), as has been mentioned"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003013_tia.1986.4504803-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003013_tia.1986.4504803-Figure1-1.png",
        "caption": "Fig. 1. Brushless self-excited three-phase synchronous motor for normalspeed drive.",
        "texts": [
            " It is feasible to synthesize these waveforms using a microcomputer-based PWM technique. By this technique the control of brushless excitation can be attained, the torque characteristics are enhanced, and smooth operation becomes practicable for the low-speed drive [10], [ 1]. Experimental results are provided in the following discussion. II. PRINCIPLES OF THE BRUSHLESS SELF-EXCITED THREE-PHASE SYNCHRONOUS MOTOR A. Strategy for Superimposing the Stationary Field For the normal-speed drive, the circuit of the brushless selfexcited three-phase synchronous motor, as shown in Fig. 1, has been reported [3], [4]. Diode D is inserted into one phase of the stator winding and then the stationary magnetic field is superimposed on the revolving field, so ac voltages of the fundamental frequency are induced in the field windings on the rotor revolving at synchronous speed. The voltages are half- 0093-9994/86/0900-0847$01.00 \u00a9 1986 IEEE IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. IA-22, NO. 5, SEPTEMBER/OCTOBER 1986 I\"ab 0 20 _ i1b r1:I -4-, 20A 20 zic f f% -\\ ~-r /1% 12a 20AI - U2b 2 0 A \u00b0 \\%,- C 2ypiA wave rectified by diodes D2b and D2C connected to the field windings, and the rotor field is excited by the rectified currents"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001695_s0165-0114(99)00153-0-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001695_s0165-0114(99)00153-0-Figure1-1.png",
        "caption": "Fig. 1. The case study: a tubular reactor.",
        "texts": [
            " To this end, fuzzy logic can be used either as add-on technique to other approaches or as self-reliant methodology providing thereby a plethora of alternative modelling and control structures. The performance of the proposed self-tuning fuzzy controller is compared against an equivalent conventional model identi\"cation adaptive controller (MIAC), over a wide range of step disturbances and operating regions. The two schemes are compared with several methods including time integral performance criteria such as Integral of Absolute Error (IAE) [22]. The case under study is shown in Fig. 1 and concerns the control of a jacketed plug Fow tubular reactor where a \"rst-order exothermic, irreversible reaction A\u2192B takes place. Assuming constant temperature for the coolant, the state modelling equations are given by the following partial di=erential equations [22]: @CA @t + v @CA @z = \u2212 k0 exp ( \u2212 E RT ) CA; (2a) cp A @T @t + cp vA @T @z =UAt(TC \u2212 T )+ (\u2212DHR)k0 exp ( \u2212 E RT ) ACA (2b) with the boundary conditions: CA(0; t)=C0; T (0; t)=T0; CA(z; 0)=CPro\"le; T (z; 0)=TPro\"le; 0\u00a1z\u00a1l; (2c) where CA(z; t); T (z; t) are the concentration and temperature pro\"le, respectively, inside the reactor, is the mass density, v represents the Fuid Fow velocity, cp for speci\"c heat capacity, \u2212DHR denotes the heat of reaction, E is the activation energy, k0 is the Arrhenius factor, R is the thermodynamic constant, l is the length of reactor, U is the overall heat transfer coeLcient, At is the heat transfer unit area, A is the cross section, TC is the coolant temperature"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001897_robot.1997.614281-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001897_robot.1997.614281-Figure1-1.png",
        "caption": "Figure 1: Description of the quadruped",
        "texts": [
            " In a third section, we present how a computed torque control law can be defined for a walking robot. Then we define the ballistic motion for this robot (section 4). In section 5 , the reference trajectory is defined. Finally, we present and comment some simulation results. 2. Desgiption of the robot and gait studied Our aim is to control a quadruped robot which consists of a platform and four identical legs, and to study different gaits for this robot which involve simultaneous motion of two legs. 2.1 The robot studied Three types of gait are possible (fig. 1): gallop when the front legs move together as the rear legs (fig. 1 b); walk when the legs on the same side move together (fig. IC); trot when diagonal legs move together (fig. Id) In order to simplify the dynamic model we use the virtual legs introduced by Raibert [9]: one virtual leg symbolizes two real legs with simultaneous motion (fig. le-f). The three gaits differ by the motion of the platform. In this paper, we study only the first gait, and limit the number of actuators to obtain the simplest model of the virtual quadruped with feet. This model is given in fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003207_019-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003207_019-Figure2-1.png",
        "caption": "Figure 2. Experimental device for testing the micromotors (a) and matrix of petals formed on a glass substrate (b).",
        "texts": [
            " For example, to achieve parameters similar to those displayed by the film motors, it is necessary that \u03b5 be higher than 10 000, which is observed for some types of ceramics. A Ar value larger than that observed during the rolling on the ferroelectric film can be achieved by using a higher voltage, since the greater thickness of ferroelectric ceramics allows one to apply a voltage that is higher by a factor of 2\u20135 than that used for rolling on the ferroelectric film. The prototype of the \u2018ceramic\u2019 electrostatic motor has the same construction as the micromotor based on ferroelectric films [6], see figure 2(a). This allows one to reliably compare experimental data obtained for both types of micromotors. Figure 3 shows the schematic of the \u2018ceramic\u2019 electrostatic micromotor. The stator consists of a ferroelectric ceramic plate with an electrode applied to its bottom surface fixed on the substrate. A moving plate (slider) with thin metallic films (petals) of length l, that are created on its surface by methods of microelectronic technology (see figure 2(b)), moves with respect to the stator along the guides. The motion consists of several stages of petal shape change. When the voltage pulse is applied between the petal in its initial state A (part of the petal is mechanically pressed to the stator surface, ferroelectric ceramics, see F) and the electrode, the petal begins from its end to be attracted to the ceramic surface by the electrostatic forces. After this the slider starts to move, as larger parts of the petals\u2019 surface are rolled on the ferroelectric surface, and petals are bent and mechanically stressed (B)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003902_.2005.1469807-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003902_.2005.1469807-Figure2-1.png",
        "caption": "Fig. 2. The geometric relationships between the relevant parameters and variables utilized in the guidance-based path following scheme.",
        "texts": [
            " Then consider a geometric path continuosly parametrized by a scalar variable R, and denote the inertial position of a point belonging to the path as p ( ) R2. The desired geometric path can consequently be expressed by the set: P = \u00a9p R2 | p = p ( ) R \u00aa , (1) where P R2. For a given , define a local reference frame at p ( ) and name it the Path Parallel (PP) frame. The PP frame is rotated an angle: ( ) = arctan \u00b5 0 ( ) 0 ( ) \u00b6 (2) relative to the inertial frame, where the notation 0 ( ) = x ( ) has been utilized. Consequently, the -axis of the PP frame is aligned with the tangent vector to the path at p ( ), see Figure 2. The error vector between p and p ( ) expressed in the PP frame is given by: = R>(p p ( )), (3) where: R ( ) = cos sin sin cos \u00b8 (4) is the rotation matrix from the inertial frame to the PP frame, R (2). The error vector = [ ] > R2 consists of the along-track error and the cross-track error , see Figure 2. Also, recognize the concept of the off-track error, represented by | |2 = > = 2 + 2. Define the positive definite and radially unbounded Control Lyapunov Function (CLF): = 1 2 > = 1 2 ( 2 + 2), (5) and differentiate it with respect to time along the trajectories of to obtain: \u02d9 = ( cos( ) ) + sin( ). (6) We can clearly consider the path tangential speed as a virtual input for stabilizing , so by choosing: = cos( ) + , (7) where 0 becomes a constant gain parameter in the guidance law, we achieve: \u02d9 = 2 + sin( )",
            " Obviously, such a variable should depend on the cross-track error itself, such that = ( ). An attractive choice for ( ) could be the physically motivated: ( ) = arctan \u00b5 4 \u00b6 , (9) where 4 0 becomes a time-varying guidance variable utilized to shape the convergence behaviour towards the path tangential, i.e. 4 = 4( ) satisfying A.3. It is often referred to as the lookahead distance in literature dealing with path following along straight lines [6], and the physical interpretation can be derived from Figure 2. Other sigmoidal shaping functions are also possible candidates for ( ). The desired azimuth angle is thus given by: ( ) = ( ) + ( ) (10) with ( ) as in (2) and ( ) as in (9). We also need to state the relationship between and : \u02d9 = p 02 + 02 = cos +p 02 + 02 , (11) which is non-singular for all paths satisfying assumption A.1. Hence, the derivative of the CLF finally becomes: \u02d9 = 2 + sin = 2 2p 2 +42 , (12) which is negative definite under assumptions A.2 and A.3. The last transition is made by utilizing trigonometric relationships from Figure 2. Note that the speed by definition cannot be negative. Elaborating on these results, we find that the error system can be represented by the states and . It can be rendered autonomous by reformulating its time dependence through the introduction of an extra state: \u02d9= 1 0 = 0 0, (13) see e.g. [7]. The new and extended system can be represented by the state vector x = \u00a3 > \u00a4> R2 \u00d7 R \u00d7 R 0, with the dynamics: x\u0307 = f(x). (14) The time variable for this new system is denoted with initial time = 0, such that ( ) = + 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003209_1.2061007-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003209_1.2061007-Figure2-1.png",
        "caption": "Fig. 2 Schematic diagram of hydraulic expansion",
        "texts": [
            " The surface of the tubesheet holes was finished to meet commercial specifications. The roughness value of the surface of the tubesheet holes is Ra12.5* m. Prior to tube expanding, preparation work for expansion was carried out first. It included numbering the tube and tubesheet, respectively, measuring and recording the original inside and outside diameters d1, d of the tubes, and the tubesheet hole diameter D. The expanded joints were fabricated by commercial hydraulic expanders, as shown in Fig. 2. The high-pressure fluid enters the hydraulic bag through the hole in the mandrel; at the same time, the pressure is transferred to the tube and plastically deforms the tube wall, starting from the inner surface. The pressure is increased until the outside tube wall contacts the tubesheet bore. Any further increase in the hydraulic pressure will cause the expansion of the tubesheet hole, and the tube will be deformed into the grooves during expansion. When the hydraulic pressure is released, the tube and tubesheet will spring back and the joint connection between tube and tubesheet is created"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003371_s00170-006-0833-7-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003371_s00170-006-0833-7-Figure1-1.png",
        "caption": "Fig. 1 The 4SPS+SPR parallel machine tool",
        "texts": [
            " However, under a wrench working load with six components, how to solve the active/passive forces of the 5-dof parallel machine tools is a challenging issue. In this paper, a 4SPS+SPR parallel machine tool with 5-dofs is proposed. The analytic approach and the CAD variation geometry approach [19] are proposed for analysing its kinematics and solving the active/passive forces. 2 The 4SPS+SPR parallel machine tool and its simulation mechanism 2.1 The 4SPS+SPR parallel machine tool and its dofs A 4SPS+SPR parallel machine tool includes a tool, a platform m, a base B, four SPS-type active legs and one SPR-type active leg, as shown in Fig. 1. Here, m is a regular triangle a1a2a3 with o as its centre and B is an equilateral pentagon A1A2A3A4A5 with O as its centre. Four identical SPS-type active legs ri (i=1, 2, 4, 5) connect m to B by spherical joint S at a1 and a3, prismatic joint P and spherical joint S at Ai. One SPR-type active leg r3 connects m to B by revolute joint R at a2, prismatic joint P and spherical joint S at A3. Let {m} be a coordinate o\u2013xyz fixed on m at o. Let {B} be a coordinate O\u2013XYZ fixed on B at O. Let {Ba} be a coordinate o\u2013XaYaZa attached on m at o"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003124_3-540-26415-9_80-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003124_3-540-26415-9_80-Figure5-1.png",
        "caption": "Fig. 5. Pitch-Yaw-Pitch (PYP) Configuration. a) A cad rendering showing the three modules and its rotation angle ranges. The module angles \u03d51, \u03d52 and \u03d53 are set to 0. b) A picture of the robot",
        "texts": [
            " The difference in phase determines the coordination between the two articulations. If the modules rotates in phase( \u03c6 = 0), no locomotion is achieved. The same happens when \u03c6 = 1800. The best coordination is obtained when \u03c6 \u2208 [110, 150]. For negative values ( \u03c6 \u2208 [0,\u2212180]), the locomotion is done in the opposite way. Fig.3b shows the position of the articulations at five instants, when A = 400, \u03c6 = 120 and T = 20. Three Y1 modules are employed in this configuration. The outermost modules rotate in the pitch axis and the one at the center in the yaw axis (Fig.5). Only one more module is added, but three new kind of gaits can be realized: 2D sinusoidal movement, lateral rolling and lateral shift. The same sinusoidal function is applied (equation 1) but in this case i \u2208 {1, 2, 3}. When \u03d52 is fixed to 0, this configuration has the same shape as in Fig.5a and therefore, it is very similar to PP configuration. It only can move on a straight line, forward and backward. The experimental results are shown in Fig.4b. The velocity of the movement increases with the amplitude and there is a phase window in which the coordination is better. For the same amplitude, the space roved is less than in PP configuration but the phase window is wider. As the distance between the outermost modules is greater than in PP configuration, it is most difficult for this two modules to carry out the locomotion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001396_robot.1991.131590-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001396_robot.1991.131590-Figure7-1.png",
        "caption": "Figure 7: i f h Degree of freedom of the grasp and the workpiece shown schematically.",
        "texts": [
            "2 Grasp- Workpiece System A workpiece is meant to be the mating part of the grasped object, e.g., in a light bulb insertion task, bulb will be the grasped object while the holder will be its workpiece. The workpieces of interest are assumed to be passive and can be described by positive definite M,, B, and K,. This is true for a large class of workpieces and environments (Hogan, 1988). The goal here is to analyze the stability of a grasped object interacting with such workpieces. Consider that the grasped object is already in contact with a workpiece, Figure 7. .4ssuming that the contact between the grasped object and the workpiece enables transmission of motion and force in all degrees of freedom, and that their actual values are precisely known, one can write the combined motion equation of the object-workpiece system as Mg,X + B,,X + K,,(x - x,~) = 0 where, M,, = M + M,, B,, = B + B,, and K,, = K + K,. A stability of this combined system, analyzed on lines similar to a grasp alone as described in the last Section and which is also detailed in Shimoga (1991), indicated the necessary condition for this system to be stable is that M,,, Bow, K,, > 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002650_j.ssci.2005.11.003-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002650_j.ssci.2005.11.003-Figure1-1.png",
        "caption": "Fig. 1. Adjustable ramp with a Brungraber Mark II slipmeter measuring a terrazzo tile.",
        "texts": [
            " Specifically, the objectives of this study were to (i) investigate the effect of inclined angle of a surface on COF values measured using the BM II under various footwear, floor, and surface conditions, and to (ii) establish a statistical model to describe the measured COF on a surface with different inclined angles under different footwear materials, floors, and surface conditions. To conduct friction measurements on an inclined surface, a ramp supported by a metal rig was fabricated and used in the study. The ramp encompassed certain features. First, the ramp must be able to be adjusted to achieve a horizontal position as the base level. Second, the inclined angle may be easily adjusted. Third, the floor on the ramp may be easily changed for measurements of various floor conditions. Finally, the BM II must be operable on the ramp. Fig. 1 shows the adjustable ramp with a BM II slipmeter on it. Three inclined angles were tested: 0 , 10 , and 20 . On the BM II slipmeter, there is an aluminum support on the lower end of the strut which suspends an aluminum shoe holder for the attachment of a footwear pad. Both the aluminum support and shoe holder are connected by a hinge. The aluminum support is aligned with the strut before the footwear pad strikes on the floor. The hinges allow forward rotation of the support and the footwear pad upon striking on the floor for a possible slip movement"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003690_bf02919180-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003690_bf02919180-Figure4-1.png",
        "caption": "Fig. 4 Impact between balls",
        "texts": [
            " In order to predict the time of impact, the relative normal distance and its time derivatives are used. The predicted time is used to estimate a time step such that the colliding bodies will not be allowed to penetrate each other. Control of the simulation time step is continued until either the prediction rules are no longer true or the detection rule becomes satisfied (Han and Gilmore, 1993). The coefficient of restitution between balls e has been measured as 0.98 through preliminary experiments and the frictional effect between balls is negligibly small. For the bal l -bal l impact shown in Fig. 4, the principle of momentum conservation is expressed as Eq. (9). ml vlx + m2 Vzx =mx V~x + m2 V~x (9) vlx + V2x= v{x + V~x Newton's hypothesis gives the kinematic relationship shown in Eq. (10). e(Valx--Vazx) :(Va2x--V'alx) (10) Then, the velocity Vax at a contact point equals to the velocity Vx of the center of the billiard bali. From Eq. (9) and (10), the post-impact ve- locities of balls are obtained as Eq. (I1). , 1 - - e , 1 + e vlx - = ~ V l x - e ~ Vax ( l l ) , 1 +e , 1--e V2x ~ Vlx \u00b1 - - ~ Vzx Here, Vy, Wx, coy, coz don't change after collision since there is no friction between balls"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001390_robot.1997.606894-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001390_robot.1997.606894-Figure4-1.png",
        "caption": "Figure 4: Vectors Pi and P,! corresponding to the desired goal configuration and an arbitrary configuration of the end-effector. Both are defined w.r.t. 7;.",
        "texts": [
            " We now describe how g(6, i) i s implemented (for a revolute joint, the case for prismatic joint is similar). It is analytically derived by symbolically differentiating the cost function c(.) in equation 4 w.r.t. q i . It is computationally advantageous to represent the goal frame w.r.t. frame Fi. Let P; = (zi, yi, zi), i = 1 . . . 3 denote the vectors that represent the tips of unit axes vectors (1 , ; and i) of F'g w.r.t. Fi in configuration f,, i.e. T(li,) . Similarly, P,! = (xi, yi, zj), i = 1 . . . 3 denote the vectors that represent the tips of unit axes vectors F'g w.r.t. Fi (see Figure 4) in an arbitrary configuration q of the robot. With this formualtion, the z coordinate (for a revolute joint, hence we explicitly use Bi instead of q i ) remains constant and therefore simplifies the symbolic differentiation of the metric d. For example, in the expression for d, in 3, d: = ( 2 1 - zi * cos(&) - y: * sin(Oi))'+ (yl - * sin(8i) + y; * (21 - z ; ) 2 the term (21 - ~ ' 1 ) ~ is a constant and therefore has no influence in the optimization. Differentiating d(iT(2g) , i T(f(q^)) w.r.t"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000077_cp:19991029-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000077_cp:19991029-Figure4-1.png",
        "caption": "Figure 4: Orientation of the fault compomnts in the stator fixed reference frame.",
        "texts": [
            " Thus a resulting current space phasor for a fault in phase 1 can be calculated with equ. 8. The phasor is,& is fixed in the stator frame, but is pulsating with synchronous frequency. It can be represented by two phasors gip,, and iip,. one rotating in the positive and one in the negative direction. This failure leads to reduced mean values of the flux and the developed torque. With respect to the fundamental electric frequency (1\" harmonic) there is a Znd harmonic in the torque, in the mechanical speed, in the magnitude of the flux and in the stator voltage space vector. In figure 4 the magnitude of the resulting current vector is shown as a function of its angle in the stator frame for a simulated fault, at speed 0, = 0.6, load torque m, = 0.9 and -15 . The fault is in part-coils 0 and 1 with -22'. These angle is marked with a dashed line (11) I - together with the missing windings. It can he seen that the corresponding minimum of the stator current phasor magnitude is at an stator angle of about -1 lo degrees which is a result of the two components !A, and lip,, caused by the fault",
            " The magnitude of the induced MMF will therefore be proportional to i, and its orientation will be spatially fixed in the stator fixed reference frame, pulsating with respect to the time with the fundamental stator frequency. The voltage equation for the short circuit winding becomes O=r, . i , (r)+x, .isc(r)+Re{(i' ).e-'*=} (13) (with v' as the flux linkage of the rotor) As in the case of an open stator coil, the pulsating MMF can be decomposed in a positive and a negative sequence component &, , and as shown in figure 4. This figure shows the point where the current in the short circuit winding jSc is maximal and the two components are aligned. The phase shift between the induced voltage , o ~ ( ~ ' , ) and the current iX .eln= is determined by the ratio of the parameter rsc which is the resistance, and the parameter X, which stands for the leakage inductance of the short circuit winding. --U -R --R - The magnitude of the short circuit current (deviation of the resulting MMF from the symmetrical MMF) is now dependent on the fundamental stator frequency (for the fault with open windings a load-dependence was evident)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001060_0003-2670(92)85135-s-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001060_0003-2670(92)85135-s-Figure1-1.png",
        "caption": "Fig 1 Cathodic stripping voltammograms of bare Pt electrodes in 1 M H2S04 after anodic polarization at +25 V vs SCE u untreated, 1 1 s, 2 3 min, 3 5 min",
        "texts": [
            " method for on-wafer fabrication of free-chlorine sensors is described The sensor structure consists of a planar three-electrode electrochemical cell covered with a poly(hydroxyethyl methacrylate) hydrogel membrane This membrane is photohthographically patterned on-wafer In order to guarantee good adhesion of the membrane to the electrode surface a special oxidation step consisting of a treatment in an oxygen plasma followed by a silanization procedure has been developed The optimal operational polarization voltage of the integrated sensor for detection of hypochlorous acid was found to be 0 mV vs the on-chip Ag/AgCI reference electrode in a solution of 0 1 M KCI Sensors with membrane thicknesses of 10 and 50 \u00b5m are found to give linear calibration curves between 0 1 and 5 mg 1 -1 free chlorine, with sensitivities of 2 0 and 0 4 nA (mg respectively Keywords Sensors, Chlorine detection, Diffusion membrane, Silicon based sensor There is an increasing need for the determination and continuous on-line monitoring of residual water disinfectant Although several alternatives, like ozone, bromide, iodine or chlorine dioxide, exist for disinfecting purposes, none can compete with chlorine with respect to its effectiveness, easy applicability, presistence and low Correspondence to A van den Berg, Institute of Microtechnology, University of Neuchatel, Rue A -L Breguet 2, CH2000 Neuchatel (Switzerland) 0003-2670/92/$05 00 \u00a9 1992 - Elsevier Science Publishers B V All rights reserved cost [1] At the normal pH values of drinking water (pH 6 5-9), chlorine is present in the form of hypochlorous acid, HC1O, or its conjugated base, the CIO- anion [2] However, since the disinfecting reactivity of HCIO is about 10000 times higher than that of the CIO - anion [3,4], we will focus on the detection of hypochlorous acid Different methods exist to detect dissolved chlorine, most of them based on electrochemical principles A potentiometnc approach, as pro- 76 posed by Schlechtriemen and Sohege [5] for the detection of chlorine gas is less appropriate for on-line monitoring because of its logarithmic response, giving the sensor a large dynamic range but a relatively low precision Detectors based on amperometnc detection respond linearly to concentration variations, and are thus more promising In this case, use is made of the strong oxidative nature of the hypochlorous acid, which enables its electrochemical reduction at a relatively anodic potential thus excluding interference of other oxidants like dissolved oxygen Conventional analyzers often use rotating disk electrodes that provide sufficient sensitivity and selectivity, but are rather bulky systems that are not easily introduced on a large scale for on-line monitoring [6] The same holds for FIA-based systems that use iodometric [7,8] or direct amperometric detection [9] A macroscopic membrane-covered amperometric detector fabricated by conventional techniques with good sensing properties has been described by Ben-Yaakov [10], but this approach lacks the possibility of easy mass-fabrication Finally, an alternative optical detection as recently proposed by Piraud et al [11] for the moment does not attain the required detection limit of about 0 01 mg 1 - I and the measurement system cannot be easily miniaturised The sensor we present here is based on a Clark-type device It uses a planar three-electrode electrochemical cell covered with a thin hydrogel membrane to detect the hypochlorous acid The distinctive feature of our approach is that the entire sensing element is realized on silicon with standard IC-fabrication techniques, implying that the sensing element can be easily and reproducibly mass-produced Thin-film platinum working- and counter-electrodes, and a partially chloridized silver reference electrode were used The latter can be used as a reference electrode since the Cl - concentration in drinking water is fairly constant The electrode reactions taking place at the working electrode (WE) and counter electrode (CE) are respectively WE(cathode) HC1O + 2e ) OH- + Cl - CE(anode) 211 20 0 02+ 4H++ 4e A van den Berg et al / Anal Chim Acta 269 (1992) 75-82 To prevent the convective effects such as stirring from influencing the mass flow to the working electrode, we used a diffusion limiting membrane (DLM) to define a stagnant surface layer m which diffusion is the only process determining the mass transfer and thus the measured current Under potentiostatic operation at a properly chosen working potential, the measured current is proportional to the amount of reduced free chlorine Recently, we have proposed the use of a poly(hydroxyethyl methacrylate) (polyHEMA) hydrogel layer as DLM for the detection of hydrogen peroxide and oxygen [12] This membrane has the advantage that it can be photolithographically polymerized and patterned enabling the fabrication of the complete cell with IC-compatible methods With this technology, polyHEMA layer thicknesses of between 10 and 100 \u00b5m can be realized In this way an optimal trade-off between a high sensor current and a rapid response on one hand (thin membrane) and a signal insensitive to stirring on the other hand (thick membrane) can be chosen Special attention has been paid to the adhesion of the polyHEMA membrane It is known that chemical pretreatment of oxide surfaces such as SI02 and A1203 with methacrylic functional silane strongly improves the adhesion [13] However, such a treatment can not be directly applied to the surface of a platinum electrode Therefore we investigated methods to oxidize and subsequently functionalize a platinum electrode, with the extra requirement that the method should be applicable on-wafer EXPERIMENTAL Basic device fabrication The basic structure consists of a three-elec- trode cell realized on a silicon wafer The working- and counter-electrodes consist of a 1500 A 0 thick Pt layer on top of a 500A thick Ti adhesion layer The reference electrode is made by chemical chloridisation of a 1 \u00b5m thick Ag layer Further details of the fabrication of the device are given in [14] A van den Berg et al / Anal Chun Acta 269 (1992) 75-82 Instrumentation and methods Cyclic voltammetry measurements were per- formed using a PAR 273 potentiostat For all cyclic voltammetric measurements a solution of 1 M H2SO4 and a scan rate of 100 mV s-i were used, except for the determination of the interference of oxygen reduction relative to the hypochlorous acid reduction, where a solution of 0 1 M KCl with 0 01 M phosphate buffer (pH 5 8) and a scan rate of 10 mV s -i were used For potentiostatic measurements a potentiostat built in-house was used The plasma oxidation of the platinum electrodes was carried out using an oxygen plasma in an Alcatel GIR 300 plasma etch machine Measurements of polyHEMA membrane thicknesses were carried out with an Alphastep 200 step height profiler Visual inspections after the measurements confirmed that the scan of the stylus did not cause any damage to the membranes Electrode surface modification Electrochemical oxidation of the platinum electrode surface was carried out by polarizing the electrodes in 1 M H 2SO4 at +25 V vs SCE during 5 min Chemical oxidation was carried out in 0 25 M (NH 4)2 S 20 8 , 0 5 M HCIO, or 1 M HNO3 Plasma oxidation was carried out in an oxygen plasma at a frequency of 13 5 MHz, a pressure of 0 1 mbar, and using a power of 100 W Silanization of the electrode surface was carried out by dipping the electrodes in hexamethyldisilazane (HMDS) (Fluka) Subsequently, the electrodes were blown dry in nitrogen Functionalization of the surface with methacrylic groups was performed by treating the electrodes for 1 min with a solution of 10% (trimethoxysilyl)propyl methacrylate (TMSM) (Aldrich) and 0 5% H20 in toluene at 60\u00b0C Membrane deposition The monomer mixture consisting of 57 5 wt % hydroxyethyl methacrylate (HEMA) (Fluka), 38 wt % ethyleneglycol (EG) (Merck), 1 wt % dimethoxyphenylacetophenone (DMAP) (Aldrich), 2 5 wt % polyvinylpyrrolidone K90 (PVP) (Aldrich) and 1 wt % tetraethyleneglycol 77 dimethacrylate (TEGDM) (Fluka) was placed by pipette on the wafer in an amount corresponding to the required membrane thickness A Mylar sheet was then pressed onto the mixture which was allowed to spread out over the wafer until the required coverage of the wafer was obtained Then the monomer mixture was selectively photopolymenzed with UV light Exposure times of 30 s to 3 min were used This was followed by development in ethanol The sensors were preconditioned in 0 1 M KCl prior to measurement RESULTS AND DISCUSSION Surface modification of the electrodes In the fabrication process of the completed cell with hydrogel membrane, a crucial element concerning the durability is the membrane adhesion to the electrode surface In order to be able to apply the frequently used method of surface silanization, the surface of the platinum electrodes must first be oxidized A well-known standard method to do this is electrochemical oxidation [15] The formation of oxide (mono)layers at the electrode surface can be monitored by reducing the oxide in a cathodic scan starting at high anodic potential In Fig 1 stripping voltammo- 78 grams of platinum, untreated and electrochemically oxidized for 1 s, 3 min and 5 min, respectively, are shown In this figure, two different cathodic waves can be clearly distinguished one corresponding to a quickly formed, and easily reduced oxide (reduction potential about +400 mV vs SCE), and a second wave corresponding to an oxide form that is only formed after a few minutes of polarization at + 2 5 V vs SCE, and reduced at approximately -50 mV vs SCE The presence of these two waves is in good correspondence with the results reported in [14], where they were attributed to two different forms of platinum oxide We will also designate the two waves as A and B for the more anodic and more cathodic waves, respectively, in accord with the nomenclature used in [15] In order to see which one of the two oxides is necessary for the silanization, we performed a simple silanization reaction with HMDS which is comparable to the somewhat more elaborate reaction with TMSM Such a reaction should passivate the formed oxide, and disable its electrochemical reduction In Fig 2 the effects of the silanization on the appearance of both oxide peaks is shown From the three curves representing untreated oxide, oxide treated in HMDS for A tan den Berg et al / Anal Chem Acta 269 (1992) 75-82 30 s, and oxide treated in HMDS for 5 min, two conclusions can be drawn The first and most important conclusion is that the oxide represented by wave A does not react with HMDS The second conclusion is that wave B reacts only relatively slowly with HMDS, and that it takes about 5 min to obtain a fully silanized oxide From the above results it can be concluded that in order to be able to silanize the electrode surface, the formation of platinum oxide of type B is necessary Since electrochemical oxidation is not easily applicable on whole wafers, we investigated other chemical treatments that could provide the platinum type B oxide Unfortunately, treatments with oxidants such as nitric acid, and ammonium peroxodisulfate did not result in the appearance of the type B oxide The only treatment which did give both oxide waves was a treatment in oxygen plasma, as shown in Fig 3 From this figure it can be concluded that a 5-min treatment of the platinum electrode in an oxygen plasma results in similar A- and B-type oxide waves as obtained with the electrochemical oxidation Membrane deposition The deposition of the polyHEMA hydrogel membranes was carried out as described in the A van den Berg et al / Anal Chtm Acta 269 (1992) 75-82 experimental part Some difficulties were encountered when we tried to wash away the unpolymerized regions from the wafer in the development step Therefore we had to modify the mask in such a way that only every second basic electrode was covered with the polyHEMA membrane A SEM micrograph of a part of a wafer covered with membranes is shown in Fig 4 From this figure, it can be concluded that a satisfactory lateral resolution of some tens of microns is obtained, which is largely sufficient for our purpose The homogeneity of the membrane thickness over the wafer was investigated by step-height measurements On 32 evenly distributed membranes over the wafer a mean thickness of 618 \u00b5m was found with a standard deviation of 7 3 \u00b5m An important part of the thickness variation was caused by a continuous varying thickness of the membranes over the wafer If closely located membranes were considered, typical standard deviations of 3-4 \u00b5m were found Sensor characterization A first characterization of the electrodes was carried out to determine the optimal polarization potential for the detection of free chlorine Therefore, cyclic voltammograms were taken of the bare platinum electrodes in background electrolyte under nitrogen and with added sodium hypochlorite A background electrolyte a solution of 0 1 M KCI with 0 01 M potassium dihydrogen- phosphate (pH 5 8) was taken to ensure that all the free chlorine was present as hypochlorous acid In order to examine the interference of oxygen, a third cyclic voltammogram was recorded in background electrolyte and ambient air, as shown in Fig 5 From the cyclic voltammogram of the reduction of hypochlorous acid (at E < + 700 mV vs SCE) and of oxygen reduction (E < + 300 mV vs SCE), a polarization potential \"window\" between + 300 and + 400 mV vs SCE can be determined where the hypochlorous acid reduction is relatively potential independent, and there is no oxygen reduction interference It must be remarked here that the finally desired detection limit for free chlorine is in the micromolar range, whereas the figure shown is obtained with a concentration of 1 mM hypochlorous acid The above mentioned conclusions were verified with potentiostatic measurements carried out with mounted and encapsulated three-electrode devices covered with a polyHEMA membrane of approximately 10 \u00b5m thickness In Fig 6, the sensor current as a function of the free chlorine concentration at three different polarization potentials is measured At the most cathodic potential (- 100 mV vs on-chip reference electrode) an offset current due to oxygen reduction is found At 0 mV this offset current is largely suppressed, whereas the same sensitivity to free chlorine is 79 80 A van den Berg et al / Anal Chum Acta 269 (1992) 75-82 2 1 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003762_j.jappmathmech.2006.03.010-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003762_j.jappmathmech.2006.03.010-Figure2-1.png",
        "caption": "Fig. 2.",
        "texts": [
            "10)) with this control comes to the equilibrium (1.6), is called the controllability domain.10 This domain, which we shall denote by Q, is described10 by the inequality (1.11) that is, the set Q of initial states from which the system can be brought into the equilibrium (1.6) is only bounded with respect to the unstable coordinate y. Inequality (1.11) describes a strip in the plane of the variables , \u2032, the boundaries of which are two parallel straight lines at the same distance from the origin of coordinates. This strip Q is shown in Fig. 2. If the initial velocity \u2032(0) = 0, then the constraint on the initial angle, at which the pendulum can be brought into equilibrium (1.6) has the form (1.12) Note that under the limiting control actions (t) = \u2213 0 the states (1.13) are equilibrium states, and they lie on the boundary of the controllability domain. The states will be equilibrium states for non-linear equation (1.3) when (t) = \u2213 0. If the initial angle (0) = 0, the constraint on the initial velocity, at which it is possible to bring the pendulum into equilibrium (1",
            "10) describes the behaviour of the \u201cunstable \u201dvariable y, which corresponds to the positive eigenvalue 1/a, while Eq. (2.11) describes the behaviour of the \u201cstable \u201dvariable z, which corresponds to the negative eigenvalue (\u22121/a). With a = 1 and c = 1 relations (1.9) and (1.10) are obtained from (2.10) and (2.11) respectively. We denote by P the set of initial states, for each of which a control (t) \u2208 W exists such that the solution of Eq. (2.9) (of system (2.10), (2.11)) with this control comes to the equilibrium (1.6). This controllability domain P is described10 by the inequality (see Fig. 2) (2.12) On returning in (2.12) to the initial parameters of the system, we obtain the inequality (2.13) (2.14) If the initial angle (0) = 0, then the constraint on the initial velocity, at which the pendulum can be brought into the state of equilibrium (1.6), has the form (2.15) We will now compare the controllability domains Q and P, which have been constructed for a pendulum with a fixed and moving suspension point O respectively. First, we note that the strip P (2.12) is wider than the strip Q (1.11) since c > 1 and a < 1 (see Fig. 2); it can thereby be said that it is larger, although the areas of the two domains are infinite. However, the domain Q does not wholly belong to the domain P, since the lines, bounding the domain Q, are inclined at a smaller angle to the abscissa axis than the lines, bounding the domain P. At the same time, it should not to be forgotten that the domains P and Q are constructed for the linear equations (1.8) and (2.9) and linearization is permissible is the values of the angle and the angular velocity \u2032 are sufficiently close to zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000348_1.3101835-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000348_1.3101835-Figure8-1.png",
        "caption": "Fig 8. Schematic of a fast-response skin friction gage for very short duration tests (from B0wersox, Schetz and Deiwert, 1995).",
        "texts": [
            "asmedigitalcollection.asme.org/ on 01/30/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use $202 MECHANICS PAN-AMERICA 1997 severe, i . e . thermal protection and surface temperature matching. For such short run times, the surfaces hardly have time to respond to the heat flux, even for surprisingly high heat flux values. The main challenges are first, of course, frequency response itself and second the effects of acceleration loads. We have developed the basically simple design shown in Fig. 8 (Bowersox, Schetz, Chadwick and Deiwert (1995)) that meets the needs of this kind of testing: The notion is to use a light material (a high-temperature plastic) so that the mass of the system is very low, and the acceleration forces are negligible compared to those from the wall shear. Also, the plastic material has favorable mechanical properties that permit designing a gage with b6th a high natural frequency (- 1 O's kHz) and a measurable strain resulting from the wall shear. Finally, the plastic has a low thermal conductivity which protects the strain gages from the heat"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003801_iros.2006.282533-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003801_iros.2006.282533-Figure5-1.png",
        "caption": "Fig. 5 Parameters used in dynamic modeling",
        "texts": [],
        "surrounding_texts": [
            "Experimentations have been done with the prototype. The tests have been performed with trajectories called \"Adept motions\". These trajectories are classical industrial motions used to characterize pick-and-place robots and correspond to a round trip motion. The controller used for these experimentations is a P controller applied on the actuated velocities and a P-I controller on the joint positions. Fig. 4 shows the desired trajectory (a-plot) and the obtained trajectory (b-plot) for a test performed with a velocity (v) equal to 5 m.s-1 and an acceleration (a) equal to 150 m.s-2 (_ 15 G). The obtained cycle time, corresponding to a round trip, is 0.25 s. This test shows that the robot is able to have a good behavior at very high dynamics. However, we can notice that the overshoot is important. Indeed, the P-I controller is not accurate enough, and the use of a dynamic control, and later, a predictive control [15] should give better results. In order to implement such control laws, dynamic modeling of the robot is necessary. The following section (part IV) will focus on its derivation. In addition, the quality of this controller requires a good precision of the dynamic parameters. Thus, the estimation of these parameters have to be done, and is presented in part V. A. Parameters and simplifications Let's first define geometrical and dynamical parameters that have been introduced: - Pi: center of actuated revolute joints - Ai: geometrical point situated at the middle of the two centers of spherical joints of forearms on actuated side of forearms - Bi: geometrical point situated at the middle of the two centers of spherical joints of forearms on traveling plate side of forearms - 0 is the controlled angle in absolute coordinates, - Q , Q and Q are the vector of joint positions qi velocities 4' and acceleration ij - X, X and X are the vector of operational positions [x y z O]T, velocities [x y z o] and acceleration [x y z - h is the length of the parallelogram of traveling-plate, - ui is the unit vector collinear to the axis of actuator, - ia: inertia of arms, ifa: inertia of forearms, im : inertia of gears and actuator, - Li is the length of arms, and 1i is the length of forearms"
        ]
    },
    {
        "image_filename": "designv11_24_0003690_bf02919180-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003690_bf02919180-Figure1-1.png",
        "caption": "Fig. 1 Cue points and the throw direction",
        "texts": [
            " The theoretical issues are implemented into a viable graphic simulation program and its efficacy is demonstrated through the experimental validation of the billiards game. The resulting analysis results are verified quantitatively and qualitatively using high-speed video camera. 2, Striking the Cue Ball It is difficult to model analytically and quantitatively the stroke process with the cue because of interposition of a human player. Therefore, the stroke must be modeled qualitatively and empirically for simulation purpose. There are 4 elements that must be considered for striking the cue ball as follows (see Fig. 1). -Cuc points: struck point on the cue bail, divided into 9 different points (C, L, R, F, D, LF, LD, RF, RD) - Stoke force : amplitude of imparted force - Stroke method : 3 classified methods (normal shot, draw shot, follow shot) -Throw direction: direction of stroke (direc- tion of stroke force) 3. Rolling Motion of Balls on the Table For the movement of a spherical ball over a fiat surface, three types of resistive force can be considered. There is a drag force due to the air, a resistive force due to the deformation of the surface and the ball in the contact zone, and eventually a sliding force if the motion is not a pure rolling motion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000733_s0921-8890(99)00044-5-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000733_s0921-8890(99)00044-5-Figure3-1.png",
        "caption": "Fig. 3 shows a schematic diagram of the robotic interception problem in its general 3D form. The acceleration command of the IPNG is computed as",
        "texts": [
            " (2b) (3) Optimal proportional navigation guidance (OPNG): L = Uopt(O)er + Vopt(O)eo, (2c) where Uopt and Vopt are optimal velocities of the interceptor in the radial and tangential directions, respectively. In [15], it was reported that the IPNG yields solutions, toward the end of interception, similar to those given by the OPNG. Although, the IPNG may be of less practical use in missile guidance compared to PPNG, its mathematical tractability and robustness to the initial conditions of the interceptor makes it especially suitable for robotic interception. Fig. 2. Interception via a PN-based technique in a plane. Fig. 3. Interception via IPNG in its general 3D form. M. Mehrandezh et al./Robotics and Autonomous Systems 28 (1999) 295-310 where r represents the position-difference vector between the target and the robot. In Eq. (3), ~os can also be expressed as a function of r and/\" as / Olos= --~-- \u2022 (4) By substituting Eq. (4.) into Eq. (3), one obtains aIpNC = ~T~{~ x (r x r)}. (5) Since/\" x (r x i9 = r(/ ' . i9 - r ( r . \u00a2), Eq. (5) can be rewritten as aIPNG = Kp(t, )~)r 4- Kd(t, ~.)/', (6) where t denotes time and the coefficients Kp and Kd are defined as follows: / Irl ]2, gd(t,)~) - - ~ ( r \u2022 /-) Kp(t, )"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002483_robot.1991.131611-Figure9-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002483_robot.1991.131611-Figure9-1.png",
        "caption": "Figure 9: Coordinate system f o r distance constraint.",
        "texts": [
            " When a set of assignments provides six independent constraints, the position of the object can be found. Expanding, and setting the complex part of the solution to 0, o = ro sin (00 - 0 2 ) + r l sin (e1 - 02) + (9) (10) D sin (0 - 8 2 ) - r3 sin (03 - 02) solving for 8 , (11) 1 sin0 = (r3 sin (03 - 02) - T 1 sin (e, - 8,) + T o sin (eo - 8 2 ) ) + 82 and noting that sin-' 3: is defined only for -1 5 z 5 1 we obtain : A Vertex Pair Constraint - T I sin (01 - 02) + T O sin (00 - 6'2) 5 1. (13) ) Using the coordinate system shown in Figure 9 the the range of values on edges rl and T P where a line of length D can be placed, can be computed. The solution desired is the range of positions along 7 1 where the line of the given lengt,h can be drawn to 7 2 . To begin, note the equations for the endpoints of the edges and the fixed length line: Thus we conclude that r1 can take on values in the range: Po = r0ereo Pl = Po + Tlefel Pz = PI + De\" p3 = T3e103 PZ can also be written as, B Triangle Orientation v P2 = P3 $Tze'ez . (6) B.1 Three Edges By substitution using the above equat,ioiis ~2 can be obtained in terms of T I : Assume that the three finger edges are joined as shown in Figure 10"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002646_1.2067688-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002646_1.2067688-Figure1-1.png",
        "caption": "FIG. 1. Definition of frames involved in the calculation.",
        "texts": [
            " Finally, we show that the Voigt and Reuss averages coincide if, and only if, the fiber axis is equivalent to 100 or 111 , and that the VRH average of M approximates the iterative Hill average by errors 1%. Three right-hand orthogonal frames of reference hereafter as frames for short are used in the calculation in this \u00a9 2005 American Institute of Physics5-1 ense or copyright; see http://jap.aip.org/about/rights_and_permissions paper. The first is the crystallographic C frame, to which literature data on single-crystal elastic constants are referred. Next, the biaxial modulus of the hkl -fiber-textured film is defined with respect to the film F frame Fig. 1 , which is so defined that F3 is parallel to the out-of-plane direction of the film i.e., along the fiber axis hkl , while both F1 and F2 lie within the film plane. The selection of F1 and F2 is immaterial due to the transverse isotropy of the polycrystalline film resulting from the uniaxial symmetry, i.e., rotational invariance, around the fiber axis.3,5 Note that it is the biaxial modulus defined by F1 and F2 that is of most interest in many applications, which explains why the term \u201cpolycrystalline films\u201d rather than \u201cpolycrystals\u201d was chosen in the title of this paper. In Fig. 1, we also define an X frame for a random grain with its X3 axis along F3, while X1 will parallel F1 after rotating around X3 counterclockwisely by . Obviously, for a definite hkl fiber axis, only is needed to describe the X frame relative to the F frame. We further assume that the grain size is small enough as compared with the film, yet big enough so that the grain boundaries remain trivial. The stress-strain relationships of linear elasticity are described by the generalized Hooke\u2019s law, in tensor notation, as9 ij = cijkl kl ij = sijkl kl, 1 where ij is the stress, ij the strain, cijkl the elastic stiffness, sijkl the elastic compliance, the Latin subscripts range from 1 to 3, and summation is performed for repeated subscripts",
            " Note that au is only a function of the rotation once the fiber axis hkl is defined. Volume averaging is involved in relating the effective elastic constants of the polycrystalline film to those associated with its constituents. Generally, a volume average depends on both the orientation of each grain and the volume 10 fraction associated with that orientation. For a polycrystal- ense or copyright; see http://jap.aip.org/about/rights_and_permissions line film with an ideal fiber texture, the orientation of each grain is fully described by the rotation Fig. 1 , and the volume fraction corresponding to each value is the same. Consequently, the presence of fiber texture reduces a volume average into an orientation average of as cijkl F = 1 2 0 2 cijkl F d and sijkl F = 1 2 0 2 sijkl F d , 7 and where the sign \u00af denotes appropriate volume averaging over all grains. We now consider several averaging schemes relating the polycrystalline behavior to the single-crystal elastic constants. The Voigt scheme assumes a homogeneous strain in each grain and averages over stress,11 while the Reuss scheme assumes constant stress throughout the material"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000634_s0301-679x(00)00027-x-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000634_s0301-679x(00)00027-x-Figure5-1.png",
        "caption": "Fig. 5. Horizontal misalignment combinations.",
        "texts": [
            " 2), on the direct stiffness and damping coefficients in the horizontal direction, on the maximum vibration amplitude at the mid-span and on the unbalance response at the mid-span are presented below. Apart from the unbalance response, for which only a single misalignment combination is considered, these illustrations of misalignment effects are for a range of horizontal misalignments (non-dimensionalised with respect to the bearing radial clearance) of pedestal 2, viz MA1, ranging from 25 to 5 and for a range of similarly non-dimensionalised horizontal misalignments of pedestal 3, viz MA2, also ranging from 25 to 5. The grid points in Fig. 5 summarise the misalignment combinations used. Fig. 6 shows the three-dimensional surfaces of the relative deflection of the rotor at mid-span in the y (vertical) and z (horizontal) directions, non-dimensionalised with respect to the bearing radial clearance for the above noted misalignment combinations. Note that the surface for deflections in the z direction is virtually a plane, so that projection onto a conveniently angled plane would collapse those results into a straight line. Fig. 7 shows the three-dimensional surfaces of the appropriately non-dimensionalised direct stiffness and damping coefficients of bearing 2 or 3 (the same because of symmetry here) in the horizontal and vertical direc- tions respectively for the above noted misalignment combination. If one views the elevations or projections of these surfaces on an auxiliary vertical plane normal to arrow A in Fig. 5, all the points fall into narrow curved bands, in many cases the bands becoming sufficiently thin to be, to all intents and purposes, curved lines. As illustrated above, the changes in bearing reaction forces due to misalignment not only alter the static deflection line, but alter the journal steady state eccentricities in the bearings, thereby altering the dynamic coefficients of the bearing supports. This in turn affects the vibration behaviour of the system when subjected to external excitation. For illustrative purposes, consider the unbalance excitation given in Table 4. Fig. 8 shows the three-dimensional surface of the maximum vibration amplitude at the rotor mid-span, non-dimensionalised with respect to the bearing radial clearance, for the above noted combinations of misalignments. Again, if one views the elevation or projection of this surface on an auxiliary vertical plane normal to arrow A in Fig. 5, all the points fall into a narrow curved band. Note that this ability for different misalignment combinations to yield virtually the same vibration response creates potential difficulties for any misalignment identification procedure seeking to determine the alignment state based on response measurements. Fig. 9 compares the unbalance response (maximum amplitude) at the rotor mid-span pertaining to the aligned rotor (ie aligned at 3000 rpm) with that pertaining to a misalignment of MA1=3, MA2=24 at 3000 rpm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003754_bf02844262-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003754_bf02844262-Figure7-1.png",
        "caption": "Figure 7 Angular momentum vector.",
        "texts": [
            " 27 becomes: pressure shifts forward from the centre of mass because of the uneven distribution of air pressure over the surface, and a small moment is created. This behaviour is similar to that of a spinning top. The longitudinal axis of the ball turns so as to reduce the small angle back to 0, as does the spinning top. As a result, the ball\u2019s longitudinal axis continues to point in the direction of its trajectory. Eqn. 29 is the finite-difference equation of the rotational motion, where \u2206L \u2192 represents the change in the angular momentum vector, as shown in Fig.7. N \u2192 is the moment vector and \u2206t is the time interval. \u2206L \u2192 = N \u2192 \u2206t (29) This equation means that \u2206L \u2192 and N \u2192 point in the same direction. Since \u2206L \u2192 is downward in the gravitational field, N \u2192 causes the nose to veer to the right from the kicker\u2019s point of view. As a result, the ball tends to hook to the right due to the sideslip. The direction of the hook depends on the direction of the angular velocity vector. If P < 0, the direction of the hook is in the opposite direction. Comparisons for three different initial flight path angles at \u03980 = 30\u00b0 are shown in Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000088_bf01248238-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000088_bf01248238-Figure5-1.png",
        "caption": "Fig. 5. The on-line monitoring system using microdialysis for the glucose sampling and the 'wired' GOx based carbon paste electrode for the amperometric detection. Flow rate 2.5 pl/min. Same carrier as for Fig. 4a",
        "texts": [
            " For comparison, experiments with ferrocyanide were done with bare carbon paste electrodes, demonstrating diffusion dependence for this system (Figs. 4a and 4b). The flow rate studies demonstrate that the enzyme-based system was not controlled by external diffusion of glucose. The uncoated electrodes and the coated electrodes were characterized by a 10-90% rise time of ,-~ 1 min and 2 min, respectively, when the glucose concentration was changed from 2.5mM to 5 mM. The on-line glucose monitoring system is shown in Fig. 5. The glucose sampling was performed with the microdialysis probe immersed in well stirred glucose solutions. 25 20 15 10 5 0 O 9 I . e 9 2 9 J- - .41 f- ~ - , - r l , , , , l ~ 84184 , , , l l , ' l ' l l ' i ' l 84 I0 20 30 40 50 60 70 g lucose /mM Fig. 6. Calibration plots obtained for cross-linked electrodes (1), cross-linked and EAQ-coated electrodes (2), cross-linked and EAQ-coated electrodes in the microdialysis system (3). Conditions as for Fig. 4a The use of EAQ-coated cross-linked 'wired' enzyme electrodes placed downstream in the microdialysis system showed adequate sensitivity, a broad linear range, and effective interferent rejection"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002395_iros.2001.973348-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002395_iros.2001.973348-Figure3-1.png",
        "caption": "Figure 3: kinematic model",
        "texts": [
            " Here we assume that an object is a ball, and it rolls on the arm with friction between them. It is easy to analyze because we don't have to think about slipping and its posture. Since the object moves on the arm, it takes off faster than the velocity of the edge of the arm. So, the object can arrive father than that of the case with grasping the object and holding off it. With the variety of arm's motion during the object rolls on the arm, this manipulation can toss the object in various paths. 2.2 Kinematic model The kinematic model of this manipulation is as shown in Figure 3. The world coordinate system C is fixed to the shoulder joint. And the object coordinate system C' has same origin, X' is fixed on the arm, and Y' is normal to the arm. The arm is even and its mass is M . The object is a ball and its mass is m. The length of the arm is L, the height of the joint is H. N is normal force to the object, F is Coulomb friction. 8 is angle of the arm. And torque of the joint is T. 2.3 Analysis of kinematic model The process of this manipulation has two steps. Before and after leaving the object"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000419_ecc.1999.7099923-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000419_ecc.1999.7099923-Figure2-1.png",
        "caption": "Fig. 2: The idea of the r-sliding controller",
        "texts": [
            " u = - \u03b1 sign( \u03c3 + |\u03c3| 1/2 sign \u03c3), 3. u = - \u03b1 sign( \u03c3 + 2 (| \u03c3 | 3 +|\u03c3| 2 ) 1/6 sign( \u03c3 + |\u03c3| 2/3 sign \u03c3)), 4. u = - \u03b1 sign{ \u03c3 + 3 ( \u03c3 6 + \u03c3 4 +|\u03c3| 3 ) 1/12 sign[ \u03c3 + ( \u03c3 4 +|\u03c3| 3 ) 1/6 sign( \u03c3 +0.5 |\u03c3| 3/4 sign \u03c3 )]}, 5. u = -\u03b1 sign (\u03c3(4) + \u03b24 (|\u03c3| 12 + | \u03c3 | 15 + | \u03c3 | 20 + | \u03c3 | 30 ) 1/60 sign( \u03c3 +\u03b23 (|\u03c3| 12 + | \u03c3 | 15 + | \u03c3 | 20 ) 1/30 sign( \u03c3 + \u03b22(|\u03c3| 12 + | \u03c3 | 15 ) 1/20 sign( \u03c3 +\u03b21|\u03c3| 4/5 sign \u03c3 )))) The idea of the controller is that a 1-sliding mode is established on the smooth parts of the discontinuity set \u0393 of (6) (Fig. 2). That sliding mode is described by the differential equation \u03c6r-1,r = 0 providing in its turn for the existence of a 1-sliding mode \u03c6r-2,r = 0. But the primary sliding mode disappears at the moment when the secondary one is to appear. The resulting movement takes place in some vicinity of the subset of \u0393 satisfying \u03c6r-2,r = 0, transfers in finite time into some vicinity of the subset satisfying \u03c6r-3,r = 0 and so on. While the trajectory approaches the r-sliding set, set \u0393 retracts to the origin in the coordinates \u03c3, \u03c3 , "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001108_1.1308033-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001108_1.1308033-Figure2-1.png",
        "caption": "Fig. 2 Foil bearing model for flat surface guide",
        "texts": [
            " Moreover, based on the assumptions of Gaussian distributions of asperities, the simple relations to predict the friction coefficient between web and guide surfaces are formulated, and the variation of friction coefficient with velocity is shown for various values of web tension. Web Spacing Analysis for Flat Surface Guide. Before analyzing the web spacing for two types of stationary guides, let us introduce the outline of web spacing analysis for ordinary flat surface guide. The foil bearing model, as shown in Fig. 2, is generally applied to analyze the web spacing in the web wrapped region ~Region II!, in which the film pressure and web spacing are obtained theoretically by solving the following Reynolds equation and web elastic equation simultaneously. ] ]x S h3p ]p ]x D1 ] ]z S h3p ]p ]z D56mUw ]~ph ! ]x (1) Et f 3 12~12n2! \u00b92\u00b92h1 T R S 12R ]2h ]x2 D5p2pa (2a) where \u00b92 is defined as follows: \u00b92[ ]2 ]x2 1 ]2 ]z2 (2b) When the guide is rotated, for example, when the guide is used as drag roller, a sum of web velocity and roller surface velocity, Uw1Ur , should be used instead of Uw in Eq",
            " 4, is introduced. The averaged flow model for the Reynolds equation @13,14# can be used to determine the equivalent spacing heq . In that case, however, the equivalent spacing is given by the numerical solutions. For web transporting system designers, it is more convenient to obtain the closed form solution of equivalent spacing. So, in this paper, we have tried to obtain the closed form solution by applying a mass conservation equation as shown in the following. In Region II ~web wrapped region! in Fig. 2, the shear flow ~Couette flow! is predominant, then the volume rate of air flow in the moving direction of web is approximately expressed as follows: q> Uw 2 ~h0L1nSg!5 Uw 2 heqL (9) where, for the triangular groove, the cross sectional area of the groove Sg is given as: Sg5hgbg/2 (10) and the equivalent spacing heq is given from Eq. ~6! as follows: heq5RS 6mUw T D 2/3S 0.5892 1.614 l 1 1.764 l2 D (11) Evaluating the web spacing h0 from Eq. ~9!: h05heq2 nSg L (12) Journal of Tribology rom: http://tribology"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000555_s0890-6955(97)00031-x-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000555_s0890-6955(97)00031-x-Figure1-1.png",
        "caption": "Fig. 1. Cutting forces and contact normal and shear loads on the tool faces.",
        "texts": [
            " The objective of this work is to develop a feasible method for fast identification of maximum mechanical stress working in a cutting tool, and to predict the premature failure of cutting tools with the use of previously identified critical stress of a cutting tool, or tool property profile, and current identified maximum stress of the cutting tool, or load profile, in a cutting process. Cutting tool fracture, Part I 1693 In metal cutting, tool faces, including the rake face, major flank face and minor flank face, are subjected to both normal and shear loads [5, 10, 11] due to the pressure from chip and machined surfaces, and friction between the tool face and chip and machined surface, as shown in Fig. 1. The resultant force working in the tool can be resolved into three orthogonal directions, including tangential, axial and radial direction, and can be measured by a force dynamometer. Through proper transformation, the total cutting force in each direction is actually the summation of the loads on the tool face in the corresponding directions as follows: bl /cr bl lcf lcr lcf Fr=ff~rx(x,y) dxdy+ff~'yz(X,z)dxdz+ff~'xz(y,z)dydz (1) 0 0 0 0 0 0 bl /cf bl /cr /cf /cr F,,=ffoy(X,z)d dz+ff zy(X,y) dy+ff 'x,(y,z, dydz O 0 0 0 O 0 (2) lcr lcf lcf bl bl lcr FR=ff y,z)dydz+ff y (x,z) dz+ff (x,y)d dy (3) 0 0 0 0 0 0 The boundary conditions for this summation are as follows",
            " In simulations, it is possible to investigate the state of load for a cutting tool under different load conditions by simply varying the value of the load functions which may cover the whole range of cutting data. The simulation results become real when they are multiplied by a scaling factor, i.e. the measured cutting force. Through the use of load functions in the study of the state of load in a cutting tool, the large number of cutting experiments, which are often expensive and time consuming, can be avoided. A cutting tool is usually subjected to multiaxial stresses in a cutting process. If we consider a small element of a cutting edge which is in equilibrium, as shown in Fig. 1, then, in the most general case, each face may be subjected to the total force. Each force may be resolved into components parallel to three coordinate directions, and if each of these nine components is divided by the area of the face upon which it acts, the total stress in this element is then described by the nine stress components. This collection of stresses is called the stress tensor, designated S. In tensor notation, this is expressed as [ ~ \u00a2 y x = ~,y (20) \"/'XZ Tyz O'Z 1696 J .M. Zhou et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002619_095440605x31481-Figure10-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002619_095440605x31481-Figure10-1.png",
        "caption": "Fig. 10 Cutting geometry of a CC1-gear, R/m \u00bc f/m \u00bc 10",
        "texts": [
            " It should be noted that the female cutters that saddle the tooth have to be here in one piece/plane each, as implied by the required synchronization of the motions, unlike the case of CV3-gears. This gives rise to adverse cutting conditions. This is the form of CC-gears generated by one set of cutters on one cutter head (or a rack), in a singleindexing cycle, while all points on each cutter are constrained to trace out circular paths of the same radius R. Thus, the tool rake face maintains a fixed attitude relative to the gear blank (Fig. 10). This is achieved by either of the two methods: (a) the individual cutters are made to rotate about their own shank axes at the same rate and in the opposite sense of cutter head rotation; (b) a cutter (for one tooth space) or a cutting rack (for a few teeth) is imparted an oscillatory, parallel, arcuate motion in a plane tangent to the gear pitch cylinder; viz. an arcuate gear planer. The outside- and inside-cutting straight edges sweep out each of an oblique cylinder as shown in Fig. 11. The resulting tooth traces are identical circular arcs, the transverse tooth thickness and space are equal, and meshing gears have line contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000926_bf02602986-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000926_bf02602986-Figure1-1.png",
        "caption": "Fig. 1. Measurement of the sliding friction in guidewires.",
        "texts": [
            " [ 1] were the first to de sc r ibe Teflon coa t ing o f g u i d e w i r e s as a m e a s u r e to reduce s l iding f r ic t ion. A b r e a k t h r o u g h t o w a r d s very low fr ic t ion was a c c o m p l i s h e d by in t roduc ing a hydrophil ic p las t ic coa t ing , first d e s c r i b e d by T a k a y a s u et al. [21 in 1988. As ,,viii be shown in the discussion, a substantial ,~liding friction is only to be reckoned with in bent parts of the catheter. For this reason, the following arrangement is chosen for measurement (Fig. 1): the wire is drawn through a circular loop (radius 2 cm) of a 7F polyethylene catheter (internal diameter 1.57 ram) with a tractional velocity of 10 cm,'sec. On the opposite side of the traction, the catheter loop is held with a thread which is connected to a spring balance of suitable strength. In order to simulate practical conditions as tar as possible with the medium in which the movement occurs, measurements are carried out with the wire and the catheter loop under water. The force read off on the spring balance using this experimental design corresponds to the sliding friction",
            " The g r e a t e r the s t i f fness o f the wire , the g rea t e r this force . F o r this r ea son , the s t i f fness is a lways one of two fac to r s that d e t e r m i n e f r ic t ional r e s i s t ance . The o the r f ac to r , the coef f ic ien t o f f r ic t ion, d e p e n d s on the su r face c h a r a c t e r i s t i c s o f the bod ies sl iding o v e r one a n o t h e r and on the m e d i u m b e t w e e n them. The coeff ic ient o f f r ic t ion can on ly be d e t e r m i n e d exper i - men ta l ly (Fig. 1). B e c a u s e in par t the cond i t ions of such a m e a s u r e m e n t a lways have to be e s t ab l i shed a rb i t r a r i ly , abso lu t e va lues are o f no in te res t , but on ly the d i f f e rences b e t w e e n d i f fe ren t typ ica l t y p e s o f sur face . T h e s e d i f f e rences , the re la t ive coeffic ien ts of f r ic t ion , a re ma n i f e s t e d when the m e a s u r e d values of frictional resistance are divided by the stiff'hess of the respective wire or when the correlation of the sliding friction with stiffness is represented graphically (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003768_j.mechmachtheory.2005.10.010-Figure11-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003768_j.mechmachtheory.2005.10.010-Figure11-1.png",
        "caption": "Fig. 11. The sun-worm axial section of spherical roller enveloping.",
        "texts": [
            "5 mm and the length of the sun-worm with l = 90 mm, the tooth profile of the sun-worm generated by the enveloping movement of the cylindrical roller can be obtained. The axial section of the sun-worm tooth profile is shown in Fig. 10. The axial tooth profile is a straight line. The sun-worm tooth profile generated by the enveloping movement of the spherical roller can be obtained by substituting Eqs. (1), (26), and (28) into Eq. (7) with, u 2 [0, 2p], i21 \u00bc 1 8 , q = 8 mm, a0 = 119 mm, r2 = 62.5 mm and the length of the sun-worm with l = 90 mm, the axial section of the sun-worm can be obtained and is shown in Fig. 11. The axial tooth profile is a curve. The undercutting function is given by Eq. (9) in meshing between a planet worm-gear and the sun-worm. If this function intersects a zero line or a zero plane, the undercutting condition in Eq. (10) is satisfied and the undercutting range can be given by the limit curve in Eq. (10). Substituting both generating surface function and meshing function of the conical roller meshing model in Eqs. (14), (16)\u2013(19) into Eq. (9), with given planet worm-gear rotational angle u2 and meshing parameters as u = 4 mm, i21 \u00bc 1 8 , q = 8 mm, b = 10 , a0 = 119 mm, r2 = 62"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000956_fuzzy.1995.409884-FigureI-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000956_fuzzy.1995.409884-FigureI-1.png",
        "caption": "Figure I : Helicopter aerodynamics components pallet 831",
        "texts": [],
        "surrounding_texts": [
            "In particular, a method to help the tuning phase based on the rules evolution is presented and illustrated.\nThe results obtained through simulation are described and commented.\nI. Introduction\nFuzzy control has shown to be useful in handling non-linear or imprecise control problems that depend on the operator skill, as is the case of helicopters guidance [Sugeno et a1 931.\nIn [Cavalcante 941, it is proposed a hierarchical structure to a helicopter navigation system. This structure presents three levels: the mission interpreter level, the task level and the control level.\nThe adjustments on the knowledge base are specially hard to be done due to the existence of many variables and possibilities of change. This paper shows the design and tuning of the navigation system fuzzy controller, and proposes a method to help the designer in the tuning phase.\nSection I1 introduces the helicopter as a controlled system, its controls and movements, as well as control problems, like cross-couplings and inherent delays.\nThe design of the fuzzy controller is shown in section 111. The knowledge base design was based on pilots observation and helicopter experts interviews and it depends on the task actually being executed. It is divided into blocks, one for each helicopter command.\nThe tuning phase is discussed in section IV, and the rules evolution method proposed to help the tuning phase is presented. The adjustments of the take off task collective block illustrates the use of this method.\nSection V shows the results obtained through simulation of a mission with three tasks: take off, azimuth change and hover.\nThe conclusions and future work are presented in section VI.\n11. Helicopters\nLets now introduce the concepts involved in helicopter guidance.\nHelicopters are vertical take off and landing aircrafts that use rotating blades to obtain forces to lift and move. Its controls allow several kinds of operations, like hover flight, vertical climb and descent, horizontal flight in any direction and autorotation.\nIn figure 1 are shown the main aerodynamic components of helicopters:\nmain rotor, which generates thrust and maneuverability to the aircraft;\ntail rotor, which counteracts the helicopter body torque reaction;\nvertical and horizontal stabilizers, which contribute to maintain the aircraft in normal flight position (leveled off and nose forward ).\nThe helicopter has six degrees of freedom, named (considering a three axes system with origin in the helicopter center of gravity) [prouty 901:\nmovement along x: longitudinal; movement along y: lateral; movement along z: vertical; movement around x: roll; movement around y: pitch; movement around z: yaw. The vertical movements (take off and landing) depend on the relation between the aircraft weight and the lift force generated by the rotating blades. If this force is greater than the weight, the helicopter accelerates up; if it is less than the weight, it accelerates down; and if they are equal, the aircraft remains hovering at a constant altitude. In order to increase and decrease the intensity of the lift force the pilot acts on the \"collective pitch control\" or simply \"collective\". The blades rotating velocity, controlled by the throttle command, is considered constant, supposing the existence of an independent control system.\nThe horizontal movements (longitudinal and lateral) occur when there is a horizontal force component. In order to generate this horizontal component, the lift force is inclined towards the desired direction. To control this inclination the pilot acts on the \"cyclic pitch control\", or simply \"cyclic\".",
            "The \"lateral cyclic\" tilts the lift force left or right sideward, and the \"longitudinal cyclic'' tilts the lift forward and backward. These horizontal movements start with the helicopter's body inclination to the desired direction. So, if a forward motion is desired, the aircraft tilts the nose down. If the movement is to the right, the aircraft rolls right.\nThe pilot changes the aircraft azimuth acting on the \"tail rotor collective control\", or simply \"tail\". This control alters the force generated by the tail rotor, whose function is to react to the helicopter turning tendency [Collier and Thomas 861.\nDue to helicopter construction characteristics, some of the commands result in undesired movements, distinguishing the existence of crosscoupling modes. Some of the couplings on helicopter movements are:\nwhen the lift force is inclined, creating a horizontal component, the vertical component intensity decreases, causing altitude lost;\nin the longitudinal movement, due to the transverse airflow, the aircraft nose tends to pitch, while in the lateral movement, the helicopter tends to roll;\nthe tail rotor force may cause lateral movement and rolling moment.\nThe helicopter couplings listed above should be foreseen and counterbalanced by the navigation system, using the four controls: collective, lateral cyclic, longitudinal cyclic and tail.\n111. Fuzzy Controller Design\nDue to helicopter complexity, the navigation system is decomposed herarchically into levels, as described in [Cavalcante 941.\nMission interpreter: analyses the mission, breaks it down into tasks, such as take off, hover or landing, for instance, that will be executed individually and sequentially by the task level;\nTask level: in this level, the actual task is executed. The task goal, as well as the existing couplings, define the knowledge base to be used by the fuzzy controller. This level also verifies if all the conditions defined in the task were achieved, like distance to the desired point, aircraft leveled off and so on.\nControl level: implements the fuzzy control of the helicopter, firing the rules of the knowledge base chosen by the task level.\nThe lowest level, called control level, consists of a fuzzy controller, whose design and tuning is described in this paper.\nThe fuzzy controller algorithm is based on [Viot 931, and presents the following characteristics:\ncontinuous fuzzy sets, triangular- or trapezoidalshaped;\ndecision-making using forward inference; min-max composition function; center of gravity defuzzification method. Let us now describe in detail the design of the fuzzy controller knowledge base. Each helicopter task has a goal, and the fuzzy controller knowledge base must reflect th~s goal, in order to execute the proper task action. The task level is responsible for choosing the knowledge base used by the fuvy controller, according to the current task being executed and taking into account the existing couplings.\nEach task knowledge base are split up into four blocks, one for each helicopter command: collective, tail, longitudinal and lateral cyclic. These blocks define the input and output variables, the fuzzy sets and the control rules to be used by the fuzzy controller. The design of these blocks is described below.\nA. Input and Output Variables\nThe input variables are errors (altitude error, position error and yaw angle error) and variation of errors. The controller goal is to zero error and variation of error.\nThe collective block uses as input variables the altitude error and the variation of altitude error, and the tail block uses the yaw angle error and the variation of yaw angle error. The cyclic blocks (longitudinal and lateral cyclic blocks) use position error (lateral and longitudinal error) and its variations, attitude angle error (pitch and roll angle) and its variation.\nThe helicopter has inherent delays associated with its controls, not reacting immediately to a command. Therefore the pilot uses smooth corrections, or impulse commands. The observation of a pilot practice shows that, in fact, he or she uses different procedures for each of the controls. In the case of the collective and tail controls, they are weight dependent, with adjustable trim point to each flight situation. The pilot uses smooth corrections around",
            "this instantaneous trim point. That is why the output variables of collective and tail blocks are the variation of the collective and tail commands. In the case of the cyclic controls, the pilot makes the corrections around fixed zero points. So, the command itself is the output variable in cyclic blocks.\nB. Fuzzy Sets\nIn the collective and tail blocks, seven fuzzy sets are used (NB negative big, NM negative medium, NS negative small, ZE zero, PS positive small, PM positive medium and PB positive big) to represent the values of the input variables (altitude error and altitude error variation). The cyclic lateral and longitudinal blocks use only five fuzzy sets (NM,NS,ZE,PS and PM) for the position error and three sets (Neg, Ze and Pos) for variation of position error, angle error and variation of angle error. The fuzzy sets number was reduced in the cyclic blocks, in order to decrease the number of rules and to make the tuning phase easier.\nFigure 2a displays the input variables fuzzy sets of collective and tail blocks. The ZERO sets are tiny, because they express the error tolerance in steady state. The SMALL sets are useful in the overshoot avoidance rules. The MEDIUM sets are used in most corrections, while the BIG sets are used only in extreme situations.\nAll the blocks use five fuzzy sets for the output variables, shown in figure 2b. In the collective and tail blocks. the MEDIUM sets are used in extreme situations, because they imply great corrections, and they try to drive the system towards medium input variables values. The SMALL fuzzy sets are the most used ones, since they express corrections to small or medium errors. The output variables fuzzy sets ZERO\nare very small, and indicate the equilibrium point (Trim point) where the command increment is minimal, as mentioned in item 111-A. A ZERO output does not mean a ZERO command, but ZERO command increment.\nOtherwise, in the cyclic blocks, the ZERO fuzzy sets indicate no output, while the SMALL and MEDIUM sets mean small and medium comands, respectively.\nC. Rules\nAs mentioned in item 111-A, the helicopter commands should be smooth, as in the case of the collective and tail controls, or small and fast, as in the case of the cyclic controls. At the same time, the rules should include the pilot ability to foresee overshoot and couplings. In order to attenuate the commands, the rules should result preferentially in SMALL sets. The overshoot avoidance actuates in rules where the input error is SMALL, and with an opposite signal to the error variation. This situation indicates that the system is tending to ZERO, and it may overshoot it. So, in this case, the command should be reversed, so that the system stops near ZERO.\nIn the cyclic blocks, the rules should consider not only the position error and its variation, but the aircraft attitudes. A large inclination may cause guidance problems, and should be corrected by a reverse command.\nSuppose a situation that the helicopter position error is small and decreasing. The overshoot avoidance needs to be activated, reversing the cyclic lateral command. If the roll angle is positive and increasing, the inclination should be reduced, reversing the cyclic lateral command. This situation is described by the following rule: \"IF position error is Positive Small, position error variation is Negative Small, roll angle is Positive Small and roll angle variation is Positive Small THEN lateral cyclic is Negative Small.'' This is an example of the simultaneous overshoot avoidance and attitude correction.\nThe next section shows how the tuning phase was done.\nV. Tuning Phase\nIn a fuzzy controller design, the tuning phase plays a very important role in the knowledge base adjustment. This phase necessarily involves simulation, the results obtained being analyzed and the adjustments in the knowledge base made in order to improve the fuzzy controller performance.\nTo allow the rules firing evolution analysis, it is proposed in this work a method, called rules evolution tuning method. T h s method indicates, in the linguistic rules table, the sequence and the transition between the rules tiring. It is based in a method proposed in [Braae and Rutherford 791 and"
        ]
    },
    {
        "image_filename": "designv11_24_0002193_87-gt-110-Figure14-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002193_87-gt-110-Figure14-1.png",
        "caption": "Fig. 14 Campbell diagram of squeeze film backed cylindrical bore bearing",
        "texts": [
            " For both operating conditions of the new design the instability at speeds above 580 s -1 is due to a subharmonic vibration of the \"unbalanced\" rotor, the frequency being a definite fraction of the running speed. The vibrational amplitudes increased with unbalance, but the amplitudes remained limited. 8 Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use Squeeze film backed cylindrical bore bearing The Campbell analysis (see Fig. 14) for both operating conditions indicated no stability threshold up to a rotor speed of 1033 s -1 . Synchronous vibrations increased with unbalance, while a critical speed (cylindrical mode) at 320 s -1 could be detected in the Campbell diagram of the unbalanced case. Self-excited vibrations were quite strong at low speed, but were limited with amplitudes reaching approximately 50 % of the total bearing clearance. At higher speeds, this instability was stabilized in relation to unbalance. These test results agreed with the stability analysis shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000067_s1474-6670(17)47335-6-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000067_s1474-6670(17)47335-6-Figure1-1.png",
        "caption": "Fig 1 Position and orientation variables",
        "texts": [
            "Ill :;,=\u00b7 cLl\u00b7~,r: 1, ~h;] Gil<ily;is of the limiting behaviour of the curvature of the path generated by the proposed control laws is carried out and verified by simulation. In section 5 an extension of the app:-r,;:vll ,~,)Cl('~!\":'.i')g the use of a set of objective functions is discussed, whereas section 6 provides ~;ome concluding remarks. Let us ccnsider a unicycle-like vehicle initially positioned at a non-zero distance with respect to a goal fra.me <g>, whose motion is governed by the combined action of both the angular velocity wand tl:le linear velocity vector :Ye, always directed as one of the axis of its attached frame <a>, as depicted in Fig. 1. Then, a set of kinematic equations can be directly devised, which involves the vehicle Cartesiar. position x , y and its orientation angle 1/;, all measured with respect to the target frame point <g>; i.e. the equations { i ,= U cos 1> Y.= U sin 1> 1>=:..: (1) belonging to the class ill ~= L !i(Z)Ui (2) i=l with zERn and UiER. It is well known that an equiliuriullI l1UiUL ur sudl sysLellls C'lllilUL ue asymptotically stabilized via a smooth feedback law if, in correspondence of it, the!i are continuously differentiable, linearly independent vectors, and m<n (Brockett 1983), as it actually happens for equations (1)",
            " However, if the independence assumption about the fi is violated, the pOSSIbIlity of asymptotically stabilizing the equilibri'LlIIl point via smooth feed back is not excluded. by Brockett's theorem and a trivial example is represented by the following system whose equilibrium point (0,0) is glohally and asymptotically stabilized by any positive and constant control action. As concerns unicycle vehicles, another set of kinematic equations can be devised using the quantities e, a and () depicted in Fig. 1, i.e. l e = -ucos a \u2022 sin a a=-w.+ u-e. szn a ()= u-e (4) As a matter of fact, equations (4) allows for a set of state variables which well resemble the same ones everyday used within our car-driving experience. Note also that, since based cn the use of a sort of polar coordinates, (4) actually result to be valid only for non zero values assumed by the distance errors e, since both angles a and () are undefined quantities in correspondence of e = 0 ; thus implying that the generally existing one to-one correspondence with"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000476_s0045-7949(99)00201-1-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000476_s0045-7949(99)00201-1-Figure1-1.png",
        "caption": "Fig. 1. Description of the motion of a triangular sti ened shell element in a co-rotational system.",
        "texts": [
            " Based on the foregoing discussion, this study presents a geometrically nonlinear shear deformable stiffened shell element that incorporates arbitrary orientation of eccentric sti eners within the element and that accounts for large displacements and rotations. A distinct feature of this element, compared to previous laminated sti ened shell elements, is that the element formulation accounts for arbitrary cross sections of laminated sti eners. The new sti ened shell element is developed by combining the formulations for shallow shell and shallow beam elements for mechanical loading. The formulation combining these kinematically compatible elements utilizes the co-rotational form of the total Lagrangian description of motion (Fig. 1). The formulation begins with the principle of virtual work: dWe 0Vs d0eT s t Dt 0 ss d0Vs 0Vb d0eT b t Dt 0 sb d0Vb 1 Between time t and t+Dt, 0es and 0eb represent the components of the incremental Green strain tensor in vector form associated with the shell and beam el- ements, respectively. The components of the Piola\u00b1 Kirchho stress tensor for both elements are contained in vectors denoted by t Dt 0 ss for the shell element and t Dt 0 sb for the beam element. The lower-left subscript indicates the con\u00aeguration by which the quantity is measured"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003936_13506501jet75-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003936_13506501jet75-Figure3-1.png",
        "caption": "Fig. 3 Dimensions of wheel and rail discs",
        "texts": [
            " Figure 1 shows a twin-disc rolling contact machine [6] used for the experiments. The machine has two 150 kW DC motors to control a disc of 300 mm in diameter (termed a wheel disc) and another disc of 170 mm in diameter (termed a rail disc), respectively. The wheel disc was made of real wheel material in accordance with JIS (Japanese Industrial Standard), used in Japanese Railways, and the rail disc, cut from a real rail. Table 1 indicates material compositions and properties of the wheel and rail discs. Figure 2 details how the rail disc was cut from a real rail. Figure 3 depicts an elevation of the contact between wheel and rail discs in the axial direction. The wheel disc (\u00d8 300 mm) was designed to have a flat geometric shape and the rail disc (\u00d8 170 mm) was curved with a radius of 600 mm at its crown in order to simulate higher contact pressure. The two discs can rotate independently at different running speeds (maximum 100 km/h) to simulate the slip phenomenon (maximum 100 per cent), and they can also move independently in the lateral direction (maximum +7 mm) to simulate a hunting motion, thereby creating random contact between wheel and rail with various worn profiles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000253_1.2801489-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000253_1.2801489-Figure1-1.png",
        "caption": "Fig. 1 Two possible simplexes",
        "texts": [
            " Since our goal is temperature regulation, we consider X\\ as an exogenous system and only focus on the temperature equation fif = e, \u2014 e sat > 0 & = -r\u201eej*, r \u201e > 0 Toie^uj* ~ (d - 9)], r 9 > 0 di i f 9i G [ 6*;min, ^ imax] .mill IT \"i \u2014 \"i.min .max I I \" i \u2014 \"i.max \u2022 Performing the min-max optimization to find a;* and a* is needed to complete the controller design and requires con structing a simplex, &s. There are, however, an infinite number of simplexes which contain the hypercube, \u00a9. For instance, two possible choices are depicted in Fig. 1. The effects of either simplexes on the nonlinear adaptive controller were investigated through simulations performed in MATLAB. The simulation parameters values are listed in Table l ( a ) - ( c ) and the results are depicted in Figs. 2 - 3 . Figure 2 demonstrates that excellent tracking is achieved re gardless of the choice of simplex. We note that e^ converges to \u00a3 which was set to IK. As e was decreased, the steady-state value of Cc decreased as well. We observed however that param- Journal of Dynamic Systems, Measurement, and Control DECEMBER 1998, Vol"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003801_iros.2006.282533-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003801_iros.2006.282533-Figure3-1.png",
        "caption": "Fig. 3 Traveling plate ofH4 and 14 and orientation of the axis of actuators",
        "texts": [
            " All these characteristics cannot be achieved at the same time neither by Delta, nor H4, nor 14. 1) Delta robot The main weak point of Delta robot is the central telescopic leg providing the rotational motion. This RUPUR (R: revolute, U: universal, P: prismatic joints) chain suffers from a short service life, and involves a bad stiffness of the rotation motion. In order to avoid the central telescopic leg, the concept of articulated traveling plate has been introduced with H4 and 14. 2) H4 robot The traveling plate of H4 is realized with three parts linked by revolute joints (see Fig. 3a). A complete study of singularities of this robot including the notion of \"internal singularities\" has been developed in [11] and demonstrates that placing actuators in a symmetrical way, i.e. at 90\u00b0 one relatively to each other involves singular postures. Thus, the robot has to be built using a particular arrangement of motors, whose axes are presented in Fig. 3a with arrows. This non symmetrical arrangement entails a non homogenous behavior in the workspace and a limited stiffness [14] of the robot. 3) 14 robot The internal mobility of 14 is obtained with a prismatic joint (Fig. 3b). The advantage of this architecture is to authorize a symmetrical arrangement of the actuators. As demonstrated in [12], it is possible to place the actuators at 90\u00b0 one relatively to each other. However, this architecture is more adapted to machine-tool application than to high speed pick-and-place. Indeed, commercial prismatic joints are not suitable for high speed and high accelerations, and have a short service life under such conditions. This inconvenient is due to the high pressure exerted on the balls of these elements at high acceleration conditions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000657_1.2833796-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000657_1.2833796-Figure1-1.png",
        "caption": "Fig. 1 (a) Rotor and stationary sleeve (case of grooved rotor)",
        "texts": [
            " Examples of its successful application include elastohydrodynamic lubri cation (EHL) (LutDrecht et al , 1987), dynamically loaded jour nal bearing with cavitation (Woods and Brewe, 1989), and dynamic simulation of plain cylindrical journal bearing lubri cated by gas (Kobayashi, 1996). This paper will present an orbit simulation procedure, which combines MG with the divergence formulation (Castelli and Pirvics, 1968), as an engineering tool to study both stationary and time-dependent problems of HGJB. The present study considers a simple bearing system com posed of a rotor and a stationary sleeve, as shown schematically in Fig. 1, assuming that the rigid rotor is ideally balanced and has a total of two degrees of freedom which correspond to the translational displacements Xcg and y^g. A herringbone-grooved pattern is formed on either the sleeve surface or the rotor sur face. Also, let us make the usual thin film lubrication assump tions so that the isothermal and compressible Reynolds equation in dimensionless vector form can be given by V -[PH^VP - APffi] = A djPH) dT (1) 148 / Vol. 121, JANUARY 1999 Copyright \u00a9 1999 by ASME Transactions of the ASME Downloaded From: http://tribology",
            " = angular rotor speed, rad/s w = stability parameter, =^cmlfy \u2022 = inner product ||jc||2 = Li norm of x Sub-, Superscripts i,i = grid indices k = control volume cell index M = finest grid level index m = grid level index n = time step index Journal of Tribology JANUARY 1999, Vol. 121 / 149 Downloaded From: http://tribology.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jotre9/28680/ on 06/14/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Rotor \\ \u00bb-2 'mmmm, a^~S I ^ M ^ B ^ Ridge / ^ ^ ^ Groove ^'mMmmMm. Stationary sleeve b \u00bb Fig. ^(b) Coordinate system; O = sleeve center; * i^ for smooth rotor and stationary grooved sleeve; **</> for grooved rotor and stationary smooth sleeve Fig. 1 HGJB system /'lz=o = 1 and the circumferential periodicity condition that (8a) {%b) Now we apply the semi-implicit Crank-Nicolson formula, the superiority of which over other formulas for nonsteady gasbearing problems has been demonstrated by Michael (1963) and Coleman (1972), to Eqs. (6a) and (6/?). As a result, we obtain the following that is satisfied whichever member is grooved 4 I (GM + e^j AA</)AZ ^ '\" \"s//i3r' - /\u0302 s:;' 2 H^, Ar (9) with the definition that fic PH' dP tan Pg dcj) dP_ dz Ji~,j-l/2 A0 2 (lb) where / - j denotes the left control volume face, and 7 \u2014 denotes the bottom side of the jth grid line, etc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000718_s0020-7403(99)00013-2-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000718_s0020-7403(99)00013-2-Figure2-1.png",
        "caption": "Fig. 2. Coordinate system S s , S m , S 2 and S t applied for generation.",
        "texts": [
            "inv a 0 , (2) where N s and a o are tooth number and pressure angle of the shaper, respectively, and inv is the involute function. The unit normal n s to the shaper surface is given by n s \" Lr s Lh s ] Lr s Lu s K Lr s Lh s ] Lr s Lu s K \"!C cos(h os #h s ) sin(h os #h s ) 0 D. (3) We represent the face-gear tooth surface, & 2 , in coordinate system S 2 by the following matrix equation: r 2 (u s , h s , u s )\"M 2s (u s )r s (u s , h s ), (4) where M 2s is the homogeneous transformation matrix from coordinate system S s to S 2 given in appendix. The auxiliary coordinate system S t (x t , y t , z t ) in Fig. 2 is set up to facilitate the coordinate transformation. The angle c m between axes z m and z 2 is determined by c m \"180!c, where c is the half-shaft angle of the face-gear. The rotational angles of the face-gear, u 2t and the shaper, u s , are related by u 2t \"u s N s /N 2 where N 2 and N 4 denote the tooth numbers of the face-gear and the shaper, respectively. The equation of meshing is represented as Eqs. (5) and (6) [1,6]. Such equations insure that the generating and the generated gear tooth surfaces are always in tangency during the generating process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001108_1.1308033-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001108_1.1308033-Figure3-1.png",
        "caption": "Fig. 3 Foil bearing model for hollow porous guide",
        "texts": [
            " Applying the least square method to the numerical solutions of web spacing, the formula for the web spacing h0 at x50 for the flat surface guide is derived as follows @1#: h05RS 6mUw T D 2/3S 0.5892 1.614 l 1 1.764 l2 D (6) Equation ~6! is valid for l.0.2 and b.6, which covers almost all range of actual applications of web transporting systems @1#, where: l5 L 2R S 6mUw T D 21/3 , b5BS 6mUw T D 21/3 (7) Web Spacing Analysis for Hollow Porous Guide. Comparing with the flat surface guide as described above, a new type of hollow porous stationary guide as shown in Fig. 3 has an advantage to control the web spacing suitably according to the variation of operation conditions in the web transporting systems @2#. The Transactions of the ASME /data/journals/jotre9/28698/ on 02/07/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F stationary guide system consists of the web and hollow porous guide. Pressurized air is added from inside the guide to the hydrodynamic air flow in the web spacing. Then, the web spacing and friction characteristics are improved by the hybrid effects of hydrodynamic pressure due to web movements and hydrostatic pressure due to pressurized added flow through the guide"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003858_j.measurement.2005.11.012-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003858_j.measurement.2005.11.012-Figure8-1.png",
        "caption": "Fig. 8. Determining distance of beam intervals.",
        "texts": [
            " h \u00bc 1 2 a t1 \u00fe t2 2 h i2 : \u00f06\u00de The time duration t3 (fall down time of athlete) and how the athlete fall down on the floor does not important in this method. In laser operated system the determination of the time of leaving from the floor is necessary to get the time duration t1 as in contact operated system. Optoelectronic sensors are used here as floor sensor. The zone is scanned with definite intervals of infrared beams, where the athlete\u2019s feet stay before jump. Selecting interval of beams is an important point during designing the floor sensor. To determine the distance between beams let us use the diagram shown in Fig. 8 and suppose that the distances between the beams (expressed as d) are equal. In Fig. 8 d\u2014the distance between adjacent beams, g\u2014the minimum shading part of athlete\u2019s shoe at start of jump and m\u2014the distance between the center of beams and the floor. The distance between the center of beams and the floor is constant and this error can be taking into consideration during writing calculation programs for microprocessor. This error is additive. Distance between the beams should so selected that should d < g. Also the shoe of athlete should hinder at least two beams during start the jump"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003710_j.jsv.2006.04.008-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003710_j.jsv.2006.04.008-Figure1-1.png",
        "caption": "Fig. 1. Journal whirling in a six-recessed hybrid bearing: (a) configuration, (b) perturbed orbit of journal center, and (c) coordinates of recess edges.",
        "texts": [
            " ARTICLE IN PRESS C.H. Chen et al. / Journal of Sound and Vibration 297 (2006) 635\u2013648 637 2.1. Lubrication equations of hybrid bearing For an iso-viscous, incompressible lubricant situated in a hybrid bearing clearance assuming of laminar flow without inertial effect, the non-dimensional Reynolds equation of lubricant can be derived from Navier\u2013Stokes equation and expressed in the Cartesian coordinates system as q qy h\u0304 3 qP\u0304 qy \u00fe D L 2 q qz\u0304 h\u0304 3 qP\u0304 qz\u0304 \u00bc L qh\u0304 qy \u00fe s qh\u0304 qt . (1) As shown in Fig. 1, the journal center rotates about its steady-state position (eo, fo) with a small whirl which is decomposed into radial and tangential components represented by Re(epe it) and Re(eofpe it), respectively. This small journal whirl will induce small perturbations of the film pressure and film thickness which are composed of steady-state part subscripted by o and dynamic parts subscripted by e and f. Thus, the pressure and film thickness distributions can be expressed, respectively, by P\u0304 \u00bc P\u0304o \u00fe epe itP\u0304e \u00fe eofpe itP\u0304f, (2a) ARTICLE IN PRESS C",
            " The expression for the outflow of lubricant from the recess is given by Q\u0304r \u00bc Z yr yl h\u0304 3 d qP\u0304 qz\u0304 z\u0304\u00bcz\u0304b dy\u00fe Z z\u0304t z\u0304b Lh\u0304d h\u0304 3 d qP\u0304 qy y\u00bcyl dz\u0304 \u00fe Z yr yl h\u0304 3 d qP\u0304 qz\u0304 z\u0304\u00bcz\u0304t dy\u00fe Z z\u0304t z\u0304b Lh\u0304d h\u0304 3 d qP\u0304 qy y\u00bcyr dz\u0304; \u00f05\u00de where y1 and yr are referred to both bounds of circumferential coordinates and z\u0304b and z\u0304t are referred to both bounds of axial coordinates, respectively, of the downstream edges of restrictor inlet at the rth recess as shown ARTICLE IN PRESS C.H. Chen et al. / Journal of Sound and Vibration 297 (2006) 635\u2013648 639 in Fig. 1(c). Similarly, the static and dynamic pressures of downstream of restrictor inlet in recesses can be obtained by substituting Eqs. (4a)\u2013(4c) into Eqs. (3) and (5), and equating coefficients of static and dynamic perturbations on both sides gives P\u0304do \u00bc 1 Q\u0304ro d z , (6) P\u0304de \u00bc 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 P\u0304do p Z d \u00f0Q\u0304e \u00fe ic cos yd \u00de, (7) P\u0304df \u00bc 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 P\u0304do p Z d \u00f0Q\u0304f \u00fe ic sin yd \u00de, (8) where z \u00bc 1 and Z \u00bc 0 for capillary restriction, and z \u00bc 2 and Z \u00bc 1 for orifice restriction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002193_87-gt-110-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002193_87-gt-110-Figure2-1.png",
        "caption": "Fig. 2 Cross-section of RR 151 turbocharger",
        "texts": [
            "org/about-asme/terms-of-use INTRODUCTION The market for small turbochargers, particularly for high speed diesel engines in the range of 600 - 2000 KW per turbocharger unit, has demanded improved overall efficiency as well as a higher flow capacity of the RR 153 turbocharger [1] shown in Fig. 1. It was assumed that this could be achieved by a redesign of the compressor and turbine stages without the need to alter the original rotor-bearing system. However, the selection of a mixed flow turbine for the new turbocharger - the RR 151 (see Fig. 2) - instead of a radial turbine as used in the RR 153, changed the vibration behavior of the rotating machinery drastically. The increased weight of the turbine due to a 40 % increase in flow capacity resulted in significantly higher rotor vibrations. Consequently, only 70 - 80 % of the required speed range could be covered safely. These results, discovered during performance testing of the turbine and compressor, indicated unsatisfactory bearing performance. This led to an intensive experimental and analytical investigation of the vibrational behavior of this new turbocharger design, the outcome and insights of which are the subject of this paper"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002247_0094-114x(87)90067-x-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002247_0094-114x(87)90067-x-Figure4-1.png",
        "caption": "Fig. 4. A n I l - l ink chain.",
        "texts": [
            "x is the mobility number of peripheral loop. (b ) Peripheral loop with a multiple joint. If n links (or loops including peripheral loop) form the multiple joint falling on the peripheral loop L12 . . . . . i, we obtain['/] s - I a -2 A2 . . . . . , - - E f / - 2 ) \" F.,+,) j - I i - I + + (n -- 2)F,, (16) Y with variable general constraints, and for constant general constraint n - I n - 2 A2 . . . . . , = ~. f j - 2 ~ Gt,+I) j = l i = I + (n -- 2)(D + F,), (17) where F, is the DOF of the joint which forms multiple joint. Example 3 Figure 4 shows an I l-link pin jointed kinematic chain with one external multiple joint. The multiple joint is formed by five links. Therefore, M 2 = l , n=5, D = 3 , F , i = l , 2 . . . . . 1 4 = l . From Fig. 4 J,2 =J23 = J 3 , = 3 and hence F12=~3, F23--3 , F34=3. From equation (4) ~ = 2 , f 2 = 2 , A = 2 , A = 2 . Hence from equation (17), the DOF of the peripheral loop mechanism shown dotted is obtained as fn~ = (2 + 2 + 2 + 2 ) - 2(3 + 3 + 3)+ ( 5 - 2 ) ( 3 + 1) -----2. To facilitate the synthesis of a multi-loop kinematic chain, the mobility properties of individual loops are obtained to calculate overall mobility. The following results of loop freedom matrix properties of partial or total freedom chains are given without proof for a better understanding"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003956_tia.2005.863899-Figure19-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003956_tia.2005.863899-Figure19-1.png",
        "caption": "Fig. 19. Flux distribution of synchRel under the full-load condition (without flux barriers).",
        "texts": [],
        "surrounding_texts": [
            "Next, an attempt was made to validate the simulated model of synchRel by comparing its performance with that of an actual motor. The synchRel was mounted on the test bed together with a direct current (dc) generator mechanically coupled to it for loading purpose. A small permanent magnet dc machine was also coupled to its shaft to measure the speed transient. First, the moment of inertia (J) of the synchRel, combined with the other two dc machines, was determined from the coasting curve of the machine set [18]. The value of J was found to be 0.023 kg \u00b7 m2. The simulated model of the synchRel was then run with the new value of J . The full-load torque (5.9 N \u00b7 m) was applied at 0.5 s. The transient stator current, speed, and rotor loop current (a loop next to interpolar gap) of the synchRel are shown in Figs. 23\u201325, respectively. The corresponding loading transients of the actual motor were obtained using a data acquisition system. They are shown in Figs. 26 and 27, respectively. The terminal voltage of the permanent magnet dc motor has a lot of ripple as shown in Fig. 27 (top). Hence, the acquired data is filtered using a digital finite impulse response (FIR) filter and plotted as shown in Fig. 27 (bottom). Though the simulated result of the speed dip upon loading is about 1 rad/s lower than the experimental one, the settling time for both simulation and the experiment is about 0.1 s. Furthermore, the simulated and the experimental transients show similar damping characteristics. Thus, it can be said that the loading transients of the simulated model have shown a close match with the corresponding transients obtained from the experiments. The steady-state performance of the simulated and the actual synchRels were also compared. The no-load and full-load simulated currents of the synchRel are shown in Fig. 28. The corresponding experimental results are shown in Fig. 29. A comparison of these figures reveals an excellent average match between the simulation and experimental results. While the root mean square (rms) values of the line current of the simulated machine under the no-load and full-load conditions are 1.82 and 3.32 A, respectively, the corresponding rms values of the line current of the actual machine are 1.8 and 3.3 A, respectively. Later, when this model was extended for operation under supply voltage unbalance [19] and stator interturn fault conditions [20], the stator currents seemed to be comparable even at the harmonic amplitude level. Hence, at this point, it is felt that sufficient refinements, as far as stator fault diagnosis is concerned, have been obtained with the MWFA-based model. A closer match between the simulated and experimental results cannot possibly be achieved unless nonlinear magnetic characteristics of iron, pole corner saturation, and flux barrier effects are accurately modeled. This would essentially mean a finiteelement-based model."
        ]
    },
    {
        "image_filename": "designv11_24_0002466_iros.1993.583931-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002466_iros.1993.583931-Figure7-1.png",
        "caption": "Fig. 7 Movement of M O robots over a long distance",
        "texts": [
            " Tlie ielative aiiglc bctwecii each robot and tlie global system can be deteriiiiiicd by incaxiring t lie rclative angle bctwceii tlic local coordiiiatc systciiis of tlie two robots, aiid accuinulating this angle from tlic time tlie global coordinate systein is fixed. from robot A to B and b froin robot B to A are incasurccl siinultaiieously, thcn robot B can deteiniinc tlie relative aiiglc B betaweell tlic local coordinate systcins of tlie two robots; B cquals the anglc Iietwccn vcctors U\u2019 and -b. In this casc, U\u2019 is tlic rcceived vcctor d simply iiidicatcd bascd on tlic local As Fig 7(a) shows, if two rclativc-vcctors --f - + + -4 -4 coordinate system of robot B, ancl -b is tlie iiivcrtcd vcctor of b . In the following, tlie scquence of inovciiicnts of two robots over a long distance is described bascd 011 Fig. 7(b). In this sequeiice, the above-mentioned proccss of nieasuriiig tlic rclative angle between coordinatc systenis is necessary cacli time the stay-robot transinits position inforination to tlic move-robot. However, tlie description of this process has been omitted. As described before, each robot can be tlic niove-robot or the stay-robot. In tlie Fig. 7(b), suffix z indicates each robot at time 7 . Robot A0 initially fixes tlie global cooidinate system so that tlie origin corresponds to its initial position and tlie 2- axis shows its direction to inove. Then, robot A0 ineasurcs relative-vector 7;: and transmits it to robot B1. Aftcr that, A. tries to moves along the x-axis and becoines Al. Hcrc, robot B1 measures relative-vcctor bl to A1 aiid trailsinits tlic position information. Tlie sanie sequence is repcatcd until robot A reaches its destiiiatioii point and bccoines A,,",
            " A,, is indicated by + + + + Robot Brccogiiizes its posit,ioii in tlic same inaniier, 4.2 Error estimation in position recognition During tlie iiioveiiiciit of two robots ovcr a long distaiicc, sinal1 ineasureinent errors accumulate in tlic dctcriiiiiiat,ioii of relative-vectors. Tlicrefoi-e, a t tlie destination point,, the recognition of tlie position in tlic global coordiiiatc systciii inay be scriously incorrect. Tlic followiiig discusses tlic rccognitioii crror of the position a fkr inoveiiieiit ovcr a long distance. As shown in Fig. 7(b), tlic inovcinciit, of t,wo robots ovcr a long distance is done by mutual moving aiid obscrvatioii. At each staying point, tlic stay-robot dctcriiiiiics tlic rclativc- vector. Finally, all of tlie relative-vectors are sumiiicd by Eq. 10 and the obtained vector A , givcs the recognition of tlie position to robot A,. Thcrefore, the recognition error of the position after movement over a long distance is equal to tlie sumination of measurement errors from the dcterniination of rclative-vectors. Here, the recognition error of the position after movement over a long distancc is indicated by vector R . According to Eq. 10, A , is derived from 2n relative-vcctors. When a relative-vector is measured, another relative-vector must also bc measured (Fig. 7(a)). Therefore, if tlie rccognition crror R is estimated by its inaxiiiiuiii value, then the maxiiiiuiii value of the measuremcnt error TmaX must be multiplied 4n times. obtained by the above process. The horizontal axis represents d which is equal to the distance from robot B 1.0 the z-axis approximately shown in Fig. 7( b). The left-vertical axis rcprcsents the maximum error I R ,naxl in the position recognition after the moveinelit over a long distance. In the cdculation, I,, is fixed at 20 [cin] and the entire length A , of the movement is fixed a t 100 [in]. The othcr parainetcrs are set according to Tablc 1. The right-vertical axis rcprescnts n. During tlie inovenient, robot A stops 72 times. This value of 72 is sclected from integers so as to iiialte the calculated value I R maxi mininiuin for each d, and this selected value of n is also shown"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001861_tia.2003.818995-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001861_tia.2003.818995-Figure1-1.png",
        "caption": "Fig. 1. Rotor with inter-bar resistance.",
        "texts": [
            " Transversal resistances existing in the rotor circuit of cage induction motors, the end-ring impedance and skin effects in the rotor bars are taken into account. The circuits theory (independent current method) is used to define a tree in the rotor circuit with branches and loops. The developed methodology is valid for any number of phases. In this paper it is used to verify the effect of the rotor skewing on the inter-bar currents of a three-phase induction motor and on its performance with different inter-bar resistance values. By using the multi-slice technique to represent the rotor skewing the structure is divided in slices as shown in Fig. 1. The angle difference between them, , is defined by the skew angle and the number of slices . From the Maxwell\u2019s equations and introducing the magnetic potential vector and the electric potential we obtain in each slice the partial differential equation given in (1) [7]. The cuts in the structure are symmetrical and the length of each slice is 0093-9994/03$17.00 \u00a9 2003 IEEE . The coefficients and are the magnetic reluctivity and the electric conductivity, respectively [9], (1) The number of turns in series in each coil of the stator winding is . The current, cross section, and dc resistance of each slice of this coil are , , and respectively. , , and are the voltage drop, resistance, and cross section of each slice of the massive conductor. Transversal resistances are inserted between the rotor bars as shown in Fig. 1 where bars are modeled by the FEM. By using the circuits theory (independent current method) one tree with edges is selected where the loops of this tree are defined as the inferior ring segments, the inter-bar resistance, and the last superior ring segment. The tree branches are the bar segments and the superior rings segments. The tree selected is shown in Fig. 2 where the heavy lines represent the branches and the thin lines represent the loops. is the end-ring segment impedance and is the voltage of each bar segment modeled by finite elements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003101_acc.1994.734996-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003101_acc.1994.734996-Figure1-1.png",
        "caption": "Fig. 1: Schematic view of a rotating arm Compact Disc mechanism.",
        "texts": [
            " Moreover, the system behaviour varies from player to player due to the required manufacturing tolerances of CD players in mass-production, which explains the need for robustness of the controller Further, an increasing amount of all CD based applications is for portable use. Thus, additionally power consumption and shock sensitivity play a decisive role in the performance assessment of controller design for CD systems. In this paper we will concentrate on the possible improvements of both the track-following and focusing behaviour of a Compact Disc player, using robust control design techniques. 2 Compact Disc Mechanism In Fig.1 a schematic view of a Compact Disc mechanism is shown. The mechanism is composed of a turn-table DC-motor for the rotation of the Compact Disc, and a balanced radial arm for trackfollowing. An optical element is mounted at the end of the radial arm. A diode located in this element generates a laser beam that passes through a series of optical lenses to give a spot on the information layer of the disc. An objective lens, suspended by two parallel leaf springs, can move in a vertical direction to give a focusing action"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001307_physrevlett.84.2164-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001307_physrevlett.84.2164-Figure1-1.png",
        "caption": "FIG. 1. Section of the shear cell ring (placed in a vertical position for the three-axis geometry) defining the three axes y, = ? y, z . The scattering vector is defined by q ki 2 kf , where ki is the incident beam and kf is the diffracted one.",
        "texts": [
            " Because of its high instrumental resolution and of the absence of inelastic contribution (measure of the elastic signal alone), the neutron spectrometer chosen to characterize the position, width, and intensity of the smectic reflection is a three-axis spectrometer. Since this spectrometer scans only the horizontal plane, the shear cell ring was placed vertically. So, the incident beam, crossing one ring side (coinciding with the center of the reciprocal space) scans the two axes contained in the horizontal plane which are the velocitygradient = ? y axis and the neutral axis z (Fig. 1). The wavelength was 4.18 \u00c5. Distances obtained with the 2D small-angle neutron scattering multidetector PAXY have also been added. In this case, the incident beam is along the neutral axis z and crosses the shear cell tilted at 2\u00b1\u20133\u00b1 to the horizontal so that one side intercepts the beam; the 2D multidetector explores the plane containing the velocity and the velocity gradient y, = ? y [as already described elsewhere [3(b)] ]. Finally, for the perpendicular orientation, only the 2D multidetector was employed to access as described in [3(a)] to the y, z plane",
            " Vigoureux (to be published). [3] (a) L. Noirez and A. Lapp, Phys. Rev. E 53, 6 (1996); (b) Phys. Rev. Lett. 78, 1 (1997); 78, 70 (1997). [4] R. Muller, C. Picot, Y. H. Zang, and D. Froelich, Macromolecules 23, 2577 (1990). [5] (a) L. Noirez, G. P\u00e9py, P. Keller, and L. Benguigui, J. Phys. II (France) 2, 821 (1991); (b) L. Noirez, C. Boeffel, and A. Daoud-Aladine, Phys. Rev. Lett. 80, 7 (1998); 80, 1453 (1998). [6] (a) L. Noirez, P. Davidson, W. Schwarz, and G. P\u00e9py, Liq. Cryst. 16, 1081 (1994) (Fig. 1 therein corresponds to the polymer deuterated on the main chain); (b) P. Davidson and A. M. Levelut, Liq. Cryst. 11, 469 (1992). [7] (a) S. I. Ben Abraham and P. Oswald, Mol. Cryst. Liq. Cryst. 93, 383 (1983); (b) P. Oswald and M. Kl\u00e9man, J. Phys. (Paris), Lett. 43, L-411 (1982); (c) R. Ribotta and G. Durand, J. Phys. (Paris) 38, 179 (1977). [8] W. Renz and M. Warner, Proc. R. Soc. London A 417, 213 (1988). [9] G. K. Auernhammer, H. R. Brand, and H. Pleiner, Rheol. Acta (to be published). [10] K"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000775_00207729808929507-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000775_00207729808929507-Figure1-1.png",
        "caption": "Figure 1. Fuzzy membership functions of s; and \"Is;'",
        "texts": [
            "; - CjUfsj - iSj la;(X;} - a;(XjIOjj)1 s H(Xj), Ib;(Xj) - bi(XjIOij)1 :::; G(Xi), Suppose that Ojj and 0ij are the optimal parameter vector of 0lj and 02i; define Oji and 0ii to be as follows: OJ; = argmin [sup liJi(XjIOli) - a(X;}I] , (17) Ol/En ll X/EMI Oii = argmin [sup Ihj(X;i02i) - h(Xj)I] , (18) 8uEn2/ X/EMj where 0lj and 02j are feasible fields of eli and 02j, respectively. M; is a subspace of R\", and Wi = iJi(XjIOjj) - a;(X;} + [hi (XjIOjj) - bi(X;}]Uci, the 'minimum approximation error'. Assumption 4: Suppose that the fuzzy logic approxima tion errors satisfy the following inequalities: D ow nl oa de d by [ E rc iy es U ni ve rs ity ] at 1 8: 22 2 5 D ec em be r 20 14 Fuzzy indirect adaptive control 153 The above fuzzy sets are taken to be triangle-shaped fuzzy sets; their membership functions are depicted in Fig. 1. Using intuitive inference, we can build the following fuzzy control rules: Rj j : IF Sj is Cj j, then Ufsj is F6_j ,;, j = 1,2, ... , 5. (26) where x, = s.]<pj, and when ISjl :::: <pj it is easy to check that Ufsj = -sgn (Sj( t)). Theorem 2: If each subsystem is defined by (3) with the adaptive control law (13), (20)-(24) and the assumptions hold, then the tracking error for each subsystem will asymptotically converge to a neighbourhood of zero. From the ith rule, we obtain the fuzzy relation Proof: Take the following Lyapunov function candidate: Rji = c; X F6_j ,; , that is Rj;(s;, Ufsj) = Cjj(Sj) /I F6- j,j(/\u00b7'"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002689_j.mechmachtheory.2004.12.016-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002689_j.mechmachtheory.2004.12.016-Figure6-1.png",
        "caption": "Fig. 6. All possible configuration of Assur 5-link in Example 2.",
        "texts": [
            " 1 2 3 4 5 6 \u00f0\u2018\u00fe m2\u00de3 \u00fe \u00f0 1:037m2 :7800e 1m\u00fe :4563e 2\u00fe :1786\u2018\u00de\u00f0\u20182 \u00fe m2\u00de2 \u00fe \u00f0:5146e 3\u2018 :1639e 3m :2526e 2m2 \u00fe 1:166\u20184 :1142\u20183 \u00fe :6473e 2\u20182 :7222e 2\u2018m :3929e 1m2\u2018\u00fe 3:357m2\u20182 :5969m3\u2018 :6881e 1m\u20182 3:731\u20183m\u00fe :2984e 1m4 \u00fe :5942e 1m3 \u00fe :6807e 5\u00de\u00f0\u20182 \u00fe m2\u00de \u00f0:1243e 12\u00f0 :9800e5m2 \u00fe 5600m \u00fe 140\u2018\u00f0 30: 1750:\u2018\u00fe 1400m\u00de\u00de2\u00de \u00bc 0 The algebraic equation by using the second method is \u00f0x2 \u00fe y2\u00de4 \u00fe \u00f0 :32213x2 \u00fe \u00f0 75:612\u00fe :85902y\u00dex\u00fe 24:081y \u00fe 402:10 :57268y2\u00de\u00f0x2 \u00fe y2\u00de3 \u00fe \u00f037:582x3 \u00fe \u00f0951:92 80:175y\u00dex2 \u00fe \u00f055:121y2 4400:4 1061:8y\u00dex 370:88y2 \u00fe :14688e6\u00fe 2663:4y 20:044y3\u00de\u00f0x2 \u00fe y2\u00de2 \u00fe \u00f0 1096:1x4 \u00fe \u00f016771:\u00fe 1753:8y\u00dex3 \u00fe \u00f010122:y :42459e6 1578:5y2\u00dex2 \u00fe \u00f05767:6y2 \u00fe 701:53y3 \u00fe :28828e6y\u00dex 8729:1y3 :16269e6y2 175:38y4\u00de\u00f0x2 \u00fe y2\u00de \u00fe 4384:6y4 87692:y3x\u00fe :49327e6y2x2 :54807e6yx3 \u00fe :17127e6x4 \u00bc 0 The first equation is combined with a line equation, 12\u2018 + 25m + 1 = 0, to get the solutions, while the second one is combined with a circle, x2 + 12x + y2 25y = 0. Six sets of solutions can then be solved as listed in Table 5. All 6 possible configurations of this Assur 5-link are plotted and shown in Fig. 6. 5 ons for Example 2 \u2018 m x y 2.7250E 02 2.6920E 02 18.57 18.35 5.7144E 02 1.2571E 02 16.69 3.67 1.3890E 02 3.3333E 02 10.65 25.56 4.3411E 03 3.7916E 02 2.98 26.03 1.6867E 01 1.2096E 01 3.92 2.81 2.9772E 02 5.4291E 02 7.77 14.16 One special problem may arise when the line passing through both origin and the pivoted point, such as the point C in Example 2, is a nontrivial solution. For this specific line, both \u2018 and m now approach infinity. On the other hand, the origin becomes a nontrivial solution if the second method is used"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002672_tmag.1983.1062820-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002672_tmag.1983.1062820-Figure2-1.png",
        "caption": "Figure 2 : Curvilinear finite elements a - six-noded element.",
        "texts": [
            ", t} with : c = - A is the vector potential and A . are the nodal values of A - aoi: ani, bn. are the coefficients of the Fourier serles of the functions ( a, (c, 6 ) ) chosen on the AGE curvilinear boundaries [2j. (See APPENDIX). - S is the number of commpn nodes to the AGE and the adjacent finite elements subdividing the rotor. On the AGE-2 curvilinear boundaries the functions Ct.(c,B) are represented b y the second order Lagrangian pAlynomials obtained from the shape functions of the classical second order curvilinear finite elements [2] (Fig.2 , Fig.3.). In the case of periodicity condition the coeffi- cient An (see eq. ( 7 ) ) is given by X = 3 . When we consider one pole-pitch as a solution domain A- can be \\m<tten as : n 6 0 Where B1 = % ; in this case, the first term of ( 7 ) is equal to zero. 2 Not e that the use of the curvilinear elements gives a better consistency with the AGE than the first order straight side elements. Examples : -- To check the validity of the AGE-2 model we compare a known solution (A = kr6 - COs(6 e ) ) to both of the classical finite element method and the proposed one"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000041_1.1392031-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000041_1.1392031-Figure4-1.png",
        "caption": "Figure 4. Schematic illustration of the hydraulic arrangement: (A) electrochemical cell, (B) counter electrode, (C) independent current feeders, (D) centrifugal pump, (E) heat exchanger, and (F) valving and bypass system.",
        "texts": [
            " Figure 3d presents 2934 Journal of The Electrochemical Society, 146 (8) 2933-2939 (1999) S0013-4651(98)08-021-5 CCC: $7.00 \u00a9 The Electrochemical Society, Inc. the configuration where all the graphite layers are short\u2013circuited to each other. This configuration is similar to a traditional flow-through electrode if the thickness of the separators can be neglected. Two intermediate configurations (a five\u2013section and a two\u2013section arrangement) were also used, as shown, respectively, in Fig. 3b and c. Flow system.\u2014Figure 4 presents a schematic illustration of the hydraulic arrangement, consisting of the electrochemical cell (A) connected to a centrifugal pump (D) and to a heat exchanger (E). The heat generated by the pump and by Joule heating during electrosynthesis corresponds to approximately 1 kW at the maximum current density employed and is evacuated by the heat exchanger to ensure isothermal operation. The system is operated at 208C, well below the 408C D\u2013arabinose degradation temperature. A valving and bypass system (F) allows the electrolyte flow rate to be varied between 0 and 60 L/h"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003364_roman.2006.314484-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003364_roman.2006.314484-Figure5-1.png",
        "caption": "Fig. 5. Movements of humans (X-Y plane) (Human Hand)",
        "texts": [
            " manner as the handing-over motion. The subjects are 20 healthy students (10 pairs) from 20 to Fig.7 shows the histogram of the undamped natural 24. All the subjects are right-handed. frequency w, which is estimated by the analysis of the handshake motion between humans. This figure shows the B. Analysis result undamped natural frequency w for trials 1-5, 26-30, and Figs.4-6 show an example of the trajectory of the hand- 46-50. In the first time meeting (trials 1-5), the distribution shake motion between humans. Fig.4 and Fig.5 show the of the undamped natural frequencies has two peaks (w = 6, paths on the X-Z plane and X-Y plane, respectively. Fig.6 w = 15). However, in the trials 26-30, the distribution of shows the velocity profiles. the undamped natural frequencies has only one peak at w = In the X-Z plane, the subjects at the request side and 15. This tendency is also exhibited in the trails 46-50. This response side move their hands upward along a smooth result shows that the subjects have mastered the handshake curved path, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002976_tec.2003.821833-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002976_tec.2003.821833-Figure3-1.png",
        "caption": "Fig. 3. Principle of the compensation method.",
        "texts": [
            " This fact gives the presented method the name compensation method and it is used in the following 0885-8969/04$20.00 \u00a9 2004 IEEE manner: by having two impedance circle diagrams with additional information about the slip, the rotor temperature difference between points of identical slip can be determined. The first impedance circle diagram is called the reference diagram (ref) and the other the measurement diagram (meas). Fig. 2 shows the schematic structure of the test machine. Machine nameplate data are summarized in Table I. The principle of the compensation method is given in Fig. 3: There are the measured impedance circle diagrams of two starts of the test machine presented. The impedance phasor moves clockwise during the starting operation. The points of the measurement diagram and of the reference diagram have identical slip but not identical phasors. Because the rotor temperature during the measurement start was about hotter than during the reference start, the point corresponds to point of the reference. How to use this qualitative effect to quantify the temperature difference is shown in Section III"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002566_s0022-0728(83)80533-6-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002566_s0022-0728(83)80533-6-Figure1-1.png",
        "caption": "Fig. 1. Voltammetric curve for 4.6\u00d7 10 -4 M MPPD in 0.1 M Et4NC104 +CH3CN at a Pt rotating-disc electrode (diameter 1 mm, N = 10 rot. s - l ) . (1) MPPD in the neutral medium; (2) after oxidation at 0.20 V to one electron per molecule; (3) after complete oxidation at 0.70 V; (4) as (1) except for addition of n-Bu 4 NOAc, 1,4\u00d710 -3 M AcOH buffer; (5) as (4) after oxidation at 0.10 V to two electrons per molecule.",
        "texts": [
            " Indeed, a continuous decrease of the absorption of PHi-\" (560-800 nm range) was observed with the simultaneous growth of a band at 510 nm after a partial oxidation at 0.25 V (nap p < 0.5), whereas this decay was very small after a complete one-electron oxidation under the same conditions. In the second case PHi-\" showed a half-life of one day in a closed spectroscopic cell. A total transfer of 2.0 mol of electrons m o l - 1 was measured during oxidation at 0.75 V and the resulting solution gave a voltammetric curve with two cathodic waves with El~ 2 values equal to those shown by MPPD (Fig. 1, curve 3). The absorption spectrum showed the existence of a mixture of PH 2+, as the main species, and of PH +. After addition of two equivalents of HC104, the protonated form PHi- gave one anodic wave at 0.53 V (na_ p = 1.6) and an oxidation at 0.80 V was completed with 2.0 mol of electrons mol -~ ' fo r the generation of PH 2+ in a nearly quantitative yield. Periodic moni tor ing of the absorpt ion spectrum (see Table 1) showed that the acidic solution of PHi-\" was stable for some hours. Similarly, oxidation at 0",
            " As an example, solutions of D P P D with two equivalents of the basic buffer n -Bu4NOAc, A c O H or 2,6-1utidine gave two-electron waves at - 0 . 1 7 and 0.06 V respectively, and after oxidat ion at 0.20 V the quinone diimine P was identified by compar ison with the properties of an authentic sample [27]. Controlled acidification of this solution gave the monopro - tonated diimine PH + (Table 3). A solution of M P P D with three equivalents of the acetate buffer gave a two-electron wave at - 0.30 V (Fig. 1, curve 4). The coulometry at 0.1 V showed the consumpt ion of 2.0 mol of electrons m o l - i for the quanti tat ive generat ion of the stable diimine P (Table 3). Successive additions of HC104 were followed by absorpt ion spectroscopy and showed the consecutive format ion of PH + and of PH~ +. After addit ion of two equivalents of 2,6-1utidine, the cyclic vo l tammogram of M P P D exhibited a quasi-reversible two-electron process (AEp = 0.09 V) with a limited stability of the dioxidized species PH + in this medium",
            " The observation of PHf\" at short times concurrently with the observation of the spectrum of PH + as the main dioxidized species is consistent with an EEC r mechanism where the reproportionation (3) is mainly replaced by the deprotonation (6) followed by reaction (9) and (5). PH 2 - 2 e ~ PH 2+ (1) + (2) PH~ + ~ P H + + H + (6) As for the pure EE process, the maximum of (AR/R)pH;. on the cathodic part of the pulse is a further proof for the existence of a homogeneous redox reaction. With the actual EECr process the overall reaction is characterized by a broad maximum on curve 2 of Fig. 1 l, the broad shape results probably from the kinetic control of reaction (5). Control experiments showed that the one-electron oxidation of phenylenediamines 1 under DPSC conditions gave the spectra of 1 +\" identical to the spectra obtained in bulk solution (Table 1). For modulation pulses spanning the two waves the spectra were mainly due to 2. The gross feature of the A R / R - t transients for 3,7-dimethoxyphenothiazine were again observed with amines 1 in CH3CN. As an example, optical monitoring of PHi-\" at 700 nm during a potential step 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003854_tmech.2005.852450-Figure11-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003854_tmech.2005.852450-Figure11-1.png",
        "caption": "Fig. 11. Theoretical result of reachable area obtained by rotating the active (first) link counterclockwise (\u03c3min < \u03c3 < \u221e).",
        "texts": [],
        "surrounding_texts": [
            "From the above discussions, the tip of the free link can reach all the points on the stable equilibrium surface in Figs. 2 and 3 and these points are stable. In this section, we investigate the reachable and stabilizable areas for the tip of the free link. Physical parameters of the experimental setup which correspond to the subsequent experiment are m1 = 1.10 \u00d7 10\u22121 kg, m2 = 2.14 \u00d7 10\u22122 kg, l1 = 1.02 \u00d7 10\u22121 m, l2 = 1.00 \u00d7 10\u22121 m l1g = 5.70 \u00d7 10\u22122 m, l2g = 1.65 \u00d7 10\u22122 m, I1 = 2.60 \u00d7 10\u22124 kg\u00b7m2, I2 = 1.74 \u00d7 10\u22125 kg\u00b7m2. The values of the dimensionless parameters, \u03c3 and c, in (7) and (8) are as \u03c3 = m2l2g g (I2 + m2l22g )\u03c92 = 1.43 \u00d7 102 \u03c92 c = m2l1l2g I2 + m2l22g = 1.49 where the parameter \u03c9 expresses the excitation frequency of the active link. The excitation amplitude of the active link a\u03b81 is set at 0.055 in the subsequent experiment. We can numerically obtain the equilibrium points of the tip of the free link from (8) for combinations of \u03c3 and \u03b81off . Furthermore, their stabilities are examined by (7). For the excitation frequency range between 0 and \u221e, all stable equilibrium points are plotted as Fig. 10, where \u03b81off is changed in the range from 0 to \u03c0. The reachable and stabilizable area in this figure expresses one of the cases when we rotate the active (first) link counterclockwise. The origin of this figure is the origin O in Fig. 1. This area and the reachable and stabilizable area for the case when we rotate the active link clockwise, i.e., for the range of \u03b81off from 0 to \u2212\u03c0, are symmetric with respect to the x-axis. As a result, the union of these areas is the reachable and stabilizable area of the tip of the free link. Furthermore, taking into account the limitation of the power of the motor used in the subsequent experiment, i.e., the limitation of the excitation frequency in the subsequent experiment (the highest excitation frequency is \u03c9max/(2\u03c0) = 50 Hz), the reachable and stabilizable areas are modified as Figs. 11 and 12 for counterclockwise and clockwise rotations of the active link, respectively. Here, the minimum value of \u03c3 corresponding to the maximum excitation frequency \u03c9max is expressed as \u03c3min = 1.43 \u00d7 102 \u03c92 max . (9) The configurations of the manipulator, in which the tip of the free joint is at the positions, (b)U\u2212, (a)U 0, (b)U +, (c)U +, and (d)U +, are also represented in Figs. 11 and 12. It is seen from these figures that the reachable and stabilizable area becomes a little smaller due to the limitation of the excitation frequency."
        ]
    },
    {
        "image_filename": "designv11_24_0002960_tac.2004.825651-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002960_tac.2004.825651-Figure1-1.png",
        "caption": "Fig. 1. Schematic configuration of a multibody attitude system in a uniform gravitational field with a reaction wheel and a proof mass actuator.",
        "texts": [
            " According to Noether\u2019s theorem and the assumption that the system is initially in equilibrium, we have , . This implies . Thus, we obtain the simplified control model: , , where is the shape acceleration control. The previous equations, with viewed as an input, have been studied for numerous examples of multibody systems with -invariant potential [37]. 2) Multibody Attitude Systems: Consider the following class of multibody attitude systems: the base body rotates about a fixed pivot point in a uniform gravitational field; see Fig. 1 for a schematic configuration illustrating a base body, a reaction wheel and a proof mass actuator. A base body fixed coordinate frame is chosen with its origin located at the pivot point. The configuration manifold is , where represents the base body attitude, and . Here, represents the base body angular velocity expressed in the base body frame and is the usual isomorphism. The reduced kinetic energy is given by where is symmetric and positive definite for all . The inertial coordinate frame is chosen with the origin located at the pivot point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002229_1.346386-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002229_1.346386-Figure4-1.png",
        "caption": "FIG. 4. Schematic representations of the energy-band-gap splittings and shifts at k =, 0 due to biaxial strain in the crystallographic direction perpen dicular to the biaxial stress planc.",
        "texts": [
            " Strain-induced band shifts The dependencies of the band edges under strain, which have been extensively investigated from theoretical and ex perimental points of view in compound semiconductors, 17-19 provide the framework to explain the measured PL shifts and to determine quantitatively the values of the strains. For a zinc-blende-type material, the valence band at k = 0 con sists ofa fourfoldP3/2 (J = 3/2, mj = + 3/2, \u00b1 112) and 11 twofold Pl/ 2 (J = 1/2, mj = \u00b1 112) multiplet. The expect ed behavior of the upper valence bands and lower conduc tion band under biaxial strain is shown in Fig. 4. Note that under biaxial strain, the P3/2 multiplet band is split into 3340 J. Appl. Phys., Vol. 68, No.7, 1 October 1990 heavy- and light-hole valence bands labeled as VI (J = 3/2, m = + 3/2) and V2 (J = 3/2, mj = \u00b1 112), respectively. l~ addition, the hydrostatic component of the strain shifts the center of gravity of this pair and the Pl/2 multiplet band, V, , relative to the conduction band. Thus, the band gap de cr~ases (increases) with biaxial tension (compression) as the valence bands move toward (away from) the conduction band"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003109_2004-01-3027-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003109_2004-01-3027-Figure1-1.png",
        "caption": "Figure 1. Shifting Clutch Powertrain Model",
        "texts": [
            " In previous work we examined the stability requirements for continuously slipping clutches, particularly the torque converter clutch [2, 3]. The objective of this paper is to analyze powertrain stability and shift quality during the engagement of a shifting clutch in an automatic transmission and determine how stability and shift quality are affected by the friction-related properties of the ATF and friction material \u2013 \u00b5, \u2202\u00b5/\u2202v, \u2202\u00b5/\u2202P and \u2202\u00b5/\u2202T. The basic elements of the powertrain model are the engine, turbine and driveline (Figure 1). The engine has inertia Ie (all components tied to the crankshaft) with speed \u03c9e(t) and brake torque \u03c4e(\u03c9e). The turbine has inertia It (components from the impeller of the torque converter to the turbine side of the shifting clutch), viscous damping ct and speed \u03c9t(t). The turbine is assumed to be rigid compared to the driveline. The torque converter clutch damper is not included. The driveline includes all powertrain components from the output side of the shifting clutch to the road. The reference \u201cvehicle\u201d speed, \u03c9v, is assumed to be constant during the shift, and Id, cd, and kd are the equivalent inertia, damping, and stiffness between the output of the clutch and the reference speed \u03c9v"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003266_1.2179462-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003266_1.2179462-Figure8-1.png",
        "caption": "Fig. 8 The FC2 , FC3 range as a parallelogram \u201eFC1 =0.907, no solution\u2026",
        "texts": [
            " Once the interval for FC1 is found, we vary the value of FC1 lume representation in this interval and check if a solution exists. Starting from one Transactions of the ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F side of the interval, say FC1 min * , we check if a solution exists by computing the ranges for the other two force components FC2 and FC3 for the current FC1 value using Eqs. 17 and 18 , and check if there is a set of values for FC2 and FC3 in these ranges that also satisfies the EC3 * conic section inequality equation Eq. 19 . Figure 8 shows this process of checking the existence of a solution for a value of FC1 in its interval. The ranges for the two force components FC2 and FC3 are represented as a parallelogram on the force space graph as shown in Fig. 8. For this particular FC1 value, the FC2 ,FC3 parallelogram does not intersect with the conic section EC3 * , and thus no solution exists for this FC1 value. This process is continued until a solution intersection between Fig. 7 Finding the initial range for FC1 Using EC1 * and EC2 * rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/27/201 the FC2 ,FC3 parallelogram and the conic section EC3 * is found, or until the end of the FC1 interval is reached. For this example system, a solution is found before the end of the FC1 interval is reached, and this first intersection between the parallelogram and the conic section is shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002290_1.1538192-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002290_1.1538192-Figure1-1.png",
        "caption": "Fig. 1 Typical traction contact",
        "texts": [
            " Copyright \u00a9 2Journal of Tribology rom: http://tribology.asmedigitalcollection.asme.org/pdfaccess.ashx?url= Overall, the relative motion between the contacting surfaces of an EHD contact is manifold and complex. To simplify the study the authors embraced Johnson approach @1#, who considered that each point on the contact area has three distinct components of slip such as: 1! The longitudinal relative motion ~slip! that occurs along the rolling velocity along x-axis. This relative motion occurs whenever any power is transmitted through the contact, Fig. 1. 2! Relative motion occurring in a direction perpendicular to the rolling velocity along the y-axis ~side slip!. This relative motion is caused by the misalignment of the shafts that support the rolling elements in contact. 3! The relative rotational motion about an axis normal to the contact area known as spin motion along z axis. This relative motion is the by-product of the kinematics of the variable speed traction drives. The slip and side-slip velocities are constant over the contact area. The spin takes place along the common normal to the contacting surfaces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003766_0278364906061159-Figure11-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003766_0278364906061159-Figure11-1.png",
        "caption": "Fig. 11. Connection of head unit.",
        "texts": [
            " This device is a foot pump. When using this device with the Slime Scope, an accumulator and a pressure reducing valve will be installed between them. The tube unit (Figures 9 and 10) is made of airtight and flexible material that can also bear the inner pressure. We used Kevlar fiber lined with urethane rubber, which is not expensive. The model we developed this time has a hose that is 80 mm in diameter, 0.5 mm in thickness, and 3000 mm in length. The tube specifications are shown in Table 1. As shown in Figure 11, the head unit and tube unit are fixed by a power supplying wire inside the tube. Therefore, when the tube expands at the velocity u, as shown in Figure 11, the inner wire will come out at twice that speed, 2u. As a result, Table 1. Tube Unit Specifications Diameter of tube 80 (mm) Length of tube 3000 (mm) at Virginia Tech on March 14, 2015ijr.sagepub.comDownloaded from at Virginia Tech on March 14, 2015ijr.sagepub.comDownloaded from Table 2. Head unit specifications Diameter 90 (mm) Weight 400 (g) Fig. 13. Head unit. extra wire will pile up at the end. To make the head unit follow the tube, it is necessary to wind up the excessive wire length. Therefore, we added a wire-rewinding device to the head unit (Figure 12)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001203_oca.4660140405-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001203_oca.4660140405-Figure3-1.png",
        "caption": "Figure 3. Geometry for defining inequality (22)",
        "texts": [
            " (Note that Ef is considered as a fixed target.) This boundary consists of the circular arcs with their respective centres at 01 and 0 2 of radius (17) as shown in Figure 2. Therefore the point Ef(xer,Yef) is called \u2018permissible\u2019 if it satisfies the inequalities (18) (19) Let Se, be the set of permissible points Ef(xef ,Yef) and a&, be the boundary of this set (see Figure 2), determined by the circular arcs A I A z A ~ and A3&AI. Now we construct a circle of radius RO with its centre at O(0,O) as shown in Figure 3, denoted in the sequel as CR,, c Se,. This allows us to consider the evader\u2019s motion, starting at Eo(Ro cos $0, Ro sin $ 0 ) E Se,, to the boundary a&, and the respective motion of the pursuer in the interception. Owing to symmetry, it is sufficient to consider the upper part of a&,, determined by the circular arc A3&A1 and denoted in the sequel as a S f . We further assume that during the interception the evader trajectory remains in Sef, i.e. P = d(ri + R:) X b + (Yet- rpI2 2 r i + R f . df + (Yef + rp)\u2019 Z r i + R : E(t) = [xe( t ) ,~e( t ) l E Ser V t E 10, tfl (20) Let tem(Zef,Jef) be the minimum time for the evader to reach a given fixed point &(Zer,Jer) \u20ac from the circle CR,,. Let tp(Zef, Per) be the time of capture at Ef along a trajectory belonging to category (a). On the basis of these definitions the inequality fp(gef, Per) < te,(Zef, Per) V(Zef, Per) E 8s:: (21) is the sufficient condition for satisfying (1 8)-(20). is fixed, it is clear (see Figure 3) that the fastest evader movement from the circle CR,, to the point Efc aStr is along the straight line passing through the points 0 and Ef. This line defines the point Eo, on C R ~ . From Figure 3 it can also be seen that the time tern(&, Yef) decreases as & \u20ac as,\u201c, moves from A3 to A4 and it increases as E f \u20ac moves from A4 to A1. Moreover, tp(Zer, Per) increases as Ef E aSZr moves from A3 to A,. Since the point & \u20ac It can thus be concluded that one can replace (21) by tp(xef, Per) < te,(Zef, Per) v(Eer, Per) 6 8s;\u2019 (22) and consequently u/2 Q $0 Q u. Moreover, as Ere 8s:' moves from PLq to AI, $0 varies from u/2 to u and vice versa. From Figure 3 we have by inspection that for the 'limit' trajectory where ) ([c: + (Rf/Ro)21 -&p cos $0 a i! cos-1 The formulae (24) and (25) allow us to replace (22) by fP(&P, $0) Gfe(&p, $0) v$o [+, a1 a f P / a & P > 0 It is easy to verify that and afe/a&, < 0, $o\u20ac [+, a1 Since f P ( 0 , $ 0 ) = 0 f e w , $ 0 ) = ( I / Ve)(l - Rf/RO) > 0 fP(&P, $0) =fc(ep, $0) and the equation has a unique positive solution iP($o) V$O E [a/2,a], characterized by fP(&P, $0) < f e ( & p , $ 0 ) VEp \u20ac [O, ip($O)l fP(&P, $0) >fe(&p, $0) VEp > iP($O) &p G iPP$O) v$o \u20ac [+, a1 Thus the inequality satisfies (31)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002596_j.1749-6632.1984.tb29825.x-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002596_j.1749-6632.1984.tb29825.x-Figure3-1.png",
        "caption": "FIGURE 3. Electrochemical cells used for electroenzymatic or electromicrobial reductions. A: With a rotating cylindrical cathode, catholyte volume of about 150 ml. I - Glass cell; 2 = 60 mm (height) x 50 mm (diameter) lead cathode with circular perforations midway; 3 - insulated steel wire, contacted to the cathode with its end dipped into the mercury pool 4; 4 - mercury contact; 5 = cylindrical perspex separator with perforations for suppressing vortex formation by the rotating cathode; 6 = counter electrode; 7 = contact to the working electrode; 8 = reference electrode; 9 = perspex cell cover; 10 = tube for electrolyte sampling; 11 = thermostating coat; I2 = Nafion membrane, separating catholyte from anolyte, tightly clamped between the mainframe of the cell cover and the Teflon nut 16; 13 = openings for thermometer, gas inlet and outlet; 14 = flexible Luggin capillary for measuring potential variations along the surface of the cathode; 15 = Teflon rotor with magnet and rings firmly fixing the cylindrical electrode onto the rotor; 16 = Teflon nut; and 17 = tube with sintered glass for bubbling inert gas. B: With mercury pool cathode, catholyte volume 7-20 ml. 1 = glass cell; 2 - mercury cathode; 3 = platinum wire for electrical contact; 4 = anode; 5 = anode compartment closed at one end by a VycorR tip; 6 = reference electrode; 7 and 8 = rubber caps as oxygen-tight seals for reference electrode, gas inlet and outlet, and for withdrawing of samples through syringe.",
        "texts": [
            ": PREPARATION OF CHIRAL COMPOUNDS 177 rate of reduction of enoates with reduced methylviologen is about I .5 times faster than that with saturating concentrations of NADH. Some kinetic data can be seen from TABLE 4. The pH dependence of Reaction 5 can be seen in FIGURE 2. That for Reaction 4 is given el~ewhere.'~ As shown in TABLE 5 , enoate reductase from C. sp. La I can be purified in a rather simple way with satisfying yieldsz6 Electroenzymatic or the later described electromicrobial reductions can be conducted in different electrochemical cells. FIGURE 3 shows rather simple and more sophisticated ones. In cell A, 1 mmol of product can be produced per hour. We assume that the volume productivity can be enlarged by a factor of 3 by rather simple means. In cell B, 50-100 pmol product/h can be produced. Besides enoate reductase, we detected a further versatile enzyme for stereospecific reductions. This so far unknown 2-0x0-acid reductase from Proteus mirabilis as well as Proteus vulgaris catalyzes in a nonpyridine nucleotide-dependent reaction the reduction of 2-0x0-carboxylates (Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000273_0167-8442(94)00004-2-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000273_0167-8442(94)00004-2-Figure3-1.png",
        "caption": "Fig. 3. Testing device.",
        "texts": [
            "68a 7 + 92.355a 8 (24) The part KF~ in Eq. (17) for extension can be written as Fy Vr~-~- yt ( a ) (25) K Fy = _ - ~ where use is made of Eq. (9). The shape factor Yt(a) for the gear tooth is assumed to be the same as that for the compact tension specimen, i.e., + m a - x 2 d x The specific form of Yt(a) is already given by Eq. (20). To summarize, Eq. (17) takes the form K = - ~ ~ cos 4) - ~ sin 4) Ym(~) s 1 - - - i n 4~Yt(a ) (27) 6L 3. Experimental approach The experimental setup is shown in Fig. 3. The gear test piece [1] has 18 teeth supported 190 mm apart. The distance L in Fig. 2(a) is 15 mm. This corresponds to a three-point bend test for determining the shape factor. The gear is made of AISI 4130 steel, the chemical composition of which is given in Table 1. The mechanical and fracture properties can be found in Table 2. A least square fit is made for the experimental data. Y(a) = 2.2486135 - 3.7173537a + 33.95a 2 - 137.5356a 3 + 210.91a 4 (28) more elaborate stress analysis would have to be made"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001020_analsci.8.553-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001020_analsci.8.553-Figure6-1.png",
        "caption": "Fig. 6 K+ measurements of sera in the normal concentration range (3.5 -5.1 mM K+) (see also Fig. 4).",
        "texts": [],
        "surrounding_texts": [
            "ANALYTICAL SCIENCES AUGUST 1992, VOL. 8\nof the activities of the sample solution at(s) versus IOEMFx/s should equal ai(r). Using the Debye-Hi ckel formalism22 a(r) was calculated to be 104.5 mM and 3.13 mM for Na+ and K+ respectively. This is indeed the case for our ab initio measurements. For aqueous solutions the agreement between the fitted values and the theoretical values is very good. The slope of the correlation line for K+ measurements equals 3.14 mM and the one for Na+ measurements is 104.1 mM (see Figs. 4, 5 and Table 1). For sera in the normal concentration range (e.g. 3.5 -\n557\n5.1 mM K+, 136 -145 mM Na+) the a(r) values for K+ measurements is 3% too low, whereas for Na+ measurements they are 3% too high. Liquid junction errors, therefore, are not giving a systematic bias. For both electrolytes the standard deviation syx found is very similar to the one obtained when measuring aqueous solutions (K+, 0.02 mM versus 0.06 mM; Na+, 1.4 mM versus 1.2 mM; see Table 1 and Figs. 6 and 7). As far as sera in the pathological concentration range are concerned (e.g. 2.5 - 7.6 mM K+,115 -161 mM Nat, respectively) the K+ measurements are in very good agreement with the theoretical value (3.15 mM found\nplasticizer and PVC as the matrix. The diffusion barrier as presented in Fig. 2 was employed. The y-axis shows the activities a1(s) of the potassium reference solution values (of the following concentrations: 2.75, 3.25, 4.25, 5 and 5.75 mM K+, respectively), the x-axis indicates the expression 10EMFx/s.\n10EMFx/ s.",
            "558 ANALYTICAL SCIENCES AUGUST 1992, VOL. 8\ncompared to 3.13 mM expected, see Fig. 8). The Na+ values are still 3% too high, compared to the theoretical value (108 mM measured compared to 104.5 mM expected, see 4 mM. Deviations\nof the measured a;(r),",
            "ANALYTICAL SCIENCES AUGUST 1992, VOL. 8\ntheoretical values, are only found when measuring serum samples, not aqueous solutions. They may therefore be explained by uncertainties in the calibration of FAES, by uncertainties in the protein/ lipid volume effect of 7%, by unusual liquid junction potentials of the reference electrodes in contact with serum samples or by uncertainties due to the Debye-HUckel formalism, which perfectly describes aqueous systems, but not necessarily serum samples. The increase in the standard deviation for assays of sera in the pathological concentration range as compared to those in the normal concentration range (4.0 versus 1.4) is not due to measuring errors but most\nprobably to biological phenomena like protein or bicarbonate binding.23,24 This hypothesis is supposed by similar results obtained by independently performed measurements with a sodium glass electrode (111.2 mM= a;(r), syX=4.3 mM). As the results clearly show, a correction for changes in the liquid junction potential AED using the Henderson formalism15 is obsolete (see also Table 1). Thus, not only assays without any previous sensor calibration have become accessible, but in addition they need much less assumptions on calculations. Therefore, the described measurements could easily be performed in a doctor's office. Nevertheless, the most challenging action supported by the symmetric ion-selective assembly will be the standardization of ion activities in reference materials.25 The efforts of official centers in Japan, USA and Europe aim at defining primary standards for ion-selective measurements. Uncertainties in ion activity evaluations were mainly attributed to the influence of proteins on the liquid junction potential and were shown to be attributable to membrane asymmetries induced by the biological sample. The presented procedure allows to evaluate, quantify and eliminate different sources of errors and is thus suitable for the determination of ion activities ab initio.\nThis work was partly supported by the Swiss National\nScience Foundation and by Ciba-Corning Diagnostic Corp.\nReferences\n1. U. Oesch, D. Ammann and W. Simon, Clin. Chem., 32, 1448 (1986). 2. N. Fogh-Andersen, T. F. Christiansen, L. Komarmy and 0. Siggaard-Andersen, Clin. Chem., 24,1545 (1978). 3. U. Oesch, D. Ammann and W. Simon, in \"Methodology\nand Clinical Applications of Ion Selective Electrodes\", ed. A. H. J. Maas, F. B. T. J. Boink, N.-E. L. Saris, R. Sprokholt\nand P. D. Wimberley, p. 273, Interprint A/ S, Copenhagen, 1986. 4. H. W. Buhler, G. G. Rumpf, L. F. J. Durselen, U. E. Spichiger and W. Simon, \"Calibration free measurements with ISEs in clinical chemistry: the benefit of symmetrical\n559\ncells\", ed. A. H. J. Maas et al., p. 315, Elinkwijk, Utrecht, 1989.\n5. J. Koryta (ed.), \"Medical and Biological Applications of Electrochemical Devices\", John Wiley and Sons, Chichester, New York, Brisbane, Toronto, 1980. 6. M. Kessler, L. C. Clark, D. W. LUbber, I. A. Silver and\nW. Simon (ed.), \"Ion and Enzyme Electrodes in Biology and Medicine\", Urban & Schwarzenberg, Munchen, Berlin, Wien,1976. 7. J. D. Czaban, Anal. Chem., 57, 345A (1985). 8. P. Nabet, Analysis, 15, 379 (1987). 9. M. Rouilly, B. Rusterholz, U. E. Spichiger and W. Simon, Clin. Chem., 36, 466 (1990). 10. E. Wang, Diss. ETH Zurich, No. 9035, 1989. 11. K. Cammann, \"Das Arbeiten mit Ionenselektiven Elek-\ntroden\", 2nd ed., Springer-Verlag, Berlin, Heidelberg, New York, 1977. 12. R. G. Bates, \"Determination of pH. Theory and Practice\", 2nd ed., p. 73, Wiley, New York, London, Sydney,\nToronto, 1973. 13. J. A. Illingworth, Biochem. J., 195, 259 (1981). 14. A. K. Covington, P. D. Whalley and W. Davison, Anal. Chim. Acta,169, 221 (1985). 15. R. Dohner, D. Wegmann, W. E. Morf and W. Simon, Anal. Chem., 58, 2585 (1986). 16. L. F. J. Durselen, D. Wegmann, K. May, U. Oesch and\nW. Simon, Anal. Chem., 60,1455 (1988). 17. C. G. Fraser, \"Interpretation of Clinical Chemistry Labo-\nratory Data\", p. 124, Blackwell Scientific Publications, Oxford, 1986. 18. J. G. Batsakis, R. N. Barnett, R. K. Gilbert, G. F. Grannis and T. Peters, \"Analytical Goals in Clinical Chemistry, College of American Pathologists (CAP)\", CAP Conference, Aspen 1976. In Proceedings of the Aspen Conference on Analytical Goals in Clinical Chemistry, ed. F. R. Elevitch, College of American Pathologists, Vol. 3, 1976, p. 1. 19. D. P. Brezinski, Analyst [London], 108, 425 (1983). 20. G. G. Guilbault, R. A. Durst, M. S. Frant, H. Freiser, E. H. Hansen, T. S. Light, E. Pungor, G. Rechnitz, N. M.\nRice, T. J. Rohm, W. Simon and J. D. R. Thomas, Pure Appl. Chem., 48,127 (1976). 21. G. G. Rumpf, L. F. J. Durselen, H. W. Buhler and W. Simon, \"Opportunities and limitations in the use of ISEs in clinical chemistry: Assays without calibration?\" in \"Contemporary Electroanalytical Chemistry\"\n, ed. A. Ivaska et al., p. 305, Plenum, New York, 1990.\n22. P. C. Meier, Anal. Chim. Acta, 36, 363 (1982). 23. R. L. Coleman and C. C. Young, Clin. Chem., 28, 1936\n(1982). 24. H. G. J. Worth, Analyst [London], 113, 373 (1988). 25. U. E. Spichiger and G. Rumpf, \"What Do Ion Sensors Really Measure?\", in Proceedings of the 13th International Symposium of IFCC/JSCC-WGSE on Methodology and Clinical Applications of Blood Gases, pH,\nElectrolytes and Sensor Technology, October 6 - 9, 1991, Hakone, Japan, Vol. 13.\n(Received March 30, 1992) (Accepted May 18, 1992)"
        ]
    },
    {
        "image_filename": "designv11_24_0003032_s1474-6670(17)55336-7-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003032_s1474-6670(17)55336-7-Figure3-1.png",
        "caption": "Fig . 3 . Dr i ving - ax i s coor d i na t e Gys t ems for two typ i cal robo t s",
        "texts": [
            " NUMBER OF ARITHMErIC OPERATIONS FOR THE INVERSE DYNAMICAL SYSTEM By observing today's modern industrial robots we define a today's industrial robot as follows to distinguish it from a general open chain: A today's industrial robot is a manipulator, 1) whose joints are either perpendicular or parallel to one another, i.e. 9' and 3 are multiples of 900; 2) of which the principal axes of every link align wi th the coordinates of the corresponding body-fixed frame; 3) whose distance vectors from the origins to the respective centers of mass have maximal only 2 non-zero components because of geometrial symmetry. To demonstrate the efficiency of the algorithm derived above we select two typical robots: a horizontal arm and a Stanford arm. Their geometrical parameters and coordinate frames are shown in fig. 3. The numbers of arithmetic operations for every step are presented together TABLE 1 Number of Arithmetic Operations Driving Axie Coordinate System Transmittin g Axis coo rdi nat e Syste m General Open Chain s i c: n-ID M: '2'(n-.) + \"9. - 3 - 93 ( '-K, ) _ 106Kl A: 96n -2 s Ic : n-ID M: 123 (n-m ) ... 125 m - 3 - 7 4 (I -Kl ) - \" OKl A: 97 ( n-:n ) \u2022 10 l m - 2 - 79 ( '-K , ) - 8 9 Kl - 68( '-Kl ) - 8 7Kl Today's s Ic : n-ID s I c : n-m Industrial M: 7 3 (n-lII) + 53m - 2 (I-K 2 ) M: 73 (n-. ) + 53"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003487_acc.1995.520970-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003487_acc.1995.520970-Figure1-1.png",
        "caption": "Figure 1: Acrobot Schematic",
        "texts": [
            " In particular, the Kuhn-Tucker optimality conditions {see Bazarra and Shetty [l]} are checked, andor a standard nonlinear programming code is given the found answer as an initial guess for checking. Also, if the Kuhn-Tucker conditions are not satisfied, i.e., if the multiplier associated with a tight constraint uk 5 u ~ , ~ ~ ~ or uk 2 u ~ , ~ ~ ~ has the wrong sign, this fact is used in the next initial guess for TS by assuming that uk was supposed to have been at its other bound. Simulation Case Study The learning algorithm was applied with success to the problem of the acrobot, illustrated below in Figure 1. The initial state of the system is the \u201cstraight down\u201d position (i.e., 0, = 0 , 0, = 0 ) at rest, and the desired terminal state is the \u201cstraight up\u201d position (i.e., 0, = x , 8, = 0), also at rest. moments of inertia of the two links by m, , m, , I , , I , (which take into account the motor inertia at the second joint), their center of mass positions by I,, , l,, , which are measured from the joint of each respective link, the link lengths by I , , and l2 , and the gravitational acceleration by g"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000944_s0094-114x(96)00075-4-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000944_s0094-114x(96)00075-4-Figure3-1.png",
        "caption": "Fig. 3.",
        "texts": [
            " Substituting equations (12) and (14) into the above equation and comparing them with equations (15) and (16), respectively, we find that the following relationships exist among co, v and ,t*, fl*: v = ~* da fl, da 7 ? o , = dv ~z,,fda']2 ,d2a \"~ = \\ d / j 2 + ct -d-\"~' do9 ~,,/do\"X ~, d2a (18) The above equations reveal the kinematic meanings of ~* and fl*. They are all invariants of spatial motion. Based on the Appendix, the spherical image curve Cm of ~=~ rolls on the spherical image curve Cr of ~f~, shown in Fig. 3. Therefore, there is a unified form of instantaneous invariants for planar, spherical and spatial motion [l] and a spatial motion up to nth order can be represented by these instantaneous invariants as well as their derivatives. 5. THE P O I N T S W I T H SPECIAL KINEMATIC M E A N I N G IN THE M O V I N G BODY The point in a moving body with special values of velocity and acceleration has some special characteristics in kinematics. It can be readily located by what we have discussed hereinafter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001320_adma.19920040605-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001320_adma.19920040605-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of a typical ISFET device, showing the associated electrical circuitry needed to maintain a constant drain-source current.",
        "texts": [
            "'~] During the last decade, Berg~eld[~] and Matsuo, Esashi and T n ~ m a [ ~ ] independently introduced, for the first time, the concept of the ion sensitive field-effect transistor (ISFET). These have some significant advantages, when compared to conventional ISEs, such as smaller size, all solid construction, a short response time and the possibility of fitting more than one sensor on to an area of a few square mm. Furthermore, the application of modern integrated-circuit technology makes possible bulk and cheap ISFET production. A typical ISFET device is shown schematically in Figure 1 . The basic principlesL6 - 91 can be summarized in the following way. A classical n-channel insulated-gate FET consists of a p-type silicon substrate with the source and the drain diffusion separated by a channel, which is overlaid by an insulator and a metal gate. An ISFET differs in that the metal gate is now removed and a solution (analyte) is in direct contact with the gate insulator layer(s), while the electrical path is closed using a reference electrode in the solution. The device is necessarily protected by a suitable incapsulant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003947_icma.2005.1626582-Figure14-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003947_icma.2005.1626582-Figure14-1.png",
        "caption": "Fig. 14. Double Tube System consisting of Straight Outer Tube and Curved Inner Tube",
        "texts": [
            " In their evaluation, compared with the conventional method, PUBS can be executed easily and in a short time by using this system. VI. CONTROL METHOD OF CURVED MULTI-TUBE CATHETER FOR SOLID ORGANS In this section, the application of CMT catheter to solid organs like brain and liver is described. If we use the control method for hollow-organs like uterus and bladder to control CMT catheter for solid organs, the CMT catheter breaks the tissue of solid organ. So, we present the control method of CMT catheter for solid organs in this section. Figure 14 shows a curved double tube catheter. This curved double tube catheter is the most simple formation of CMT catheter, and it is considered that CMT catheters of this type are applicable to various medical treatments. Figure 14(a) shows Straight Outer Tube, and Figure 14(b) shows Curved Inner Tube. Figures 14(c) and (d) show the two states of the curved double tube catheter. As shown in Figure 14(c), the curved double tube catheter becomes almost straight in Stat 1 by the difference of the rigidity of tubes. Figure 15 shows the control method of the curved multitube system for solid organ. When this method is used for solid organ, the tissue of the solid organ does not destroyed. VII. VARIOUS APPLICATIONS OF CURVED MULTI-TUBE CATHETER We have started the joint studies with the laboratories in the graduate school of medicine of Osaka University in the fields of liver-paracentesis, venepuncture, and brain surgery"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003809_detc2005-84681-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003809_detc2005-84681-Figure7-1.png",
        "caption": "Figure 7: Test configuration and modal identification results.",
        "texts": [
            "org/about-asme/terms-of-use D Spindle body mode shapes are complex to analyze. Many local modes are present and the couplings between them are significant. The modes are substantially dampened and the mode decoupling hypothesis is not verified. For this structure the beam model is not satisfactory and only solid three-dimensional finite element modeling makes it possible to translate the complexity of its dynamic behavior. Moreover, the MAC criterion established on the first three identified bending modes is unsatisfactory (see figure 7). The identification process did not enable an acceptable dynamic characterization of the spindle body and in this case the \"infinitely rigid\" model is retained. ownloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/03/2016 T The rear guide (see figure 8) is the connection between the spindle body and the rotating shaft. It allows axial thermal expansion of the shaft thanks to a ball bush. Measurements present many high frequency modes. However the measurement coherence criterion does not guarantee good identification conditions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002547_s10010-005-0011-3-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002547_s10010-005-0011-3-Figure1-1.png",
        "caption": "Fig. 1. The system",
        "texts": [
            " [20] calculate limit cycles for a two degrees of freedom rotor. Yamauchi and Someya [28] study the dynamic characteristics of gear couplings and the related self-excited vibrations analytically and experimentally. Li and Yu [18] develop a linear finite element model for the rotor and add non-linear elements for the couplings. Interaction of torsional and lateral motions and various misalignments are taken into account. Steady state responses and spectra are obtained numerically. 2 The system; equations of motion 2.1 The system The rotor shown in Fig. 1 consists of two massless rigid shafts, No.1 (length l3) and No.2 (length l4), mounted on two rigid bearings A and C, and on the flexible bearing B, which is suspended by spring-dashpot elements, stiffnesses kx , ky, viscous dampings dx , dy in the horizontal and the vertical directions, respectively. The attachment points D, E of the suspension elements can be slid by ax and ay to produce special (angular) misalignments in the gear coupling gc (point mass mgc) which connects the two shafts. Shaft 1 carries the rigid disk dk of a turbine (mass mdk, moments of inertia Jp, Jd along polar axis and diameter) which is unbalanced (eccentricity eu ) but sits otherwise straight",
            " This, of course, requires a time dependent torque MT = MT (t). The goal is to study in a systematic way the instability and small lateral oscillations of the rotor which originate by the interaction of the strongly non-linear frictional characteristic of the gear coupling and the otherwise linear system. Of special interest are the influences of misalignment and unbalance. 2.2 Equations of motion The deflections of the rotor are measured by its displacements x = x(t), y = y(t) at the bearing B; for (x, y) = (0, 0) is the rotor straight, see Fig. 1. In the Appendix the basic assumptions of the model are explained and the equations of motion for x, y are established. They read in vector notation: Mu\u0308+ (D+\u2126G+ f(v)C1) u\u0307+ (K+\u2126 f(v)C2) u = Fe +Fu(t) . (2) Here, u, M, D, K are, respectively, the displacement vector, the matrices of mass, of damping and of stiffness, u = ( x y ) , M = ( m 0 0 m ) , D = ( dx 0 0 dy ) , K = ( kx 0 0 ky ) , (3) G, C1, C2 represent the gyroscopic and the two gear coupling matrices, G = Jp/l2 2 \u00b7 ( 0 1 \u22121 0 ) , C1 = MF/l2 \u00b7 ( 1 0 0 1 ) , (4) C2 = MF/l2 \u00b7 ( 0 1 \u22121 0 ) , where v = \u221a (x\u0307 +\u2126y)2 + (y\u0307 \u2212\u2126x)2, f(v) = tanh(v/v\u2217) v , Fe is the vector of the adjustment forces and the weight, Fu contains the unbalance forces: Fe = ( kxax kyay \u2212 W ) , Fu = eumu\u21262 ( cos \u03a6(t) sin \u03a6(t) ) + eumu\u2126\u0307 ( sin \u03a6(t) \u2212 cos \u03a6(t) ) ",
            " 31, 6 for the notation) v(0) = v0 = (x\u0307(0), y\u0307(0), x(0), y(0))T = (vR, vR, eR, eR)T \u00d710\u22122 . (23) Figure 5 presents in 9 diagrams the results for \u21261 = \u2126N . The first two diagrams (counted row-wise) show for the time section 0 < t/TR < 29 (left parts of the diagrams) the slow growth of the displacements x(t) and y(t) which agrees well with the second variational solution \u03b4uS2(t), cf. Eq. 21 and the small growth constant \u03c3S2 shown in Fig. 4 for \u21261 = \u2126N . During the time 0 < t/TR < 29 the gear coupling nearly \u2018sticks\u2019, the bearing B (see Fig. 1) spirals slowly outwards, almost on a circle, see the magnified diagram 7. For more details, polar coordinates are introduced: x(t) = r(t) cos \u03a8(t) , y(t) = r(t) sin \u03a8(t) . (24) The diagrams 3 to 6 show, for the stretched subinterval 26 < t/T R < 35, the functions r(t), r\u0307(t),\u03a8\u0307(t) and tanh (v(t)/v\u2217). From diagram 5 follows that for t/TR < 29 the system rotates almost like a rigid body with \u03a8\u0307(t) = \u2126N/\u03c9R. In diagrams 3 and 4 (for t/TR < 29) again, as in diagram 7, the slowly creeping motion can be recognized which, as expected, replaces the frozen motion",
            " The procedure of the Appendix, here developed to establish the non-linear equations of motion for a two degrees of freedom rotor including one gear coupling, can be applied to obtain a higher-order system as a basis for a more detailed investigation. A machine with two shafts, connected by a pair of gear couplings, requires easily a model with 12 to 16 degrees of freedom. There are many parameters, and to gather (numerical) experience a large amount of calculations will be necessary. The deflections of the rotor are measured by its displacements at the bearing B (cf. Figure 1), x = x(t), y = y(t) . (43) Lagrange\u2019s energy method (see [24]) is applied to establish the equations of motion for x, y. Let the displacements have small magnitudes, |x|, |y| l2. From the outset, the equations of motion are linearized with respect to x, y (and the time derivatives x\u0307, y\u0307) with exception of the characteristic of the gear coupling which is a strongly nonlinear function of (x, y, x\u0307, y\u0307). Then it is sufficient to express the kinetic energy and the potential by linear and quadratic forms of (x, y, x\u0307, y\u0307). By linearized geometric relations follow from Figs. 1 and 17 the displacements xdk , ydk of the disk\u2019s centre of mass: xdk = x \u00d7 l1/l2 + eu cos \u03a6(t) , ydk = y \u00d7 l1/l2 + eu sin \u03a6(t) . (44) The inclinations of shaft 1 (i.e. the disk) are measured by the angles \u03c6x , \u03c6y as rotations about the x- and the y-axis, respectively. From Fig. 1 follows \u03d5x = y/l2 , \u03d5y = \u2212x/l2 . (45) For small magnitudes |\u03d5x |, |\u03d5y| 1 are the angles represented by vectors (cf. the twin arrows \u03d5x , \u03d5y in Fig. 1, and \u03d5mx , \u03d5m y in Fig. 18c). The displacements of the gear coupling (see Fig. 1) are xgc = x \u00d7 l3/l2 , ygc = y \u00d7 l3/l2 . (46) The small (misalignment) angles \u03d5mx , \u03d5m y at the gear coupling are read from Fig. 1: \u03d5mx = y/l2 + y \u00d7 l3/(l2 \u00d7 l4), \u03d5m y = \u2212x/l2 \u2212 x \u00d7 l3/(l2 \u00d7 l4) . (47) (See the explanations following Eq. 53 for the correct orientations.) The kinetic energy T of the system contains translatory and rotary motions T = 1/2\u00d7 ( mdk(x\u0307 2 dk + y\u03072 dk)+mgc(x\u0307 2 gc + y\u03072 gc)+ Jd(\u03d5\u0307 2 x + \u03d5\u03072 y) ) +1/2\u00d7 Jp [ \u2126+ (\u03d5\u0307x\u03d5y \u2212 \u03d5\u0307y\u03d5x)/2 ]2 . (48) The expression in the last line represents gyroscopic terms (cf. [3]); its third and fourth order terms have to be dropped after resolution of the brackets. The potential U contains the elastic bearing suspensions and the weight: U = 1/2\u00d7 ( kx(x \u2212ax) 2 + ky(y \u2212ay) 2 ) +mdkg ydk +mgcg ygc , (49) g \u2013 gravity acceleration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002383_robot.1996.506891-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002383_robot.1996.506891-Figure1-1.png",
        "caption": "Figure 1: Curve-Face with a five joint kinematic model.",
        "texts": [
            "2 Curve-face contact The bottom rim of the peg contacts the plane of the hole. This is modelled by means of a five degrees-offreedom virtual manipulator (Fig. l), with twist and wrench Jacobians J,f and G,f [5]: 0 0 0 0 -c, \u201c 1 - T O 0 1 0 1 0 0 o o o o s , 0 I , G c f = O 1 o c , o O S a 0 0 O I J c , = - - - 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 Gc, = 0 0 1 0 \u2018 (10) 0 1 - - 0 0 0 0 - r is the peg radius. s, and c, are, respectively, the sine and cosine of a, the angle between the axis of the peg and the contact normal (Fig. 1). This contact situation has two identifiable geometrical uncertainty parameters: the rotation angle 19 of the peg about its own axis, and the angle a between the peg axis and the contact normal. 3.3 Three point contact There are three distinct contacts: 1. surf: the contact between the outer surface of the peg and the rim of the hole. 2. riml and rim2 the two contacts between the bottom rim of the peg and the rim of the hole. These two contacts are positioned symmetrically with respect to the plane through the peg\u2019s axis and through surf",
            "2 Identification This section shows the results of the off-line identification of uncertainties in the different contact situations. As mentioned in Section 3, only the curve-face and the three point contact have identifiable uncertainty parameters. Fig. 5 shows the result of the identification of geometrical uncertainty parameters in the curve-face contact. The angle between the peg's axis and the contact normal remains constant, about 0.85 rad; whereas the rotation angle of the peg about its own axis is small. This means that the contact point belongs to the Y-2 plane (Fig. 1). Fig. 6 shows the identified uncertainty parameters of the three point contact. Due to friction disturbancies on the forces measurements, only the kinetic energy error term of (4) is minimized. In the top figure the identified alignment error (full line) is compared with the specification (dashed line). When the alignment error is small, the insertion can start. The rotation angle about the peg axis (bottom figure) is small. This means that the surfcontact belongs to the Y-2 plane (Fig. 2). 4.3 Monitoring The detection of the transitions between the different contact situations is based on the total energy error function of the expected model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003505_robot.2006.1642018-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003505_robot.2006.1642018-Figure1-1.png",
        "caption": "Fig. 1. Stable grasping of a 3-D object with parallel surfaces in a dynamic sense. The third finger (middle finger) is used for stopping the spinning motion \u03c9X around the X-axis that may be induced by the gravity.",
        "texts": [
            " John Napier says in his book [1] at page 55 that \u201cThe movement of the thumb underlies all the skilled procedures of which the hand is capable.\u201d \u201cWithout the thumb, the hand is put back 60 million years in evolutionary terms to a stage when the thumb had no independence movement and was just another digit. One cannot emphasize enough the importance of finger-thumb opposition for human emergence from a relatively undistinguished primate background.\u201d Finger-thumb opposition is defined by a movement in which the pulp surface of the thumb is placed squarely in contact with the terminal pads of one or all of the remaining digits (see Fig.1). According to the literature of research works on multi-fingered robotic hands [2] \u223c [4], however, there is a dearth of papers that are concerned with dynamics and control of stable precision prehension or grasp of an object through finger-thumb opposition. Rather, most research works were concerned with kinematics and plannings of motions realizing force/torque closure for secure grasping (in a static sense) by using multi-fingers with frictionless contacts [2] \u223c [4]. Two exceptional papers [5] [6] treated the problem of rolling contacts and analyzed kinematics and dynamics of multi-fingered hands with rolling contacts",
            "00 \u00a92006 IEEE 2124 is proposed, which does neither use the knowledge of object kinematics nor external sensing. Stability of closed-loop dynamics of the fingers-object system in a dynamic sense is discussed and the validity of such a control method is demonstrated on the basis of numerical simulations of the derived model. II. OPPOSABLE FORCES AND CONTROL OF SPINNING MOTION Human can pinch a rigid object by using only a pair of the thumb and index (or middle) finger (see Fig.2), if the object is not so heavy and thick. However, when the distance from the straight line (X-axis in Fig.1) connecting two contact points between finger-ends and object surfaces to the vertical axis through the object mass center in the direction of gravity becomes large, there arises a spinning motion of the object around X-axis. In order to stop this spinning, the third digit is needed as shown in Fig.1. Or it is possible to consider the problem of modelling of pinching in the situation that, after this spinning motion stops, the center of mass of the object comes sufficiently close to the beneath of the X-axis and there will no more arise such spinning due to dry friction between finger-ends and object surfaces in rotational motion around the X-axis. Irrespective of this assumption, rolling contact constraints become non-holonomic and, moreover, the instantaneous axis of rotation of the object is changeable and hence induce non-holonomic constraints (see Landau & Lifschits [14])"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001518_3-540-45118-8_21-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001518_3-540-45118-8_21-Figure4-1.png",
        "caption": "Fig. 4. Parameter definition for triplet optimization (see text).",
        "texts": [
            " Criteria: Each admissible point goes through a series of tests to characterize its adequacy for use as an entry point for the robotic tool or the endoscope. There are qualitative and quantitative tests as described next: Qualitative tests concern the reachability from an admissible point to the target areas, where the point is eliminated if any of the following conditions holds: \u2013 The length of the tool between target and admissible is outside a given range, which simply means that the area cannot be operated using the concerned instrument. (d in figure 4 (a), not used for endoscope) \u2013 The angle between the admissible direction and the line relating the target to the admissible is too big, in which case the tool may damage the adjacent ribs (\u03b2 in figure 4 (a)). \u2013 The path between the admissible point and the target area is not clear; i.e., it is hindered by an anatomical structure as is shown for instance in figure 3 (b). The graphics hardware is used to perform this test in a way similar to the work described in [7]. Quantitative tests concern the dexterity of the robot, where each admissible point is graded based on the angle between the target direction and the line relating the target to the admissible (\u03b1 in figure 4 (a)). This measure translates the ease with which the surgeon will be able to operate the concerned target areas from a given port in the case of a robotic tool, or the quality of viewing these areas for an endoscope. Optimization: Finding the best triplet of ports is done in two steps: First the best endoscope position is chosen based on the above listed criteria, then all possible pairs are ranked according to their combined quantitative grade and their position with respect to the endoscope. More precisely, the triplet is ranked in a way that insures a symmetry of the left and right arms with respect of the endoscope, and favors positions further away from the endoscope to give a clear field of view (formally this corresponds to maximizing \u03c6 and \u03b8 defined in figure 4). Moreover, and in order to anticipate on the next step which is the robot positioning, port that are too close are not considered in the optimization, as they would most certainly result in a colliding state. This optimization is exhaustive; however, it does not cause a performance problem since the search is hierarchical and thus only a small number of admissible points are left for ranking after all the tests are performed. Once a suitable port placement has been found, the robot has to be positioned in a way that avoids collisions between its arms, in addition to other constraints"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001020_analsci.8.553-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001020_analsci.8.553-Figure5-1.png",
        "caption": "Fig. 5 Na+ measurements of aqueous solutions with an ionselective membrane consisting of hemisodium, BBPA as the plasticizes and PVC as the matrix. The y-axis shows the activities a1(s) of the sodium reference solution with the following concentrations of Na+ 100, 120, 140, 160 and 180 mM, respectively. The x-axis indicates the expression",
        "texts": [],
        "surrounding_texts": [
            "reference electrodes with a diffusion (convection) barrier as illustrated in Fig. 2, this phenomenon can be sup-\npressed. Thus, the measured potential remains constant during a measuring sequence as presented in Fig. 3 The quality of the membranes and their suitability foi serum assays were carefully evaluated. For sodiumn measurements, the optimized membrane consisted of hemisodium as the ligand, PVC as the matrix and BBPA as the plasticizer. The electrical asymmetry of thf membranes was well below 0.2 mV, the slope was 100\u00b1 1.1 % of the theoretical value, the standard deviation syx of the single values from the linear regression line of the calibration curve in the physiological range was about \u00b10.1 mV. The results of measurements in biological material were equally satisfying: 10 calibration-freE measurements of EMF values on serum samples withirr the physiological range coincided with the theoretical ones (see below) within 0.3 mV, the drift during thf serum measurements being 0.3 mV/ h and the asymmetry potential induced by proteins being below 0.1 mV. The membranes for potassium measurement consisting of valinomycin, PVC and BBPA showec similar properties. With these optimized membranes sera with patho. logical concentrations of sodium and potassium wen assayed. The reliability of the measurements was testec by making a comparison with independent methods especially with flame photometry, and to some extent with measurements utilizing sodium glass electrodes.\nIn the Nicolsky-Eisenman equation (1):20\nEMF[mV] = Eo slog aid KPot(aj)Z''Z' (1, J1\nwith\nEo=EDGE (2,\nand\n2.303RT S =\nziF =59 .2 mV/z1. (25\u00b0C) (3)\nEo is the standard cell potential and depends on E, a constant potential difference (depending on the reference electrodes and the temperature but not on the sample solution) and on ED, the liquid junction potential difference generated between the reference electrolyte and the sample solution. R is the gas constant (8.314 J K-1 mol-1), T the absolute temperature and F the Faraday constant (9.6487X104 C mol-1); zi, zj are the charge numbers of the primary ion I and the interfering ions J; ai, aj are the activities of the respective ions in the sample solution (moll-1); KP\u00b0t is the selectivity factor which describes the preference of the interfering ion J relative to the ion I by the ISE membrane. Ideally, all KP\u00b0t equal zero.\nThe results of measurements in aqueous solutions indicate that the membranes exhibit sufficient selectivity to make corrections for interfering ion obsolete. In addition, the slope of the ion-selective electrode is theoretical within the limits of our measurements. Since the applied membranes as well as the reference electrodes are electrically symmetric, Eo reduces to sample induced changes AED in the liquid junction\npotential ED (Eq. (2)). By utilizing the above described symmetric measuring cell with an electrolyte containing the ion I at an activity a1(r) (reference solution) in one compartment and the sample solution with an activity at(s) in the other, the cell EMF e.g. EMFx is obtained from Eqs. (1) to (3):21\nEMFx[mV] = ZED + s loga;(s)/ai(r). (4)\nWith the chosen reference solution and bridge electrolyte the change in the liquid junction potential DED due to a change from reference to sample solution is sufficiently sma11.15 By neglecting AED and rearranging Eq. (4) the following equation (5) is obtained:\nat(s) - a(r) '10EMFx/s (5)\nFor the following correlations (Figs. 5 - 10) the expressions 10EM>~x/s were plotted on the x-axis of a coordinate system. The activities of the measured ion a1(s) were arranged on the y-axis. In case of measurements of aqueous solutions, these activities were calculated using the Debye-HUckel formalism.22 For serum samples, the activities at(s) are based on values obtained by independently performed FAES measurements. All FAES values were corrected for a lipid/\nprotein volume effect of 7%. The single ion activity coefficients were calculated based on the FAES readings for the measured ion and a constant background identical to the reference electrolyte . solutions. The counter ions were supposed to be ClAccording to Eq. (5) the slope of the correlation lines",
            "ANALYTICAL SCIENCES AUGUST 1992, VOL. 8\nof the activities of the sample solution at(s) versus IOEMFx/s should equal ai(r). Using the Debye-Hi ckel formalism22 a(r) was calculated to be 104.5 mM and 3.13 mM for Na+ and K+ respectively. This is indeed the case for our ab initio measurements. For aqueous solutions the agreement between the fitted values and the theoretical values is very good. The slope of the correlation line for K+ measurements equals 3.14 mM and the one for Na+ measurements is 104.1 mM (see Figs. 4, 5 and Table 1). For sera in the normal concentration range (e.g. 3.5 -\n557\n5.1 mM K+, 136 -145 mM Na+) the a(r) values for K+ measurements is 3% too low, whereas for Na+ measurements they are 3% too high. Liquid junction errors, therefore, are not giving a systematic bias. For both electrolytes the standard deviation syx found is very similar to the one obtained when measuring aqueous solutions (K+, 0.02 mM versus 0.06 mM; Na+, 1.4 mM versus 1.2 mM; see Table 1 and Figs. 6 and 7). As far as sera in the pathological concentration range are concerned (e.g. 2.5 - 7.6 mM K+,115 -161 mM Nat, respectively) the K+ measurements are in very good agreement with the theoretical value (3.15 mM found\nplasticizer and PVC as the matrix. The diffusion barrier as presented in Fig. 2 was employed. The y-axis shows the activities a1(s) of the potassium reference solution values (of the following concentrations: 2.75, 3.25, 4.25, 5 and 5.75 mM K+, respectively), the x-axis indicates the expression 10EMFx/s.\n10EMFx/ s.",
            "558 ANALYTICAL SCIENCES AUGUST 1992, VOL. 8\ncompared to 3.13 mM expected, see Fig. 8). The Na+ values are still 3% too high, compared to the theoretical value (108 mM measured compared to 104.5 mM expected, see 4 mM. Deviations\nof the measured a;(r),"
        ]
    },
    {
        "image_filename": "designv11_24_0003180_j.tws.2005.06.001-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003180_j.tws.2005.06.001-Figure7-1.png",
        "caption": "Fig. 7. A model of the girder divided into elements\u2014a view from the inside of the girder onto membrane.",
        "texts": [
            " The calculations by the finite element method were performed using a professional program package ANSYS5.4. In view of the fact that the real girder has two planes of symmetry, a discrete model of the girder constitutes 1/4 of the real construction. In the numerical model, welds were also taken into consideration; these were divided into elements of the same material properties as the girder sheets. The calculations were made using finite four-node shell elements (SHELL 43) of six degrees of freedom in each node. The division into the elements is shown in Fig. 7. The load of the girder was obtained from the simulation of welding of the straps parallel to the girder axis. The simulation consisted in applying an appropriate temperature to all the nodes belonging to the elements corresponding to the strap used. At the next stage the construction was cooled down to ambient temperature [5]. The model of the girder had webs of the real magnitude of preliminary deflections; the imperfections reached a value of 15 mm. In Fig. 8 an image of the deformation of the surface of the girder webs is presented"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003784_s11044-006-9030-6-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003784_s11044-006-9030-6-Figure1-1.png",
        "caption": "Fig. 1 Simple towed-cable-body system model",
        "texts": [
            "1 Control model For control design, a relatively simple model of the cable system is used. The cable elasticity and flexibility are neglected and hence the cable may be treated as a straight rigid rod. In order to correctly account for the cable\u2019s inertia, the distributed mass of the cable is included. The cable is assumed to be uniform in mass with constant diameter. For simplicity in this work, only planar motion of the cable is considered. This is suitable for terrainfollowing in the vertical plane. Figure 1 shows a representation of the cable model and the generalized coordinates used to represent the position of the cable tip in the vertical plane. The instantaneous tether length is denoted by r and the orientation with respect to the local vertical is denoted by \u03b8 . The aircraft downrange is denoted by x, whereas the altitude relative to reference sealevel is denoted by h. A local coordinate frame which is attached to and moves with the aircraft is used, denoted by Oxy in Figure 1. The height of the terrain, which is, in general, a function of the downrange x, is denoted by hT. The towedbody is treated as a point mass, and the aircraft motion is assumed to be prescribed for all time. Springer Consider a general point on the cable s \u2208 [0, r ], whose inertial position is given by R = (x \u2212 s sin \u03b8 )i + (h \u2212 s cos \u03b8 )j. (1) Differentiation of Equation (1) gives the velocity of s in Oxy v = R\u0307 = (x\u0307 \u2212 s\u0307 sin \u03b8 \u2212 s\u03b8\u0307 cos \u03b8 )i + (h\u0307 \u2212 s\u0307 cos \u03b8 + s\u03b8\u0307 sin \u03b8 )j (2) If it is noted that the cable is assumed rigid, s\u0307 = r\u0307 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003589_b978-0-12-093480-5.50006-4-Figure2.2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003589_b978-0-12-093480-5.50006-4-Figure2.2-1.png",
        "caption": "FIG. 2.2 Geometric interpretation of the first-order multiplier iteration",
        "texts": [
            " The minimum is attained at the point w(A, C) for which the gradient of p(u) + X'u + | c | i / | 2 is zero, or equivalently V{p(w) + ic|t/|2}|M=M(A>c)= - 1 Thus the minimizing point M(A, C) is obtained as shown in Fig. 2.1. We have also min Lc(x, A) - \u03bb\u0389(\u03bb, c) = p[w(A, c)] + \\c\\u(X, c)\\\\ X so the tangent hyperplane to the graph of p(u) + \\c\\u\\2 at u(\u00c0,c) (which has \"slope\" \u2014A) intersects the vertical axis at the value minxLc(x,A) as shown in Fig. 2.1. It can be seen that if c is sufficiently large then p(u) + X'u + \\c\\u\\2 is convex in a neighborhood of the origin. Furthermore, the 106 2. MULTIPLIER METHODS value minx Lc(x, A) is close to p(0) = /(**) for values of A close to A* and large values of c. Figure 2.2 provides a geometric interpretation of the multiplier iteration (1). To understand this figure, note that if xk minimizes LCk(\u00b7, Ak), then by the analysis above the vector uk given by uk = h(xk) minimizes p(u) + Xku + ick|w|2. Hence, V{Kw) + i c J W | 2 } | M = U k = - A k , and Vp(wk) = -(Ak + ckwk) = -[Ak 4- ck/i(xk)]. It follows that, for the next multiplier Ak+1? we have 4 + 1 = K + ck/i(xk) = -Vp(wk), as shown in Fig. 2.2. The figure shows that if Ak is sufficiently close to A* and/or ck is sufficiently large, the next multiplier Ak+1 will be closer to A* than Ak is. In fact if p(u) is linear, convergence to A* will be achieved in one iteration. If V2/?(0) = 0, the convergence is very fast. Furthermore it is not 2.2 THE ORIGINAL METHOD OF MULTIPLIERS 107 necessary to have ck -\u25ba oo in order to obtain convergence but merely to have that ck exceeds some threshold level after some index. We proceed to make these observations precise",
            "5 is equivalent to the local convexity condition V2 xxL0{x*,X*)>0, then any positive c can serve as a threshold level. The same is true even if V2p(0) > 0. We shall reencounter this result in the context of convex programming problems in Chapter 5. (b) If V2p(0) has a negative eigenvalue, then any c satisfying c > max{ \u2014 eu . . . , \u2014 em} is sufficient for V2 xLf(x*, \u039b,*) > 0 to hold (Proposition 2.5). However, it is necessary to take c > 2 max{ \u2014 eu ..., \u2014 em} in order to induce convergence [compare with (40)]. The reason for this can be understood by examination of Fig. 2.2, where it can be seen that to achieve convergence the \"penalized\" primal functional pc must have at least as much \"positive curvature\" as the \"negative curvature\" of p. Regarding rate of convergence, we see from (43) and (44) that we have at least Q-linear convergence if {ck} is bounded and superlinear convergence if either {ck} is unbounded or V2p(0) = 0. These rate-of-convergence results cannot be improved, since for any dimensions n and m, it is possible to construct a problem with a quadratic objective function and linear equality constraints and a starting point \u03bb0 for which, if ck = c* for all /c, relation (43) holds as an equality",
            " Given Ak, cfc, and xk such that VxLCk(xk,Afc) = 0, the second-order iterate Xk + 1 is given by \u039b + \u03b9 = Xk + { V M * J [ V i L J x f c A ) r ' \u03bd / \u03b9 \u03af \u03c7 * ) } \" 1 ^ ) . 140 2. MULTIPLIER METHODS This equation can be written in terms of the primal functional p as (50) Xk + 1 = Xk + \\y2p(uk) + cj-]uk = lk + V2p(iikK, where (51) uk = h{xk\\ lk = Xk + ckuk. If we form the second-order Taylor series expansion of p around uk pk{u) = p(uk) + Vp(uk)'(u - uk) + %\u03bc - uk)'V 2p(uk)(u - uk\\ we obtain (52) VA(0) = Vp(uk) - V2p(uk)uk. Since (compare with Fig. 2.2) we have (53) Xk = -Vp(uk\\ it follows from (50)-(53) that Vft(0)= -Xk + 1 as shown in Fig. 2.6. In other words the second-order iteration yields the predicted value of \u2014 Vp(0) based on a second-order Taylor series expansion of p around uk = h{xk). By contrast the first-order iteration yields the predicted value of \u2014 Vp(0) based on a first-order Taylor series expansion of p around uk = h(xk) (compare with Fig. 2.2). In the algorithms of Sections 2.2 and 2.3, all the equality constraints were eliminated by means of a penalty. In some cases however, it is of interest to consider algorithms where only part of the constraints are eliminated by means of a penalty, while the remaining constraints are retained explicitly. A typical example is a problem of the form minimize f(x) subject to h(x) = 0, x > 0, where the dimension n of the vector x is large and h(x) = 0 represents a small number of nonlinear constraints"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001920_70.56666-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001920_70.56666-Figure8-1.png",
        "caption": "Fig. 8. Block showing grasp points and attached coordinate system",
        "texts": [
            " When the object rotates, the grasp points change relative to the \u201cobject\u201d frame, and hence, the G transform changes. 10 5 - 0 0 -5 z e U - l O + - F z f I 1 i -15, . - ! ! ! ! ! . 0 1 2 3 4 5 Time IV . DEMONSTRATION TASKS Fig. 9. Forces during insertion at 25 mm/s insertion speed. The object stiffness control system described in Section I11 was used in two simple example tasks. The Salisbury hand, mounted on a PUMA 560 robot, grasped a rectangular wooden block of dimension 50 x 50 x 300 mm at the contact points shown in Fig. 8. The stiffness of the block was given by diagonal object stiffness matrix KC,, with values -15 I 1 1 I I KO = diag [0.9 0.9 0.9 0 900 0 0 0 01. (15) 0 1 2 3 Time The rank of W is 6, as expected. The first three columns are the unisense wrenches of the grasp, and they correspond to the homogeneous solution of (3). It is simple to show that the intensities of these unisense wrenches are the same sign, and thus, contact can be maintained. The contact intensities w1, w2, and w3 used in this grasp were 5, 5, and 10 N, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003882_s0007-8506(07)60477-6-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003882_s0007-8506(07)60477-6-Figure1-1.png",
        "caption": "Figure 1: Definition of runout measurement conditions. (a) Movement direction of the probe defines the sampling cone. (b) Runout measurement via registration of one single",
        "texts": [
            " Although all CMMs equipped with a bevel gear measurement software provide runout evaluations, only a few publications exist about appropriate algorithms. This paper presents a new approach for this evaluation problem and discusses further options [4]. Additionally, a short discussion about results of investigations on different standard CMMs is attached. Runout measurement of bevel gears is defined in [5],[6] as a difference of positions of a specified probe, which radially dips in each gap of the gear. The sampling direction of this probe is perpendicular to the reference cone and the probing ball contacts both flanks simultaneously (Figure 1 (a) and (b)). During of the sampling movement, the probe follows a sampling cone. This sampling cone is oriented opposite to the reference cone and penetrates it perpendicularly. The intersection element of these two cones is a circle with the so-called tolerance or pitch diameter. The sampling cone represents the totality of all possible positions and sampling ways of the probe ball centre (Figure 1 (a)). point with a specified probe ball, contacting both flanks simultaneously. Source: [7], edited. dT: tolerance diameter (pitch diameter) \u03b4: cone angle (angle of reference cone) Rm: mean cone distance (between apex of the reference cone and the intersection point of the reference cone and the pitch diameter) Figure 2 illustrates the principle of evaluation. Figure 2 (a) sketches the top view of the runout measurement of a gear clamped at an eccentricity fe. Each gap contains one ball probe, contacting both flanks simultaneously",
            " edatum: Datum gap width e: Actual gap width dT: pitch diameter r dip: Radius of the ball probe centre position, where a simultaneous contact at both flanks occurs Thus, one could imagine the corridor as a conical slit, where the probe ball is rolling through. Consequently, the corridor centre line in Figure 8 (b) indicates all theoretically possible positions of centre points of the ball probe. This model reflects the reality only in a limited region around the pitch points. Within this region, the intersection point between sampling cone and centre line of corridor gives the virtual probe ball centre of direct runout measurement (see also Figure 1 (a)). (a) Gap with two pitch points. (b) Schematic detail A from (a). For a better estimation of the situation inside a gap, standard geometry elements with one, two or more curvatures offer better geometric models. Investigations with several standard geometric elements show that e.g. a torus fits better than a cylinder [4]. [8] exclusively used several tori for his investigations. On the other hand, the more complex the description of the geometric element is, the higher is the mathematical effort regarding the evaluation of the virtual ball probe centre points"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000523_a:1008786811464-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000523_a:1008786811464-Figure3-1.png",
        "caption": "Figure 3. Projection onto the (V, \u03b1, \u03b3 )-space of the viability kernel of D2 (leadership kernel in the absence of wind disturbance) for problem 2. Minimum value of \u03b3 in the first figure, and maximum value of \u03b3 in the second figure.",
        "texts": [
            " If this subset is not empty, then there exists an admissible control u(\u00b7) which assures that the climb rate h\u2032 remains \u2018near\u2019 a prescribed one and, in particular, remains positive. As in Problem 1, we seek the leadership kernel, Lead(D2). For numerical simulations we take h\u2032R = 35 ft/s and \u03b7 = 0.5 ft/s. First of all, we consider the situation of no windshear disturbance, that is, W \u2032x(t) = W \u2032h(t) = 0. In that case, the leadership kernel Lead(D2) is simply the viability kernel of D2 (the definition of the viability kernel is postponed in the Appendix). Figure 3 shows a projection along the h\u2032 axis of the viability kernel of D2, namely, 5V,\u03b3,\u03b1(Viab (D2)). Using Figure 3 we can check, for example, whether the initial relative angle of attack \u03b1 and speed V are too low of too high to allow a viable trajectory. Next we allow for wind disturbances subject to (8) with W \u2032x = 2.61 ft/s and W \u2032h = 0.78 ft/s in Figure 4, and withW \u2032x = 5.63 ft/s andW \u2032h = 1.57 ft/s in Figure 5. These figures show the projections onto the (V, \u03b3, \u03b1)-space of the leadership kernel of D2 for the system (12) and all wind disturbances satisfying (8); for \u03b3 only the minimum and maximum values are shown"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001455_50006-1-Figure5.10-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001455_50006-1-Figure5.10-1.png",
        "caption": "FIGURE 5.10 Rotating coil device: (a) perspective of device; (b) end view; and (c) side view.",
        "texts": [
            " We integrate this along the bar in the direction of current flow and obtain fb (dl x B ext). ~ = (dl X B ext). a r = - - B e x t dy = Bexth. (5.109) Therefore, the Lorentz force on the bar is F = iBexth. Equations of motion\" Substitute Eqs. (5.108) and (5.109) into Eq. (5.103), which gives di(t) 1 dt = L [Vs(t) - i(t)(R + R b a r) - - Bexhu(t)] du(t) 1 = --i(t)Bexth dt m dx(t) dt = u(t). These equations need to be solved subject to initial conditions (5.88). D EXAMPLE 5.6.3 Consider the rotary device shown in Fig. 5.10a. This represents a basic direct-current (dc) motor. In this device, a magnetic field B ex t (assumed constant) is produced between two pole pieces by a field current i I through a coil that is wrapped around the pole pieces. A rectangular coil is mounted between the pole pieces and is free to rotate about the z-axis. When a current i passes through the coil it experiences a torque that causes it to rotate as shown. 372 CHAPTER 5 Electromechanical Devices A split ring with brushes is connected to the terminals of the rotating coil so that the current through it reverses direction every half turn",
            " There is no mechanical torque and Eqs. (5.102) reduce di(t) 1 f c dt = L [Vs(t) - i ( t ) ( R + Rcoil) q- oil dco(t)_ i ( t )~ [r x (dl x Bext) ] 9 dt Ym Jcoil to dO(t) [(r x r) x Bext] .dl] = og(t). (5.110) dt where L and Rcoi~ are the inductance and resistance of the coil, and Ym is the moment of inertia of the coil about the z-axis. We need to evaluate the induced voltage and torque integrals in Eq. (5.110). We use a Cartesian reference frame at rest with respect to the pole pieces as shown in Fig. 5.10a. We choose a rotation angle O, which is measured with respect to the y-axis in a counterclockwise sense about the z-axis as shown in Fig. 5.10b. Induced voltage: We determine the voltage induced at the terminals of the coil by summing the contributions from its various segments. The coil has four segments; relatively long left and right side segments, and two shorter end segments (Fig. 5.10b,c). We evaluate the side segments first. To evaluate the induced voltage we need [(r x r) x B ext]. dl along these segments. We know that, ~(t) = co(t)~., and from Fig. 5.10b we find that - b s in(0)~ + b cos(0)~ (left side) r = b s in(0)~ - b cos(0)~\" (right side). Therefore, - e)(t)b cos(0)~ - o~(t)b s in(0)~ (left side) x r - (o(t)b cos(0)~ + og(t)b s in(0)~ (right side). Note that B ex t is in the x-direction, Bex t - Bext~. Therefore, og(t)bBex sin(0)~ (to x r) x Bex t - - -c~162 (left side) (right side). Because dl = dz~ for both segments we have co(t)bBex t sin(0) dz [(o,) x r) x BCxt].dl = -~ (left side) (5.111) (right side). We evaluate Eq. (5.111) along the side segments with the integration in the direction of the current"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003925_001-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003925_001-Figure5-1.png",
        "caption": "Figure 5. Illustration of the proof of lemma 3: \u2018overlapping\u2019 optimal trajectories form a locally optimal trajectory.",
        "texts": [
            " From the principle of optimality, x\u2217(t) (t \u2208 [0, t1 + \u03c3 ]) and x\u2217(t) (t \u2208 [t1, T \u2217]) are each locally optimal with respect to their corresponding endpoints. Suppose that \u2016x\u2217(t1 + \u03c3) \u2212 s\u2016\u221e \u03b51 for any s \u2208 SQ and that x\u2217(t) (t \u2208 [0, T \u2217]) is not a local minimum. Then, there must exist \u03b5 < min(\u03b5, \u03b51/2) (with \u03b5 as defined in condition 1) and another optimum x(t) \u2208 D \u00d7 [0, T ] satisfying \u2016x(t) \u2212 x\u2217(t)\u2016\u221e < \u03b5 and C(x(t), 0, T ) < C(x\u2217(t), 0, T \u2217). Note that \u2016x(t1 + \u03c3) \u2212 s\u2016\u221e \u03b5 for any s \u2208 SQ. Construct two trajectories y1(t), y2(t) (t \u2208 [t1, t1 + \u03c3 ]) that connect x(t) and x\u2217(t) (see figure 5) and satisfy condition 1 (with x\u2217 or x playing the role of x1, and y1 or y2 standing for x2). In particular, let y1, y2 be such that x\u2217(t1) = y2(t1), x \u2217(t1 + \u03c3) = y1(t1 + \u03c3), x(t1) = y1(t1), x(t1 + \u03c3) = y2(t1 + \u03c3). Now, condition 1 implies that C(y1(t), t1, \u03c3 ) < C(x(t), t1, \u03c3 ) + L\u03c3, C(y2(t), t1, \u03c3 ) < C(x\u2217(t), t1, \u03c3 ) + L\u03c3. (7) Because x\u2217(t) (t \u2208 [0, t1 + \u03c3 ]) and x\u2217(t) (t \u2208 [t1, T \u2217]) are each locally optimal, the following holds, C(x\u2217(t), 0, t1) + C(x\u2217(t), t1, \u03c3 ) < C(x(t), 0, t1) + C(y1(t), t1, \u03c3 ), (8) and C(x\u2217(t), t1, \u03c3 ) + C(x\u2217(t), t1 + \u03c3, T \u2217 \u2212 t1 \u2212 \u03c3) < C(x(t), t1 + \u03c3, T \u2212 t1 \u2212 \u03c3) + C(y2(t), t1, \u03c3 )"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001474_s0167-8922(08)70580-7-Figure6.7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001474_s0167-8922(08)70580-7-Figure6.7-1.png",
        "caption": "FIGURE 6.7 Flat circular pad bearing with orifice controlled flow.",
        "texts": [
            " It is also possible with this method of controlling the lubricant flow, to vary stiffness to suit specific design requirements as opposed to the fixed values of stiffness provided by the constant flow device. It can also be noted that the lubricant viscosity is eliminated when equating the flow through the capillary to the total lubricant flow. Hence the bearing stiffness in this case is independent of temperature since the effect of viscosity on flow through the bearing is balanced by the viscosity effect on flow through the capillary. . Stiffness With an Orifice In some applications an orifice is fitted to the lubricant supply line as shown in Figure 6.7. Although this device is very simple it controls lubricant flow quite effectively and allows some freedom in the selection of load and stiffness characteristics. The flow rate through an orifice of diameter 'd is: where: Q d is the flow rate through the orifice [m3/sl; is the diameter of the orifice [ml; Chapter 6 HYDROSTATIC LUBRICATION 327 p, P, P C, is the discharge coefficient. is the lubricant supply pressure [Pal; is the bearing recess pressure [Pal; is the lubricant density [kg/m31; Equating flow through the orifice to the total lubricant flow through the bearing (6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002058_iros.1997.649050-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002058_iros.1997.649050-Figure1-1.png",
        "caption": "Figure 1: Example of manipulation utilizing dynamic deformation of rodlike object",
        "texts": [],
        "surrounding_texts": [
            "objects as presented. In m a n u f a c t w i n g processes, there are m a n y manipulat ive operations which deal wi th defomaahle objects. Evaluat ion o f t h e shapes of these ohjects is impor tan t f o r thedr manipulat ive operations because ihe i r deformation c a n m u s e both saccess of siich Operations i f it is zltilized efleetively and the i r failure if t h e de format ion i s unezpecied. Furthermore, i f deformable objects are operated paickly, the dynamical effect of ihem, cannot be neglected w h e n we evalualie t he i r shapes. Thm, both, s tat ic an.d dyn.amie analysis of objects deformation is required so tha t t he shape of t h e objects can be evaluated on a c o m p u t e r an advance. In this paper, we wall an,alyse t h e dynmmic deformat i o n of deformable rodlake objects. First, a, geometr i c representat ion t o describe the shape of a rodtake object wi th dynam,ie deformation is introduced. T h e potent ial and the kinet ic energy of the object and t h e geometric constraints tmposed o n it are t h e n f o r m u - lated. T h e shape of the dynamical ly deforming object can be derived by tnk l im i z ing th,e digerence between the kinet ie energy and the potent ial energy u n d e r th.e geometric constraints. Next, a procedure t o compute the defoamed shape i s developed by u s e of E d e r ' s approach. Fin)allg, s o m e numer ica l examples are &own in order to dem.onslrcaie h o w the proposed approach computes the shapes of deformed rodlike objects.\n1 Introduction In manu\u20acacturing, the automation of handling and manipulative processes which deal with deformable objects such as rubber tubes, sheet metals, cords, leather products, and paper sheets has been done but it is not enough to satisfy our requests. In manipulative processes, if the shape of deformed objects can be utilized actively, we can operate them successfully. If i t is unexpected, however, the operations mag result in failure. Modeling of deformable objects is thus necessary in order to evaluate the shape of them on a coniputer in advance arid t,o derive task strategies to carry out manipulative operations successfully by a.voiding\ndeforrnation or by utilizing it. Zheng et a1 derived strategies to insert a flexible beam into a hole without wedging or ja.\"ing[l]. Villarreai ett al developed strategies by use of the buffer zone, which represents the complia,nnce of flexible parts[2]. We have developed a modeling technique of rodlike objects such as wires considering its static deformation[3]. Nakaga.ki et al have been studying insertion task of a flexibie wire int.0 hole[4]. However, these studies do not consider the dynamical effect of deformable objects when they deform. Modeling of dynamic deformation becomes important because the dynamicai effect of them cannot be neglected if they are operated quickly by humans or machines. Furthermore, by considering dynamic deformation, we can derive new task strategies which cannot be derived when only static deformation is considered. For example, when we manipulate a rodlike object, slowly as shown in Figure l-(a.j, it will impact against an obstacle. But, quick manipulation can avoid impacting as shown in Figure I-(b) even if a manipmla.tor tracks the same trajectory. Also, we can identify whipping or lariating ias one of good strategies t o operate the far end of a deformable rodlike object such as a whip or a lariat quickly. Therefore, it is important for quick ninnipulation of deformable objects to eva.luate the shape of them which deform\nProc. IROS 97 0-7803-4119-8/97/$1001997 IEEE",
            "197\ndynamically in advance. In this paper, we will analyse the dynamic deformation of deformable rodlike objects. First, a geometric representation of dynamic deformation of a rodlike object in 3-dimensional space is established. Secondly, the potential and the kinetic energy of the object and the geometric constraints imposed on it are formulated. Thirdly, procedure to compute the deformed shape is developed by use of Euler\u2019s approach. Finally, some numerical examples are shown in order to demonstrate how the shapes of deformed rodlike objects are computed using the proposed approach.\n2 Modeling of Rodlike Object Deformation\n2.1 Geometric Representation of De-\nIn this section, we will formulate the geometrical shape of a rodlike object, which moves and deforms dynamically in three-dimensional space. Let L be the length of the object, s be the distance froin one endpoint of the object, along it, and t be the time. Let us introduce the global space coordinate system and the local object coordinate system at individual points 3n the object and at each time, as shown in Figure 2, LD order to describe the motion and the deformation 3f a rodlike object.\nLet 0-zyz be the coordinate system fixed on space znd P(s,t) - (qC be the coordinate system fixed on zn arbitrary point of the object at distance s and Lime t . Select the direction of the coordinates so that h e <-axis, qaxis, and C-axis are parallel to x-axis, yw i s , and z-axis, respectively, in natural state where the object neither move nor deform. Theii, the moion and the deformation of the object are represented 3y the relationship bet ween the local coordmate sys,ern Pjs,t) - Jq( and the global coordinate system 3-zyz. Let us describe the orientation of the local :oordmate system with respect to the space coordilate system by use of Eulerian angles, 4 ( s , t ) , O(.s,t),\nformed Rodlike Objects\nand $(s, t ) . Namely, rotational transformation from coordinate system P(s, t ) - (q< to coordinate system 0-zyz is expressed by the following rotational matrix:\nFor h e sake of simplicity, cos 19 and sin 8 are abbreviated as CO and So, respectively. Note that the Eulerian angles depend upon para.meters s and t .\nBy using above rotational matrix, a unit vector along (-axis at the natural state is transformed into the following vector due to the object motion and deformation:\nLet a: = [ t ( s , t ) y(s, t ) z(s, t ) IT be spatial coordinates corresponding to point P(s, t ) along 2-, y-, and z-axis, respectively. The spatial coordinates can be computed by integrating the above vector. Namely,\nx = 5 0 + 1 \u2019 6 d s (2)\nwhere XO denotes the coordinate at the end point corresponding to s = 0, which is represented as a function of time t .\nLet us describe the curvature of the object and its torsional ratio at time t in order to express bending and torsional deformations of the object. Let 40, Bo, a:id pb0 be Eulerian angles at the end point corresponding to s = 0. Then, these are represented as a function of time t . Let tc(s,t) and x ( s , t ) be the curvature and the torsional ratio at point, P(s,t), respectively. \u2018The curvature and the torsional ratio can be described by use of Eulerian angles 4, 8, $, arid Bo as follows:\nNext, let us describe the velocity and the angular velocity of the object at time t , in order to express motion of the object. Let t~ be the velocity of the object, at the point P(s, t ) , namely,\nFurthermore, let w1 (s, t> and w ~ ( s , t ) be the angular velocity for deformation around the axis which intersects with the central axis perpendicularly, and that around the central axis at point P(s, t ) , respectively as shown in Figure 3. It is found that these two angular"
        ]
    },
    {
        "image_filename": "designv11_24_0000526_0017-9310(96)00146-9-Figure9-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000526_0017-9310(96)00146-9-Figure9-1.png",
        "caption": "Fig. 9. Distributions of tangential stresses tr~ in elastomer thermal-protective coating of a cylindrical tube under the action of internal pressure and heat flux, figures at curves are time t(s).",
        "texts": [
            " A level of pore pressure is essentially higher than that for the first type, it is connected with essentially lower gas-permeability due to small porosity ~pO. Maximal values ofp reach 15 MPa. By a high level of internal pressurep\" we can explain that radial stresses aR prove to be only compressing (Fig. 8). Therefore for the given combination of the material, the structure and the thermo-force action conditions, tangential stresses tro are the most dangerous. At intensive pyrolysis process shrinkage tensile stresses a~ appear in the coked zone (Fig. 9); their magnitudes are rather high max ao ~ 43 MPa. It is the tangential tensile stresses a , that become the cause of destruction of the material in the coked zone, when strength properties of the material fall down under the limiting values. The present paper gives the statement of the coupled problem on deforming and internal heat-mass transfer of elastomer ablating materials with finite deformations. The suggested system of equations allows to determine stress, temperature and pore pressure fields in porous reacting materials withstanding finite deformations (up to tens of percents), for example, in elastomer thermal-protective coatings of combustors of rocket engines, solid propellants (energetic materials), etc"
        ],
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    },
    {
        "image_filename": "designv11_24_0002471_135065002760199943-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002471_135065002760199943-Figure1-1.png",
        "caption": "Fig. 1 Engine support for the experimentation",
        "texts": [],
        "surrounding_texts": [
            "The engine support of the experimentation is a highspeed gasoline engine, indirect injected, 2 l, four cylinders and 16 valves (\u00aering order, 1\u00b13\u00b14\u00b12). The bore and stroke are 86 mm. The engine has a maximum brake horsepower of 97.4 kW at 5500 r/min and a maximum torque of 180 N m at 4250 r/min. The crankshaft has \u00aeve main bearings and eight counterweights. These bearings are numbered from the side of the \u00afywheel. The \u00aerst three main bearings are studied. The bearings are half-grooved, their diameter and width being 60 mm and 18.4mm respectively. The bearings have caps independent of each other (F ig. 1). The casing rolls and the bearing caps are \u00afaked graphite cast iron. The crankshaft is spheroidal graphite cast iron. The support of the half-bearings is steel (thickness, 1.6 mm) and the antifriction alloy of the bearings is aluminium\u00b1tin. On each crankshaft bearing, four eddy current gap sensors have been \u00aexed in the same plane (F ig. 2). Their diameter and length are 4 mm and 13 mm respectively. These sensors were selected for their insensitivity to the environment properties that separate them from the target (ageing of oil, impurities and soots). Moreover, J01901 # IMechE 2002 Proc Instn Mech Engrs Vol 216 Part J: J Engineering Tribology at UNIV OF PITTSBURGH on March 14, 2015pij.sagepub.comDownloaded from they are extremely precise (uncertainty of the measure +1 mm), with a high resolution and a very reduced size. Thus the oil-\u00aelm thickness is measured at four points per bearing and the corresponding crank pin trajectory is deduced from the following relations: ex \u02c6 h3 \u00a1 h2 \u00a1 h4 \u2021 h1 2 2 p ey \u02c6 h3 \u00a1 h2 \u2021 h4 \u00a1 h1 2 2 p In the width of the bearings, the sensors are placed on the edge for reasons of feasibility and because of the groove on the upper half-bearings of the crankcase (this position does not allow measurement of the misalignment of the shaft into the sleeve because there are no sensors on the other side of the bearing). The distance between the median plan of the bearing and the axis of the sensors is 7 mm for the bearing 1 and 5.5 mm for bearings 2 and 3. The sensors are numbered from 1 to 4 for bearing 1, from 5 to 8 for bearing 2 and from 9 to 12 for bearing 3 (F ig. 3). The two screws of the bearing cap 3 are instrumented with a stress sensor. Only the reaction of the bearing cap can be detected from the efforts measured in the screws because they are sensitive only to the efforts directed towards the cap."
        ]
    },
    {
        "image_filename": "designv11_24_0003917_0278364905058242-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003917_0278364905058242-Figure8-1.png",
        "caption": "Fig. 8. The collection of feasible three-limb postures in contact c-space.",
        "texts": [
            " Then we show that the approximation of a convex set by p maximal cubes is a convex optimization problem. The set F ijk of feasible three-limb postures is specified in eq. (2) as a union of three sets, each corresponding to a different pair of two-limb postures. The following lemma asserts that each of these sets is convex in contact c-space. LEMMA 2. In each cell Ii \u00d7Ij \u00d7Ik of contact c-space, the set F ijk of feasible three-limb postures is a union of three convex sets. Note that any of the convex sets comprising F ijk may be empty. For example, in Figure 8 each set F ijk is either empty or consists of a single convex set. Proof. The three sets that comprise F ijk have a similar form. Hence it suffices to consider only one of these sets, say P ij k\u0304 \u2229P i\u0304jk \u2229Rijk. The prisms P ij k\u0304 and P i\u0304jk are defined by the intersection of linear inequalities. Each prism is therefore a convex polytope in contact c-space. Next consider the reachability set Rijk. The existential quantifier in eq. (1) acts on a set, denoted R\u0304ijk, which is defined in the five-dimensional space (s1, s2, s3, c): R\u0304ijk = { (s1, s2, s3, c) \u2208 Ii \u00d7 Ij \u00d7 Ik \u00d7 IR2 : max{\u2016x(s1)\u2212 c\u2016, \u2016x(s2)\u2212 c\u2016, \u2016x(s3)\u2212 c\u2016} \u2264 R } ",
            " Finally, the two walls at the tunnel\u2019s top form an opening cone. These geometric features are significant, since the robot must use friction effects in order to traverse such features. The walls are parametrized by path length in counterclockwise order (Figure 12). Thus s = 0 and s = 270 correspond to the bottom and top of the tunnel\u2019s right side, while s = 270 and s = 540 correspond to the top and bottom of the tunnel\u2019s left side. Using this parametrization, contact c-space is the cube [0, 540]\u00d7[0, 540]\u00d7[0, 540] depicted in Figure 8. The center point of contact c-space at (270, 270, 270) represents three-limb postures where the three footpads touch the upper point of either side of the tunnel. Topologically, one ought to put a cube-shaped puncture at the center of contact c-space, since the top points on the left and right sides of the tunnel are physically distinct. Topologically, when one introduces a small cube-shaped puncture at the center point, contact c-space becomes a set embedded in a three-dimensional torus. This fact has been noted in the context of three-finger grasps by Leveroni and Salisbury (1995)",
            " Hence the vertices (0, 0, 0) and (540, 540, 540) certainly lie outside the set of feasible three-limb postures presented below. First consider the computation of the feasible three-limb postures in contact c-space. Figure 7 shows the collection of two-limb equilibrium postures in the (si, sj ) plane. It can be seen that these postures form a convex polygon in each planar cell. The edges of these polygons consist of frictional equilibrium constraints and the cell\u2019s boundaries. Note that the figure is symmetric with respect to the si = sj axis, reflecting the possibility of switching limbs between the two contacts. Figure 8 shows the collection of feasible three-limb postures. These postures are intersection of pairs of prisms whose polygonal cross-section appears in Figure 7. In this particular tunnel, all prism intersections automatically satisfy the reachability constraint. (This is an artifact of our tunnel environment, coefficient of friction, and robot radius.) The collection of feasible three-limb postures has a sixfold symmetry consisting of six symmetric \u201carms\u201d: every non-empty cell represents an assignment of the three limbs to a triplet of walls, and there are six such assignments"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003754_bf02844262-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003754_bf02844262-Figure4-1.png",
        "caption": "Figure 4 a) Inertial coordinate system. b) Body-fixed coordinate system. c) A definition of the Euler angles.",
        "texts": [
            "50 \u00d7 10\u20138\u03b14 (3) CL(\u03b1) = 6.25 \u00d7 10\u20133\u03b1 + 2.41 \u00d7 10\u20134\u03b12 \u2013 3.44 \u00d7 10\u20136\u03b13 (4) CY(\u03b1, \u03c9) = (\u20131.50 \u00d7 10\u20133 + 6.49 \u00d7 10\u20134\u03c9 \u2013 8.35 \u00d7 10\u20135\u03c92)\u03b1 + (\u20134.11 \u00d7 10\u20135 \u2013 3.82 \u00d7 10\u20135\u03c9 + 2.64 \u00d7 10\u20136\u03c92)\u03b12 + (4.94 \u00d7 10\u20137 + 2.74 \u00d7 10\u20137\u03c9 \u2013 1.77 \u00d7 10\u20138\u03c92)\u03b13 (5) Cm(\u03b1) = 1.51 \u00d7 10\u20132\u03b1 \u2013 1.69 \u00d7 10\u20134\u03b12 (6) The differences between the data calculated from the formulae and the wind tunnel data are estimated to be within SD = 0.034 for CD, SD = 0.061 for CL, SD = 0.089 for CY and SD = 0.076 for Cm. The inertial right-handed coordinate system is shown in Fig. 4a. The origin is defined as the point of intersection of the goal line and the left touchline from the kicker\u2019s view on the ground, where the XE axis is in the horizontal forward direction, the YE axis is in the horizontal right direction and the ZE axis is in the vertical downward direction. The body-fixed coordinate system is shown in Fig. 4 b. The origin is defined as the centre of mass of the ball. Its xb axis is aligned with the longitudinal axis, and yb and zb are aligned with the transverse axes, with the zb axis passing through the valve. The sequence of rotations conventionally used to describe the instantaneous attitude with respect to an inertial coordinate system is shown in Fig. 4c (Stevens, 1992). Starting from the inertial coordinate system: 1 rotate about the ZE axis, nose right (positive yaw \u03a8) 2 rotate about the y1 axis, nose up (positive pitch \u0398) 3 rotate about the xb axis, right wing down (positive roll \u03a6). 52 Sports Engineering (2006) 9, 49\u201358 \u00a9 2006 isea In terms of coordinate transformations we then have ( ) = [mij] ( ) (7) cos\u0398 cos\u03a8 (sin\u03a6 sin\u0398 cos\u03a8 \u2013 cos\u03a6 sin\u03a8) (cos\u03a6 sin\u0398 cos\u03a8 + sin\u03a6 sin\u03a8) [mij] = ( cos\u0398 sin\u03a8 (sin\u03a6 sin\u0398 sin\u03a8 + cos\u03a6 cos\u03a8) (cos\u03a6 sin\u0398 sin\u03a8 \u2013 sin\u03a6 cos\u03a8) ) (8) \u2013sin\u0398 sin\u03a6 cos\u0398 cos\u03a6 cos\u0398 U V W X "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002512_026635118700200301-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002512_026635118700200301-Figure8-1.png",
        "caption": "Fig. 8. Structure with 90\u00b0-60\u00b0-30\u00b0 elements.",
        "texts": [
            " However, as the apex angle increases the clear width and head room also increase, even though the length of erected module decreases. At the same time the number ofelements, and hence the number of hinges, increase. All of the illustrations of usable buildings as well as the data in the tables have made use of elements in the form of isosceles triangles. In Figs. I and 2 an indication was given that other forms of triangular element were acceptable. Whilst other forms are usable they would probably not find ready acceptance except in special circumstances. The reason can be seen in Fig. 8. In this illustration the 90\u00b0- 60\u00b0-30\u00b0 element has been used and it is immediately apparent that for the side walls to contact the ground over their entire length, the structure must be skewed. Whilst in some instances this feature may be architecturally desirable it would in general make planning, handling and erection somewhat difficult. So far only structures have been considered which are erected in a straight line and rest predominantly on a levelsurface with the long edges of the modules essentiallyparallel",
            " The additional two degrees of freedom correspond with the end shape becoming a four-bar mechanism instead of a three-link structure and the end must be braced accordingly. C. G. Foster, S. Krishnakumar Physically unfolding the device and erecting it on the ground is quite simple. Predicting, mathematically, where the nodes would be is quite another problem. For regular isosceles elements in a structure erected on flat ground the calculation of node positions can also be simple. Small departures from this regular form can quickly compound the shape calculations. Even the relatively simple form of structure with 90\u00b0-60\u00b0-30\u00b0 elements erected on level ground (Fig. 8) leads to a set of seven simultaneous quadratic equations. However, since the device can be made statically determinate it is always possible to determine the locations of all nodes regardless of how complex the geometry may be. The complete technique for performing these calculations together with a suitable computer program (in BASIC) is given elsewhere (Ref. 10). Essentially, the technique relies on the fact that the side of the element is of invariant length. If there are two elements hinged together and the locations of three of the nodes are known, while that of the fourth (at one end of the hinge) is unknown, then this node must be a fixed distance from each of the other three nodes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002619_095440605x31481-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002619_095440605x31481-Figure7-1.png",
        "caption": "Fig. 7 Geometry of grinding a CV2-gear using a flaring-cup that swivels about a \u2018vertical\u2019 axis, fm \u00bc 208, w/k \u00bc 0.2, and k/R \u00bc 0.95",
        "texts": [
            " Firstly, the grinding wheel contacts the tooth flanks in a confined spot that wanders about, rather than along an arc across the whole face, thereby obviating burns and allowing coolant into the grinding zone and swarf out of it. Secondly, the adjustable eccentricity can be used to maintain constant grinding radii if, upon repeated dressing, the grinding wheel rim thickness changed (by equal amounts on the outside/inside). Two decades later, another method of generatinggrinding CV2-gears was disclosed by Koganov et al. [30], then by Shejnin et al. [31]. As shown in Fig. 7, a flaring-cup grinding wheel of 608 mean cone angle is mounted on a spindle that is inclined at 608 to the generating rack pitch plane. (In reference [30], the wheel is made up of two nested ones on concentric, contra-rotating spindles.) The grinding wheel rim is bevelled in its axial section to a generating rack tooth shape, and it touches both flanks of a tooth space at a point each. The rest of the grinding surfaces gradually clear the flanks as the wheel cross-section in the pitch plane forms a crescent",
            " The inside and outside generatrices in the plane that contains the cone and the oscillating axes mimic the machining process of Fig. 6, yet in a serpentine route. This grinding method offers the advantage of not imposing bounds on the number of teeth; it could even be used to finish CV2-racks. (A flaring-cup milling cutter could be used to generate CV2-gears and racks according to the same method.) It is worthwhile to study the geometry of this method a little deeper. By completing the construction lines in Fig. 7 it can be shown that the crescent section is delimited by two ellipses of minimum radii of curvature (at their vertices) given by rcav,vex \u00bc k cosfm sin (60+ fm) w tan (60+ fm) (5) Proc. IMechE Vol. 219 Part C: J. Mechanical Engineering Science C01505 # IMechE 2005 at UNIV OF VIRGINIA on July 12, 2015pic.sagepub.comDownloaded from For fm \u00bc 208 and w \u00bc 0.2k, the curvature radii will be rcav \u00bc 0.9189k and rvex \u00bc 1.2236k. The mean tooth-trace radius R should equal the mean value of these two curvature radii with a small bilateral allowance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003639_s00397-005-0003-0-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003639_s00397-005-0003-0-Figure1-1.png",
        "caption": "Fig. 1 Schematic of small amplitude oscillatory shear flow, showing the orientation (h) and the velocity field and the other geometric variables used in the problem (adapted form Burghardt 1991). The wall stress oscillates with a given frequency x",
        "texts": [
            " The equations that describe the flow processes in nematic liquid crystals consists of the linear momentum balance, the internal angular momentum or director torque balance, and also the constitutive equations for the dissipative and elastic stress tensor, and for the viscous and elastic torques acting (Chandrasekhar 1992; de Gennes and Prost 1993; Larson 1999). The materials of interest in this paper are uniaxial rod-like (calamitic) nematic liquid crystals (NLCs) whose orientation is defined by a unit vector known as the director n. Here we analyze the small-amplitude oscillatory shear flow between two flat plates, when the flow is driven by an imposed oscillatory stress at the wall (see Fig. 1). The geometry of the problem is described with a rectangular coordinate system defined by unit triad (dx, dy, dz). The shear flow velocity is the x coordinate direction, while the velocity gradient is parallel to the y coordinate direction. The initial orientation of the director is homogeneous and along the y-coordinate: n(y,t=0)= (0,1,0). In the presence of a small-amplitude harmonic wall-stress, the linearized velocity and director field are: v \u00bc 0; v y; t\u00f0 \u00de; 0\u00f0 \u00de; n \u00bc h y; t\u00f0 \u00de; 1; 0\u00f0 \u00de; where h is the tilt angle between the y-coordinate and the director n"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000847_70.833184-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000847_70.833184-Figure2-1.png",
        "caption": "Fig. 2. A manipulator before and after a failure of the first joint. The joint error ~q induces motion of the interest point r (a point on the hand in this case). Two possible measures of the point\u2019s motion, denoted e , are shown: path length assuming stationary healthy joints and Euclidean distance.",
        "texts": [
            " For some failure modes, will be a function of . (Examples will be given in Section VI.) Let point , whose Euclidean-space error is of interest, lie at the tip of vector in Denavit\u2013Hartenberg (D\u2013H) frame , . (This article uses the frame-labeling scheme of Paul [27].) The point so chosen is completely general\u2014any location in any frame. Then, the point error represents a measure of point \u2019s motion caused by . Two possible values, path length assuming stationary healthy joints and Euclidean distance, are shown in Fig. 2. Let be the perpendicular vector from the line passing through , the -axis of D\u2013H frame , to the tip of , Path length is appropriate when the focus is on the process of the failure, and Euclidean distance is appropriate when the focus is on the result of the failure. Examples showing when each of these is applicable are given in Section VI. In the ensuing text, however, will be used in the general sense and not restricted to either of these values. The scalar can be found through (4) where is the vector from the origin of D\u2013H frame to D\u2013H frame "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003449_tmag.2004.824720-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003449_tmag.2004.824720-Figure4-1.png",
        "caption": "Fig. 4. Time variation and distribution of flux density and loss distribution of motor with semiclosed rotor slots at synchronous speed.",
        "texts": [],
        "surrounding_texts": [
            "transformation of the currents waveforms. The sum of the harmonic secondary copper losses can be also calculated from the waveforms of the harmonic secondary current densities at each finite element in the rotor cage as\n(3)\nwhere is the time-harmonic order observed from the rotor coordinate system (moving coordinate system [3]).\nOn the other hand, the torque of the motor is calculated by the nodal force method [4] as\n(4)\nwhere to is the nodes included in the rotor region, and are the radius vector and the nodal force of th node. However, the negative torque caused by the harmonic core losses is not included in (4) because the eddy current and hysteresis phenomena in the laminated core are neglected in the finite element analysis. In this paper, we take into account the effect by the second step in Fig. 1, as follows.\nAlthough many methods are proposed to calculate the core loss, it is suitable for the purpose of this paper to calculate the sum of the harmonic core losses from the harmonic magnetic inductions [5] as\n(5)\nwhere are the sums of harmonic eddy current and hysteresis loss of the core, is the density of the core, and and are the th harmonics of the radial and peripheral components of the flux density. and are the experimental constant obtained by the Epstein frame [6]. This expression can also be considered to be valid for the calculation of rotor harmonic core losses with the time harmonic order observed from the rotor coordinate system.\nFirst, let us consider the harmonic torque generated by the harmonic rotational magnetic field whose space-harmonic order is and the time-harmonic order is observed from the stator coordinate system. In this case, the harmonic torque can be calculated from the rotor harmonic loss due to the electric machine theory as\n(6)\nwhere is the mechanical angular speed and is the slip of the rotor from the harmonic rotational magnetic field, that is\n(7)\nwhere is the synchronous speed, is the slip of the rotor from the fundamental rotational field, and when the harmonic field is the forward wave and when the backward wave. Substituting (7) into (6), we have\n(8)\nThis expression implies that the harmonic torque is always negative when the rotor slip is small and is much larger than\n. It is true of the major harmonic fields at the rotor when the motor is driven by the sinusoidal power supply. For example, in the case of the stator slot ripples, and slot number plus minus . In this case, (8) can be approximated as\n(9)\nConsidering the transformation between the stator and rotor coordinate systems, this expression is also valid for the harmonic torque caused by the harmonic losses generated at the stator. Thus, we can calculate the negative and the total torque considering the harmonic core losses as\n(10)\n(11)\nFig. 2 shows the system for the measurement of the negative torque of the induction motor at synchronous speed. First, the induction motor is rotated without the power supply using the synchronous permanent magnet motor. At this moment, the input power of the permanent magnet motor includes not only the own losses, but also the mechanical loss of the induction motor. Next, the power is supplied to the induction motor. The input power of the permanent magnet motor increases according to the voltage of the induction motor. It can be considered that this increase corresponds to the negative torque generated by the induction motor.\nThe total torque of the induction motor at the load condition is also measured using the torque detector with the analyzing",
            "recorder. The average torque is obtained from the 32 000 data at steady rotation with the sampling time 100 s.\nTable I shows the specification of the measured motors. Two types of the motor are investigated to clarify the effects of the harmonic fields. One is with the closed rotor slots and the other is with the semiclosed slots, which will cause relatively large slot harmonics.\nFigs. 3 and 4 show the calculated results of the time and space variation of the magnetic field and the loss distribution of the motors with the closed and semiclosed slots, respectively. In the case of the closed slots, the time variation of the magnetic field\nat the stator is nearly sinusoidal. On the other hand, in the case of the semiclosed slots, the waveform at the stator includes the harmonics caused by the rotor slot ripples due to the movement of the rotor. This harmonics must cause the part of the negative torque. The large harmonics caused by the stator slot ripples also appear at the rotor teeth tops of both motors. As a result, the losses concentrate at the rotor surface. In the case of the semiclosed slot, the high loss density area is larger than the case of the closed slot.\nThe measured and the calculated negative torques at synchronous speed are shown in Fig. 5 for the accuracy estimation. Considering the difficulty to measure and calculate the harmonic characteristics accurately, it can be said that the results",
            "agree well and that the proposed method is applicable to calculate the negative torque of the induction motors. Both the measured and calculated results indicate that the negative torque in case of the semiclosed slots is larger than the case of the closed slots, whose reason can be explained by Figs. 3 and 4. In the case of the semiclosed slot, the negative torque is nearly 5% of the rating output, which must not be negligible for the vector-controlled motors.\nFig. 6 shows the measured and calculated total torque due to the load. The calculated result by the conventional method is also shown. The conventional method clearly overestimates the total torque in case of the semiclosed slot. On the other hand, the accuracy of the torque calculation is improved by the proposed method.\nThe negative torque of induction motors caused by the slot ripples is investigated from both sides of the measurement and the electromagnetic field analysis. In the analysis, the negative torque is calculated from the harmonic losses of the motor ob-\ntained from the results of the time-stepping finite element analysis with the assistance of the electric machine theory. It is clarified that the negative torque of the motor with the semiclosed rotor slots is not negligible and that the accuracy of the torque calculation is improved by the proposed method.\n[1] K. Yamazaki, \u201cInduction motor analysis considering both harmonics and end effects using combination of 2-D and 3-D finite element method,\u201d IEEE Trans. Energy Conversion, vol. 14, pp. 698\u2013703, Sept. 1999. [2] , \u201cA quasi 3-D formulation for analyzing characteristics of induction motors with skewed slots,\u201d IEEE Trans. Magn., vol. 34, pp. 3624\u20133627, Sept. 1998. [3] , \u201cGeneralization of 3-D eddy current analysis for moving conductors due to coordinate systems and gauge conditions,\u201d IEEE Trans. Magn., vol. 33, pp. 1259\u20131263, Mar. 1997. [4] A. Kameari, \u201cLocal force calculation in 3D FEM with edge elements,\u201d Int. J. Appl. Electromagn. Mater., vol. 3, pp. 231\u2013240, 1993. [5] J. G. Zhu and V. S. Ramsden, \u201cImproved formulations for rotational core losses in rotating electrical machines,\u201d IEEE Trans. Magn., vol. 34, pp. 2234\u20132242, July 1998. [6] K. Yamazaki, \u201cEfficiency analysis of induction motors for ammonia compressors considering stray load losses caused by stator and rotor slot ripple,\u201d in Conf. Rec. 2001 IEEE Industry Applications Conference 36th Annual Meeting, vol. 2, 2001, pp. 762\u2013769."
        ]
    },
    {
        "image_filename": "designv11_24_0001466_978-1-4471-1021-7_60-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001466_978-1-4471-1021-7_60-Figure4-1.png",
        "caption": "Figure 4: The snakeboard's instantaneous center of rotation",
        "texts": [
            " (5) can be expressed as a constraint distribution: 'D - {!.... b!.... ~ ~ ~ ~} q - span a 8x + 8y + C 80' 81/1' 8\u00a2b' 8\u00a2, ' (17) where a = -l[cos \u00a2b cos( \u00a2, + 0) + cos \u00a2, cos( \u00a2b + 0)] b = -l[cos \u00a2b sin( \u00a2, + 0) + cos \u00a2, sin( \u00a2b + 0)] c = sin(\u00a2b - \u00a2,). (18) The vertical distribution was defined in Eq. (11), and the constrained fiber distribution is: Sq = 'Dqn VqQ = span{ a :'1) + b :y + c :,,}. Sq corresponds to instantaneous rotations of the snake board about the point where the two wheel axes intersect (Fig. 4). The nonholonomic momentum of Eq. (16) is: pc =< ~~;(eC)Q(q) > q A' \u2022 \u2022\u2022 = (mR2 + Jc)O + Jr c1/; + JwC(\u00a2b + \u00a2,), (19) R is the radius from the instantaneous center of rotation to the snakeboard's center of mass. Thus, pC corresponds to the snakeboard's angular momen tum about the instantaneous center of rotation. If the front and back wheels were fixed, this momen tum would be conserved, as the fixed wheels pro vide a holonomic constraint of rotation about the fixed center. However, since the constraints are variable, the snakeboard's momentum can be al tered by internal forces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002475_jctb.280360804-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002475_jctb.280360804-Figure2-1.png",
        "caption": "Figure 2. Schematic representation of the H z 0 2 detection system. E(ox/red) are the redox forms of a peroxidase enzyme and MED(ox/red) the redox forms of a mediator of electron transfer.",
        "texts": [
            "22 This enzyme represents a major fraction of the total soluble protein in muscle, and its release into the bloodstream is associated with several forms of muscle damage including acute myocardial infarction. The analytical methods described so far have exploited the ability of the ferricinium ion to act as an electron acceptor. However, ferrocene and its derivatives can also act as electron donors, as in a recently developed electrochemical assay for hydrogen per~xide . '~ The essential features are shown schematically in Figure 2. The fundamental reaction is the enzymic reduction of substrate (i.e. H202) by peroxidase. Native enzyme is regenerated by subsequent electron transfer from a gold or pyrolytic graphite electrode to the enzyme, via a redox mediator. This not only provides a direct assay for hydrogen peroxide (Figure 3), capable of detecting -lo-\", but can also be a component of other analytical systems in which hydrogen peroxide is a product of one or more further chemical reactions. An electrochemical method for detection of cholesterol has been devised which incorporates the peroxidase-coupled assay"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000922_s1474-6670(17)58102-1-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000922_s1474-6670(17)58102-1-Figure2-1.png",
        "caption": "Fig. 2 . Feet lbac k func tion v ddilled ill (11 ) . jl/ I I < ro/,2- which prf'vpnt:s 6 ['mm Iwnmlillg t.oo large, a~ we :-<.hall see.",
        "texts": [],
        "surrounding_texts": [
            "(1 ) Onc(~ t.he slat~ !JrUi (>nt,pred .!\\'u , switch to a feed bi.'\\.(..'k (:o u~rol It:! which sttthilizes link :l ill its inve r ted s i-ate; (:-~) \\-\\,ith link ;) sta hili ?'cJ , a pply a fef'dback contl'Ol 'i f ;}\nwhi<.:h swings link \"2 lllt.O a. neigld.JO rhood .'V\"u-u of tbe- cquilibrilllllll1a.nifo ld V-U: (--1) On cc Lhf~ s t.ale' lii-l ~ ent.(,J'cr\\ .Vu - u . SWil.ch t ( ) a [(:ed back (\"oml'o l 1\"4 which st.lI hili z('s bOlh link 2 and link a on U-U .\n13(~('a.us(:' of the Bwit.ch illg nature of t.1[( ' cont.rol , the rcsld t is a pplicable t.o the f.; in~le inverted pendulum, in eith er it\" rot.ational o r it.s t ranslat io na l \\'miants. FUrt.hermore, \\Vi' s tress thrll. cad, (Jf UlCS I? \"0111/'01.\" is llonliHear f eed buck , and hot feed - fOl\"wa.rd . lu(k'cd . \\ ... \u00b7itll the :;witching logi c, our nmt rol la.\\v n Ul 11P: {'oll sid('r~d a. single, stat ic Jlolllinf';'lJ' ('c'I' dhack .\n\\Ve Iwgin by defining a cont.ro l ltu\" J. (} , v), that c.a1l4 .. :eJs Ihe ro r('(' ~ applied t,n lin k 1 hy link.') '1 ilnd :1, effective l}' det;()up ling tht' :'iy~'-CIII. Solv iug {I ) fo r iir, <.\u00b7\u00b7quatillg the ri:'~lllt with the lle\\ ... \u00b7 ill pll t, 1) , and :mh'illg for 'U = /to give::;\n(2)\nwhe re' .3. ::;: 1/1'11 Jlt n 1JI';Q - 111'f:! III:13 - 1I1'T:3\"I'n is the cle \"c' [minal.<..\" or the ine rlla matr ix . I\\ou .. l.h .. 1. (2) is globa lly defined. :\\pply illg (2) \\.n (1) a lld d('fining t,he') stat.es et = fl r .. ~:! ----== 1; 1 . '/ :1 :::; 1/:\\. I\" l ::::: <rl\u00b7 'f: ! = '1:1. 'h = 1/ 3, we ('n n rt'\\vril.e ( I ) ill 110rnll1..1 for m (Isido!'i 1~1.\"9):\n(I =6 f!.:: .;::: //\nf/ ' = // 2\nI\\'u 1\\' [1 h\u00b74 - -. SIIl -'/ 1 -- - .-11\"!. '1\" 1/ . -I' (\u00b7os -'11 {\\\"2 / \\ \"2 \\ ~\n. - ~~ + \"\"1 (2 '11 )-'1 '/ :1 = '!:}\n(:l)\n(4)\n(5)\n(6 )\n(7)\n(8)\nHen'. l.lw nlap from v t.o ~1 = '1 1 i . ...; m'ld<.' linear , a Hd t.lw dYllarllic~ 1' C' IJl\"c'st:'lltillg lillk:2 (Il l , f1\" ' ) and link ~~ (1/:i . '1-11 a rE' d(~coup led from o ne-rw()t lwf. .\\Jure' that t.he' ze ro dYIHIl UIC6,. ckfiued by sl' tt.ing~! == ( :! ::::: U. are eXil C' Uy I-IloSI' f or 1,\\ .... 0 1IIlfon :,~d Iw nrlu lll!ll:oj .\n2.1 Swing- Up of L'lnA: ,1\nIn rle~ iglling till' link :~ swi n~-Hp cont.ro l. It l . we mnkc use of thp. fv llowing two o bscr vations. Fi l'~ t., beca.lI sl' U (l\nder.o upl e:-; the J Yl1il.m il:s of link '2 from ~he t.he rest ( ) f the sy s tcrll ~ Wf' may ignore (5) (Ind (6) . Of co urse. 'l l tlu<i '12 will b., ('x ci I-eel by \u00b7lll . bw \"he ir (almofit.) g lo bnl ex\" p oncu l.ial sta bili t.y (till' ;!;0rO dynamic::::; are expo nen t iall.\" ~table ) ju:';t.ifleJ:; this s illLplifje; ~t.iou, Se.c:o udly, h <..'Cause ~I is rot.at:ionai , and because eil,:h ~quilibl'illlll tnanifo kl is iu vari ant wit-h r~~JlN : l. to ~ 1. \u00b7-ye C;Ul ignore' the beha.v ior of {I (:.~) during 1.Iw swing-u p flpe rHtio ll . O IlU-~ I.he sys t.PnJ is :;tabi!ized OH U - U, t.he:\" (:Oll t ro t call mo\\,(' tlw syst.c rn 1.0 the or\"ig iu <1.iong V - U . s ho uld ~ l rlrirt. d u r ing :> wing-u p . (T llis c~a l1ll ot, 1.)(' j ust.ified fo r Uw t.ra.nsJat,jollal ill v~ ~ n,(-'d pc ndulum sys tem . 1)('C'i)u:-<e in dl a.1. C(lS(: , t\u00b7, Im .... limite d tr r\\.\\'d .)\nIn addition to t he ~w t.wo Ob::i\u20acT -!at.iolls . \\v(' wjlllll~gJf'c t, tile higher-order centripetal te1TWj ~ in(2fll ) ~ a nd ::; in( 2 7;t~ ) S4during tlw df8igll of t.he s\\\\o' illg -up co uL;\"ol: they a.I'C ll~t ig llore(1 ill ou r s imul a tio ns & l ' xpCl'irn(,l1 t,~, or cours.e. To jn:;tify j,hi~ ~ ilnplificat. i o ll , \\\\le will ;>;ho w t.ha.t ~\"! remains :-:;lllall during swing-up. !\\ote that. t his ;).-:;s lImprioH 11(1.\"3 1 )f~ I ~ 1l IJ lacle f1'l'q u(~ nt.Iy hy o tile\" IT::;cil lT lw r b :')t.udy ing I . hf~ ~W illg- Up prohl nlll foJ' ~l)(' rotn l. jonal illvnicd J,l f.' IHlldUlI1 . e.g. , (Fu rut.a d al . l!l!)1 , \\ Vik l 1111'1 eI al. H)~M )\nThe s im plif ied d Yllfllllics (' hat \\w' conside r wlwll desjgu ing \"(I. ] ar(' lI lt' refo l'I'\n6 ~::: /1\n'II;~ = 1}4\n. !\\'j. h\u00b7w 1\\. ;) ' 14 :::: --.- :0:; 111 113 - - .-11\" + I)\u00b7 -. co:\"; '1/3 . [\\ :1 (\\ :1 }\\ :-I\n(9)\n(Ill)\n( 11)\nT he key icl (-,;,l is 1,0 considel' /1 1.0 l)c n il ill p ut. 10 tlL <;' U/  t r: nwi dynalltlcs (G ~tz and He,l rid: I !:-.HJ;\u00b7; ) ( 10)- (1 1), an ilpproac ll t.hat ha.~ bt'en applied t.o l.lie .,:>wing-up t\u00b7o nl.l'o l o f t.hp: (J.clViJo t (Spong IDfl4 ), By c,'.spntjally ignorillg (0). wc:' are left. I,,\u00b7 i t.l l a se<\"ond-ordcr 1I00dincar syst.elll , whic h ca u be a.nalyzecl usin~ 1\u00b7 ... el! -f'Sf cl b Ji~l lCd phase plane Illct.hods .\nNow , \\,owilder t,11!' ro llowilJg hl'llr i!'l t, i /.~ swing-up con trol f Ol\" ( IOH 11):\n_ { \"I (I) . oos('/3) . O1\"ota\" ('14) V I - Il if 1'131 < rr / 2 if 1'1,,1> ,,/ 2. ( 12 )\nwhere (/'1 (I) > () is a. tillle-va.ry i llg qu:tnti i.y 1:0 J)(' de fined . T Ilt' fund-ioll // i ~ illu st.rated in Figu]'(' 2 for fix c~ rI a I . The ideiL h(~hllld i lli :'> control i ~ 1.0 \"\u00b7pUIllP\" en e rgy in to lin k ;1 by a.ece lcral.ing ir ill the same d irecti.on t hat i t. is rota.t, ing .. but on ly whE'1l il. is pE' lI da ll t. , i .f' .. IJ/:51 < rr ( 2. Note th at. thi s .... d p ~ in;d n{' ( x~ kn'\\t , ion\" i . ...; ~moorli ilud i)olllldco .",
            "T! Ji~ (\\ )[ 11.1'0 1 will cause::; 1t:3 and //.1 ill (,II(' ;,;iJllplitied m(xl!:' ! (11\u00bb)-( 11. ) t.o ent.e r a s lable limit- cycle. whose '\u00b7amplif.ude)' i:'i C:\\. contiuuous]y inccl:'a.-;ing fllUdlOH of a j for ~ufficiently Sn1<:t1l a l . Th i ~ i::; not diftkulL t.o prove. sillce the internal dynamics (10)- ( It) are secoud-ordei\". a ml Bendixon 's Thf' On.'lll appli c:-i. A::; a.1l illll .~t.ratjoll, w(' slio,.,. the phas(' par\u00b7 tr' lil. of I.h(' illl ern<'ll dynalllic\u00b7! fol' {I. I --= ::'0 in Figure :L Now, Wf may propo:;f' t., ... \u00b7o lhe :>Wi llg-lIp l:'t.rategic:'. for U1 . [il,I1('1' determin e a Jlxf'd (11 \\\\'lli<:h caw'if's I,he limit cycle (0 e ntN .Vu . o r 1.0 :-;lowl)1 ill c r('as~' (1 1 (I) as a. fUll ction o f lilllf' llmil Lllf' limit. eyel!' int(' l'sf'cl:; .\\\"u. F.')I' 01\\1' S'y~rem , til l\" value of (I] = :LO sIK('eeds in i li is :'!;oal, a~ can bf! .'\";(\"l'lI ill l'i p; lI H' :L\nOf COlll',e , , in,,\" <ott) = j;,=~,' I'(T) tiT , 16(1 )1 mighl be ('urnI.' large , cOllt,raci icl.illg Ollr .\"implif~/ ing assumption of ig no rillg t.he (~eJ1l.ripeta.1 fo re-e . o r 'A'OI\":;e, plI ~hing the s t.ate trnjcctory Ollt. of JVu . f-I ow(.~ve r , hfX'3U:\"(,. J/ I is bOllwJed . Hlld i~ ,11\\ odd rll llcl.ion of t/1. and is \"1,11 f'ven fUllcLion of '/J' a.nd hl'(: all~e 113 and '/.:1 r:oll vl:.' rge t.o pC'r iodic functio lls, //1 (I) .. IS Cl fuuct.ioll o f tinw a):.;o COIIW' l'g('S t.o a. pf'l'iocli r fUlJrt.io ll wl1o~I' \" 0(' \"\",I ut\"\u00b7 i:-. 'f,1'ro. Pllysically , sillce 1/:3 uucI IJ4 cOIl\\'ergf' t.o <.l \"sY llll llf'lric\" lillIit. \"yde , J/ lrllJs l. <11.':'0 b e periodic and :o;yrulIlerri,: ;- lbOIII. O. Thus, ~2 COll y\"rg ps I n a pn io ciic fHlwt.io ll \\\\\u00b7 iI.II all ,)II i-;(>t., whi c.h would he\u00b7 cl IU' I,n ('/11' t ra nsi t' llI I11 CH rr('d d 11 rill g , '011 \\' (,l'gE' n('~ or '13 and 1}.1 1.0 Ut{' s{,abl (' lill li ! cycle . FIgllf~ ;1 ~hows thE' t.inH:' history of 6( / ) 1'01' t.lw sanw Sillllll\"ltio ll of (9)-(11) , sul} .if'CI \\.0 (12) and adf) := :L Tile DC of[':.,e\\. is v(~ry small, and ~:! {l ) plil inly converges (l) a p\"'l\"i<.d ic fllllct.ioll.\nThus_ t.I ... :; \\\u00b7.., ing- up conf.!'o l fo r liu K :~ is\n\\ .. \u00b7IJ('rf' /l.u Itnd III ,uf' delint'd in (~) alld (l~J, respf'cLive\\y. alld jJ ~ (t) is '>Itile r a lix( 'd const ant .. o r a s lowly illcrea. ... in~\n-'5L -20 -~-\n_4 -3 - 2 - 1 1 1 4 3 2 Link 3 Position q3(t)\nFi ~. :{ . Pha.\u00b7w por l.L\u00b7ail. ft r t.he ext.t'l'llal sy:-;;tem (10)-( 11) w it.11 (;olHrol (11) , inil.ia l condilion [~,(ll) 1/,,(0) 114(OW- = [0 ll.O[) oV and a = :1. ThL' origin is now IIn:-;; table, and t.he limit (; . ,.-dc is st.a.ble, 'oVhi ch can b(\u00b7~ :-;hown with Bendixoll's Thf'ol'cul.\nfllll ct.ion with lIIaximum valu f' :: .\nThe control that ~(lbjlizes Iink.\\ in its invert.ed po~il.ion is s imply:Ht LQB -<k s iglt.",
            "wl)(']'(\u00b7 .... :-1 :=..' \u00b1 ] indicate~ whidl direction link ;_~ swingl'l up , a.nd V:J i1'; a. IICW illl) UL 1.0 hi' u:\u00b7wd to swing-up link ~ during tbe next plta::je. \\Vlwn UIP . \"j.;:t.le hecumes suffi  '\u00b7'(,Htly dos(' to Uw rnflll ifold D-V , Wllich i:'> rletcrmined Clllpll'ically. then I-iw ('ontroller swi!dw~ to '/1.2, and COIll  mences t.ht\" swi ng-up \\'ontrol of link 2. Note that (jl does IwL appeal' in (l ;{).\n1.:-: ,.,' wi1lg- lI l ) of L lIlt :! .\nThe . .;wing-up con trol fo r lill ) .. '2 l::i ,,,,i lllil ar in spirit, to Lhat or link :t Wt:. ddilW a. \u00b7\u00b7desin'd <w<.'elel'a.l,ion\" rl:'ed back\nv .\u2022 = {\",(I) . cos{'Jd . ,,,clan(,),) If lIlt! < rr/2 ( 14 ) . 0 .1 11/11 > ,,/2 .\nwhere 112(1) > O. which is subst.itl.lLed int,o (13), giving\n1l:1 = uo(q, q. v:- )_ ( 15)\nTlw controller can .-;wit.(:h 1..0 (1 il ) as S{J{)1l as li nk :3 is sta bilized ill it. ... iuvel'tf'd p(~\"iitioll, JIl !'onLr i:ls t t.o t.he previ o us 5wing-lIl' ('ollt,rol, lilt' theor(,l,i (\u00b7al prouf of ~x istellce of i1 lirllit cyclf' i!'i IIlo re ( 'o lllplc~ , ])(' ('::,\\US(' ( la) has 1f-f'c1hack LI',! 10 s ta bil iz(' liuk :L T1ti ~ noL ouly cou pks the dYl1iUlIics, i)l lt. I\"(,L lders dw map from v:~ t,o < I llf)!J - lninimum pha.se , I'\\ond .lu:-k :;:-. Oll r ~ illlUl at. io ll :o:. ; ~'1I1 ('xperi l!lC'lI l,a,{ re:; ult~\nindicate t.hat\n(1) VJ also iuduces a stable limit. (,)'cl f:' in the (f}1, fJ:d d y nallli es ; (:2 ) Ihat t.his limit cycle 's \"rU lIplil,ud(' '' is an incl'()n.sillg\nfUl wtio n o f Cl ? and (:q that ~h e r(' ('xi SlS <-111 Cl'.!. to fo[\"(\" (' tllf' tl 'ajedury throngh\n:Vu -u ,\nT luls , \\-\\\u00b7e CFI.lI adopt the ImIne s tl'at,I'!(Y, iJl which we slowl y illl:: rease H:1 (1) unt il '/1 reaches \u00b1lr, o r wc can a. priori drt,Cl'lllil](> t.h e value of fl:, at w\u00b7hich t.hi:-l occurs , and lIse 1.lIi :-; fix l.'d v:=\\ III\\ ' .\n2.4 S'taiJil izol-/un abo/If U-U\n\\\\~ hell tlte full stal,f~ passes withiu .. \\ tu - u, a fina.l LQH. <.'o nt.ro llc-r ilS (\u00b7 ngag:r d t,hilt. st,ahilir,c:-; I.hf' sy ... lem about v U and hri ngs t ilt' sl.a.Lt\u00b7 ~ 1 bn~\u00b7k [0 dl f' (>]\" i ~ill . if d(\"::;ir('d:\nwhere s:! = \u00b1l indicate::; the d .rection t.hat link 1 swings up, and qi({f.) iH a ue.-; ired t raj f!c:tory u :;~ d Lo move the pendulllm back t.o l.he o rigin aft.er swing- lip .\nA siIllulatio n of ti ll:' comp/eLe :- i\\ving-up controll~r for the Illode l of o ur expNllllcnt.a l p< lld ululll ( l ) is plou.ed in Figure ;). For t. bi~ sinllllatio JI al = (1. 2 ::::: :~ tll'e fi x(\u00b7cI . Note I.he l:' IJlall a mo unt. 0 1\" dl'i ~l in qdl). and t.lw small Ifh(t)1 mailltaiJlf'd t,ltwugholl1. t.he s\"ving-up phase.\n:1. EX PERJMEN'L\\L RES ULTS\nT llP ~wing- l1p cont.roller ha.<; be;~n s llccc~sfully a pplied to o ur experimental t,(~st- bed at. the Oniversity of Toronto, phoLographed in FigUl'e G. The \u00b7:ont.roller is implement.cd 0 11 a TMS:120C:lO IlSP, which is hosl.ed by \" 48(i-b'L,pd PC, Links:2 ;,\\nd:\\ a t\" t~ sensed \\\\' it.h <ulalog poi~ and 12-bil. :\\-1) conver! cr.-;, wltil f' lillk J i.\" S(' Il .o;cd 1l~illg: an optical position encoder . \"1\"11(' pendulullI is act.uated wit.h a. ill expen~ i vf:\" DC 1l1O(.or driven by a vo ltage arn pli fieL 'l'h ~ sampl r J\"CLt t' i:-5 set, H( 2UO Hz .\nFor t.h(' swing- up CO lltro l. (/1(1,) = ;) ami (t:dt) =;~ work wel l. as l.h., :5imulat.ions have indicat.ed . The j o int. t.ra j ec tories al\u00b7e provitk\u00b7d ill Figu !',' 7 . i\\'ote that Lhe stabil izing cont.rollers //:- and \"It.1 an swit.clted for larger de viat:ioll s fWIlI D-U ami V-U, respectively, whC'n C:O lIl  pnred t,o ilw s illl lllalio ns in F 'g ul'e I). 'Ne set> th Fl L III drirts little froll1 i(,~ initial cOlldir.ioH, a.nd t.lta!. (il l' ~rn aiJl :;\n:; Illa(l t.J1l\u00b7OlIg llo ll1. t. 1H' sw in~- lI p . [lw m ost. diflic.:-:ul t. PMt. 0 1\" the (' xpm\u00b7jll H' nt. I::; Llw fi li al balall('illg comrol ( tri). which yidd f; a. ~llIn, 1 1 rep;ioll of aU.rClC1.i on and ia...:b rohlls tness to ]XI,ramr'I (' r 1I11 ce rt.alu t,'y'. For !!Iorf:' px]w rilnen t it-i r es!IIL.':i . Sf'f' http: //wWlJ ,toronto. edu nn 1.lw \\V\\V\\V ."
        ]
    },
    {
        "image_filename": "designv11_24_0002247_0094-114x(87)90067-x-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002247_0094-114x(87)90067-x-Figure2-1.png",
        "caption": "Fig. 2. A (K = ) 5-loop chain.",
        "texts": [
            " (12) j = l i=l The above equation is true only when (n~- 1) independent loops meet at the external multiple joint. It may not be valid when two different chains are hinged at the common point. A mechanism may have both internal or external multiple joints and in that case equations (1 1) and (12) may be combined and written as K Mt F= ~ f ~ - ~ ' ~ j + ~ (m2-m~--2)/2\"F,,, j - I i= l M2 + ~ (n~-3n~+E)/2\"F.,. (13) i = l In general, multiple joints are revolute joints, therefore, F.~ = F.~ = 1. Example 1 Figure 2 shows a 13-1ink plane kinematic chain with revolute pairs. It has one external double joint formed by links, 1, 2 and 6, three internal multiple joints--two double joints formed by links 3, 7 and 10, 5, 1 1 and 12, and one triple joint formed by links 6, 7, 8 and 9. There are five independent loops L . j = 1,2 . . . . . 5. Therefore, M , = 3 , M 2 = l , m l = 3 , m2=3, m3=4, hi=3, Fi, i = l , 2 . . . . . 17=1, K = 5 . From Fig. 2, \"]'12----1, J13=2, Ji4 = 1, J l s=2 , ,]23=3, .]24 = 1, J2s'--O, J~=3, J3s= I, J4s = 3. From equation (4) A = I , A = 2 , A=2, A=3, A = I F , : = I . F~3=2 , FI,=I, F15=2, F23=-3, F24=1, F25=0. F ~ = 3 , F35 = 1, F~s = 3. Hence from equation (13) F=(1 + 2 + 2 + 3 + I) - ( 1 + 2 + 1 + 2 + 3 + 1 + 0 + 3 + 1 +3) + \u00bd[(32 - 3 - 2) + (32 - 3 - 2) + (4: - 4 - 2)] +\u00bd(32-3 \u00d7 3 + 2 ) = 2 . The above shows that if only the DOF of the independent loops and connecting mechanisms are given, equation (13) can determine DOF of the complete mechanisms with constant general constraint"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003854_tmech.2005.852450-Figure13-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003854_tmech.2005.852450-Figure13-1.png",
        "caption": "Fig. 13. Experimental setup.",
        "texts": [
            " Here, the minimum value of \u03c3 corresponding to the maximum excitation frequency \u03c9max is expressed as \u03c3min = 1.43 \u00d7 102 \u03c92 max . (9) The configurations of the manipulator, in which the tip of the free joint is at the positions, (b)U\u2212, (a)U 0, (b)U +, (c)U +, and (d)U +, are also represented in Figs. 11 and 12. It is seen from these figures that the reachable and stabilizable area becomes a little smaller due to the limitation of the excitation frequency. We experimentally confirm the theoretically obtained reachable and stabilizable area of the tip of the free link (Fig. 13). The active (first)link is actuated by an AC servomotor with a rotary encoder (Mitsubishi Corp., HC-MFS73 [maximum torque: 7.2 N\u00b7m, rated output: 750 W)]. The free (second) link does not have an actuator or a sensor. A CCD camera (Sony Corp., XC-77) is used for collecting the data of the stable equilibrium points of the tip of the free link; this data is not used for any motion control. The experimentally obtained reachable and stabilizable areas of the tip of the free joint are shown in Figs. 14 and 15, which are in the cases when we rotate the active link counterclockwise and clockwise, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003122_acc.2003.1239789-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003122_acc.2003.1239789-Figure6-1.png",
        "caption": "Figure 6: A sectional view of the brake chamber",
        "texts": [
            " Next, we choose the brake chamber and the air hose as the control volume under consideration. We assume all fluid properties in the control volume to be uniform at any instant of time. We assume frictional losses in the hose to be negligible. The Mach number of the flow in the hose was measured at the entrance of the brake chamber. For various test runs, the value of the Mach number was found not to exceed 0.2. Hence, we can neglect the effects of compressibility of air for the flow through the hose 1131. Applying mass balance to the control volume (see figure 6). we obtain, m b = p d p (11) where nib is the rate of change of the mass of air in the control volume, p is the density of air inside the control volume at any instant of time, and A, is the cross-sectional area of the valve opening. Next, let us consider the mass of air inside the control volume at any instant of time, mb. Since we treat air as an ideal gas, where Pb is the local static pressure inside the control volume, v b is the volume of the control volume and Tb is the local static temperature inside the control volume",
            " The volume of air inside the control volume at any instant of time can be written as, V\" I i f q < p , vb = { vo] +A@b tf 0 5 Xb < X b m (14) V\"2 I f Xb = X b m u where V,, is the initial volume of air in the control volume before the application of the brake, Vo? is the maximum volume of air in the control volume, A b is the cross-sectional area of the brake chamber, xb is the stroke of the brake chamber diaphragm, i.e., the stroke of the push rod, xbmw is the maximum stroke of the push r d a n d P, is the minimum pressure required to start the motion of the push rod. Proceedings of the American Control Conference 1419 Denver. Colorado June 4-6.2003 Let us now consider the dynamics of the brake chamber (refer to Figure 6). The equation of motion of the brake chamber diaphragm can be written as (we neglect any friction in the brake chamber), where Mb is the mass of the brake chamber diaphragm, Kb is the spring constant of the brake chamber return spring and &bi is the pre-load in the brake chamber diaphragm return spring. Neglecting the inertia of the brake chamber diaphragm, and using (15) and (14) in equation (13), and simplifying yields, Using equation (10) in (11) and comparing with equation (16) yields, This is the governing equation for the pressure transients in the brake chamber during the apply phase with the term f, being the supply pressure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001540_0168-874x(91)90017-s-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001540_0168-874x(91)90017-s-Figure1-1.png",
        "caption": "Fig. 1. Definition of displacements, rotation, forces and moments.",
        "texts": [
            " It is the purpose of this paper to derive the natural shape functions for uniformly twisted helix elements without approximations except those using the governing equations. For a brief review of the historical development of the governing equations, the reader is referred to Ref. [81. Mottershead [10] also used exact shape functions, employing an energy approach. The stiffness matrix is obtained by integrating the matrix produc t of shape funct ion differentials. N o explicit forms were given. The explicit stiffness matrix is derived here by means of the transfer matrix [11]. Governing equations Let the center line of the helix shown in Fig. 1 be measured by its arc length s, 0 ~< s ~< l. Let the unit vectors of tangent, normal and binormal along s be t, n, and b, respectively. Then the Frene t -Ser re t formulae [12] are d t / d s = Kn, d n / d s = - x t + # b , d b / d s = - gn , (1) which define the curvature x and the torsion g. Let the displacement vector ( u ) = [u v w]T and the angular displacement vector ( 0 ) = [0 q, tp] T defined at s along the local n, b, and t axes. Then it can be proved [8] that the strain vector ( c ) and the change in the curvature-twist { k } are given by i d _ (2) 0' 0 G 0 0 ds G 0 0168-874X/91/$03"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003172_detc2005-84638-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003172_detc2005-84638-Figure3-1.png",
        "caption": "Fig. 3 - Schematic of assembly errors of hypoid gear set",
        "texts": [
            " (13) Dynamic mesh force can be defined as dmdm ckF \u03b4\u03b4\u03b4 += . (14) A typical face-milled hypoid gear is analyzed. The design parameters are shown in Table 1. Here, in this example, the pinion is left hand type and rotate in the clockwise direction (as seen from larger pinion end). So, the concave side of pinion and the convex side of gear are in contact. Four types of assembly errors, including shaft angle error, pinion offset error, gear and pinion axial position error, are studied here as shown in Fig. 3. Gear contact pattern results are obtained by applying the quasi-static analysis for numerous types of assembly errors. Mesh parameters like mesh point, line-of-action vector, mesh stiffness and static transmission error are obtained by processing the detailed results. 2 Copyright \u00a9 2005 by ASME erms of Use: http://www.asme.org/about-asme/terms-of-use Figure 4 shows the contact pattern results on pinion and gear for different shaft angle errors. It can be seen the maximum values of contact pressure for negative error (- 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001474_s0167-8922(08)70580-7-Figure6.3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001474_s0167-8922(08)70580-7-Figure6.3-1.png",
        "caption": "FIGURE 6.3 Film geometry of conical hydrostatic bearing.",
        "texts": [
            " In some mechanical systems it is, however, very convenient to support oblique loads while allowing rotation and non-flat circular pad bearings are suitable for this purpose. Examples of non-flat bearings used in mechanical equipment are bearings based on a conical or hemi-spherical shape. The typical geometries of these bearings are shown in Figure 6.2. Non-flat circular pad bearings can be analysed in the same manner as already discussed for flat circular pads. For example, the geometry of the conical bearing is shown in Figure 6.3 and the following analysis is applicable. 314 ENGINEERING TRIBOLOGY spherical, c) conical, d) hydrostatic screw thread. Over the flat part of the bearing surface, hydrostatic pressure is equal to the supply pressure while a nearly linear decrease in pressure prevails in the conical bearing region. The pressure profile is then very similar to the flat pad bearing pressure profile already discussed. In the conical bearing, pressure does show a fully asymptotic profile outside the constant pressure region because the bearing radius 'I' increases at a slower rate with respect to distance travelled by the escaping fluid"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002290_1.1538192-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002290_1.1538192-Figure2-1.png",
        "caption": "Fig. 2 Spin test rig",
        "texts": [
            " There are many other contributions regarding the spin\u2019s influence on the traction performance of an EHD contact. All of them concur on the negative impact that the spin has on the contact performance and majority of the contributors propose solutions to ameliorate the spin effect. In this paper the authors present an evaluation of the effect of the spin on the performance of the EHD contact. In order to study the effect of the spin motion upon an EHD contact traction performances, a simple test rig was built. A schematic representation of the test rig is shown in Fig. 2. The test rig comprises two co-axial steel discs, which can rotate under controlled conditions and represent the device\u2019s input and output. A steel ball is placed between the disks and can rotate freely in a cage. The disks are pressed one against another using a controlled force so the rig would have full control upon both EHD contacts. By adjusting the value of the radius \u2018\u2018R\u2019\u2019 the rig can develop different values for the spin in the contacts. The dimensionless spin is defined as the ratio between the maximum value of tangential spin velocity and the value of rolling velocity and is given by the ratio of \u2018\u2018a/R ,\u2019\u2019 with \u2018\u2018a\u2019\u2019 the contact radius"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003952_iecon.2005.1569191-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003952_iecon.2005.1569191-Figure1-1.png",
        "caption": "Fig. 1. Impedance model of the interaction",
        "texts": [
            " When the robot is implementing the task, the robot may come into the unexpected collision with a human operator or a work piece. In this case only motion control strategy, which makes the robot much stiffer than the environment, cannot accommodate the interaction between robot and environment. The approach to control robot with considering the interaction with the environment is required to manipulate the dynamic relation between the interaction state variables (e.g., position, velocity, and force) as illustrated in Fig. 1. The relation is described by the equivalent mechanical components, and it is usually represented by inertia J f or mass M f , damper D f , and spring K f . Impedance control has been introduced to control the dynamics of interaction force Fint and the state variables [5]. However, several strategies appeared in the literatures on impedance control for industrial robot utilize the force sensor to detect the interaction force [6]\u2013[8], which are practically impossible to detect the collision occurred on the manipulator structure",
            " IMPEDANCE CONTROL IMPLEMENTATION WITH POSITION CONTROL OF INDUSTRIAL ROBOT In this paper, the impedance behavior of the robot end-point is chosen as Freact = M f X\u0308int +D f X\u0307int +K f Xint (1) where the parameters M f , D f , and K f are, respectively, mass, damping, and stiffness of the desired mechanical impedance 18780-7803-9252-3/05/$20.00 \u00a92005 IEEE Fint \u03c9Mint \u2212 + Kp Kv + S 1 + \u2212 S 1 \u03c9Mint \u03b8\u03c9\u03c9 1 Jf Df Kf \u2212 + + + Joint space impedance model \u03b8int 1 s 1 s Ideal acceleration control system Rg Rg Rg +\u03b8Mint \u03b8int \u03b8int M M M cmd + Fig. 2. Impedance model implementation with ideal acceleration control system between the end-point position error Xint and the reaction force Freact . To implement the impedance model in Fig. 1, the acceleration control scheme of the decouple joint is required. This control scheme can implement the ideal impedance model as shown in Fig. 2. However, the motion control system of industrial robot ordinarily consists of the position control system with minor speed control loop and minor current control loop. Therefore, it is difficult for industrial robot to implement the impedance control with acceleration control scheme. Generally, the position control used in industrial robot is the PD control scheme"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003768_j.mechmachtheory.2005.10.010-Figure21-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003768_j.mechmachtheory.2005.10.010-Figure21-1.png",
        "caption": "Fig. 21. Schematic of tooth profile manufacturing process.",
        "texts": [
            " 20 gives the contact stress between a planet worm-gear and the sun-worm in the meshing process for conical, cylindrical, and spherical rollers. It can be seen that the values of contact stress for the spherical roller is the smallest and the values of the contact stress for the cylindrical roller is the largest among conical, cylindrical and spherical shape rollers. The sun-worm tooth profile is generated by the enveloping movement of the meshing rollers. Based on the relative movement between the planet worm-gear and the sun-worm, the enveloping manufacturing method by fly-blade in the hobbing machine is proposed. Fig. 21 illustrates the schematic of a manufacturing process. While manufacturing as in Fig. 21(a), the sun-worm work piece is mounted on the shaft of the hob and rotates with the shaft. The fly-blade is fixed at a working-table and rotates with the working-table. The drive ratio between the sun-worm and the fly-blade is determined by adjusting transmission gears of the hobbing machine, and finally the sun-worm tooth profile is machined by the combination movement of the work piece and the fly-blade. Fig. 21(b) shows the grinding process of the sun-worm tooth profile, the CBN grinder is driven by high speed motor and the movements is the same like the manufacturing process. In the abovementioned process, the fly-blade and the CBN grinder are designed according to the normal tooth profile of the sun-worm and the sun-worm tooth profile generated by conical, cylindrical and spherical rollers can be manufactured. But for the spherical roller meshing, the grinding manufacturing for sun-worm tooth profile is fulfilled by the ball-end grinder illustrated in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002512_026635118700200301-Figure15-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002512_026635118700200301-Figure15-1.png",
        "caption": "Fig. 15. Lightweight construction employing wrapped structural foam.",
        "texts": [
            " Two techniques have been suggested to achieve light weight. In the first, the panels would be made principally of expanded polystyrene foam with a protective sheeting (e.g. aluminium). Some reinforcing may be needed along the edges since this is the area where the major forces and stresses are found. The hinge itself could easily be made of a continuous polypropylene strip. This construction is relatively simple and makes use of existing building construction ideas. A cross-section of the hinge made by the second technique is illustrated in Fig. 15. In this system a lightweight structural-strength foam (e.g. closed-cell polystyrene foam) is completely wrapped in an adhesive sheet to protect the foam from undesirable atmospheric effects (e.g. ultraviolet radiation). The covering sheet is continued over the joint to form the hinge. This form of hinge is essentially the same as that used in the models of Figs 3 and 9. The experience gained 137 with this type of hinge on models shows that it has a very good performance provided there are no sharp edges to start a tear along the fold line"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003917_0278364905058242-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003917_0278364905058242-Figure6-1.png",
        "caption": "Fig. 6. Four subcubes in contact c-space with parallel and non-parallel orientation vectors.",
        "texts": [
            " The following lemma gives a sufficient condition for reachability of a target posture T . LEMMA 3. Let S and T be start and target three-limb postures. A sufficient condition for T \u2208 R(S) is that the subcube graph contains a path from S to T whose nodes change orientation at least once along the path. The sufficient condition is also necessary when T lies outside the planes passing through S and orthogonal to the axes of contact c-space. A proof of the lemma appears in Appendix A. The necessary condition is depicted in Figure 6(a). The figure shows four subcubes whose orientation vectors are aligned with the s3-axis. The path on the subcube graph fromS toT contains no change of orientation, and R(S) is trapped in a plane passing through S and orthogonal to the s3-axis. Figure 6(b) shows the situation when one subcube has an orientation vector along the s1-axis. In this case R(S) fills the entire subcube having the rotated orientation vector, as well as the subsequent subcubes along the path. The change-of-orientation condition can be identified by the following simple criterion. If the sequence 2. The orientation vectors impose a non-holonomic constraint which has been first observed by Koditschek (1994) in the context of manipulation planning. of footholds from S to T requires repositioning of all three limbs, the sequence contains at least one change of orientation as required by the lemma"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000920_s1474-6670(17)48874-4-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000920_s1474-6670(17)48874-4-Figure2-1.png",
        "caption": "Figure 2: Reference frames",
        "texts": [
            " The attitude control is devoted to communication link purposes and to put the capsule nose in upwind direction as to obtain a stabilizing effect from the aerodynamic torques due to the capsule shape. Simulations are performed by using the ESA-I\\1IDAS dynamic simulator in pres ence of athmospheric disturbances and corrupted Earth-magnetic field measures. 2 THE MODEL In this section the model of the satellite will be de rived. To this end we must first introduce the ref erence frames usually used in a satellite attitude control problem and then the dynamics equations. 2.1 The reference frames The coordinate systems used in attitude control are shown in Fig. 2. The inertially fixed coordinate system Xo, Yo, Zo with the axes origin in the Earth center is used to determine the orbital position of the satellite. The attitude motion of a spacecraft is most commonly described in terms of an \"airplane\" three axis coordinate system, namely roll, pitch and yaw. The nominal yaw axis, Z, is along the vector from the center of mass of the spacecraft to the center of mass of the Earth, and the nominal pitch axis Y Denote by { = (<jJ, 0, 1/;)T the vector of error angles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003307_elan.200503459-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003307_elan.200503459-Figure2-1.png",
        "caption": "Fig. 2. Linear sweep voltammetric response recorded at a Pt microdisk 10 mm radius in a raw Grappa sample (alcohol content 73 vol%) spiked with 5.0 10 5 M Cu2\u00fe. Forward scan: Ein\u00bc 0.3 V, Ef\u00bc 0.4 V, scan rate 5 mV s 1; backward scan: preconcentration at 0.4 V for 10 s, scan rate 50 mV s 1.",
        "texts": [
            " In the forward scan, however, the first wave was well developed, the nucleation loop on the backward scan was present only for the highest copper concentration (i.e., >0.5 mM) and occurred at more negative potential values. Nevertheless, in any case, a stripping peak was obtained on reversal of the scan, provided that a sufficient long time elapsed once the applied potential was over the plateau region of the second wave. An example of a typical response obtained for a raw grappa sample with an alcohol content of 73 vol% and spiked with 5 10 5 M Cu2\u00fe is shown in Figure 2. In this experiment, the forward scanwas run at 5 mVs 1 from 0.3 V to 0.4 V, at the latter potential a 10 s preconcentration time was applied, then the anodic scan was run at 50 mV s 1. As is evident, two well developed waves are observed in the cathodic scan, wave (I) being conceivably due to the formation of a copper (I) soluble species. This was actually confirmed by CV responses obtained by setting the reversal potential in the plateau region of wave (I). Under the latter conditions, no stripping peak in the anodic scan was observed, even if delay times up to 60 s were applied before starting the anodic scan"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002564_2004-01-1307-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002564_2004-01-1307-Figure3-1.png",
        "caption": "Figure 3. Configurations computed: (a) Base-model, (b) Config. 1, (c) Config. 2, (d) Config.3, (e) Config. 4, and (f) Config. 5.",
        "texts": [
            " 1: a 3D front-wheel deflector, 50 mm in height and about 270 mm in length. The shape of the deflector follows the end curve of the wheelhouse. The idea is to protect the front-wheels and the link arm from the upcoming flow and, thus, reduce drag contribution of these parts. \u2022 Config. 2: a 3D front-wheel deflector, 50 mm in height and about 500 mm in length. The shape of the deflectors follows the end curve of the wheelhouse. The idea is to protect the wheel and the link arm from the upcoming flow, as well as to reduce the amount of flow into the wheel house. \u2022 Config. 3: a 3D front-wheel deflector, 50 mm in height and about 115 mm in length. The shape of the deflectors follows the end curve of the wheelhouse. The idea is to reduce the exposed area of the deflector, while still protecting the front-wheel from the upcoming flow. \u2022 Config. 4: a 3D front-wheel deflector, 25 mm in height and about 270 mm in length. The shape of the deflectors follows the end curve of the wheelhouse. Just as in Config. 1, the idea is to protect the wheel and the link arm from the upcoming flow, while reducing the exposed surface represented by the deflector by decreasing its height. \u2022 Config. 5: a 2D front-wheel deflector, 50 mm in height and 285 mm in length and 150-200 mm in front of the wheel-house. The objective is to protect the wheel and the link arm from the upcoming flow, and reduce the effect on the front lift coefficient. The different cases studied are shown in Figure 3. A rectangle has been drawn around the deflectors to help the reader visualization. Table 2 presents Cd and dCd values computed in this study. The dCd values are calculated with the basemodel as reference. Table 2 also gives the changes in Cd in terms of percentage values compared to the reference case. The drag coefficient, Cd, is defined as: AU5.0 F Cd 2 x \u03c1 = , where Fx is the total force is the streamwise direction, A is the frontal area of the car, and \u03c1 and U have been defined previously. The results on Table 2 show that the deflectors of Configs",
            " Note that on Table 3 the values presented for the front and rear wheels include the contribution of the brakes, and that the floor includes both wheel houses. Note also that the values for the cooling package include the drag contribution due to the pressure loss through the condenser, radiator, charge air cooler, and fan. In Configs. 1 to 5, it is observed that the main effect of the front-wheel deflector is on the drag reduction of the front and rear wheels. Configs. 1 to 4 also cause a significant reduction of the drag contribution of the underbody and front suspension (except for Config. 3 and 5). It is, however, possible to further reduce drag by designing and correctly placing a front wheel deflector which is not so frontally exposed to the flow and this way avoid relatively large stagnation zones. Such a parametric study is not included in this work, rather, it is suggested as a wind tunnel analysis. A proper way to understand the values on Table 3 is in connection with distribution plots of non-dimensional static pressure, Cp, defined as 2 refs U5.0 pp Cp \u03c1 \u2212 = . Figures 4 and 5 show a comparison between the base-model and Config",
            " It is also important to look at the influence of the various configurations on the lift coefficient. The lift coefficient, Cl, is defined as: AU5.0 F Cl 2 Z \u03c1 = . It is, however, more relevant to divide Cl into front lift coefficient, ClF, and rear lift coefficient, ClR. These coefficients are defined as AU5.0 F Cl 2 ZF F \u03c1 = and AU5.0 F Cl 2 RZ R \u03c1 = , with Cl = ClF + ClR. The results of the lift coefficient are summarized on Table 4 for all cases studied. From Table 4 it is can be seen that all deflectors, with exception of the deflector in Config. 3 and 5, increase the front lift, ClF. The 25 mm deflector of Config. 4 causes a less dramatic increase compared to the other deflectors tested. A slight decrease in the rear lift is also observed with this deflector in comparison with increase ClR observed in other cases. The increase of front lift, can be attributed to the higher pressure areas created in front of the deflector as shown in Figure 7 (b) for the case of Config. 1. Greater or smaller higher pressure zones are created by the other deflectors studied and are reflected in the values of ClF"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001377_robot.1996.503846-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001377_robot.1996.503846-Figure1-1.png",
        "caption": "Figure 1: Experimental robot with 2 links and 7 joints.",
        "texts": [
            " The constraint environment is modeled as a spring with a large spring constant, therefore Lagrange multiplier AA is given by AA = K,,,NAp = K,,,N(JeA@ + JeAe) , (9) where Ken, are the environmental stiffnesses, Ap are the deflections of the constraints, n = are the unit vector normal to the constraints, and N = nTn. equations of motion can be written as IVPl Substituting Eq. (9) into Eq. (8), the approximated 0 or in a more compact form LAr = M(0)Aq + K\"Aq. (11) 3 Simulations and Experiment To clarify the discussion, the motions of an experimental flexible manipulator ADAM (Aerospace Dual Arm Manipulator) are considered. ADAM has two arms and each arm consists of 2 elastic links and 7 rotary joints [lo]. In this paper, however, only the left arm of ADAM (Fig. 1) is considered. The discussion is restricted to only the vertical motion of joints 2, 4 and 6 (65, 04, e,) while joint 6 always preserves an angle of n/2 [rad] with respect to constraints. Based on the above model, two simulations are performed. The results, achieved by a precise model constructed by commercial dynamic analysis softwarle packages, are compared with experimental results. 3.1 Experimental setup The experimental manipulator ADAM is driven by DC servo motors with hardware velocity control"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002816_tmag.1984.1063462-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002816_tmag.1984.1063462-Figure1-1.png",
        "caption": "Fig. 1. Resolution of B , H, & M along two orthogonal axes",
        "texts": [],
        "surrounding_texts": [
            "T h i s p a p e r d e s c r i b e s a f i n i t e e l e m e n t f o r m u l a t i o n f o r m o d e l i n g p e r m a n e n t m a g n e t s i n e l e c t r o m a g n e t i c d e v i c e s . The method was used t o p r e d i c t f l u x d e n s i t i e s o f a i r s t a b l i z e d e l e c t r i c a l m a c h i n e u n d e r n o l o a d c o n d i t i o n . S e a r c h co i l measurements of f l u x d e n s i t i e s i n t h e d e v i c e were used to v e r i f y t h e v a l i d i t y o f t h e m o d e l , a n d a n a g r e e m e n t well w i t h i n 5% was o b t a i n e d . INTRODUCTION I n many p r a c t i c a l a p p l i c a t i o n s i n v o l v i n g t h e d e s i g n o f p e r m a n e n t m a g n e t d e v i c e s , a c c u r a t e c o m p u t a t i o n o f t h e m a g n e t i c f i e l d s is e s s e n t i a l f o r a r e a l i s t i c p r e d i c t i o n o f t h e i r p e r f o r m a n c e c h a r a c t e r i s t i c s . V a r i o u s numcr i ca l t e c h n i q u e s t o a n a l y z e p e r m a n e n t m a g n e t s h a v e S e e n r e p o r t e d i n t h e l i t r a t u r e [ 1 , 2 , 3 , 4 , 5 , 6 ] , b u t many o f t h e s e m o d e l s c o n t a i n a s s u m p t i o n s w h i c h r e s t r i c t t h e i r g e n e r a l u s e . T h i s p a p e r d e s c r i b e s a f i n i t e e l e m e n t f o r m u l a t i o n f o r m o d e l i n g p e r m a n e n t m a g n e t s o f a r b i t r a r y s h a p e a n d d e i n a g n e t i z a t i o n c u r v e . A l t h o u g h t e m e t h o d is g e n e r a l l y a p i c a b l e t o n o n l i n e a r a n i s o t r o p i c m a g n e t s , it h a s b e e n u s e d i n t h i s p a p e r to a n a l y z e a samarium cobal t rnagnet hav ing a l i n c a r d e m a g n e t i z a t i o n c h a r a c t e r i s t i c s .\nXAGNETIC FIELD FORf4ULATION\nTo o b t a i n a s o l u t i o n f o r t h e m a g n e t i c f i e l d due t o p e r m a n e n t m a g n e t s t h e f o l l o w i n g a s s u m p t i o n s a r e made: 1) t h e B-8 c u r v e o f m a g n e t i c a l l y s o f t i r o n is assumed t o be s i n g l e v a l u e d , i .e. h y s t e r e s i s is n e g l e c t e d . 2 ) t h e d e m a g n e t i z a t i o n c u r v e is t h a t o f a s t a b i l i z e d m a g n e t , i .e . t h e r e c o i l l i n e is s i n g l e v a l u e d . 3 ) e d d y c u r r e n t e f f e c t s are n e g l e c t e d . 4 ) a two d i m e n s i o n a l a n a l y s i s is assclmed.\nT h e t o t a l m a g n e t i c f l u x d e n s i t y i3 i n a n y m a g n e t i z a b l e n a t e r i a l i s g i v e n by.\nB =\u2019 pia + a) where &,H is r e l a t e d to t h e f i e l d a n d p.M i s r e l a t e d to t h e m a t e r i a l . F o rp e r m a n e n t magne t - - M = M o + X I ~\nwhere flo i n t h e r e m a n e n t t r i n s i c m a g n e t i z a t i o n o f c o n s t a n t m a g n i t u d e , a n d x is t h e s u s c e p t a b i l i t y w h i c h i s a f u n c t i o n o f H i n a non- l i n e a r m a t e r i a l . S u b s t i t u t i n g ( 2 ) i n t o (1) o n e f i n d s\nwhere\nOne s h o u l d n o t e t h a t po pr is a smooth f u n c t i o n o f B or H a n d t h e r e f o r e w o r k i n g i n terms of t h i s p r o d u c t will b e c o n s i s t e n t w i t h t h e Newtonn Raphson i t e r a t i o n s c h e m e [ 7 ]\n- I n t h e case o f i s o t r o p i c mater ia l t h e v e c t o r s B , 3, and M c a n be c o n s i d e r e d c o l i n e a r a n d p and pe pr are r e d u c e d f r o m t e n s o r s t o I scalars, I n t h e g e n e r a l c a s e t h e v e c t o r s X, H I and P 4 c a n be r e s o l v e d a l o n g two m u t u a l l y o r t h o g o n a l c o o r d i n a t e a x i s , s a y p and q , w i t h p b e i n g t h e d i r e c t i o n f t h ei n t r i n s i c r e m a n e n t m a g n e t i z a t i o n ( e a s y a x i s or p r e f e r e d a x i s ) a n d q its o r t h o g o n a l .\nT h e r e f o r e , e q u a t i o n ( 3 ) becomes\nE q u a t i o n 4 i s r e p r e s e n t e d b y t h e c u r v e 1 i n F i g 2 .\nI n o r d e r to i n c o r p o r a t e t h e d e m a g n e t i z a t i o n c u r v e o f p e r m a n a n t m a g n e t s i n t o a g e n e r a l p u r p o s e c o n p u t e r c o d e s u c h as WENAP [ S I , a s h i f t i n t h e B-H c u r v e t o w a r d s t h e o r i g i n must be made s i n c e i n s u c h p r o g r a m s o n l y\n0018-9464/84/0900-1933$01.00@1984 IEEE",
            "m a g n e t i c a l l y s o f t m a t e r i a l s w e r e c o s i d e r e d . T h i s r e q u i r e m e n t c a n b e met by d i v i d i n g t h e f l u x d e n s i t y B i n t w o p a r t s , a p a s s i v e p a r t which is z e r o a t H=O. and a magnetomot ive p a r t g i v e n by Hc. T h e r e f o r e , e q u a t i o n s ( 4 ) and ( 5 ) c a n b e w r i t t e n as\nB = * q 'o'rqHq\nwhere po F;\" is a s s o c i a t e d w i t h c u r v e ( 2 ) i n F i g . 2 , 'faand t h e n a g n e t o m o t i v e t e r m -\u20acIC is f i e l d i n d e p e n d e n t . T h i s s h i f t o f t h e 3p-IIp c u r v e m e a n s p h y s i c a l l y i n t h e case o f a two d i m e n s i o n a l i s o t r o p i c ~ magnet , a n o n - h y s t e r e t i c m a g n e t w i t h poprr wrapped i n a c u r r e n t s h e e t o f s t r e n g t h -1ic A m p p e r u n i t l e n g t h o fe m a g n e t . R e a r r e n g i n g eq. ( 6 ) and (7) a n d t a k i n g t h e c u r l o f e a c h s i d e , o n e o b t a i n s\nC u r l H 7 = C u r l (B 7 /u u* ) P P P P o r p\n+ C u r l H T C P\nS i n c e n o m a c r o s c o p i c u r r e n t s e x i s t i n t h e magnet\nD e f i n i n g a vector p o t e n t i a l - B = C u r l X (11)\nN h e t h e r t h e r e g i o n c o n t a i n p e r m a n e n t m a g n e t OK n o t , we o b t a i n\nWhere\ni s a n e q u i v a l e n t c u r r e n t d e n s i t y . If there i s some a c t u a l c u r r e n t d e n s i t y Ji; i n the s y s t e m , e q u a t i o n ( 1 3 ) becomes\nNote, t h a t g e n e r a l l y , both J and J m are n o t p r e s e n t a t the same p o i n t .\nApp ly ing Stoke 's theorem t o e q u a t i o n (14), w e h a v e\nr\nI m is a n e q u i v a l e n t c u r r e n t s h e e t , R i s t h e o p e n s u r f a c e r e g i o n c o n t a i n i n g t h e p e r m a n e n t magnet , and C is i t s p e r i p h e r y . I n t h e case o f a u n i f o r m m a g n e t i z a t i o n o f t h e p e r m a n e n t : m a g n e t , t h e c u r r e n t s h e e t e x i s t s o n l y a t t h e boundary be tween the pe rmanen t mag i l e t and the o t h e r materials. I n the c a s e o f a non u n i f o r m m a g n e t i z a t i o n , IIc may va ry f om e l e m e n t ' t o c l e m e n t , a n d t h e r e f o r e a c u r r e n t s h e e t e x i s t s o n t h e c i r c u m f e r e n c e o f e v e r y s i n g l e e l e m e n t w i t h i n t h e p e r m a n e n t m a g n e t r e g i o n . I n two d i m e n s i o n a l f i n i t e e l e m e n t f o r m u l a t i o n , c u r r e n t s h e e t s c a n e a s i l y b e r e p r e s e n t e d b y o n e d i m e n s i o n a l e l e m e n t s . I n order t o r e p r e s e n t c u r r e n t s h e e t s by o n e - d i m e n s i o n a l e l e m e n t s , t h e c o n t r i b u t i o n o f t h e Jm term to t h e f u n c t i o n a l [PJ] is t o be c a l c u l a t e d . T h u s\nr\nWhere Q( ' s are a p p r o x i m a t i n g p o l y n o m i a l s [SI. For o n e d i m e n s i o n a l e l e m e n t s o f f i r s t o r d e r , e q u a t i o n ( 1 7 ) becomes\nhi do = Ji dR = 2 a ( 1 8 )\nC o n s i d e r i n g n e x t , two e l e m e n t s w i t h a n i n t e g r a t i o n p a t h as shown i n f i g u r e 3\nF i g u r e 4 shows a twe lve po le pe rmanen t magne t rotor . The d i r e c t i o n o f m a g n e t i s a t i o n of t h e magnets a r e c i r c u m f i r c n t i a l , a s shown i n t h e f i g u r e . The magnets a re mounted t in s lo t s , i n s u c h a f a s h i o n so as. t o p r o v i d e n a g n e t i s a t i o n i n t h e clockwise a n d a n t i c l o c k w i s e d i r e c t i o n s .\nT h i s a r r a n g e m e n t l e a d s t o t h e f o r m a t i o n o f m a g n e t i c n o r t h a n d s o u t h poles on the rotor s u r f a c e . S i n c e t h e p roblem is sy inmet r i ca l a b o u t h e pole a x i s , o n l y h a l f a pole p i t c h i s a n a l y z e d ."
        ]
    },
    {
        "image_filename": "designv11_24_0003564_epepemc.2006.4778433-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003564_epepemc.2006.4778433-Figure5-1.png",
        "caption": "Fig. 5. Trajectory of LIPM",
        "texts": [
            " In this paper, it is assumed that the term of the double support phase is enough short to be ignored. In addition, trajectory planning of the swing leg is also proposed. This is planned to change the length of stride and to suppress the reaction force in x direction at landing. In this research, it is assumed that the ground is plain and no external force works on the robot other than gravity. In LIPM, a biped robot is treated as an inverted pendulum that has COG as a mass point and massless legs that is able to expand or contract. This model is shown in Fig. 5. The movement of COG is restricted on a line and the equation of motion is shown in (7). The line is called the constraint line. (7) is about COG in x direction. The origin of coordinates is set at the ankle of the supporting point. x\u0308 = g Zc x (7) x and x\u0308 denotes COG position and acceleration in x direction. Zc is the point at the intersection of the constraint line with the perpendicular line which goes along the supporting point. g means gravity. Since (7) does not include z element, COG motion in z direction does not interfere in the motion in x direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003258_detc2005-84712-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003258_detc2005-84712-Figure4-1.png",
        "caption": "Figure 4. Wunderlich mechanism in a singular configuration q0.",
        "texts": [
            " Discussion: In q0 the kinematic tangent space is a twodimensional vector space, i.e. \u03b4diff (q0) = 2. The local (and global) DOF is \u03b4loc (q0) = dimCq0 V = dimCq0 V ( IK ) = 0. q0 is a regular point of deg (q0) = 2. Thus V = P 2 = {q0}, P i = \u2205, i 6= 2, \u03a3 = \u2205. The mechanism is paradox-in-thesmall and paradox in the usual sense [14, 15]. In [38] Wunderlich combined four 4-bar mechanisms to a kinematotropic 12-bar mechanism. Copyright c\u00a9 2005 by ASME se: http://www.asme.org/about-asme/terms-of-use Do I. Kinematic tangent cone to V : The reference configuration q0 is shown in figure 4. The kinematic tangent space Tq0 V ( IK ) is a two-dimensional vector space. The kinematic tangent cone Cq0 V ( IK ) = C\u2032 q0 V ( IK ) \u222aC\u2032\u2032 q0 V ( IK ) is the union of a two-dimensional cone C1 q0 V ( IK ) and a onedimensional cone C2 q0 V ( IK ) . II. I-Tangent cone to V : It holds Cq0 V ( IK ) \u223d Cq0 V ( I ) . III. Tangent cone to V : It holds Cq0 V = Cq0 V ( IK ) . IV. Discussion: The kinematic tangent space is a threedimensional vector space. The kinematic tangent cone is the union of a two-dimensional vector space C\u2032 q0 V ( IK ) and a one-dimensional vector space C\u2032\u2032 q0 V ( IK ) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003996_tase.2005.846289-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003996_tase.2005.846289-Figure5-1.png",
        "caption": "Fig. 5. Staircase effect with two fabrication modes.",
        "texts": [
            " However, it is possible to build each part so that the angle between every facet normal and the build direction is closer to 90 and the volumetric error for each facet could be reduced. The following is a comparison of the results for a given surface fabricated at a different orientation. According to (3), to fabricate the wedge shown in Fig. 4 with a specified sectional error , layer thickness is (11) where and are the height and width of the wedge. Additionally, assuming that the deposition speed is constant at and the offset between the deposition paths is , the time needed for the deposition of this wedge is Time (12) As shown in Fig. 5, let us consider the time for a wedge to be fabricated in two orientations that are perpendicular to each other. The following relationship can be obtained by considering and in these two modes: (13) Time Time (14) From this example, it can be seen that, for these two different fabrication modes, to achieve the same resultant error, the time needed for deposition is directly related to the ratio of . In Section IV-B, a novel orthogonal LM system is introduced, which automatically selects between these two fabrication modes so that the overall performance of the system can be improved"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003411_ip-rsn:20041177-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003411_ip-rsn:20041177-Figure3-1.png",
        "caption": "Fig. 3 Antenna heading and target pointing frame",
        "texts": [],
        "surrounding_texts": [
            "Most modern homing missiles make use of PN (proportional navigation) guidance law using LOS (line-of-sight) rates. In homing missiles with a seeker, the LOS rate can be estimated by a low-pass filter or Kalman filter using tracking error measurements of the seeker [1, 2]. It is well known that the conventional low-pass filter approach requires a more accurate seeker system than the Kalman filter approach. On the other hand, the LOS rate dynamics model is necessary for the Kalman filter approach [3]. Many ASM (anti-ship missile) systems adopt sea skimming technologies in the vertical plane to enhance survivability and ECCM (electronic counter countermeasure) capability. Since sea-skimming ASM systems are designed basically to fly maintaining a prescribed altitude, the homing guidance loop is constructed only in the horizontal plane [1]. Therefore, the seeker for ASM systems is often designed to aquire horizontal LOS rates only. In this case, the seeker takes advantage of saving key hardware components of the antenna control loop and makes no effort to obtain the vertical LOS rate information. The guidance algorithm for sea skimming missiles is conventionally implemented independently in the horizontal plane and in the vertical plane under the assumption that the pitch and yaw planes of the missile are coincident to the the vertical and horizontal planes, respectively. This implies that a roll stabilisation loop must be designed to keep the roll angle very small. Unfortunately, however, the roll stabilisation performance is degraded by various factors such as missile dynamics uncertainties, unexpected wind gusts, seeker control loop imperfection, and so on. The unexpected large roll motions produced by these uncertainties can generate poor LOS rate measurements through a roll coupling effect. Consequently, an LOS rate estimation scheme considering the roll motions is necessary to improve the guidance performance. In the previous work [3], the Kalman filter based on a simplified LOS dynamics model was set up to handle the measurement delay for the IR (infrared) seeker system. The simplified model does not fully include the roll coupling effect and the derivation of a more precise model for LOS angle behaviour remains as a further research topic. Besides the roll coupling effect, the nonlinear and timevarying nature of the seeker detection gain is a frequently encountered error source in RF (radio frequency) seeker systems [4]. Since the calculation of LOS tracking errors in the seeker system is influenced by detection gain variation, it may cause severe degradation of LOS rate estimates. In particular, the conventional low-pass filter approach may cause unreliable homing performance because it makes direct use of the tracking errors to estimate LOS rates. In this paper, a more precise LOS rate dynamics model reflecting the roll coupling effects for two-axis gimballed seeker systems is derived. The detection gain variation is considered as a norm-bounded parameter uncertainty. A robust LOS rate estimator to cope with both roll coupling and detection gain uncertainty is proposed by applying a new robust Kalman filter theory to the model. The proposed robust Kalman filter is the first attempt to extend the Krein space estimation theory [5, 6] to the robust filtering problem. It has a similar structure to that of the conventional Kalman filter, and the steady-state robust filter gain can easily be obtained by solving the algebraic Riccati equation. Since it is easy to design and implement the proposed filter for real-time applications, and thus it is a practical result. A numerical example is given to show the estimation performance and the robustness of the proposed LOS rate estimator."
        ]
    },
    {
        "image_filename": "designv11_24_0002937_j.jbiomech.2004.08.023-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002937_j.jbiomech.2004.08.023-Figure1-1.png",
        "caption": "Fig. 1. Real springboard and the rotational mass\u2013spring rigid bar model (dashed). Real board stiffness can be adjusted by moving the fulcrum support horizontally. The rigid bar (modeled springboard) is hinged at point O, which is the point of intersection of the perpendicular bisector of O to loaded and unloaded board (Kooi and Kuipers, 1994).",
        "texts": [
            " A Maxiflex \u2018\u2018B\u2019\u2019 springboard was previously characterized by a 1-D mass\u2013spring model. Equivalent board mass mb and stiffness k for fulcrum settings S \u00bc 1; 5, and 9 were measured by Sprigings et al. (1990) and interpreted by Miller et al. (1998). Cubic spline interpolations for mb and k at other settings were calculated (Cheng and Hubbard, 2004). However, in order to model both the horizontal and vertical board tip motion, a rotational mass\u2013spring system which simulated board tip motion accurately (Kooi and Kuipers, 1994) is used in the present study. Fig. 1 shows a real springboard and the modeled board. The equivalent board mass (mb \u00bc 7:00 kg), bar length (l \u00bc 2:80 m), and rotational spring constant (k \u00bc 39 531 N m) generate a vertical board tip displacement equivalent to fulcrum setting=7, while the values (mb \u00bc 6:32 kg; l \u00bc 2:53 m; k \u00bc 38 877 N m=rad) correspond to fulcrum setting=1 in the 1-D model. Cubic splines interpolate corresponding mb, l, and k at other fulcrum settings (Table 1). A planar four-segment human model with frictionless revolute joints and joint torque actuators is used to simulate springboard standing jumps"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002509_s1474-6670(17)51725-5-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002509_s1474-6670(17)51725-5-Figure1-1.png",
        "caption": "Fig. 1 - A four-link planar robot ann",
        "texts": [
            " After some manip ulation it can be shown that the projection matrix takes the form (21) Comparing this with the expression (l3) of the RG method, as applied to self-motions, it is easy to see that (22) I :I(i Therefore, the two methods provide in this case the same direction in the joint space, up to the iteration dependent scaling factor .e. This was not unexpected, since for these robots the null-space of the Jacobian is one-dimensional. It is possible to show that this scal ing factor is equivalently rewritten as det 2 Ja .e = det ( J JT) s;: 1. (23) This general result applies indeed to the previous ex ample. NUMERICAL RESULTS The proposed redundancy resolution method has been applied to a 4-R planar robot arm with all links of unit length (see Fig. 1), both for internal self-motions and for end-effector trajectories. For positioning tasks, this robot has two degrees of redundancy and thus it is suit able to fully illustrate the different behavior of the RG and the PG methods. Using absolute joint coordinates, the Jacobian of this arm is J(q)=[-81 Cl (24) Different objective functions H (q) were tested for op timization. In order to maximize the joint range avail ability, the criterion proposed by Liegeois (1977) was used. For the 4-R arm, this is written in terms of abso lute coordinates as (25) where [(Jm,ilOM,il is the admissible range for joint i and Bi is its center"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001455_50006-1-Figure5.37-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001455_50006-1-Figure5.37-1.png",
        "caption": "FIGURE 5.37 Permanent magnet brushless dc motor.",
        "texts": [
            "248) we find that the response time of an actuator with a shorted turn is much shorter than without one. Finally, an alternate linear motor configuration with a shorted turn is shown in Fig. 5.36. The response time of this actuator has been analyzed by Wagner [18]. Permanent magnet axial-field motors are used for low-torque, servo and speed control applications. They are also referred to as brushless dc motors, and are commonly used as spindle motors for both disk and cassette tape drives [19]. A typical motor configuration is shown in Fig. 5.37. The motor consists of a set of equally spaced stator coils, fixed 422 CHAPTER 5 Electromechanical Devices beneath a cylindrical multipole rotor magnet with flux return plates positioned above the magnet and below the coils to enhance the field in the motor cavity. During normal operation, the coils are energized in a synchronous fashion as they pass under the transition region between adjacent rotor poles. They are synchronized so as to impart a continual steady torque to the rotor. Hall effect sensors are mounted on the stator near the coils to sense the rotor's magnetic field and synchronize the activation of the coils",
            "255) ~rA w where Nac is the number of active coils, Nturn is the number of turns in each coil, lw is the length of the wire in each coil, and r~ and A~ are the conductivity and cross-sectional area of the wire. In our case there are 4 active coils, Nac = 4. Notice that Eq. (5.255) constitutes one equation with three unknowns: Nturn, 1~, and A,,. Therefore, additional information is needed. One approach to obtaining the unknowns is to specify the orientation, shape, and dimensions of the coil. To this end, we specify the motor cavity height h, which puts an upper limit of h - t m on the height of the coils (Fig. 5.37). We choose the cross-sectional area Ac and mean length per turn l t (Fig. 5.39). Given the coil dimensions, we write the following additional relations, Nturn A., A c = (5.256) 5 and l w = f o N t u r n l , , (5.257) where fp is a wire packing factor and f~ is a geometric factor. For precision wound coils fp ,~ 0.69. The three unknowns Xturn , lw, and A w are obtained via the simultaneous solution of Eqs. (5.255), (5.256), and (5.257). 426 CHAPTER 5 Electromechanical Devices Once the orientation and geometry of the coils are known we compute the torque constant K t",
            "260) are known except for B 0, the field in the gap region. This can be determined using the results of Examples 5.13.1 or 5.13.2 [21-23]. Once we know R e, V, K t, and K e we use Eqs. (5.253) and (5.254) to determine the no-load speed CONL and stall torque T s. We then plot the speed-torque curve co vs T (Fig. 5.38). As the operating speed co is given, we can determine both the operating point of the motor and its efficiency. EXAMPLE 5.13.1 Develop a two-dimensional model for the field in the gap region of an axial-field motor (Fig. 5.37). Assume the magnet has a linear second quadrant demagnetization curve of the form B = #H +/ toM S, (5.261) where Br /~ = - - . (5.262) Hc SOLUTION 5.13.1 We reduce the three-dimensional motor geometry to an approximate two-dimensional geometry [21]. This is done by introducing a cylindrical cutting plane at the mean radius of the magnets. This cylinder is then imagined to be unrolled into a two-dimensional surface of infinite extent into and out of the page, as illustrated in Fig. 5.40a. This two-dimensional geometry can be reduced further by exploiting the symmetry that results from the repeating magnetic structure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003947_icma.2005.1626582-Figure9-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003947_icma.2005.1626582-Figure9-1.png",
        "caption": "Fig. 9. Definition of Variables in CMT Catheter for PUBS",
        "texts": [
            " The tip position of Inner Guide shown in Figure 6 is controlled by the rotations of Inner and Outer guides, and the linear motion of the total system. Figure 8 shows a photo of curved multi-tube catheter for PUBS. By controlling the rotation of outer guide tube and inner guide tube, the linear motion of total system, and the linear motion of PTC needle, the tip of PTC needle can take the prescribed position or posture without hurting the abdominal wall and the uterus wall. III. KINEMATICS OF CMT CATHETER Figure 9 shows the definition of variables in CMT catheter for PUBS. The homogeneous transformation matrix for the tip of the inner guide tube is given as in the following:\u23a1 \u23a2\u23a2\u23a3 a b c d e f g h i j k l 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 where d, h and l indicate the x, y and z coordinates of the tip of inner guide, respectively. a = C\u03b81C\u03b11C\u03b82C\u03b12 \u2212 S\u03b81S\u03b82C\u03b12 \u2212 C\u03b81S\u03b11C\u03b12 b = \u2212C\u03b81C\u03b11S\u03b82 \u2212 S\u03b81C\u03b82 c = C\u03b81C\u03b11C\u03b82S\u03b12 \u2212 S\u03b81S\u03b82S\u03b12 + C\u03b81S\u03b11S\u03b12 d = \u2212r2C\u03b81C\u03b11C\u03b82C\u03b12 + r2C\u03b81C\u03b11C\u03b82 +r2S\u03b81S\u03b82C\u03b12 \u2212 r2S\u03b81S\u03b82 +r2C\u03b81S\u03b11S\u03b12 \u2212 r1C\u03b81C\u03b11 + r1C\u03b81 e = S\u03b81C\u03b11C\u03b82C\u03b12 + C\u03b81S\u03b82C\u03b12 \u2212 S\u03b81S\u03b11S\u03b12 f = \u2212S\u03b81C\u03b11S\u03b82 + C\u03b81C\u03b82 g = S\u03b81C\u03b11C\u03b82S\u03b12 + C\u03b81S\u03b82S\u03b12 + S\u03b81S\u03b11C\u03b12 h = \u2212r2S\u03b81C\u03b11C\u03b82C\u03b12 + r2S\u03b81C\u03b11C\u03b82 \u2212r2C\u03b81S\u03b82C\u03b12 + r2C\u03b81S\u03b82 +r2S\u03b81S\u03b11S\u03b12 \u2212 r1S\u03b81C\u03b11 + r1S\u03b81 i = \u2212S\u03b11C\u03b82C\u03b12 \u2212 C\u03b11S\u03b12 j = S\u03b11S\u03b82 k = \u2212S\u03b11C\u03b82S\u03b12 + C\u03b11C\u03b12 l = r2S\u03b11C\u03b82C\u03b12 \u2212 r2S\u03b11C\u03b82 +r2C\u03b11S\u03b12 + r1S\u03b11 + l1 iC\u03b8 = cos \u03b8CS\u03b8 = sin \u03b8j IV"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001407_robot.1993.291878-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001407_robot.1993.291878-Figure2-1.png",
        "caption": "Figure 2: Assembly states for a Peg-in-Hole task.",
        "texts": [
            " For example, the basic peg-in hole task is composed of two primitive motions: move the peg to the hole position and move it down into the hole. The combination of primitive motions is different for each peg-in-hole task. Our approach is to represent each assembly task as a set of primitive motions based on the human worker\u2019s movement and then to analyze tasks using the corresponding primitive motion sets. We divide the workspace into several assembly states based on the manipulated object\u2019s position with limits of translational freedom [lo]. For the peg-in-hole task, there are three states (Fig. 2). The first state is the initial space with the peg is in free space with no constraints. The second state is where the peg is located over the hole, and the last state is where the peg is in the hole and physically constrained. The division of space into assembly states is based on a geometrical model of the parts. For each tasklevel specification, the division into states should be the same regardless of whether the hole is wide or narrow or whether the peg is square or round. The observed human movements are classified according to the assembly states, and the assembly movement sets for the tasks are matched according to these states"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002432_cca.2002.1038699-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002432_cca.2002.1038699-Figure6-1.png",
        "caption": "Fig. 6. Sample of a sequence of scanned images in automatic navigation.",
        "texts": [
            " AUTOMATIC NAVIGATION IN TETRANAUTA In automatic navigation, the user just tells the final destination to system and it makes all required movements to reach it. Wheelchair control must be completely automatic, avoiding any user contribution to its local movements' (apart from stopping to change a new destination or select a new navigation mode). In TetraNauta, this kind of navigation uses local sensing of lines painted on the floor. The sensing system is based in a low cost CCD color camera. Analyses of camera images get topological parameters used in VPF functions for the guiding system. Fig. 6 shows a sample situation to demonstrate how the guiding system uses VPF. ' That is. all movements needed to follow the user selected mute. We combine effects of two attractive VPF to meet both objectives: a line AWV makes the wheelchair to move toward the line, while an point AVPF moves it toward the end of the line. The global effect of both VPFs is that wheelchair moves towards the desired location, not in any way but following the l i e , because the line AVPF has not effect once the wheelchaii is aligned with the line"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001608_s0022-0728(00)00446-0-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001608_s0022-0728(00)00446-0-Figure1-1.png",
        "caption": "Fig. 1. Coordinate system for the microdisc electrode and bipolar impulse excitations.",
        "texts": [
            " In this work the mass transport diffusion-controlled kinetics in an ECL cell with a microdisc electrode under bipolar impulse non-steady electrolysis are considered. The microdisc in an ECL cell is electrolysed by bipolar * Corresponding author. Tel.: +38-572-409107; fax: +38-572- 409113. E-mail address: svir@kture.kharkov.ua (I.B. Svir). 0022-0728/01/$ - see front matter \u00a9 2001 Elsevier Science B.V. All rights reserved. PII: S0022-0728(00)00446-0 voltage impulses of sufficient amplitude to form reduced and oxidised organoluminophor forms. It is possible to separate the model into two time phases (Fig. 1), where the first phase is anodic, when the positive voltage impulse is applied to an electrode, and the second is cathodic, which corresponds the negative voltage impulse. Anodic phase: (Ag\u2212e\u2212 A+) Diffusion mass transport is described by the following equation system #c+ #t =D #2c+ #r2 + 1 r #c+ #r + #2c+ #z2 n (1) c++cg=c0 (2) where c+ and cg are the concentrations of A+ and Ag correspondingly, D is the diffusion coefficient, which is considered equal for every kind of species in the solution, and c0 is the initial luminophor concentration. The initial and boundary conditions for the above system are: t=0 r]0 z]0 c+(r, z, t)=0 0B tBT1 05r5rd z=0 c+(r, z, t)=c0 r]rd z=0 #c+ #z ) z=0 =0 r\\0 z c+(r, z, t) 0 r=0 z]0 #c+ #r ) r=0 =0 r z\\0 c+(r, z, t) 0 (3) where rd is the radius of the microdisc, and r and z are the spatial co-ordinates (Fig. 1). Table 1 Convergence results for regular and irregular grids when t=1.1025\u00d7 10\u22123 s (t=0.09) a Grid Convergence This work ConvergenceGavaghan [2] /% /% 29\u00d729 7.273.494 3.8987 3.47 57\u00d757 7.093.501 3.8377 1.85 5.65 3.79923.555 0.83113\u00d7113 3.611225\u00d7225 4.17 3.7851 0.45 2.97 3.76913.656 0.03449\u00d7449 a The analytic solution of the flux is f(t)=3.768 from Aoki and Osteryoung [14] for this representative time point t=0.09. The cathodic phase is characterised by the equation system: #c+ #t =D #2c+ #r2 + 1 r #c+ #r + #2c+ #z2 n \u2212kbic+c\u2212 (4) #c\u2212 #t =D #2c\u2212 #r2 + 1 r #c\u2212 #r + #2c\u2212 #z2 n \u2212kbic+c\u2212 (5) #c* #t =D #2c* #r2 + 1 r #c* #r + #2c* #z2 n +kbic+c\u2212\u2212kfc* (6) c++c\u2212 +c*+cg=c0 (7) where c\u2212and c* are the concentrations of species A\u2212 and species 1A*, kbi is the bimolecular interaction rate constant, kf=8fl/t is the pseudo-monomolecular rate constant of \u2018light\u2019 homogeneous ET reactions, where 8fl is the fluorescence quantum efficiency and t is the life-time of species 1A*",
            " The transient current calculated from expression: i(t)=4rdFDc0 & 1 0 #C\u2212 #G \u2212 #C+ #G dU (21) The transient ECL intensity is: IECL(T) =4pFECLNAkfc0rd 3 & 1 0 & 1 0 C*(U,G,T)R det J dU dG (22) where det J = \u2212 p 2 U2+sin2 p 2 G (1\u2212U2) cos3 p 2 G (1\u2212U2)1/2 is the Jacobian of the transformation. 3.2. Exponential expanding grid in the time direction We used a non-uniform grid for the time co-ordinate to avoid solution oscillations, which appear through the initial time singularity [2,36]. We investigated a bipolar periodic process (Fig. 1) which is why we used the transformation proposed by Feldberg and Goldstein [37] T= ln 1+a t Te ln(1+a) (23) with modification for the periodic process. This gives us an exponential expanding grid for every phase: T= ln a Tph (t\u2212Te)+1 ln(1+a) + (Nph\u22121) (24) where Tph is a current phase duration (anodic or cathodic); Te is a previous phase duration of the electrolysis; Nph is the number of the current phase. The current electrolysis time is given by t= Tph a (eln(1+a)(T\u2212 (Nph\u22121))\u22121)+Te (25) 3.3. Transformation of original co-ordinates to mapped space In order to obtain rapid conformity of simulated concentration values at any point in transformed space and original co-ordinates by \u2018light\u2019 marker in our programs, we had made the transformation of the original co-ordinates (R, Z) to mapped space (U,G) [25]: G= 2 p arctan 2Z 2+2 Z4+2Z2+2R2Z2+1\u22122R2+R4\u22122Z2\u22122R2 (26) U= 1 2 2+2 Z4+2Z2+2R2Z2+1\u22122R2+R4\u22122Z2\u22122R2 (27) 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003449_tmag.2004.824720-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003449_tmag.2004.824720-Figure3-1.png",
        "caption": "Fig. 3. Time variation and distribution of flux density and loss distribution of motor with closed rotor slots at synchronous speed.",
        "texts": [],
        "surrounding_texts": [
            "transformation of the currents waveforms. The sum of the harmonic secondary copper losses can be also calculated from the waveforms of the harmonic secondary current densities at each finite element in the rotor cage as\n(3)\nwhere is the time-harmonic order observed from the rotor coordinate system (moving coordinate system [3]).\nOn the other hand, the torque of the motor is calculated by the nodal force method [4] as\n(4)\nwhere to is the nodes included in the rotor region, and are the radius vector and the nodal force of th node. However, the negative torque caused by the harmonic core losses is not included in (4) because the eddy current and hysteresis phenomena in the laminated core are neglected in the finite element analysis. In this paper, we take into account the effect by the second step in Fig. 1, as follows.\nAlthough many methods are proposed to calculate the core loss, it is suitable for the purpose of this paper to calculate the sum of the harmonic core losses from the harmonic magnetic inductions [5] as\n(5)\nwhere are the sums of harmonic eddy current and hysteresis loss of the core, is the density of the core, and and are the th harmonics of the radial and peripheral components of the flux density. and are the experimental constant obtained by the Epstein frame [6]. This expression can also be considered to be valid for the calculation of rotor harmonic core losses with the time harmonic order observed from the rotor coordinate system.\nFirst, let us consider the harmonic torque generated by the harmonic rotational magnetic field whose space-harmonic order is and the time-harmonic order is observed from the stator coordinate system. In this case, the harmonic torque can be calculated from the rotor harmonic loss due to the electric machine theory as\n(6)\nwhere is the mechanical angular speed and is the slip of the rotor from the harmonic rotational magnetic field, that is\n(7)\nwhere is the synchronous speed, is the slip of the rotor from the fundamental rotational field, and when the harmonic field is the forward wave and when the backward wave. Substituting (7) into (6), we have\n(8)\nThis expression implies that the harmonic torque is always negative when the rotor slip is small and is much larger than\n. It is true of the major harmonic fields at the rotor when the motor is driven by the sinusoidal power supply. For example, in the case of the stator slot ripples, and slot number plus minus . In this case, (8) can be approximated as\n(9)\nConsidering the transformation between the stator and rotor coordinate systems, this expression is also valid for the harmonic torque caused by the harmonic losses generated at the stator. Thus, we can calculate the negative and the total torque considering the harmonic core losses as\n(10)\n(11)\nFig. 2 shows the system for the measurement of the negative torque of the induction motor at synchronous speed. First, the induction motor is rotated without the power supply using the synchronous permanent magnet motor. At this moment, the input power of the permanent magnet motor includes not only the own losses, but also the mechanical loss of the induction motor. Next, the power is supplied to the induction motor. The input power of the permanent magnet motor increases according to the voltage of the induction motor. It can be considered that this increase corresponds to the negative torque generated by the induction motor.\nThe total torque of the induction motor at the load condition is also measured using the torque detector with the analyzing",
            "recorder. The average torque is obtained from the 32 000 data at steady rotation with the sampling time 100 s.\nTable I shows the specification of the measured motors. Two types of the motor are investigated to clarify the effects of the harmonic fields. One is with the closed rotor slots and the other is with the semiclosed slots, which will cause relatively large slot harmonics.\nFigs. 3 and 4 show the calculated results of the time and space variation of the magnetic field and the loss distribution of the motors with the closed and semiclosed slots, respectively. In the case of the closed slots, the time variation of the magnetic field\nat the stator is nearly sinusoidal. On the other hand, in the case of the semiclosed slots, the waveform at the stator includes the harmonics caused by the rotor slot ripples due to the movement of the rotor. This harmonics must cause the part of the negative torque. The large harmonics caused by the stator slot ripples also appear at the rotor teeth tops of both motors. As a result, the losses concentrate at the rotor surface. In the case of the semiclosed slot, the high loss density area is larger than the case of the closed slot.\nThe measured and the calculated negative torques at synchronous speed are shown in Fig. 5 for the accuracy estimation. Considering the difficulty to measure and calculate the harmonic characteristics accurately, it can be said that the results",
            "agree well and that the proposed method is applicable to calculate the negative torque of the induction motors. Both the measured and calculated results indicate that the negative torque in case of the semiclosed slots is larger than the case of the closed slots, whose reason can be explained by Figs. 3 and 4. In the case of the semiclosed slot, the negative torque is nearly 5% of the rating output, which must not be negligible for the vector-controlled motors.\nFig. 6 shows the measured and calculated total torque due to the load. The calculated result by the conventional method is also shown. The conventional method clearly overestimates the total torque in case of the semiclosed slot. On the other hand, the accuracy of the torque calculation is improved by the proposed method.\nThe negative torque of induction motors caused by the slot ripples is investigated from both sides of the measurement and the electromagnetic field analysis. In the analysis, the negative torque is calculated from the harmonic losses of the motor ob-\ntained from the results of the time-stepping finite element analysis with the assistance of the electric machine theory. It is clarified that the negative torque of the motor with the semiclosed rotor slots is not negligible and that the accuracy of the torque calculation is improved by the proposed method.\n[1] K. Yamazaki, \u201cInduction motor analysis considering both harmonics and end effects using combination of 2-D and 3-D finite element method,\u201d IEEE Trans. Energy Conversion, vol. 14, pp. 698\u2013703, Sept. 1999. [2] , \u201cA quasi 3-D formulation for analyzing characteristics of induction motors with skewed slots,\u201d IEEE Trans. Magn., vol. 34, pp. 3624\u20133627, Sept. 1998. [3] , \u201cGeneralization of 3-D eddy current analysis for moving conductors due to coordinate systems and gauge conditions,\u201d IEEE Trans. Magn., vol. 33, pp. 1259\u20131263, Mar. 1997. [4] A. Kameari, \u201cLocal force calculation in 3D FEM with edge elements,\u201d Int. J. Appl. Electromagn. Mater., vol. 3, pp. 231\u2013240, 1993. [5] J. G. Zhu and V. S. Ramsden, \u201cImproved formulations for rotational core losses in rotating electrical machines,\u201d IEEE Trans. Magn., vol. 34, pp. 2234\u20132242, July 1998. [6] K. Yamazaki, \u201cEfficiency analysis of induction motors for ammonia compressors considering stray load losses caused by stator and rotor slot ripple,\u201d in Conf. Rec. 2001 IEEE Industry Applications Conference 36th Annual Meeting, vol. 2, 2001, pp. 762\u2013769."
        ]
    },
    {
        "image_filename": "designv11_24_0001788_bf02459024-Figure13-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001788_bf02459024-Figure13-1.png",
        "caption": "Fig. 13. - Plane (x', y'). k I> 1. The transformed stripes 1S~ and 2S~ are confluent on the stripe X~.",
        "texts": [
            " Let Sd be the family of stripes, of amplitude d, perpendicular to the x-axis, on the plane (x, y) (see fig. 12). Property B states that hysteresis loops with extremum values of input on the same stripe are congruent; nothing is said however about the congruency of loops with input's extrema on different stripes, 1Sd and 2Sd, of the same family. Linear transformations transform parallel lines into parallel lines. Stripes Sd, on plane (x, y), are transformed into inclined stripes S' d, on the plane (x', y') (see fig. 13). Let us call X~, the family of stripes, of amplitude d', perpendicular to x'-axis, in the plane (x', y') (see fig. 13). Definition. We shall call two stripes 1S~ and ~ confluent (on stripes of the X~, family) if they are both intersected by at least one stripe of X~, family (see fig. 13). At first, let us consider the case k > 0 (negative feedback). Let us distinguish: i) k > l , ii) k < l . i) Let 1Sd and 2Sd be two generic stripes of Sd family, and 1S'd, ~S~ the S' corresponding transformed stripes in plane (x',y'). Stripes 1S~ and 2 ~ are confluent (see fig. 13). By contradiction, let us suppose that property B is satisfied in the plane (x', y'). Then the loops 1C~, and 2C'd, (see fig. 13), belonging to stripes 1S~ and 2S~, respectively, should be congruent, and consequently all S' and S' should also be loops with extremum values of input on stripes 1 d 2 d congruent. For the general properties of l inear transformations, such a congruency should also hold for loops belonging to stripes iSd and 2S~ in the plane (x, y). But property B did not contemplate such a congruency in (x, y)-plane. Therefore, property B is not, in general, satisfied in the plane (x', y'). ii) In this case, stripes 1S~ and 2S'd are not confluent (see fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000708_1.2832460-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000708_1.2832460-Figure2-1.png",
        "caption": "Fig. 2 FMRR seal kinematic model and coordinate systems",
        "texts": [
            " The forcing functions in the system are seen to result from the initial misalignment of the flexible supports. An analytical method is presented for obtaining the general steady-state response to these forcing functions. The steady-state response determines the leakage rate of the seal and whether face contact occurs as a result of excessive steady-state runout. Kinematic Description Wileman and Green (1991) described a kinematic model for the concentric FMRR seal configuration (Figs. 2 and 3). Figure 2 shows the inertial reference frame, ^77 ,\u0302 and the principal systems for both elements, denoted x\u201ey\u201ez\u201e. Throughout the anal ysis, n is used to denote the element number, either 1 or 2, and these numbers can be assigned arbitrarily provided they are applied consistently throughout the analysis. Figure 3 illustrates the various coordinate systems as viewed along the direction of the system centerline. This vector diagram shows the relation ships between the inertial, principal, and fluid film systems described below. The inertial moments acting upon the rotors depend upon their absolute motions, and are expressed in the inertial system irj^ (Fig. 2) . It is also with respect to this system that the rotations of the other reference frames are measured. The equa tions of motion for the system are obtained by transforming the flexible support and fluid film moments into this inertial frame, then forming a moment balance between these applied moments and the inertial moments. A shaft-fixed reference frame XnY\u201eZ\u201e is associated with each of the shafts, and rotates with the shaft, so that the axis Z\u201e is parallel to axis ^, and X\u201e corresponds to ^ at r = 0 and leads ^ by the precession angle w\u201ef thereafter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000252_elan.1140090509-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000252_elan.1140090509-Figure3-1.png",
        "caption": "Fig. 3. Cyclic voltammograms of the poly(NB)-modified electrode swept in a) pH 5.4 acetate buffer, b) (a)+0.42mg/mL Hemoglobin and c) 0.42mg/mL hemoglobin at the bare glassy carbon electrode.",
        "texts": [
            " 5 potential shifted in the negative direction with a slope of 24.0mV. Therefore, it suggested a sluggish electron transfer through the polymer to the electrode. Due to the proton participation in the polymer redox conversion, the formal potential would change with the pH. With increasing pH in the range of 2.0-1 1 .O, the peak potential of both anodic and cathodic peaks shifted in the negative direction. AElA pH is -61 mV/pH in the pH region from 2.0 to 11.0. Thus, the electrode process is a two-electron, two-proton one. Figure 3 shows the cyclic voltammograms of the polymer electrode which were obtained in the absence and presence of 0.42mg/mL hemoglobin. It can be observed that there is an increasing response current corresponding to the cathodic peak, meanwhile, the anodic peak current decreases obviously. The response of hemoglobin was not observed at the bare electrode. This suggested that the redox polymer has catalytic activity for the reduction of hemoglobin. Hemoglobin in solution diffused toward the electrode surface and reacted with the reduction state of poly(NB) and that produced the oxidized state of poly(NB)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003574_1.2101858-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003574_1.2101858-Figure1-1.png",
        "caption": "Fig. 1 Schematic of brush seal",
        "texts": [
            " Common brush seal terminology involves many inherent brush seal dynamic issues, including bristle flutter, blow-down, hang-up, stiffness, instability, tip wear, pressure-carrying capacity, effective clearance, and leakage. Dinc et al. 1 have recently outlined a robust design procedure containing many complex design parameters. Developments in brush seal design indicate the significance of pressure and flow fields in dictating seal dynamics and performance. Early brush seal applications utilized a short front plate and a straight backing plate, which are illustrated in Fig. 1. Bristles are clamped between the front and backing plates with a lay angle to the rotor for flexibility. The backing plate is extended towards the rotor surface up to maximum radial rotor-stator closure in order to provide mechanical support. This typical configuration is referred to as the standard brush seal design. The bristle pack is divided radially into two distinct regions, labeled as fence height and upper regions Fig. 1 . The radial height between the bristle tips and the backing plate inner diameter is called the fence height. The rest of the bristle height out to the bristle pinch point is called the upper region. Governed predominantly by the flow field, bristles are mainly subject to three types of force: elastic, frictional, and aerodynamic. The balance of these forces dictates bristle equilibrium and brush seal dynamic behavior. Elastic forces are set by bristle mechanical properties and geometry. Frictional forces among bristles 1To whom correspondence should be addressed",
            " Over the years, various geometric modifications, e.g., pressure relief grooves, have been suggested to reduce frictional lock at the backing plate. Friction between the bristles and the backing plate is one of the main parameters determining whether the seal blows-down or remains hung-up. Based on a review of previous work, five common backing plate concepts are chosen in the scope of present study Fig. 2 . Standard configuration with straight backing plate case 1 is selected as the baseline. As shown in Fig. 1, the standard seal typically has a 0.75 mm 0.0295 in. thick bristle pack, 1.6 mm 0.0630 in. thick front and backing plates, a fence height of 1.4 mm 0.0551 in. , and a free bristle height of Transactions of the ASME ?url=/data/journals/jotuei/28728/ on 02/19/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F 10.68 mm 0.4205 in. 14,15 . Case 2 defines a single longitudinal groove in the backing plate Fig. 2 . A representative axial groove depth of 0.375 mm 0.0148 in. is selected"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000194_1.2832445-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000194_1.2832445-Figure2-1.png",
        "caption": "Fig. 2 Mass-spring model of rolling element bearing",
        "texts": [
            " Each of these stiff nesses is nonlinear in nature and has to be considered separately. This is what is done in the present work. In this section, a model for analysis of the structural vibration in rolling element bearings is developed. First the expressions for kinetic and potential energies are formulated. Using these expressions the equations of motion are derived utilizing La- grange's equation. These equations are then normalized to ob tain a comprehensive form. 2.1 Kinetic and Potential Energy Expressions. A sche matic of rolling element bearing is shown in Fig. 1. Figure 2 illustrates the mathematical model wherein the rolling element bearing is represented by a mass-spring system. Since the Hert zian forces arise only when there is contact deformation, the springs are required to act only in compression. In other words the respective spring force comes into play when the instanta neous spring length is shorter than its unstressed length; other wise separation between ball and race will take place and the resulting force is set to zero. A number of assumptions are made in the development of the mathematical model",
            " + pjb^ + xl + IXaPi cos 6'j - Ix^pfi sin 9-, + yl + lya'Pi sin 6*, + lyapfi cos 61;] r = r,,,, + Ti,., + To,. + r. (3) 2 e - - ( ( / . , - e ) Pr where Tr.e. represent the kinetic energy sum of the rolling ele ments. Tj,., To.,:, and T^ denote the kinetic energies of the inner and outer rings and the cage. The kinetic energy due to the rolling elements may then be obtained as a summation of those from each element, N Tr.e. = I T, (4) where the kinetic energy of the \u00abth rolling element may be written (Fig. 2) as r,. = {m,{% + \u00a5\u201e)\u2022{% + t) + jiM (5) As Fig. 2 illustrates, p = (p, cos 9i)r+ (pi sin 9i)]'. (6) and F\u201e = xf+ yaj (7) Differentiating with respect to time, substituting in Eq. (5) and simplifying, Ti = ^m/ipj + pj9j + xl + 2x\u201epi cos fl, - IXaPt'Oi sin 9i + yl + 2%pi sin 9i + 2%pi9i cos 9,] + {h 0? (8) Neglecting slip, the rolling contact equation for the /th rolling element and the inner ring can be written (Fig. 3) as The kinetic energy expression for the inner ring is Hence, Ti.r. = 2^a{r\u201e-ra) + j ^ ^ \" ^ Ti.r. = 2m\u201e(jC^ + fa) + 2ta4>l (11) (12) (13) Pri^i -9i)= - r ( < / . \u201e - 6 ' , . ) The position of the outer ring center is defined with respect to the inner ring center as depicted in Fig. 2. Here, Xi, and y,, refer to the coordinates defined with respect to the center of the inner ring. The displacement vector showing the location of the outer ring center with respect to that of the inner ring is then given by n = 'n, + r7b (14) or, n = ixa +Xi,)T+(y\u201e + yi,)f (15) Differentiating this with respect to time, ft = ixa +Xb)T+iya +yh)T (16) The kinetic energy of the outer ring may be written as To.r. = ^mtiFh-ri,) = lmi,i{x\u201e + 4 ) ' + (% + )ii)'] + ^hU (17) The kinetic energy of the cage is calculated by assuming that its center remains coincident with that of the inner ring",
            "org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use K... = S rtiigip, sindi + ya) 1=1 N = mgNya + X (mipig sin 0,) (20) i-i For the inner ring We may now employ Eq. (28 ) to obtain those derivatives of dXj _ 2p, - 2xi, cos $1 - 2yi, sin 6>,- 5pi V,-.;.. = m\u201eg% The potential energy of the outer ring is Vo.r. = mtgiya + yb) (21 ) (22) Noting that the deformations of springs representing the con tacts between the ith rolling element and the inner and outer races are, respectively, p, - L,o and R - Xi - L20 (Fig. 2 ) , the expression for the potential energy due to the contact deforma tion may be written as N N V\u00bb = I -2ku(p, - U? + I kkv(R - X, - L20? (23) 1=1 i = l where ku and fe, are the nonlinear stiffnesses due to Hertzian contact effects. The potential energy of the cage may be ex pressed as 2Xi _ Pi \u2014 Xj, cos dj - yt, sin dj Xi dxi _ Ixj, \u2014 2pi cos 61 _ Xj, \u2014 Pi cos 6i uXh 2Xj Xi dXi _ 2yf, - 2p, sin Oj _ yi, - pi sin Oj dyb 2xi Xi (29) (30) (31 ) 2.3 Normalization of Equations of Motion. The equa tions of motion may be normalized with respect to the physical and geometrical properties of the rolling elements, i",
            " (^ - Xi - L20) - ^ = Fx ( 26 ) i=i 0x1, where F^ is the generalized force on the outer ring corresponding to the generalized coordinate xi, and for generalized coordinate yt the equation is \" dXi mi,% + mi,yi, + mi,g - X ^2i (R - -\u00ab/ - lao) -^ = Fy (27) where f,, is the generalized force on the outer ring of the bearing corresponding to the generalized coordinate yi,. If the motion of the inner ring is known, Eqs. ( 2 5 ) , ( 2 6 ) , and (27) may be solved simultaneously to obtain the resulting bearing response. This is a system of N + 2 second order, nonlinear, ordinary differential equations. Now, to find the deformation of spring 2, Xi is defined as shown in Fig. 2. Considering this figure, Xi cos Bx + Xi, = Pi cos 9i Xi sin 0x + yi> = pi sin 9i From these two equations, we obtain the expression for Xi: Xi = [{pi cos Bi - Xb)^ + ipi sin \u00ab,\u2022 - j * ) ^ ] ' \" = [p? + x l - 2piXb cos 9i +yl- 2ybPi sin 6 I , ] ' \" (28) mtxt + mtxt - I kl{R* - xf - Ll) ' 1=1 dxt (34) , * V f * *,.;* rrib y\u201e -I- Mb yb + mbg - I kUR* - xf - L?o) 2 ^ = F* (35) (-1 dyb 2.4 Contact Stiffness. Hertz equations for elastic defor mation involving line contact between solid bodies are given by (Eschmann et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001882_1.1398549-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001882_1.1398549-Figure1-1.png",
        "caption": "Fig. 1 Principle of the EHL machine used for the experiments. The ball and the disc are accurately and independently entrained by 2 stepping motors in the range 0.5 mm\u00d5s to 3 m\u00d5s. The applied load is between 0 and 25 N \u201econtact pressure \u00cb0.5 GPa\u2026.",
        "texts": [
            "org/ on 01/28/2016 Term the lubricant supply is a key point in the understanding of the lubrication mechanism of such emulsions. The kinetics of lubricating film formation can be modelled by considering that the boundary layers only ensure a starved EHD lubrication. An analysis of the supply conditions based on the work of Chevalier et al. @14# can then be used to investigate the piezo-viscous properties of the boundary films formed in a concentrated rolling/sliding contact. 2.1 The Test Equipment. An optical EHL rig presented in Fig. 1 has been developed and used in this work. Its main principle is similar to the EHL machines already described in the literature @15,16#. Nevertheless, this apparatus is not only devoted to the measurement of the oil film thickness with an optical method but to the visualisation of the lubricated contact. The contact is formed between a 52,100 steel ball and a silica disc coated with a thin chromium layer ~thickness: 10 nm!. This disc in contact with the steel ball, forms an optical resonant cavity that enables us to precisely measure the oil film thickness @17#"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000096_jsvi.1998.1646-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000096_jsvi.1998.1646-Figure1-1.png",
        "caption": "Figure 1. Mechanical model.",
        "texts": [
            " Moreover, in reference [8], it has been shown that rattling noise in real gear-boxes does not depend in a significant way on the structural properties of the corresponding non-linear vibrations; it depends mainly on the parameter influencing the mean values of the impulsive processes. Therefore, a more adequate description by mean value on the random rattling system will need to evolve. To develop a stochastic model, a brief review about the deterministic model is necessary. In this paper, only a single stage rattling system is considered. In Figure 1, the driven gear wheel not under load can move freely between backlashes, and the free flight motion is only stopped by the backlash boundary, where an impact occurs. According to what has been mentioned above, the motion of the driven wheel can be distinguished into two phases: the free flight phase and the contact phase. The motion equation can be written in the following way: I1f 1 + d1f 1 =\u2212T1, (1) for the free flight phase and the contact phase is expressed by f + 1 =\u2212of \u2212 1 + (1+ o) Re R1 e\u0307(t), (2) in which Re and R1 are basic radii; e(t) is a harmonic rotation with amplitude a and frequency v; v1 indicates a constant play in mesh plane; I1 stands for inertia moment of driven gear wheel; f1 is angular displacement; T1 denotes a constant moment; d1 means damping ratio in free flight phase; and o is the restitution coefficient"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001060_0003-2670(92)85135-s-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001060_0003-2670(92)85135-s-Figure3-1.png",
        "caption": "Fig 3 Cathodic stripping voltammograms of bare Pt electrodes in 1 M H2SO4 after treatment in oxygen plasma u untreated, 1 30 s, 2 2 min, 3 5 min",
        "texts": [
            " method for on-wafer fabrication of free-chlorine sensors is described The sensor structure consists of a planar three-electrode electrochemical cell covered with a poly(hydroxyethyl methacrylate) hydrogel membrane This membrane is photohthographically patterned on-wafer In order to guarantee good adhesion of the membrane to the electrode surface a special oxidation step consisting of a treatment in an oxygen plasma followed by a silanization procedure has been developed The optimal operational polarization voltage of the integrated sensor for detection of hypochlorous acid was found to be 0 mV vs the on-chip Ag/AgCI reference electrode in a solution of 0 1 M KCI Sensors with membrane thicknesses of 10 and 50 \u00b5m are found to give linear calibration curves between 0 1 and 5 mg 1 -1 free chlorine, with sensitivities of 2 0 and 0 4 nA (mg respectively Keywords Sensors, Chlorine detection, Diffusion membrane, Silicon based sensor There is an increasing need for the determination and continuous on-line monitoring of residual water disinfectant Although several alternatives, like ozone, bromide, iodine or chlorine dioxide, exist for disinfecting purposes, none can compete with chlorine with respect to its effectiveness, easy applicability, presistence and low Correspondence to A van den Berg, Institute of Microtechnology, University of Neuchatel, Rue A -L Breguet 2, CH2000 Neuchatel (Switzerland) 0003-2670/92/$05 00 \u00a9 1992 - Elsevier Science Publishers B V All rights reserved cost [1] At the normal pH values of drinking water (pH 6 5-9), chlorine is present in the form of hypochlorous acid, HC1O, or its conjugated base, the CIO- anion [2] However, since the disinfecting reactivity of HCIO is about 10000 times higher than that of the CIO - anion [3,4], we will focus on the detection of hypochlorous acid Different methods exist to detect dissolved chlorine, most of them based on electrochemical principles A potentiometnc approach, as pro- 76 posed by Schlechtriemen and Sohege [5] for the detection of chlorine gas is less appropriate for on-line monitoring because of its logarithmic response, giving the sensor a large dynamic range but a relatively low precision Detectors based on amperometnc detection respond linearly to concentration variations, and are thus more promising In this case, use is made of the strong oxidative nature of the hypochlorous acid, which enables its electrochemical reduction at a relatively anodic potential thus excluding interference of other oxidants like dissolved oxygen Conventional analyzers often use rotating disk electrodes that provide sufficient sensitivity and selectivity, but are rather bulky systems that are not easily introduced on a large scale for on-line monitoring [6] The same holds for FIA-based systems that use iodometric [7,8] or direct amperometric detection [9] A macroscopic membrane-covered amperometric detector fabricated by conventional techniques with good sensing properties has been described by Ben-Yaakov [10], but this approach lacks the possibility of easy mass-fabrication Finally, an alternative optical detection as recently proposed by Piraud et al [11] for the moment does not attain the required detection limit of about 0 01 mg 1 - I and the measurement system cannot be easily miniaturised The sensor we present here is based on a Clark-type device It uses a planar three-electrode electrochemical cell covered with a thin hydrogel membrane to detect the hypochlorous acid The distinctive feature of our approach is that the entire sensing element is realized on silicon with standard IC-fabrication techniques, implying that the sensing element can be easily and reproducibly mass-produced Thin-film platinum working- and counter-electrodes, and a partially chloridized silver reference electrode were used The latter can be used as a reference electrode since the Cl - concentration in drinking water is fairly constant The electrode reactions taking place at the working electrode (WE) and counter electrode (CE) are respectively WE(cathode) HC1O + 2e ) OH- + Cl - CE(anode) 211 20 0 02+ 4H++ 4e A van den Berg et al / Anal Chim Acta 269 (1992) 75-82 To prevent the convective effects such as stirring from influencing the mass flow to the working electrode, we used a diffusion limiting membrane (DLM) to define a stagnant surface layer m which diffusion is the only process determining the mass transfer and thus the measured current Under potentiostatic operation at a properly chosen working potential, the measured current is proportional to the amount of reduced free chlorine Recently, we have proposed the use of a poly(hydroxyethyl methacrylate) (polyHEMA) hydrogel layer as DLM for the detection of hydrogen peroxide and oxygen [12] This membrane has the advantage that it can be photolithographically polymerized and patterned enabling the fabrication of the complete cell with IC-compatible methods With this technology, polyHEMA layer thicknesses of between 10 and 100 \u00b5m can be realized In this way an optimal trade-off between a high sensor current and a rapid response on one hand (thin membrane) and a signal insensitive to stirring on the other hand (thick membrane) can be chosen Special attention has been paid to the adhesion of the polyHEMA membrane It is known that chemical pretreatment of oxide surfaces such as SI02 and A1203 with methacrylic functional silane strongly improves the adhesion [13] However, such a treatment can not be directly applied to the surface of a platinum electrode Therefore we investigated methods to oxidize and subsequently functionalize a platinum electrode, with the extra requirement that the method should be applicable on-wafer EXPERIMENTAL Basic device fabrication The basic structure consists of a three-elec- trode cell realized on a silicon wafer The working- and counter-electrodes consist of a 1500 A 0 thick Pt layer on top of a 500A thick Ti adhesion layer The reference electrode is made by chemical chloridisation of a 1 \u00b5m thick Ag layer Further details of the fabrication of the device are given in [14] A van den Berg et al / Anal Chun Acta 269 (1992) 75-82 Instrumentation and methods Cyclic voltammetry measurements were per- formed using a PAR 273 potentiostat For all cyclic voltammetric measurements a solution of 1 M H2SO4 and a scan rate of 100 mV s-i were used, except for the determination of the interference of oxygen reduction relative to the hypochlorous acid reduction, where a solution of 0 1 M KCl with 0 01 M phosphate buffer (pH 5 8) and a scan rate of 10 mV s -i were used For potentiostatic measurements a potentiostat built in-house was used The plasma oxidation of the platinum electrodes was carried out using an oxygen plasma in an Alcatel GIR 300 plasma etch machine Measurements of polyHEMA membrane thicknesses were carried out with an Alphastep 200 step height profiler Visual inspections after the measurements confirmed that the scan of the stylus did not cause any damage to the membranes Electrode surface modification Electrochemical oxidation of the platinum electrode surface was carried out by polarizing the electrodes in 1 M H 2SO4 at +25 V vs SCE during 5 min Chemical oxidation was carried out in 0 25 M (NH 4)2 S 20 8 , 0 5 M HCIO, or 1 M HNO3 Plasma oxidation was carried out in an oxygen plasma at a frequency of 13 5 MHz, a pressure of 0 1 mbar, and using a power of 100 W Silanization of the electrode surface was carried out by dipping the electrodes in hexamethyldisilazane (HMDS) (Fluka) Subsequently, the electrodes were blown dry in nitrogen Functionalization of the surface with methacrylic groups was performed by treating the electrodes for 1 min with a solution of 10% (trimethoxysilyl)propyl methacrylate (TMSM) (Aldrich) and 0 5% H20 in toluene at 60\u00b0C Membrane deposition The monomer mixture consisting of 57 5 wt % hydroxyethyl methacrylate (HEMA) (Fluka), 38 wt % ethyleneglycol (EG) (Merck), 1 wt % dimethoxyphenylacetophenone (DMAP) (Aldrich), 2 5 wt % polyvinylpyrrolidone K90 (PVP) (Aldrich) and 1 wt % tetraethyleneglycol 77 dimethacrylate (TEGDM) (Fluka) was placed by pipette on the wafer in an amount corresponding to the required membrane thickness A Mylar sheet was then pressed onto the mixture which was allowed to spread out over the wafer until the required coverage of the wafer was obtained Then the monomer mixture was selectively photopolymenzed with UV light Exposure times of 30 s to 3 min were used This was followed by development in ethanol The sensors were preconditioned in 0 1 M KCl prior to measurement RESULTS AND DISCUSSION Surface modification of the electrodes In the fabrication process of the completed cell with hydrogel membrane, a crucial element concerning the durability is the membrane adhesion to the electrode surface In order to be able to apply the frequently used method of surface silanization, the surface of the platinum electrodes must first be oxidized A well-known standard method to do this is electrochemical oxidation [15] The formation of oxide (mono)layers at the electrode surface can be monitored by reducing the oxide in a cathodic scan starting at high anodic potential In Fig 1 stripping voltammo- 78 grams of platinum, untreated and electrochemically oxidized for 1 s, 3 min and 5 min, respectively, are shown In this figure, two different cathodic waves can be clearly distinguished one corresponding to a quickly formed, and easily reduced oxide (reduction potential about +400 mV vs SCE), and a second wave corresponding to an oxide form that is only formed after a few minutes of polarization at + 2 5 V vs SCE, and reduced at approximately -50 mV vs SCE The presence of these two waves is in good correspondence with the results reported in [14], where they were attributed to two different forms of platinum oxide We will also designate the two waves as A and B for the more anodic and more cathodic waves, respectively, in accord with the nomenclature used in [15] In order to see which one of the two oxides is necessary for the silanization, we performed a simple silanization reaction with HMDS which is comparable to the somewhat more elaborate reaction with TMSM Such a reaction should passivate the formed oxide, and disable its electrochemical reduction In Fig 2 the effects of the silanization on the appearance of both oxide peaks is shown From the three curves representing untreated oxide, oxide treated in HMDS for A tan den Berg et al / Anal Chem Acta 269 (1992) 75-82 30 s, and oxide treated in HMDS for 5 min, two conclusions can be drawn The first and most important conclusion is that the oxide represented by wave A does not react with HMDS The second conclusion is that wave B reacts only relatively slowly with HMDS, and that it takes about 5 min to obtain a fully silanized oxide From the above results it can be concluded that in order to be able to silanize the electrode surface, the formation of platinum oxide of type B is necessary Since electrochemical oxidation is not easily applicable on whole wafers, we investigated other chemical treatments that could provide the platinum type B oxide Unfortunately, treatments with oxidants such as nitric acid, and ammonium peroxodisulfate did not result in the appearance of the type B oxide The only treatment which did give both oxide waves was a treatment in oxygen plasma, as shown in Fig 3 From this figure it can be concluded that a 5-min treatment of the platinum electrode in an oxygen plasma results in similar A- and B-type oxide waves as obtained with the electrochemical oxidation Membrane deposition The deposition of the polyHEMA hydrogel membranes was carried out as described in the A van den Berg et al / Anal Chtm Acta 269 (1992) 75-82 experimental part Some difficulties were encountered when we tried to wash away the unpolymerized regions from the wafer in the development step Therefore we had to modify the mask in such a way that only every second basic electrode was covered with the polyHEMA membrane A SEM micrograph of a part of a wafer covered with membranes is shown in Fig 4 From this figure, it can be concluded that a satisfactory lateral resolution of some tens of microns is obtained, which is largely sufficient for our purpose The homogeneity of the membrane thickness over the wafer was investigated by step-height measurements On 32 evenly distributed membranes over the wafer a mean thickness of 618 \u00b5m was found with a standard deviation of 7 3 \u00b5m An important part of the thickness variation was caused by a continuous varying thickness of the membranes over the wafer If closely located membranes were considered, typical standard deviations of 3-4 \u00b5m were found Sensor characterization A first characterization of the electrodes was carried out to determine the optimal polarization potential for the detection of free chlorine Therefore, cyclic voltammograms were taken of the bare platinum electrodes in background electrolyte under nitrogen and with added sodium hypochlorite A background electrolyte a solution of 0 1 M KCI with 0 01 M potassium dihydrogen- phosphate (pH 5 8) was taken to ensure that all the free chlorine was present as hypochlorous acid In order to examine the interference of oxygen, a third cyclic voltammogram was recorded in background electrolyte and ambient air, as shown in Fig 5 From the cyclic voltammogram of the reduction of hypochlorous acid (at E < + 700 mV vs SCE) and of oxygen reduction (E < + 300 mV vs SCE), a polarization potential \"window\" between + 300 and + 400 mV vs SCE can be determined where the hypochlorous acid reduction is relatively potential independent, and there is no oxygen reduction interference It must be remarked here that the finally desired detection limit for free chlorine is in the micromolar range, whereas the figure shown is obtained with a concentration of 1 mM hypochlorous acid The above mentioned conclusions were verified with potentiostatic measurements carried out with mounted and encapsulated three-electrode devices covered with a polyHEMA membrane of approximately 10 \u00b5m thickness In Fig 6, the sensor current as a function of the free chlorine concentration at three different polarization potentials is measured At the most cathodic potential (- 100 mV vs on-chip reference electrode) an offset current due to oxygen reduction is found At 0 mV this offset current is largely suppressed, whereas the same sensitivity to free chlorine is 79 80 A van den Berg et al / Anal Chum Acta 269 (1992) 75-82 2 1 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003420_1.1809634-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003420_1.1809634-Figure2-1.png",
        "caption": "FIG. 2. The composition of the model: the substrate (a) and the powder bed (c) are represented by Solid70 elements to simulate three-dimensional (3D) thermal conduction. They are coupled by the Contact174/Target170 contact pair (b); the radiation and convection effects at surfaces [d\u2013g] are studied using the Surf152 elements.",
        "texts": [
            " In the model, the powder bed is treated as a continuum with a relatively low thermal conductivity before melting. The thickness of the layer is represented by an equivalent solid form, s1\u2212adL, where a is the voidage of the powder bed and L is the actual thickness of the powder bed. When the temperature of the layer is raised above its liquidus temperature, a molten layer is assumed to form. To model the thermal conduction between the powder bed and the substrate, the contact analysis capability of ANSYS is utilized (Fig. 2). Contact 174/Target 170 is a surface-tosurface contact pair that can simulate the thermal contact resistance. In fact, thermal contact conductance is used, which is the reciprocal of thermal contact resistance. In the model, a layer of Target 170 elements is generated and assigned to the bottom of the powder bed; similarly, Contact 174 elements are assigned to the top surface of the substrate. The surface effects (convection and radiation) are represented by element Surf152, which has the capability to evaluate the heat loss caused by convection and radiation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003766_0278364906061159-Figure16-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003766_0278364906061159-Figure16-1.png",
        "caption": "Fig. 16. Lock mechanics.",
        "texts": [],
        "surrounding_texts": [
            "Table 2. Head unit specifications\nDiameter 90 (mm) Weight 400 (g)\nFig. 13. Head unit.\nextra wire will pile up at the end. To make the head unit follow the tube, it is necessary to wind up the excessive wire length. Therefore, we added a wire-rewinding device to the head unit (Figure 12).\nThe head unit has a CCD camera. The specifications of the head unit are shown in Table 2.\nAs shown in Figures 14 and 15, the hermetic case is composed of the following:\n1. a winch;\n2. a slip ring;\n3. an air tank (hermetic case);\n4. lock mechanism.\nThe winch winds up the tube and wire simultaneously. The slip ring allows the supply of electricity to the outside through the wire wound up around the winch. The air tank contains the air supplied from the air compressor. The amount of tube expansion is controlled by the handle and lock mechanism.\nThis hermetic wheel case can wind up to 10 m of tube. Since the wire is inside the tube and will be wound up along with the tube, the wire will twist if no measure is taken. The slip ring prevents this twist.\nIn the next section we explain the handle lock mechanism. When air pressure is applied, the tube will expand in a forward direction. Accordingly, it will continue expanding unless the expansion is stopped. In rescue operations, however, some-\nat Virginia Tech on March 14, 2015ijr.sagepub.comDownloaded from",
            "times it is necessary to stop the tube expansion and search a certain area for a while. Therefore, the device controls the expansion amount by locking the handle to stop the tube expansion. Figures 16 and 17 show the actual handle lock mechanism. The Slime Scope controls the tube expansion by locking and releasing the handle.\n5. Test Machine\nFigure 18 shows our test machine. We used this test machine to confirm that the DETube can travel in rubble. Table 3 shows its specifications.\nIn the following, the DETube\u2019s holding power is the power needed to maintain the tube\u2019s expansion against the propelling force at the head of the DETube, with the propelling force being caused by the inside pressure. Assuming that the propelling force produced by the DETube is FT , the holding power is Fk, the force that holds the tube from outside is Ff and the loss is FL, the relationship between these can be expressed as\nFT = Fk + Ff + FL. (1)\nThe retracted tube is wrinkled since it has the same diameter as the external tube, causing friction, resulting in loss, etc.\nAs the DETube\u2019s propulsion principle is the same as the principle of a pulley, the following equation is established:\nFk = Ff . (2)\nSubstituting eq. (2) into eq. (1) yields the following equation:\nFT = 2Fk + FL. (3)\nHere FT is the product of the pressure inside the tube and the stress area, so if the holding force Fk is determined, the impact of the loss in propelling force can be calculated from eq. (3). In other words, determining the holding power is considered to be important to know the characteristics of the DETube.\nat Virginia Tech on March 14, 2015ijr.sagepub.comDownloaded from",
            "Therefore, we calculated the loss in propelling force by measuring the holding power Fk using the experiment device shown in Figure 19. Figure 20 shows the result.\nThe experiment demonstrated that the holding power was not the same as the propelling power. This discrepancy results from the friction loss, possibly because higher pressure increases the friction resistance inside the tube and thus increases the loss.\nIn addition, Figure 20 shows that the holding power remains almost the same regardless of the expansion amount. In other words, the impact of the loss is independent of the expansion amount. However, in theory, as the expansion amount becomes larger, the contact area between the external tube and retracted tube (i.e., the area where there is loss from friction resistance) will increase. As a result, the loss must be larger. However, this does not appear clearly in the experiments, since the expansion amount was small, thus resulting in a small friction resistance.\nIn the previous experiment, we studied the impact from the loss by measuring the holding power when the DETube went straight forward. However, in actual search operations in rubble, the DETube will often need to bend to go through, rather than go straight forward. Accordingly, we studied the changes of the loss when the DETube bends, using the experiment of apparatus shown in Figure 21. Figure 22 shows the result.\nFigure 22 shows that the holding power decreases as the bending angle increases. This would suggest that increasing the bending angle results in an increased loss.\nThen we studied the loss. When the DETube is bent, the contact area between the external tube and retracted tube will increase and the area affected by sliding friction will increase. Therefore, it is considered that the loss will increase.\nTo study the impact of the friction loss, we repeated the previous experiment once again after applying grease inside the tube for lubrication. Figure 23 shows the result.\nat Virginia Tech on March 14, 2015ijr.sagepub.comDownloaded from"
        ]
    },
    {
        "image_filename": "designv11_24_0002564_2004-01-1307-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002564_2004-01-1307-Figure5-1.png",
        "caption": "Figure 5. Pressure distribution on the rear wheels: (a) Base-model, and (b) Config. 1.",
        "texts": [
            " The shape of the deflectors follows the end curve of the wheelhouse. The idea is to reduce the exposed area of the deflector, while still protecting the front-wheel from the upcoming flow. \u2022 Config. 4: a 3D front-wheel deflector, 25 mm in height and about 270 mm in length. The shape of the deflectors follows the end curve of the wheelhouse. Just as in Config. 1, the idea is to protect the wheel and the link arm from the upcoming flow, while reducing the exposed surface represented by the deflector by decreasing its height. \u2022 Config. 5: a 2D front-wheel deflector, 50 mm in height and 285 mm in length and 150-200 mm in front of the wheel-house. The objective is to protect the wheel and the link arm from the upcoming flow, and reduce the effect on the front lift coefficient. The different cases studied are shown in Figure 3. A rectangle has been drawn around the deflectors to help the reader visualization. Table 2 presents Cd and dCd values computed in this study. The dCd values are calculated with the basemodel as reference. Table 2 also gives the changes in Cd in terms of percentage values compared to the reference case",
            " 1 and 2 give the highest drag reduction for the front and rear wheels, respectively. The deflector of Config. 1 is plotted in Figure 4 (b) and it shows the area of the front-wheel it protects. It is also visible by comparing Figures 4(a) and 4(b) that the front brakes also benefit from the inclusion of the deflector, as high-pressure areas have disappeared in Figure 4 (b). On the other hand, the deflector represents itself a region with high-pressure values that contribute significantly to drag increase. The plots on Figure 5 (a) and 5 (b) show that the high pressure area on the front side of the real wheels is greater for the base-model and for Config.1, explaining the results of Table 3. The inside of the rear wheels do not seem to be affected. Similar results to the ones shown in Figures 4 and 5 were obtained for the other four deflectors investigated, and therefore are not presented here. An interesting way to understand the contribution of the underbody drag to the total drag of the vehicle is by looking at the sum of local drag values (increments of 100 mm in the x-direction), as Figure 6 shows"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002971_095441005x7259-Figure10-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002971_095441005x7259-Figure10-1.png",
        "caption": "Fig. 10 Plan view of the ICE vehicle (OB LEF, outboard leading-edge flap; SSD, spoiler-slot deflector; AMT, all moving tip)",
        "texts": [
            " The control effectors include elevons, pitch flaps, all moving tips, thrust vectoring, spoiler-slot deflectors, and outboard leading-edge flaps. The conventional control effectors are defined as the elevons, pitch flap, and leading-edge flaps. The innovative control effectors are defined as the thrust vectoring, all moving tips, and spoiler slot deflectors. Challenges associated with control using the all moving tips and spoiler-slot deflectors include zero lower deflection limits, strong multi-axis effects, and effector interactions. The state, output, and input vectors in these linear models are defined below, and Fig. 10 shows the vehicle in plan view: xT \u00bc \u00bdu w qb u v pb rb f yT \u00bc \u00bd v a qb u b ps rs f axcg aycg ancg uT \u00bc \u00bdDE3 DE13 DE4 DE5 DE15 DE9 DE19 DE2 DE12 DE10 DE20 Proc. IMechE Vol. 219 Part G: J. Aerospace Engineering G02104 # IMechE 2005 at COLORADO STATE UNIV LIBRARIES on June 28, 2015pig.sagepub.comDownloaded from It should be noted that all the possible sensed quantities available with the ICE model were input to the observers. Vehicle models for the two flight conditions follow. The vehicle model possesses one unstable pole at s \u00bc 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003766_0278364906061159-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003766_0278364906061159-Figure2-1.png",
        "caption": "Fig. 2. Search in the rubble (rod-type tool).",
        "texts": [],
        "surrounding_texts": [
            "One of the major characteristics of the DETube is that it can expand without causing friction with the outside. This is because, as mentioned before, it expands by dispensing the tube from inside, so the part once extracted outside stands still against the outside environment. Another major characteristic is that it uses a pneumatic tube as an expandable unit. Because of this, it can bend easily and, with a direction instruction tool installed at the end, go along the rubble (Figure 5). On the other hand, the tube can become more rigid by increasing the inner pressure to go over a ditch (Figure 6). That is, the DETube can serve as a new mechanism to go through rubble, which meets the criteria required for tools that operate in rubble as described in Section 2 (Figure 7)."
        ]
    },
    {
        "image_filename": "designv11_24_0001683_s0094-114x(99)00016-6-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001683_s0094-114x(99)00016-6-Figure1-1.png",
        "caption": "Fig. 1. The structure of nine-link Barranov truss.",
        "texts": [
            " The early research for Assur groups in closed-form (analytical) solutions was presented by Liand [1], where planar Assur II groups were solved and six solutions are obtained. Subsequently, the same problem was studied in Ref. [2\u00b14, 7\u00b19]. Recently, one kind of sevsenlink Barranov truss or six-link Assur groups was solved by Innocenti [5]. However, all the other Assur groups which are more than six-link remain unsolved. In this paper, the displacement analysis for one kind of nine-link Barranov trusses is studied (Fig. 1). If removing some link from the structure, eight-link Assur group can be obtained. The total eight eight-link Assur groups can be obtained, in Figs. 2\u00b19, where double circle indicates the outside pair. We will \u00aex the quadrangular link ABCD to solve displacement analysis of Barranov truss. It is the same as displacement analysis for a eight-link Assur group in Fig. 2. Meanwhile, the number of assembly con\u00aegurations for other Assur groups can be determined, since they are equal to the number of Assur group in Fig. 2. The method of vector together with complex numbers is used in the paper. It has been introduced by Wilson [6]. However, the di erence with Wilson's approach is that we will directly deal with the complex number equations rather than separate it into real and imaginary parts when eliminating and solving equations. Using this method, the displacement analysis for various kind of planar mechanisms are possible. According to the vector loop relationships in Fig. 1, there are four constraint equations can be established. KF KC CA AF ME MJ JC CA AE DG DC CJ JI IG BH BC CJ JI IH Changing vector equations into complex numbers form, they are KF \u00ffl5eia2eiy2 A\u00ff C l2e iy1 1 ME \u00ffl7eia3eiy3 \u00ff l6e iy2 A\u00ff C l1e ia1eiy1 2 DG C \u00ff D l6e iy2 l8e iy3 l9e iy4 3 BH C \u00ff B l6e iy2 l8e iy3 l10e ia4eiy4 4 Here, A,B,C and D denote the coordinates of points A, B, C and D under the complex coordinate which have the form of x yi, i \u00ff1p . Since the square of distance between the points K and F is equal to KF multiplied by its conjugate complex numbers KF (in this paper, the upper line stands for conjugate complex numbers), the following equation from Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001914_rob.10048-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001914_rob.10048-Figure2-1.png",
        "caption": "Figure 2. Definition of coordinate systems and vector loop formulation of the limbs: (a) S-type LAP, (b) H-type LAP.",
        "texts": [
            " The feasible configuration search algorithm and the differential loop closure equations are respectively derived in Sections 3 and 4. The complete numerical algorithm for solving the direct kinematics problem is presented in Section 5. Section 6 gives two numerical examples todemonstrate the stability andefficiencyof the proposed method and its ability of finding multiple direct kinematic solutions. The conclusions of this work are given in the last section. AND INVERSE KINEMATICS SOLUTIONS The associated coordinate systems and the vector loop formulation of the two types of LAP are shown in Figure 2. As shown in the figure, the origins of the moving frame U-V-W and the fixed frame X-Y-Z are respectively attached to the center point C of the endeffector and a fixed reference point O of the base. The absolute position of the moving platform is denoted by the vector PC , and its orientation is described by [R] = [u v w] where [R] is a 3\u00d7 3 orthogonal matrix, in which u, v, and w are, respectively, unit vectors along the U, V, and W axis of the moving frame, expressed with respect to the fixed reference frame X-Y-Z. Accordingly, the absolute position of the center point pi of the ith joint on the moving platform can be written as: Pi = PC + [R]UVWri (1) where UVWri is the position vector of point pi relative topointC , expressedwith respect to themoving frame U-V-W. The inversekinematicsproblem involves computing the driving joint variables for given configuration (that is,PC and [R]) of themovingplatform.The closed form solutions to this problem can be derived easily, as follows. As shown in Figure 2(a), the loop closure equation for each limb of the S-type LAP can be written as: Li = Pi \u2212 Bi (2) where Bi is the absolute position vector of the center point bi of the universal joint. Since PC and [R] are known, Pi can be computed from Eq. (1). Therefore, the limb length can be obtained as: li = \u221a (Pi \u2212 Bi )2 (3) On the other hand, according to Figure 2(b), the vector loop closure equation for each limb of the H-type LAP can be written as: Li = Pi \u2212 (B\u2032 i + aiei ) (4) in which ai is the distance of the slider measured with respect to a reference point B \u2032 i on the rail, and ei is a unit vector that denotes the positive direction of the rail. Taking the square of the Euclidean norm of both sides of Eq. (4) gives: l2i = (Pi \u2212 B\u2032 i ) 2 \u2212 2(Pi \u2212 B\u2032 i ) \u00b7 ei ai + a2i (5) Since the limb length li is known for this type, the joint variable ai can be solved as: ai = (Pi \u2212 B\u2032 i ) \u00b7 ei \u00b1 \u221a l2i \u2212 (Pi \u2212 B\u2032 i ) 2 + [(Pi \u2212 B\u2032 i ) \u00b7 ei ]2 (6) Noting that there are two possible real solutions for each ai , therefore the H-type LAP can have, at most, 64 inverse kinematic solutions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002619_095440605x31481-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002619_095440605x31481-Figure8-1.png",
        "caption": "Fig. 8 CV4-gear and pinion generated by a tilted male and female cutter, respectively, u \u00bc 58, R/m \u00bc 12, fm \u00bc 208, N1 \u00bc 20, and N2 \u00bc 100",
        "texts": [
            " A pair of CV3-gears consists of two dissimilar parts; one CV2-gear proper and its conjugate, in C01505 # IMechE 2005 Proc. IMechE Vol. 219 Part C: J. Mechanical Engineering Science at UNIV OF VIRGINIA on July 12, 2015pic.sagepub.comDownloaded from line contact. The two generating racks are complementary; the \u2018second\u2019 one has its tooth spacemaintained constant in the direction of the radius vector R, rather than the tooth thickness. This is achieved by the second rack being traced out by female cutters that saddle the tooth to be cut (shape as depicted later in Fig. 8), as opposed to the male cutters. Both gears will have the same tooth trace radii, but Rcav and Rvex are interchanged. A female cutter must not be in one piece or plane; it is easier to assemble its function from a pair of single-sided cutters. The limitation on the number of teeth to be cut will be markedly tighter than that according to Fig. 4, owing to the female cutter radius to its innermost edges being small. Hence, it is suggested that the pinion should be the member to generate by the female tool, also because it produces a tooth section of higher bending strength",
            " The proposal of CV3-gears dates back to Schurr [6] and Farnum [7]. The latter used the terms \u2018singleannular or tooth-space-forming cutter\u2019 and \u2018double-annular or tooth-forming cutter\u2019. Williams [8] also used male and female cutters, but in a process of generating only the pinion, as mentioned previously in section 1. Koga [36] introduced the same process of generating CV3-gears with an additional feature to allow cutting larger numbers of teeth, even racks, without collision with the cutters on their way round. As shown in Fig. 8, the male cutters are tilted by a small angle u on their cutter head in an outward (flaring) conical form, while the axis of that cutter head is tilted by the same amount to its feed direction, such that the cutters remain perpendicular to the rack pitch plane in the midplane. For example, with u \u00bc 58, as in Fig. 8, racks with b \u00bc 308 could be produced with R/m 5 14. The opposite is done to the female cutter head, which cuts pinions of small numbers of teeth. What Koga did not state is that: (a) the male cutters render the bottom land deeper in the midplane, whereas the female cutters do the opposite; (b) the two sets of flanks of any one gear have the same pressure angle only in the midplane, the teeth will be slightly oblique (buttress) in the side planes, and the obliquity is the same and in the correct relative orientation for both gears, so that they should remain conjugate in all transverse planes; (c) the generating conical frusta have a semi-cone angle of (fm2 u) for the convex rack flank enveloped by the male cutters and for the concave rack flank enveloped by the female cutters, and a larger semi-cone angle of (fm\u00fe u) for the other two flanks, and this makes the hyperbolic deviations of the latter flank profiles in the side planes larger. In the side plane(s), the increased transverse pressure angle and circular thickness of the pinion and space width of the gear, as well as the tooth obliquities and the deeper/shallower bottom lands, are all evident from the enlarged details at the top and bottom of Fig. 8. Thus, the tooth flank geometry of CV4-racks cannot be described in simple terms, and the presence of an angle u adds another item to the specifications. Worth mentioning is that Koga [36] evaded the pitfall which Llewellin [37] had earlier run into by having suggested that both mating gears be cut by the samemale cutter head, tilted in the same clearing sense, where contradicting tooth obliquities would have resulted. In doing so, Llewellin had been aiming at compensating the tooth space widening towards the side planes by having the cutters dig Proc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003144_cp:20060181-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003144_cp:20060181-Figure2-1.png",
        "caption": "Fig. 2: DFIG equivalent model for stability studies.",
        "texts": [
            " This is done by defining the following variables: eqs = KmrrCWsYVdr eds = -Kmrrc)sVqr (1) (2) s = Lss - (L/rr) Tr = Lrr /Rr (3) (4) where Kmrr = LWLrr. The corresponding set of dynamical equations is, in pu: 1eB dt Lsiqs =-Rliqs + CWssids + Wq --e Vqs + KmrrVqr (5) W dtdsds W5 Ws; qr -ct)Ls-Rlid + \u00b1 vds +Kmrrvdr (6) We/Bff dt WosTr WO I_dte_- 2 ds Ies+ I ledI - Kmrrvdr We/B dt Ws 2 WsTr OWS) ds 1 d eds R rI i'r eds O)el dtois=-2qs O) eq Tr+ KmrrVqr (7) (8) where R1 = Rs+R2 and R2 = Kmrr2Rr. The rotor current is: iqr = -(es /Xm )- Kmrriqs idr = (eqs /Xm )- Kmrrids (9) (10) The equivalent model is shown in Fig. 2 where variables with an upper-line are complex values with the real and imaginary components equal to the q- and d-axis components respectively, e.g. the stator current is Is = iqs+jids. The current source IC2 represents the bi-directional current flowing to or from the grid. The impedance ZT is the transformer between the grid-side converter (C2) and the grid. The impedance ZI = R,+jXs' represents the equivalent impedance between the machine internal voltage and terminal voltage. 2.2 Drive train For the drive train, two common representations that are used, are the one- and two-mass model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001020_analsci.8.553-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001020_analsci.8.553-Figure1-1.png",
        "caption": "Fig. 1 Symmetric measuring cell. 1, reference electrode; 2, cell body (Teflon); 3, reference electrolyte; 4, membrane holder (poly(methyl methacrylate)); 5, membrane; 6, ARGENTHAL\u00ae reference element; 7, reference electrolyte (3 M KC1); 8, bridge electrolyte (3 M KC1); 9, ceramic diaphragm; 10, cell support (aluminum); 11, sample/refer-",
        "texts": [
            " Keywords Ion-selective electrode, clinical application, calibration-free sample, membrane technology measurement, analytical error, biological Ion-selective solvent polymeric membrane electrodes are a fully established routine tool in clinical chemistry, their main limitation being the stability of the calibration values.l-4 The present project was undertaken in order to investigate the possibility of ion assays in undiluted human blood serum without any previous sensor calibration. For that reason a symmetric electrochemical cell as presented in Fig. 1, was constructed which allows the distinction and quantification of measuring errors of various kinds. Calibration-free measurements can be carried out if the following three necessary conditions hold: 1. The ion-selective electrode (ISE) has such a selectivity for the ion I to be sensed that there is no significant interference by other ions J. 2. The ISEs must exhibit an almost theoretical slope of the electrode response. To date, carrier and ionexchanger based ISEs for determining the activities of H30+, Li+, Nat, K+ Cat, Mgt, Cl-, HC03- and C032-1,5-10 in whole blood and blood serum most of them exhibiting sufficient selectivity (see l",
            " Sodium glass electrode In order to guarantee the use of electrically fresh sodium glass electrodes (Fa. Moeller, CH-8050 Zurich, Switzerland), their glass surfaces were treated with a 5% HF solution for 5 min before each serum assay. After the etching of the outer glass layer, a new layer was conditioned by immersing the electrodes in the reference solution for at least 17 h. Membrane preparation and conditioning The membranes were prepared according to ref. 15. For conditioning, the membranes were mounted into the measuring cell (Fig. 1), both half-cells being filled with the reference electrolyte solution described above. The conditioning time was 17 to 24 h. Afterwards, both half-cells were washed with the reference electrolyte solution before starting the EMF measurements. Cell assembly and EMF measurements All measurements were performed in the cell shown in Fig. 1. Each half-cell contained about 15 ml of reference electrolyte and sample solution, respectively, which were not stirred. For the remote control, data storage, and handling, a personal computer Apple lie was used with an IEEE 488 interface, an extended RAM memory (Apple Computer Inc., Cupertino, CA), a real-time clock (Thunderwate Inc., Oakland, CA), a matrix printer RX80 (Epson Corp., Nagano, Japan), and a Graphic Plotter Color Pro (Hewlett Packard, San Diego, CA), managed by a high-level language program (UCSD Pascal 1.3). The measurements were carried out at 21\u00b11\u00b0. First, the offset of the reference electrodes was obtained 15 min after immersing them into a glass beaker containing the reference solution. In a second step the asymmetry of the ion-selective membrane was measured after a conditioning period of almost 24 h. The membrane was implemented in the symmetrically constructed cell (Fig. 1) and the asymmetry was evaluated by a pair of reference electrodes with known offset filling the same reference electrolyte in both half cells. For testing and optimization of the membrane composition the slope of the EMF function was evaluated by measuring a series of reference solutions consisting of 140, 100, 120, 160, 180 and 140 mM Na+ solutions (or 4.25, 42.5, 2.75, 3.5, 5, 5.75 and 4.25 mM K+ solutions, respectively). Solutions were changed only in one half cell, the other was charged with 140 mM Na+ and 4",
            " Before each measuremnt, one portion containing 15 ml was defrozen and analyzed the same day. Measurements in samples with pathological activities of sodium and potassium were performed in serum supplied freshly from the University Hospital, Zurich, Switzerland, which was at most kept in the refrigerator for 24 h. Measurements by flame atomic emission spectroscopy They were carried out on a IL-443 with internal lithium standard (Instrumentation Laboratory SPA, Milan, Italy). Results and Discussion By utilizing the symmetric cell of Fig. 1, the origin of various measuring errors can be determined and gradually ruled out. This is especially important because of the very narrow physiological ion activity range' which impose a severe demand on the EMF stability of the ISE system. Ideally the maximum allowable analytical error amounts to ca. 0.5 mM (0. 10 mV) for sodium and to ca. 0.10 mM (1.0 mV) for potassium assays in human blood serum.'7,'8 A main source of errors lies in the EMF stability of the reference electrodes when used in protein-containing solutions, and can easily exceed 10 mV"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002157_027836498900800302-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002157_027836498900800302-Figure8-1.png",
        "caption": "Fig. 8. Generation of an interweld path.",
        "texts": [
            " This replaces the current segment with two new segments, which must both be checked. If no interference is detected, then no further attention is required by that segment. Positions can be added, moved, or removed until an acceptable interweld trajectory is obtained. In practice, new positions can be easily generated by moving the robot joint by joint away from an interpolated position which interferes. The resulting path should follow the fundamental path as closely as possible in order to minimize the distance in joint space. Figure 8 illustrates this idea. at UNIVERSITE DE MONTREAL on June 20, 2015ijr.sagepub.comDownloaded from 41 7. Implementation and Results The interference detection and inverse kinematics techniques and the automatic welding parameter selection module have been combined with the trajectory search algorithm in a FORTRAN program called AUTOWELD, implemented on a Silicon Graphics Iris graphics computer. Given a CAD specification of the workpiece geometry and seams, AUTOWELD interactively generates a welding program composed of welding trajectories connected by joint-interpolated interweld trajectories"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003469_j.talanta.2005.04.031-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003469_j.talanta.2005.04.031-Figure6-1.png",
        "caption": "Fig. 6. Effect of the different amount of Nafion on the response using amperometry.",
        "texts": [
            " And the reduction current did not increase after the addition of glucose. The result shows that the pretreatment is necessary for the preparation of the glucose biosensor. XRD showed that Fe in CFN is the form of -Fe so the pretreatment transfers -Fe to iron ion. It is a common knowledge that iron ion is prone to complex with enzyme and protein. According to the experimental results, it is suggested that GOD was immobilized on the CNFPE after the pretreatment by covalently complex action between GOD and iron ion. Fig. 6 compares the effect of the amount of Nafion on the response of the glucose biosensor. It is observed that the amperometric response is rather small when only small amount or even no Nafion was covered on GOD film, which seems to be attributed to the easy dissolution of GOD in solution. The response decreases with the increase of Nafion when more than 10 l of 0.5% Nafion is added. It is found that the optimum amount was10 l of 0.5% Nafion. Moreover, the GOD biosensor without Nafion suffers from the interference of ascorbic acid and uric acid"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003006_tmag.2004.828994-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003006_tmag.2004.828994-Figure1-1.png",
        "caption": "Fig. 1. Flying slider in near-contact regime.",
        "texts": [
            " Finally, we present experimental and theoretical studies of bouncing vibration of a slider in a near-contact regime due to the attractive force and frictional force [6]. Manuscript received October 24, 2003. This work was supported in part by the Grant-in-Aid, Japan Ministry of Science, Culture, and Sport and Storage Research Consortium. The author is with the Department of Mechanical and Control Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan (e-mail: ono@mech.titech.ac.jp). Digital Object Identifier 10.1109/TMAG.2004.828994 Fig. 1 shows a flying head slider over a spinning disk that has microwaviness and roughness on the surface. Motion of the slider at contact is caused by the contact force normal to disk surface and the friction force in the disk spinning direction, so that the slider motion can approximately be understood by two degree-of-freedom (2-DOF) plane motion, i.e., translational and pitch motions. Regardless of flying or contact state, air-bearing stiffness and contact stiffness at the trailing edge are much stronger than the front air-bearing stiffness"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003615_acc.1994.751914-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003615_acc.1994.751914-Figure1-1.png",
        "caption": "Fig. 1 : Three-Story Building Model; (a) Case 1; (b) Case 2; (c) Case 3",
        "texts": [
            " The main feature of VSS (or SMC) control is to design controllers to drive the response trajectory into the switching surface or sliding surface on which the response trajectory moves stably toward the equilibrium position, referred to as the sliding mode. Numerical examples are worked out to illustrate the applications of VSS control and its remarkable performance. The effectiveness of the AVS systems in reducing the response of seismicexcited buildings is also demonstrated. 2. FORMULATION Equation of Motion Consider an n-story shear-beam type building in which r active variable stiffness (AVS) systems are installed as shown in Fig. 1, The building is idealized by an n-degree-of-freedom linear system and is subjected to a one-dimensional earthquake ground acceleration xo(t). The vector equation of motion is given by M ~ ( t ) + C l r i ( t ) + K X ( t ) = H * Q g ( t ) + r l $ ( t ) (1) in which X(t)=[x,,x,, ..., x,]\u2019 is an n-vector with xi(t) being the drift of the ith story unit; M, C and K are (nxn) mass, damping and stiffness matrices, respectively; q=-[ml,m2, ..., m,]\u2018 is a mass vector with mi being the mass of the ith floor ; and the prime indicates the t r a n s y e of either a vector or a matrix",
            "( 11) where hi involves only the collocated velocity measurements. 3. SIMULATION RESULTS To demonstrate the applications of the sliding mode control methods (SMC) presented and to examine their performances, simulation results are obtained in this section. Two examples are considered: (1) a three-story scaled building; and (2) an eight-story building. Example 1: A Three-Story Scaled Model A three-story scaled building model studied in 121, in which every story unit is identically constructed, is considered as shown in Fig. 1. The mass, stiffness and damping coefficient of each story unit are mi=l metric ton, $=980 kN/m, and ci=1.407 kN.s/m, respectively, for i=l, 2 and 3. Active variable stiffness (AVS) systems are installed [see Fig. 11 and the El Centro earthquake ground acceleration (NS component) scaled to 30% of its original intensity is used as the input excitation. Within 30 seconds of the earthquake episode, the maximum interstory drifts, xi, and the maximum floor accelerations, X,, are shown in columns (2) and (3) of Table 1 for the building without AVS systems"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003904_13506501jet91-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003904_13506501jet91-Figure1-1.png",
        "caption": "Fig. 1 Diagram of lip seal in position",
        "texts": [
            " The lubricant viscosity is modelled by the Gecim law, and the influence on features such as the average and minimal thickness, reverse pumping, and power loss is analysed. We consider the following hypothesis: the lip seal is perfectly elastic, the rotating shaft perfectly smooth, and the seal is perfectly centered (no whipping). Taking into account the geometric shape, the lip angle, and the spring location, the radial flexure of the lip produces an asymmetric distribution of the contact pressure ps, leading to a strong rise on the lubricant side and to a smooth decrease on the air side (Fig. 1). A new and original approach was presented in a previous article [14]. The compliant part of the seal is not assumed to have a totally elastic axisymmetric Corresponding author: Department of Structures and Interfaces, Laboratoire de Me\u0301canique des Solides, IUT IV\u2013Angoule\u0302me, JET91 # IMechE 2006 Proc. IMechE Vol. 220 Part J: J. Engineering Tribology at The University of Manchester Library on May 1, 2015pij.sagepub.comDownloaded from behaviour; it is divided into two parts with different mechanical behaviours"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002884_b:jmsc.0000021440.04191.02-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002884_b:jmsc.0000021440.04191.02-Figure2-1.png",
        "caption": "Figure 2 CVD apparatus: (a) Source gas (Ti(O-iso C3H7)4, (b) gas outlet, (c) CA thermocouple, (d) furnace, (e) brick, (f) heater, (g) rotation disk (25 rpm), (h) carbon microcoils and (i) reaction tube (quartz, 40 mm i.d.).",
        "texts": [
            " In the sol-gel process, ethyl alcohol solution (3 \u00d7 10\u22126 m3) containing TIPO and CMC (10 mg) was mixed with ethyl alcohol solution (6 \u00d7 10\u22126 m3) containing a 2 M Figure 1 Representative carbon microcoils used as a template. HCl (2 \u00d7 10\u22128 m3), and the mixture was stirred by using supersonic bath, aged (2 h), concentrated under vacuum, dried, and heat-treated or calcinated. The addition amount of TIPO was 2\u20138 \u00d7 10\u22127 m3, and the concentration ratio was 25\u2013100% (full drying). In the CVD process, the CMC was coated with TiO2 layers using a gas mixture of TIPO + H2O + N2 at 300\u25e6C for 2 h using a rotating CVD reactor as shown in Fig. 2. The rotating speed was fixed at 25 rpm. The TiO2-coated CMC was then heat-treated in N2 atmosphere or calcined in air atmosphere at 500\u2013800\u25e6C for 2 h. The amount of TiO2 deposited on the surface of CMC was estimated from the ignition loss obtained at 500\u25e6C in air using a TG apparatus. UV light (365 nm, 4 W) was irradiated onto 20 g/m3 Methyl Orange (refer to as \u201cMO\u201d hereafter) aqueous solution containing 0.03 g sample (TiO2/CMC, etc.), and the reactor volume was 1.0\u00d710\u22124 m3. The degree of decomposition of the MO molecules was measured by an UV spectrometer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001455_50006-1-Figure5.42-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001455_50006-1-Figure5.42-1.png",
        "caption": "FIGURE 5.42 Motor geometry for 3D analysis.",
        "texts": [
            "275) Field values are computed with /~ = 1.0 ~o, 1.5 #o, and 2.0 #o, and with the vertical position in the gap set to y = 2 mm. Ten values are computed for each value of #. Specifically, field values are computed at q5 = O, 5, 10 . . . . . 45 ~ (i.e., from the center of one pole to that of its neighbor). These data are shown in Fig. 5.41. Notice that the field decreases with increasing/~. 77 432 CHAPTER 5 Electromechanical Devices EXAMPLE 5.13.2 Develop a three-dimensional field solution for the gap region of an axial-field motor (Fig. 5.42). Assume that the magnet has a second quadrant demagnetization curve B = po(H + Ms~), (5.276) where the +_ term takes into account the alternating polarity of adjacent poles [22,231. SOLUTION 5.13.2 For the three-dimensional model we approximate the magnetic structure of the motor in terms of the magnetic circuit shown in Fig. 5.43. Specifically, we assume that the upper and lower flux plates have infinite permeability (p = oo), and are of infinite extent in both the vertical and horizontal directions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002554_2005-01-3472-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002554_2005-01-3472-Figure1-1.png",
        "caption": "Figure 1. Vehicle model (bicycle model)",
        "texts": [
            " Here, the drift area is defined as the area over which the rear wheel exceeds the maximum cornering force. This is precisely the area where counter steering is needed. In this study, drift cornering is achieved when the rear wheel exceeds the maximum cornering force, and controlling counter steering during drift. Here, the drift angle shows the body slip angle at the time of the drift cornering. Analysis of the movement of the vehicle was carried out using a model with two degrees of freedom (Figure 1). Tires were tested in sets of 3 or more to determine \u03d5 (Figure 2) using the following function: ( ) ( )38711 \u2212\u2212= \u03d5\u03d5f ( ) 3>\u03d5 When the maximum value was exceeded, it was assumed to be decreasing characteristic function. Friction, \u00b5 , of the rear wheel was set to a value lower than that of the front wheel for the rear wheel so as to easily achieve drift. Motion o equations mV +(\u03b2& f FlrI =& Moreover wheels a analysis, described ff = \u03b4\u03b2 r \u2212= \u03b2\u03b2 The verti which is accelerat inf WW =\u2212 outfW =\u2212 inr WW =\u2212 outrW =\u2212 The corn function o for the fro tire is bas (fFt \u03d5= where: ( ) \u03d5\u03d5 =f K\u03d5 = f the vehicle is described by the following : rf FFr +=) ( )1 rrf Fl\u2212 ( )2 , when the tire slip angles of the right and left re assumed to be equal for purposes of the front and rear wheel slip angles are as follows: The steering mo angle in cornerin of front wheel st vehicle body slip start of cornering Vrl f\u2212\u2212 \u03b2 ( )3 Vrlr+ ( )4 ( )tstepkf 0=\u03b4 cal normal load of the right and left wheels, described by the load movement and lateral ion as shown below"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003952_iecon.2005.1569191-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003952_iecon.2005.1569191-Figure5-1.png",
        "caption": "Fig. 5. Single-DOF model for flexible joint system",
        "texts": [
            " Therefore, this paper newly adopts the motion control law (4) and the structure in Fig. 4 for industrial robot. \u03c9\u0307cmd M = \u03c9\u0307Mint +Kp(\u03b8Mint \u2212\u03b8M)+Kv(\u03c9Mint \u2212\u03c9M) (2) \u03c9cmd M = Kpp(\u03b8Mint \u2212\u03b8M)\u2212Kpd\u03c9M (3) \u03c9cmd M = Kpp(\u03b8Mint \u2212\u03b8M)+Fpd(\u03c9Mint \u2212\u03c9M) \u2212 (Kpd\u2212Fpd)\u03c9M (4) The harmonic drive, which is a nonrigid drive system, is normally used as the speed reducer in industrial robot. Accordingly, the joint flexibility should be taken into account in the modeling of the robot system [12]. In this paper, the twoinertia system is adopted to model each joint of the robot as shown in Fig. 5. Here, \u03b8M is the angular position of actuating motor, \u03b8L is the angular position of robot link or the gear output, \u03b8S is the torsional angular position. The nominal model of this structure is easily obtained from resonant and antiresonant characteristic of the robot arm [4]. The external torque, which is considered as the disturbance torque \u03c4L in each joint, is computed by the disturbance observer as \u03c4\u0302L = \u03c4inert + \u03c4col + \u03c4grav + \u03c4 f ric + \u03c4react (5) where \u03c4inert is the torque from inertia variation and the coupling torque term, \u03c4col is the centrifugal and Coriolis term, \u03c4grav is gravity term, and \u03c4 f ric is friction term"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000033_jsvi.1999.2261-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000033_jsvi.1999.2261-Figure1-1.png",
        "caption": "Figure 1. Material, element and structure co-ordinates of \"ber-composite laminated cylindrical shell.",
        "texts": [
            " The doubly curved shell element has four edges (three nodes per edge) and can be used to model fairly complicated curved surface structures very accurately. The reduced integration rule together with hourglass sti!ness control is employed to formulate the element sti!ness matrix [20]. During the analysis, the constitutive matrices of composite materials at element integration points must be calculated before the sti!ness matrices are assembled from element level to global level. For \"ber-composite laminated materials, each lamina can be considered as an orthotropic layer in a plane stress condition (Figure 1). The stress}strain relations for a lamina in the material co-ordinates (1,2,3) at an element integration point can be written as Mp@N\"[Q@ 1 ]Me@N, Mq@N \" [Q@ 2 ] Mc@N, (1) [Q@ 1 ]\" E 11 1!l 12 l 21 l 12 E 22 1!l 12 l 21 0 l 21 E 11 1!l 12 l 21 E 22 1!l 12 l 21 0 0 0 G 12 , [Q@ 2 ]\"C a 1 G 13 0 0 a 2 G 23 D, (2) where Mp@N\"Mp 1 , p 2 , q 12 NT, Mq@N\"Mq 13 , q 23 NT, Me@N\"Me 1 , e 2 , c 12 NT, Mc@N\"Mc 13 , c 23 NT. The a 1 and a 2 are shear correction factors, which are calculated in ABAQUS by assuming that the transverse shear energy through the thickness of laminate is equal to that in unidirectional bending [20, 21]",
            " The constitutive equations for the lamina in the element co-ordinates (x, y, z) become MpN\"[Q 1 ]MeN, [Q 1 ]\"[\u00b9 1 ]T[Q@ 1 ][\u00b9 1 ], (3) MqN\"[Q 2 ]McN, [Q 2 ]\"[\u00b9 2 ]T[Q@ 2 ][\u00b9 2 ], (4) [\u00b9 1 ]\" cos2h sin2h sin h cos h sin2h cos2h !sin h cos h !2sin h cos h 2sin h cos h cos2 h!sin2 h [\u00b9 2 ]\"C cos h sin h !sin h cos hD , (5) where MpN\"Mp x , p y , q xy NT, MqN\"Mq xz , q yz NT, MeN\"Me x , e y , c xy NT, McN\"Mc xz , c yz NT, and h is measured counterclockwise about the z-axis from the element local x-axis to the material 1-axis. The element co-ordinate system (x, y, z) is a curvilinear local system (Figure 1) that is di!erent from the structural global co-ordinate (X,>,Z). While the element x-axis is parallel to the longitudinal direction of the cylindrical shell, the element y- and z-axis are in the circumferential and the radial directions of the cylindrical shell. Let Me o N\"Me xo , e yo , c xyo NT be the in-plane strains at the mid- surface of the laminate section MiN\"Mi x , i y , i xy NT the curvatures, and h the total thickness of the section. If there are n layers in the layup, the stress resultants, MNN\"MN x , N y , N xy NT, MMN\"MM x , M y , M xy NT and M<N\"M< x , < y NT, can be de\"ned as G MNN MMN M<N H\" P h@2 ~h@2 G MpN zMpN MqNH dz \" n + j/1 (z jt "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001026_tt.3020010103-Figure12-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001026_tt.3020010103-Figure12-1.png",
        "caption": "Figure 12(ii) Two-dimensional pressure distribution in the direction of rolling",
        "texts": [
            " The absence of almost any free bulk oil (see Figure 9) upstream of the position of the side constrictions indicates no inhibiting factors in the way of formation of secondary pressure peaks in the side constriction as is observed in the isobar plot of Figure 11. Therefore, the locus of the pressure spikes extends from the rear of the centre of the Hertzian contact to the side constrictions, following the characteristic horse-shoe constriction in Figure 9. Similar conditions prevail in the case of the isobar plot of Figure 12 (i). This isobar plot corresponds to an acutely starved 50 Johns-Rahnejat and Gohar P* x 10-3 5- - - - Hertzian ~ Experimental AA at mid-contact BB 0.1 mm from mi CC 0.2 mrn from m I I I I I - A -3 -2 -1 0 1 2 3 x Figure 12(iii) Two-dimensional pressure distributions transverse to the direction of rolling P* x 10-3 - Hertzian ~ Experimental _ - 5- -2 -1 0 1 2 Y I I Tribotest journal 1-1, September 2994. (1) 50 1354-4063 $6.00 + $2.50 Measuring Contact Pressure Distributions under Elastohydrodynamic Point Contacts 51 condition (m = 2.157, m* = 5.466), with the isobar plot conforming more closely to the Hertzian contact than that of Figure 11. The region of maximum pressures has shifted to the side constriction. However, it should be noted that no secondary pressure peaks are observed as the recorded pressure distribution along various sections in the direction of entraining motion exhibit the flat lowspeed type characteristics. The pressure profiles at various sections in the direction of entraining motion, 57, and perpendicular to it (i.e. 7) are also shown in Figure 12 (ii) and (iii). The isobar plot of Figure 13 (i) is at the same speed as the previous isobar, but at a higher load. With this higher load, the inlet meniscus has moved closer to the leading edge of the Hertzian contact and caved in upstream of the centre of the contact. The isobar plot has also shrunk in the lateral direction, indicating a more restricted side leakage under higher loads. The isobar plot has tended closer to the Hertzian contact region with increasing load, and the region of secondary pressure peaks has moved to the rear constriction, extending to the sides of the Hertzian contact (see also Figure 13 (ii), overleaf) illustrating the pressure profiles at various cross-sections in the direction of rolling"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003258_detc2005-84712-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003258_detc2005-84712-Figure7-1.png",
        "caption": "Figure 7. Planar 8R-mechanism in its singular configuration q0.",
        "texts": [
            " These are the tangent spaces to respectively two- and one-dimensional manifolds (modi). I.e. the mechanism can enter modi with different dimensions. Figure 5 shows a configura- 10 wnloaded From: https://proceedings.asmedigitalcollection.asme.org on 01/04/2019 Terms of Us tion in a mode with \u03b4loc= 1 and figure 6 shows one in a mode with \u03b4loc = 2. Due to \u03b4diff (q0) = 3 and \u03b4loc (q0) = dimCq0 V ( IK ) \u2261 max(dimC\u2032 q0 V ( IK ) , C\u2032\u2032 q0 V ( IK ) ) = 2 the point q0 is singular with deg q0 = 1. The mechanism is kinematotropic. The planar 8-bar mechanism in figure 7 is a combination of a planar 4- and 5-bar mechanism. Shown is the reference configuration q0 = 0. I. Kinematic tangent cone to V : The kinematic tangent space is identical to the kinematic tangent cone, i.e. Cq0 V ( IK ) = Tq0 V ( IK ) , where Tq0 V ( IK ) = {(\u2212r, 0, r, s + 2t,\u22122s\u2212 3t, s, t, 0) ; r, s, t \u2208 R}. II. I-Tangent cone to V : It holds Cq0 V ( IK ) \u223d Cq0 V ( I ) . III. Tangent cone to V : The tangent cone to V differs from the kinematic tangent cone. It is Cq0 V = C\u2032 q0 V \u222a C\u2032\u2032 q0 V with C\u2032 q0 V = {(\u2212r, 0, r, 0, 0, 0, 0, 0) ; r \u2208 R} C\u2032\u2032 q0 V = {(0, 0, 0, s + 2t,\u22122s\u2212 3t, s, t, 0) ; s, t \u2208 R}"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002058_iros.1997.649050-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002058_iros.1997.649050-Figure3-1.png",
        "caption": "Figure 3: Angular velocities of rodlike object",
        "texts": [
            " \u2018The curvature and the torsional ratio can be described by use of Eulerian angles 4, 8, $, arid Bo as follows: Next, let us describe the velocity and the angular velocity of the object at time t , in order to express motion of the object. Let t~ be the velocity of the object, at the point P(s, t ) , namely, Furthermore, let w1 (s, t> and w ~ ( s , t ) be the angular velocity for deformation around the axis which intersects with the central axis perpendicularly, and that around the central axis at point P(s, t ) , respectively as shown in Figure 3. It is found that these two angular 198 velocities can be described by use of Eulerian angles #J, 8, 4, $0, Bo, and $0 as follows: From the above discussion, the geometric shape of a moving and deforming rodlike object can be represented by both three variables, 4 , 8, and $, which depend upon distance s and time i, and three variables, 40, 8 0 , and $0, which depend upon time t alone. 2.2 Potential Energy, Kinetic Energy, In this paper, we will adopt the Hamilton\u2019s principle that the time integral of the difference between the kinetic energy of the object and its potential energy reaches the minimum when the object moves dynamically"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000718_s0020-7403(99)00013-2-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000718_s0020-7403(99)00013-2-Figure4-1.png",
        "caption": "Fig. 4. (a) Relationship of coordinate system S a , S 1 and S f ; (b) Relationship of coordinate system S 2 , S a , S b and S c .",
        "texts": [
            " Coordinate systems S 1 (x 1 , y 1 , z 1 ) and S f (x f , y f , z f ) are \"xed on the spur pinion and the frame of the face-gear drive as shown in both Figs. 3 and 4(a) respectively. The coordinate system S 1 can be transformed to the coordinate system S f by rotating the coordinate about axis z 1 or z f through an angle u 1 . In order to simulate the misalignment of the face-gear, auxiliary coordinate systems S a (x a , y a , z a ), S b (x b , y b , z b ) and S c (x c , y c , z c ) are set up in Fig. 4(b). The location of S a with respect to S f is shown in Fig. 4(a). Parameters *E,D and D cot c determine the location of the origin O a with respect to O f , where *E denotes the crossed displacement that is the shortest distance between the spur pinion and the face-gear axes when the axes are crossed but not intersected. In the alignment meshing, *E\"0 that is the spur pinion and the face-gear axes intersect. In the following analysis, *E is used to simulate the misalignment of the crossed displacement between axes of spur pinion and face-gear. The crossed angle, c f \"180"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002700_j.adhoc.2005.01.003-Figure13-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002700_j.adhoc.2005.01.003-Figure13-1.png",
        "caption": "Fig. 13. Data link header initiated for each of the edge neighbors.",
        "texts": [
            " Upon initiating a broadcast/flooding, the initiator si defines an arbitrary N direction (perhaps randomly) and defines the polygon neighbors accordingly. In these algorithms we assume (only for simplifying the presentation) the initiator defines the N direction as its arbitrary definition of the 0 angle. Note that when executed by the initiator, the procedure electRepresentative is called with h0,0,0i as a data-link header by the initiator. Note that the initiator defines the N direction as the arbitrary 0 angle and assumed that it is located in the center of the polygon it represents. Fig. 13 shows the initiator si located in the center of the figure, the edge polygon neighbors N, E, S and W and the data-link headers x, y, a attached to each message sent to the representatives sN, sE, sS and sW respectively. (The values x, y, a are different for each representative according to its location and the polygon it represents.) The sensor marked with sE, for example, is the sensor elected by si to be the representative of the edge neighbor E. The value a denotes the clockwise angle between the directed segment (si, sE) and the N vector (dotted line that crosses the center of the E polygon) denoting the direction of the N neighbor of polygon E"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003505_robot.2006.1642018-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003505_robot.2006.1642018-Figure2-1.png",
        "caption": "Fig. 2. The coordinates of the overall fingers-object system. The coordinates Oxyz is fixed at the frame.",
        "texts": [
            " Secondly a control signal for realizing \u201cblind grasping\u201d 0-7803-9505-0/06/$20.00 \u00a92006 IEEE 2124 is proposed, which does neither use the knowledge of object kinematics nor external sensing. Stability of closed-loop dynamics of the fingers-object system in a dynamic sense is discussed and the validity of such a control method is demonstrated on the basis of numerical simulations of the derived model. II. OPPOSABLE FORCES AND CONTROL OF SPINNING MOTION Human can pinch a rigid object by using only a pair of the thumb and index (or middle) finger (see Fig.2), if the object is not so heavy and thick. However, when the distance from the straight line (X-axis in Fig.1) connecting two contact points between finger-ends and object surfaces to the vertical axis through the object mass center in the direction of gravity becomes large, there arises a spinning motion of the object around X-axis. In order to stop this spinning, the third digit is needed as shown in Fig.1. Or it is possible to consider the problem of modelling of pinching in the situation that, after this spinning motion stops, the center of mass of the object comes sufficiently close to the beneath of the X-axis and there will no more arise such spinning due to dry friction between finger-ends and object surfaces in rotational motion around the X-axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002355_s0301-679x(03)00090-2-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002355_s0301-679x(03)00090-2-Figure1-1.png",
        "caption": "Fig. 1. Schematic representation of thrust bearing system.",
        "texts": [
            " The effect of elasticity was also observed as affected the additional load-bearing characteristics of the thrust bearing. The proposed neural network was employed as a predictor of the system. The organisation of the paper can be written as follows; Section 2 gives theoretical model of the system, which is analysed by the neural network methods. Section 3 presents the neutral network that is a proposed recurrent network. Simulation results are given in Section 4. The paper is concluded with Section 5. Fig. 1 shows the configuration of the thrust bearing. As can be seen from the Fig. 1, there are cantilevered portions (between QL) in the rear surface of the thrust bearing. QL is the length of zone A or C and Q is defined as cantilever factor. The flat surface of the bearing is deformed elastically cause of the under-cutting during the system runs. The configuration of the narrowing and enlarging oil wedges is occurred due to an approximately sinusoidal form of the bearing [5,6]. When there is no deformation (d = 0), according to the theory of hydrodynamic thrust bearing, pressure area will develop and naturally a metal\u2013metal contact would become inevitable [7,8]",
            " After the pressure area is obtained, by integrating this area, which is the basis for calculating the total lubrication load in the thrust bearing, we can obtain the load- bearing capacity for unit [6]. The load can be stated from W\u0304 = Wh2 0 /huL2b and thus the dimensionless total load is given as follow, W\u0304T 2 0 p\u0304 dx (8) In the theoretical analysis, along with undercutting the lower part of thrust bearing and the variation of the total lubrication load W\u0304T, the elastic load due to elastic deflection must also be taken into account. In Fig. 1, the work of the pressure force can be written as follows, in order to converge the oil film from h to h0 Wp 2 0 b(h h0)pdx (9) If the variation in film thickness given Eq. (1) for zone A is taken into account and the interior of the integral is made non-dimensional, W\u0304p Wd 2 0 p\u0304dx\u0304 2 1 cos px\u0304 Q cWd (10) is obtained. Here W is the load, d is the amount of sagging and c is the integral. Elastic deformation of the part whose lower area has been cut and the displacement energy is taken into account",
            " When non-linear neurons are adopted, this gives the network the ability to perform non-linear dynamics mapping and thus model non-linear dynamic systems. The existence in the recurrent network of a hidden layer with both linear and non-linear neurons facilitates the modelling of practical non-linear systems comprising linear and nonlinear parts. Some results of two approaches seemed important in the thrust bearing which is the basis for the theoretical model (the geometry of the system was described in Fig. 1). In the various under-cutting factors (Q) of the total lubrication load (W\u0304T), the variation in sagging through elastic deformation\u2019s desired and neural network results are shown in Fig. 3 for the full hydrodynamic state (p\u0304 = 0). It can be seen from the figure the neural network predictor follows desired results. Accordingly, in the various values for Q, when sagging is zero (d\u0304 = 0), the theory of hydrodynamic thrust bearing indicates that the system cannot bear loads when sagging is zero. When deformation begins at the extremities of the thrust bearing d/h will not be zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003903_iembs.2006.259950-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003903_iembs.2006.259950-Figure2-1.png",
        "caption": "Fig. 2. Front and top diagrams of a rotary FlexCVA. The worm motors act as brakes for the front and rear sprockets. When a cam deflects one belt, the deflection force is coupled to the output shaft. After the deflection, the worm motor pulls the belt flat again while the other belt drives the output shaft.",
        "texts": [
            " In other words, an infinite load force is required to prevent the driving force from deflecting the belt to some degree. As the deflection angle increases, the same driving force can be opposed by a smaller and smaller load force. A small change in the deflection amount makes a large difference in the output force for a given deflection force. This principle is used in the FlexCVA/T to vary the mechanical advantage and provide a continuously variable transmission without gears. The movement of the load due to each flexor deflection of distance h equals 2(Lf \u2013 L0). Figure 2 shows a diagram of a rotary FlexCVA. Worm gears are used as brakes to hold a sprocket stationary during the time its belt is being deflected by the cam. This technique takes advantage of the inability to backdrive a worm gear with a small lead angle. The motor driving the worm can be quite small because it rotates only when the load is on the other worm gear. The worm motor pulls the slack from the undriven belt in preparation for the next deflection. The cams are driven 180 degrees out of phase, and each cam has an increasing radius for 270 degrees of its rotation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002547_s10010-005-0011-3-Figure19-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002547_s10010-005-0011-3-Figure19-1.png",
        "caption": "Fig. 19a,b. Gear coupling: a aligned; b misaligned with left-half moments",
        "texts": [
            " \u2212 increment, variation \u03bb = \u03c3 + j\u03c9 rad/s eigen-value \u00b5,\u00b50 1 coefficients of friction \u03bd, \u03bd\u2217 rad/s angular velocities (\u03c1, \u03b3), (r, \u03a8) \u2212 polar coordinates \u03d5x, \u03d5y rad shaft inclinations (rotations about x- and y-axis) \u03a6 rad angle of rotation \u2126, \u03c9 rad/s angular velocity, frequency Fe, Fu force vectors u, v displacement and state vectors u\u0302, u\u0306 amplitude vectors M, D, G, K mass, damping, gyroscopic and stiffness 2\u00d72 \u2013 matrices f(\u03bd)C1, f(\u03bd)C2 2\u00d72 \u2013 matrices of nonlinear gear coupling effects Subscripts dk disk fx, fy with respect to rotor-fixed system \u03c6x, \u03c6y with respect to space-fixed system F friction gc gear coupling m, mx, my misalignments N emphasizes the nominal value of a parameter R reference quantity u unbalance x, y directions of x, y Flexible couplings transmit torque from driving to driven shafts without torsional slip but accommodate unavoidable misalignments due to installation errors, deflections under load, thermal expansions etc. (see [13, 23]). Gear couplings belong to the simplest and most commonly used flexible couplings. They consist of an externally toothed hub, see Fig. 19a, and a mating sleeve with internal teeth which permit relative axial sliding. Crowning (rounding) of the hub teeth and a clearance (backlash) between the meshing gears prevent jamming and allow small angular displacements (\u2018angular misalignments\u2019) between the axes of sleeve and hub (see the angle \u03b1 in Fig. 19b; |\u03b1| < 0.004 rad \u2248 0.25 \u25e6C at high speeds). The incorporation of the gear coupling into a rotor-bearing system has unwelcome side effects: The touching teeth-flanks need some slipping for lubrication, thus a minimum misalignment |\u03b1| > 0 is necessary. (A perfectly aligned shaft train is not only unattainable but also undesirable.) The Coulomb type friction forces between the sliding tooth flanks lead to energy fluxes from the driving motor to the shaft\u2019s lateral oscillations, instability and self-excited oscillations are possible",
            " The potential U contains the elastic bearing suspensions and the weight: U = 1/2\u00d7 ( kx(x \u2212ax) 2 + ky(y \u2212ay) 2 ) +mdkg ydk +mgcg ygc , (49) g \u2013 gravity acceleration. Rayleigh\u2019s dissipation function D represents the effects of the bearing dampings: D = 1/2\u00d7 (dx x\u03072 +dy y\u03072) . (50) Fig. 18a\u2013d. Coordinates: a, b stationary; c, d rotating The friction moments M\u03d5x , M\u03d5y in the gear coupling (see below) enter Lagrange\u2019s equations via their virtual work, it is negative since the friction dissipates energy: \u03b4W = \u2212(M\u03d5x\u03b4\u03d5mx + M\u03d5y\u03b4\u03d5m y) . (51) The moments acting at the gear coupling have to be considered in detail: Fig. 19 shows the non-rotating gear coupling loaded by the (given) torque MT ; Fig. 19a shows the straight coupling, Fig. 19b presents the coupling tilted by an angle \u03b1 (|\u03b1| 1) about the point H (the intersection of the shafts\u2019 axes) which is assumed to act like a hinge. The moments MT , Meq , Mf , the twin arrows shown in Fig. 19b, apply upon the left-half of the coupling during the tilting. (We neglect moments necessary to tilt the friction-free coupling due to the special shape of the gear teeth.) The moment Meq, Meq = MT tan(\u03b1/2) \u2248 MT \u03b1/2 , (52) keeps equilibrium at the tilted but frictionless coupling (its vector lies in the plane of the angle \u03b1). Because of |\u03b1| 1 the moment Meq is neglected. (Further small \u201cequilibrium moments\u201d, comparable to Meq, act also upon the tilted rotor at the disk and at the bearing C. They are neglected too"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001243_s0141-6359(01)00097-6-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001243_s0141-6359(01)00097-6-Figure2-1.png",
        "caption": "Fig. 2. Sensor locations",
        "texts": [
            " The cooling water is fed from a large tank installed adjacent to the test machine, which means that the water supply temperature is the same as the circumferential temperature. The air is provided through 12 feed holes with 0.5 mm diameter for each journal bearing. The bearing axial length and radial clearance are 60 mm and 20 m, and the air supply pressure is 0.7 MPa. Measurements were conducted on the front journal bearing. Ninety-four 1 mm diameter sheath type thermocouples (type T) were mounted in the housing, bush and air film. The thermocouples were located in nine planes (A-A through I-I) at the radial and axial locations shown in Fig. 2. Fifty-four thermocouples to measure housing and bush temperatures were fixed in drilled holes of 1.5 mm diameter, and the nominal radial distances from the bush inner surface are indicated in Fig. 2. Thirty-six thermocouples for air film temperature measurements were mounted in plugs, which were assembled in the bush, the inner surface of which was then lapped. In addition to the locations shown in Fig. 2, ten adhesive type thermocouples were used for the housing outer surface temperature measurements, one sheath thermocouple for inlet air, one for outlet air, one for the circumference and one for motor cooling water. All thermocouples were calibrated in the range between 20 and 50\u00b0 Celsius by using a platinum resistance thermometer with an accuracy of 0.02\u00b0 Celsius as a calibration standard. In the C-C plane in Fig. 2, three semiconductor pressure transducers are embedded at 30, 150 and 210\u00b0, which is the region where the attitude angle was expected to be. The radial displacement of the spindle was measured with four capacitance type transducers located at the near end of the spindle. The transducers were configured as opposing pairs, one vertical pair and one horizontal pair. The signals from these pairs were combined to yield both spindle position and the expansion due to the centrifugal force and temperature increase"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000813_bf00571701-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000813_bf00571701-Figure1-1.png",
        "caption": "Figure 1. Description of the four-legged robot.",
        "texts": [
            " Moreover, the multiplication of the two terms of (5) by T T allows to eliminate the constraint actions ( ( T A ) T A = 0), we thus obtain: r m = I(OI)O I + C ( O I , 0 I ) 0 1 -- T f -- r g, (19) with I c(oI, O x) d x d matrix of generalised inertia I = T T M T (20) d x d matrix of centrifugal and coriolis terms C ( O I, 0 I ) = T T M T + T T R M T (21) 7 TM d-dim vector of generalised driving action \"r m = T T T m (22) T f d-dim vector of generalised friction action T f = T T T f (23) 7-g d-dim vector of generalised action due to the gravity T g : T T T g (24) The mechanism shown in Figure 1 comprises a rectangular platform connected to four legs, each leg being composed of two links and one foot (called a hoof by analogy with the horse foot). The joints used are: a spherical joint between a hoof and the lower link in which the y axis is motorised, a motorised revolute joint (g axis) between the two links and two motorised revolute joints (y and z axes) between the platform and the upper link. 4.2. ROBOT LOCOMOTION The adopted strategy of locomotion of the four-legged robot is the walking"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003549_rissp.2003.1285572-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003549_rissp.2003.1285572-Figure4-1.png",
        "caption": "Fig. 4 Friction Constraint for Internal Force",
        "texts": [
            "(4) with respect to f , we obtain f = G+(ta - mg) + N k , (6 ) where G+ and N denote the pseud*inverse of G and the matrix composing the null space of G , respectively. we denote that f = if'; fzl fZ]' E R6 for 2D model. The second term of the right hand side of the eq.(6) does not affect the total forcelmoment acting on the body, and corresponds to the internal force studied in the research field of robotic hand[l3]. The matrix N can be defined as[13] eo1 e02 0 0 -eo2 -e12 N = [ --eo1 0 e12 ] , (7) where ei j (i, j = 1,2) denotes the unit vector directing from one contact point to an another one, and its defi- nition is shown in Fig.4. We note that the whole body manipulation by a humanoid robot can be realized by applying f H effectively. Diffwent from the grasp by a robot hand, the second teriwof eq.(6) affects the mtion an object. Now, we redefine the internal force for whole body manipulation as follows: Definition 1 (Whole Body Internal Force) Assume that a humanoid is standing on a floor and that the hands are contacting with an object. We define the internal force acting among the contact points and realizing the manipulation of an object as the \"Whole Body Internal Force\""
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003771_j.compstruc.2006.08.026-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003771_j.compstruc.2006.08.026-Figure1-1.png",
        "caption": "Fig. 1. The schematic plot of the solid and fluid models. The bumps are magnified for better visualization.",
        "texts": [
            " The model is a finite element simulation of an elastohydrodynamic lubrication problem, in which both fluid and solid models have simple cylindrical geometries with an uneven solid\u2013fluid interface. The flat rotating surface at the bottom is simulated by velocity boundary conditions at the lower fluid surface consistent with a rigid plate in rotation about the symmetry axis. The interfacial surface of the solid consists of sinusoidal circumferential bumps, which when undeformed are symmetrical about the axis of rotation. We adopt cylindrical coordinates (r,h,z), where the z coordinate is coincident with the axis of rotation, r is the radial coordinate in [0,R] and h is the polar angle. Fig. 1 illustrates graphically the undeformed solid and fluid models including their dimensions. The undeformed solid interface is formed of five sinusoidal circumferential bumps. In the undeformed state, the minimum fluid thickness hmin is constant for all r, and the maximum fluid thickness circumferentially grows linearly from hmin at r = 0 to a global maximum hmax at r = R. Thus, the undeformed solid\u2013fluid interface in the model is given by h\u00f0r; h\u00de \u00bc hmin \u00fe r\u00f0hmax hmin\u00de 2R \u00f01\u00fe cos nh\u00de \u00f01\u00de where \u2022 h is the fluid thickness at (r,h), \u2022 hmin and hmax are the minimum and maximum fluid thickness over the entire disc, \u2022 n is the number of asperities of the solid interface (n = 5 in our model), 1 ADINA is a comprehensive finite element software for extensive analyses of solid, fluid, and fluid flow with structural interactions: www"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002942_6.2004-5008-Figure9-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002942_6.2004-5008-Figure9-1.png",
        "caption": "Figure 9: Bench test configurations and modeling.",
        "texts": [
            " In order to generate control design models and perform detail dynamical simulations which are physically relevant, we first characterize by parameterizing the dynamics of the subsystems and total system from first princi- ples and then use a series of bench tests to determine these parameters from measured data. Specific necessary tasks to this end includes design and fabrication of specific test configurations, instrumentation, calibration, followed by model development and validation through estimation of parameters including noise levels and its associated filters. Figure 9 shows the bench test configuration for an individual ducted fan and vane system. The focus in this bench test involves characterizing (i) Fan motor and vane dynamics, and (ii) Fan and vane aerodynamics. The former basically involves the development of models to characterize fan speed and vane angle from their commands, while the latter modeling task can be anywhere from almost trivial to near impossible if the unsteady aero effects are to be included with any level of confidence. Together they determine the actual net forces and torques generated by control commands for fan speeds and vane deflection angles",
            " Figure 12 illustrates the measured unsteady effects in the vertical force component with time varying fan speeds with fixed vane angle. The 1-\u03c3 variation of 0.1 pound thrust in a single fan is not insignificant for this subscale platform, especially considering that we have not included additional factors such as vane effects and implicit bandwidth limitations in the fan motor. The above sample data were obtained experimentally, by testing the components in a ducted fan configuration, displayed in Figure 9. Static thrust vector force components were obtained from these tests, and are provided in [8]. Unsteady flow forces which are difficult to characterize are not quantified, and do not appear in the simulation model described in the next Section. In this section we present simulation results based on full nonlinear models that are constructed from first principles, bench test data refined model parameters, sampled and quantized measurements, and saturation limits on actuators. In particular, the dynamical models for the Ducted fan/vane, whose development are based on bench tests, includes asymmetrical effects which are difficult to visualize due to their 3-dimensional characteristics"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002672_tmag.1983.1062820-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002672_tmag.1983.1062820-Figure6-1.png",
        "caption": "Figure 6 : Vector potential distribution using AGE2 corresponding to a",
        "texts": [],
        "surrounding_texts": [
            "a and c' = b if i E {1,2, . . e , s )\nb and c' = a if i E {s+1, ..., t} with : c =\n- A is the vector potential and A . are the nodal values of A\n- aoi: ani, bn. are the coefficients of the Fourier serles of the functions ( a, (c, 6 ) ) chosen on the AGE curvilinear boundaries [2j. (See APPENDIX).\n- S is the number of commpn nodes to the AGE and the adjacent finite elements subdividing the rotor.\nOn the AGE-2 curvilinear boundaries the functions Ct.(c,B) are represented b y the second order Lagrangian pAlynomials obtained from the shape functions of the classical second order curvilinear finite elements [2] (Fig.2 , Fig.3.).\nIn the case of periodicity condition the coeffi-\ncient An (see eq. ( 7 ) ) is given by X = 3 . When we consider one pole-pitch as a solution domain A- can be \\m<tten as : n 6 0\nWhere B1 = % ; in this case, the first term of ( 7 ) is equal to zero. 2\nNot e that the use of the curvilinear elements gives a better consistency with the AGE than the first order straight side elements.\nExamples : -- To check the validity of the AGE-2 model we compare a known solution (A = kr6 - COs(6 e ) ) to both of the classical finite element method and the proposed one. The solution domain i s that given in Fig.4, and the equation to be solved is the Laplace's one (AA = 0 ) .\nThe rotation of the rotor, when using classical subdivision, creates a distortion of the finite elements discretizing the air-gap. Rapidly this distortion becomes inconsistent with a reasonable accuracy and makes a new discretization necessary while the AGE2 use gives results which are in good agreement with the known solution, for every relative position of the rotor (See Fig.4, 5, 6).\nb - eight-nod4 element.",
            "2302\na) A rotor point (See Fig.4a) b) A stator point (See Fig.4a) a ) Known solution (----) @ ) AGE-2 in air-gap and classical elements\nelsewhere (-----) y ) Classical second order finite elements\neverywhere (.-.-.-)\n6 = e0/3 (eo = z ) : displacement of the rotor.\n----_________ Case of a synchronous machine :\nThe field calculation is done for a three phase synchronous machine.The vector potential distributions (Fig.7) i s given for mo relative' positicms- of the rotor whenusing the AGE-2 model.\n____ Figure 7 : Vector potential distribution in a saturated synchronous machine.\nCONCLUSION\nThe AGE-2, modelling the UPAG of electric machines, has been developed and incorporated into the finite element method using second order isoparametric elements for the subdivision of the rotor and stator subdomains. The relative position of the rotor is automatically taken into acount when using sucha model. The model of the air-gap is almost perfect since the solution, in it, is determined analytically and the result accuracy depends only on the rotor and stator discretization [21. Moreover the AGE-2 use avoids the subdivision of an important part of the air-gap.\nOn the other hand the possibility of applying the anti-periodicity condition, when using the AGE2 , permits to consider only one pole-pitch for the solution domain.\n, ~ l ~ ~ l l ~ to optimize the computing time spent on solving the equation system, when using the AGE which increase the bandwidth of the matrix of the whole system [21, we used the S I C C G method 141.\nAPPENDIX\nThe coefficients aoi, ani, bni are given by the following formulas :\nThe referencies [ 6 ] , [71 show other applications of the AGE model.",
            "2303\nType I1 (See Fig.3)\n+ sin(A;e,_,)) + - 2 (cos(A.8 ) -cos(h;ei-l)~l A 3 n i+l\nwhere x = for the case of periodicity condition n Bo' and \u20aclo is the period. 2Tl\nREFERENCES\nA.A. ABDEL-RAZEK, J.L. COULOMB, M. FELIACHI and J . C. SABONNADIERE \"Conception of an Air-Gap-Element for the dynamic analysis of the electromagnetic fleld in electric machines\", IEEE Trans. Mag., vol.MAG-18, n02, March 1982.\nM. FELIACHI \"Contribution au calcul du champ 6lectromagnBtique par la rnethode des Blements finis en vue d'une rnodglisation dynamique de machines glectriques\", Thbse de Docteur-Inggnieur, Paris 1981.\nJ.C. SABONNADIERE, G. MEUNIER and B. MOREL \"FLUX : A General Interactive Finite Element Package for 2D electromagnetic field\", IEEE, Trans Mag., MAG-18, N02, March 1982.\nT.A. MANTEUFFEL \"The Shifled Incomplete Cholesky Factorization\", Sandia Laboratories, SAND 78-8226, 1978.\nP. SILVESTER, M.V.K. CHAR1 \"Finite element solution. of saturable magnetic field problems\", IEEE Trans., PAS-89, N07, 1970.\nA.A. ABDEL-RAZEK, J.L. COULOMB, M. FELIACHI and J .C. SABONNADIERE \"The calculation of electromagnetic torque in saturated electric machines within combined numerical and analytical solutions of the field equations\". IEEE Trans. Mag., MAG-17, N06, Nov. 1981.\n[7 3 M. FELIACHI, A. ABDEL-RAZEK and F. BOUILLAULT \"A synchronous machine dynamic model f o r magnetic field calculation'!,. ICEM, Budapest 1982."
        ]
    },
    {
        "image_filename": "designv11_24_0003549_rissp.2003.1285572-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003549_rissp.2003.1285572-Figure8-1.png",
        "caption": "Fig. 8: Model used in Numerical Example",
        "texts": [
            " From the above discussions, we can see that the amount of the whole body internal force becomes maximum when 61 = bz is satisfied. Since we implicitly assumed that the change of G'mg is small during the change of the foot position, this discussion becomes correct just the neighborhood of bl = bz. However, this discussion suits for our intuition that, when a human pushes a wall, the hand will slip first if a foot is close to the wall, while the foot will slip first if a foot is far from the wall. 6 Numerical Example We performed simulation for the model as shown in Fig.8 where its physical parameters are m~ = 30[kg], Fig.?: Whole body internal force with one contact between leg and ground la = 0.5[m], in11 = m21 = 10[kg], T I ] = ~ 2 1 = 0.2[kg], m12 = mzz = 10[kg], and yIz = T Z ~ = 0.2[kg]. The friction anglc a t each contact point and the joint torque limit are set as LY = 7rjS and rmax = 70IT[Nm], respectively. The results of numerical calculation of FF and FT are shown in Figs. 9 and 10, respectively. [ inn 70 100 70]T[Nni], rmin = [-io0 - 70 - ion - We obtained joint torque and performed simulation by using the ADAMS (Mechanical Dynamic, Inc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003400_008-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003400_008-Figure1-1.png",
        "caption": "Figure 1. Schematic illustration of carrousel-type sputtering apparatus (view from above).",
        "texts": [
            " In the present study we used a carrousel-type magnetron sputtering apparatus with independently controlled multiple targets and a rotating substrate holder to achieve composition control and composition homogeneity. The mechanical properties and shape memory behaviors of Ti\u2013Ni thin films prepared with this sputtering apparatus are evaluated and the feasibility of some applications using these films is demonstrated. 0964-1726/05/050216+07$30.00 \u00a9 2005 IOP Publishing Ltd Printed in the UK S216 A schematic illustration of the carrousel-type magnetron sputtering apparatus used in this study is shown in figure 1. This apparatus is characterized by a rotating substrate holder (called \u2018carrousel-type\u2019) in the center that is surrounded by several planar magnetron cathodes [4]. This geometry allows composition homogeneity by rotation of the substrate holder during multiple-cathode sputtering. Up to six substrates can be placed on the holder, and up to six targets can be powered simultaneously. In the present study, two targets of Ti\u201350 at.% Ni and pure Ti were used to obtain a desired film composition. These targets were 3 inches in diameter and 5 mm in thickness"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003917_0278364905058242-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003917_0278364905058242-Figure3-1.png",
        "caption": "Fig. 3. (a) A gait feasible three-limb posture, (b), (c) contains two distinct two-limb postures.",
        "texts": [
            " For each triplet of walls Wi,Wj,Wk, the reachability constraint is given by Rijk = {(s1, s2, s3) \u2208 Ii \u00d7 Ij \u00d7 Ik : \u2203c \u2208 IR2 (1) max{\u2016x(s1)\u2212 c\u2016, \u2016x(s2)\u2212 c\u2016, \u2016x(s3)\u2212 c\u2016} \u2264 R}, The point c appearing in eq. (1) can be interpreted as the center of a disk containing the three foothold positions, such that the disk\u2019s radius is bounded by R. As discussed in the next section, the elimination of the existential quantifier in eq. (1) results in a set which is bounded by quadratic surfaces in contact c-space. Gait feasibility of three-limb postures.A three-limb posture is gait feasible if it contains two distinct two-limb equilibrium postures (Figure 3). Let us write this constraint in the contact c-space cell Ii \u00d7 Ij \u00d7 Ik. This cell corresponds to contact with the walls Wi,Wj,Wk, and gait feasibility is satisfied by intersection of pairs of two-limb prisms associated with the three walls. There are three such pairs in the cell: (P ij k\u0304,P ij\u0304 k), (P ij k\u0304,P i\u0304jk), and (P i\u0304jk,P ij\u0304 k). Hence, the set of all feasible three-limb postures in the cell, denoted F ijk, is given by F ijk = (P ij k\u0304 \u2229 P ij\u0304 k \u2229 Rijk ) \u222a (P ij k\u0304 \u2229 P i\u0304jk \u2229 Rijk ) \u222a (P i\u0304jk \u2229 P ij\u0304 k \u2229 Rijk ) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000601_018-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000601_018-Figure7-1.png",
        "caption": "Figure 7. Change in curvature of a ball pressed against a surface.",
        "texts": [
            ") For smaller distortions the actual force is about one quarter of that calculated. This ties in neatly with the results of the contact time experiment. The pressure in the ball can be measured as the ball is squashed; although it does increase, by about 20% over the range of measurements shown, this change is obviously too small to be the major factor. The measured force agrees well with that calculated by multiplying the pressure by the contact area. The key must therefore be the way in which the wall of the ball bends round the perimeter of the flattened region. As figure 7 shows, this reduces the area of contact, compared to the simple model of a sphere intersecting a plane. The results all point to contact areas that are about one quarter of that calculated from the simple model, so that the diameter of the contact circle is halved. As noted earlier, accurate measurements of bounce height are quite challenging and care and patience are needed to get results that show the fairly slight effect of impact speed on bounce efficiency. Our results are summarized in figure 8; the lowest speeds correspond to drop heights of 20 mm and the bounce heights were measured to the nearest millimetre using the laser beam method"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003814_12.601652-Figure19-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003814_12.601652-Figure19-1.png",
        "caption": "Figure 19. Cavity monotonically increases from the fixed to free end",
        "texts": [
            "18b shows the component fabricated by homogenization DMD technique using a combination of Nickel and Cycle Time\u2026. Injection time Packing time Freezing time Clamp Open time Up to 75% Cooling Time Cooling time = Freezing time + Packing time (Injection time \u2013 Time to reach the node) Figure 16. In an injection-molding die, 75% of the cycle time is devoted to cooling. 52 Proc. of SPIE Vol. 5706 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/12/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx Chromium. Fig.19 shows a designed component similar to a turbine blade that has 50% less mass but has the similar mechanical strength when compared to conventional blade designs. Fig.20 shows creep test data for a component fabricated with Inconel 738. Implication of 50% reduction in mass in a turbine is proportional reduction in fuel lost. Integrated Design and manufacturing: Imagine the impact of \u201cDesigned Materials\u201d on society and in the environment. On can foresee is new paradigm of manufacturing where it is driven by customer\u2019s desire instead of the best available practice"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003090_iembs.2006.259233-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003090_iembs.2006.259233-Figure5-1.png",
        "caption": "Figure 5. The whole schematic of the master setup (a) frame with two cable sensors for each arm (b) left arm with sensors attached",
        "texts": [],
        "surrounding_texts": [
            "Keywords\u2014 surgery, robotics, master-slave, endoscope\nI. INTRODUCTION\nFlexible endoscopy is used to inspect and treat disorders of the gastrointestinal (GI) tract without the need for creating an artificial opening on the patient\u2019s body [1]. The endoscope is introduced via the mouth or anus into the upper or lower GI tracts respectively. A miniature camera at the distal end captures images of the GI wall that help the clinician in his/her diagnosis of the GI diseases. Simple surgical procedures (like polypectomy and biopsy) can be performed by introducing a flexible tool via a working channel to reach the site of interest at the distal end. The types of procedures that can be performed in this manner are limited by the lack of maneuverability of the tool. More technically demanding surgical procedures like hemostasis for arterial bleeding, suturing to mend a perforation, fundoplication for gastrooesophageal reflux cannot be effectively achieved with flexible endoscopy. These procedures are often presently being performed under opened or laparoscopic surgeries.\nWith the invention of medical robots like the Da Vinci [2] surgical systems, clinicians are now able to maneuver surgical tools accurately and easily within the human body [3]. Operating from a master console, the clinician is able to control the movements of laparoscopic surgical tools real time. These tools (also known as the slaves) are designed with sufficient degrees of freedom to move according to the natural hand and\nwrist motion allowing the clinician to perform intricate procedures with minimal technical difficulties.\nThus far, master-slave surgical robotic systems like Zeus and Da Vinci are either completely rigid or do not have a significant length of flexible body [4]. The slave manipulators enter the human body by means of incisions on the body. In this paper, we propose a robotic system with flexible slave manipulators that could be attached directly to flexible endoscopes. Similar to a conventional flexible endoscopic procedure (e.g. gastroscopy), the \u2018robotic endoscope\u2019 bundle could negotiate the curves and bends in the GI to reach the desired position within the gut. This system empowers the surgeons to perform more difficult surgeries that are otherwise impossible with the conventional endoscopic tool.\nII. OVERALL ROBOTIC SYSTEM\nFigure 1 shows the proposed system layout whereby the endoscopist work on the master console while gathering visual feedback from the endoscope. A computer console will interpret the readings from the master console that will in turn give instruction to the slave robotic system to perform the treatment to the patient. This system allows complicated treatment to be performed with the added benefit of easy and intuitive control for the endoscopist.\nIII. THE SLAVE MANIPULATOR\nThe 3D model of the intended slave manipulator can be seen in Fig 2. In order for the surgeon to perform the necessary dexterous actions, the slave manipulators should possess a high number of Degrees of Freedom (DOF). The emphasis of the\n1-4244-0033-3/06/$20.00 \u00a92006 IEEE. 3850",
            "project is to make the slave manipulator to be as intuitive to control as possible. As such, the DOF and joints of the slave manipulator are modeled after a simplified human arm as shown in Fig 3. Altogether there are 5 DOF for positioning of the slave and an extra DOF for manipulating the end effector and the axis or rotation. Two slave manipulators are used instead of one since it can perform actions such as pulling and cutting of polyps or suturing bleeding sites. Furthermore two slave manipulators are more intuitive to use since they resemble the two human arms.\nIn order for the slave manipulator to be able to go through human GI tract, the slave manipulator has to be small yet flexible. Due to this unique requirement, tendon-sheath actuation is used. The prime movers are located outside the human body and it transmits power to the mechanism by pulling and releasing tendons in a sheath accordingly.\nThe design of the mechanism is such that the two antagonistic tendons that control each DOF motion are independently actuated by one DC motor. In addition, the rotational displacement of each joint is directly proportional to the linear displacements of the tendon. These characteristics\nallow the serial slave manipulator to be controlled more easily. With the help of the software, the manipulator will not face singularity conditions in the prescribed range of motion for the manipulators.\nDifferent types of end effectors have been designed to perform different types of actions during surgery. One of the tools includes electrodes that can perform monopolar cauterizing. The picture of the current developed prototype can be seen in Figure 4. Take note that the attachment that held the endoscope and manipulators is not fixed to the current prototype yet.\nTo pass the endoscope and slave system to the desired site of the GI tract, an overtube can be used. Currently the size of the whole slave manipulator is approximately 25mm in diameter. Future developments will be on the miniaturizing of the slave manipulator till it is comfortable to be used on human beings.\nIV. THE MASTER CONTROLLER SYSTEM\nThe ergonomic master device is built as a 6 DOF structure to control the 6 DOF slave mechanism. As the slave manipulators resemble the human arms, the anthropomorphic data of the surgeon\u2019s arm is used as the control parameters in order to give the surgeon better perception in performing the joint-to-joint control of the slave.",
            "The schematic of the master controller is shown in Fig. 4. Two cable-actuated position sensors are used to measure the two contributing rotations of the shoulder joint that cause the up-down and in-out movement of the upper arm. Two optical rotary encoders are used to measure the flexion and supinationpronation movement of the elbow joint. Another similar encoder is used for flexion-hyperextension movement of the wrist, and the finger grip comes with an encoder inside the holder.\nA virtual plane is formed using the reference of the shoulder joint with the two position sensors. The sensor locations can be modified to meet the required workspace that lies on one side of the plane. For the full range upper arm movement, additional sensor will be needed. As the comfortable workspace for the surgeon\u2019s upper arm lies in a quarter of a spherical space, two position sensors is sufficient to get the anthropomorphic data of one arm in that range.\nThe position sensors are located in such a way that the cables do not impose any disturbance on the surgeon\u2019s vision and movement. Furthermore the tensions of the cables facilitate the surgeon as a counterweight from his own arm moments, reducing the fatigue.\nAssuming that the shoulder joint to be a ball and socket type, the point of cable-attached upper arm is determined by three spheres formed by upper arm length and two cable lengths. In Fig. 6, L1 and L2 are the two cable lengths and L3 is the upper arm length.\nIn X0Y0Z0 coordinate system,\n2 1 202 1 002 1 00 LPPPPP zyyxx (1)\n2 2 202 2 002 2 00 LPPPPP zyyxx (2)\n2 3 202020 LPPP zyx (3)\nThe point 0P(x,y,z) below the plane can be solved from above equations and it can be transformed into X1Y1Z1 by rotation matrix about Y-axis.\nz\ny\nx\nz\ny\nx\nP P P P P P 0 0\n0\n1\n1\n1\ncos0sin 010\nsin0cos\n(4) 1P(x,y,z) can be used to calculate the shoulder joint up-\ndown and in-out angles.\nThe mobility range of the master is constrained only at the upper arm by the virtual plane formed by the shoulder joint and two cable sensors. The other joints accommodate the full range of motion of the surgeon.\nA dedicated computer software is programmed to control and interface the slave and master robotic system. First it takes in real time readings from each encoder of the master device to determine the motion geenrated out by the user. This data is processed and appropriate signals are sent out to actuate the respective motors to bring about the required movements of the slave. The system framework adopts a 2-layer architecture. The bottom layer is the hardware control module that uses low-level drivers for hardware control. The top-layer modules are the kernel algorithms, which perform the signal processing to compensate for backlash and noise disturbances (more details in Section 7).\nIn vitro experiments with the master-slave system have been conducted in carrying out some tasks. By manipulating the master, users are able to manipulate the slave to carry out pick and place action as well as grabbing and cutting a soft object. In future animal trials will be conducted to verify its functionality. During experimentation, it is found that the mechanism is capable of producing at least 0.8N for each DOF.\nOne of the biggest problems in the tendon-sheath driving robot system control is the nonlinear characteristic due to the friction between the tendon and sheath [5]. As a result, delays and movement hysteresis are noticeable and can be seen in the below relationship\n1)exp()( 0 EA LT L (5)"
        ]
    },
    {
        "image_filename": "designv11_24_0003960_detc2005-84728-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003960_detc2005-84728-Figure2-1.png",
        "caption": "Fig. 2 GSAM models of planetary gearsets (a) Case 1- single pinion (b) Case 2 - double pinion",
        "texts": [
            " The sun and pinion gears in case 1 are exactly the same as the sun and SP pinions in case 2. Case 2 has an additional pinion RP and the ring gears are of course different in the two cases. In both cases the powerflow is the same \u2013 the sun gear is the input member, the ring gear is the output member and the carrier is the reaction member. The SP pinion in case 2 and the pinion in case 1 are operating under almost identical conditions except for orientation of meshes, and so will offer a good comparison between single and double pinion planetary arrangements. Figure 2 shows the GSAM models for both cases and the orientation and spatial locations of the gears can be seen 2 Copyright \u00a9 2005 by ASME l=/data/conferences/idetc/cie2005/71315/ on 04/01/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Dow Table 1 Case 1: Single Pinion Planetary Gearset Sun Pinion Ring Number of teeth 35 26 86 Nor. module mm 1.59 Nor. pressure angle deg 20 Nor. helix angle deg 21 R 21 L 21 L Face width mm 32.35 29.00 32.00 Center distance mm 51.945 51.945 Input torque Nm 1378.7 input to sun Reaction member Carrier Number of pinions 3 First we will consider the calculations for bearing loads and moments for the single pinion planetary arrangement shown in Figure 2 (a). Figure 3 shows a plot of a pinion and the forces acting on it. The forces are assumed to be concentrated at the operating pitch point in the center of the facewidth of the pinion. This approximation is commonly done and gives the bearing loads and moments in the absence of a distributed load, or when the effective centroid of the distributed load (at a given point in time) coincides with the pitch point in the center of the pinion facewidth. For clarity, only two teeth are shown on the pinion \u2013 one at the sun mesh and one at the ring mesh"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000811_1.2834592-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000811_1.2834592-Figure6-1.png",
        "caption": "Fig. 6 Planar view of a MEMs smart bearing pad",
        "texts": [
            " For a fourth order model, percent deviation ranges from 1.6-7.4 at the \u00b130 percent mini mum clearance location. 3.2 1-D Nonlinear Coefficients and Higher Order Mod eling Accuracy\u2014MEMs Smart Slider Bearing. The non linear model is applied to a MEMs active smart slider bearing (Heam et al., 1995). The MEMs smart slider bearing geometry is similar to the conventional slider bearing except that the bearing pad is populated with sensors and active actuators (Maddox, 1994). A planar view of a MEMs bearing pad is depicted in Fig. 6. Preliminary results from a MEMs smart bearing study suggest that the presence of MEMs actuators has a significant effect on the conventional bearing's steady state performance (Maddox, 1994; Masser, 1996; Wood et al., 1996). These results also suggest that a MEMs smart bearing can have controllable dynamic characteristics. This actively controllable dynamic feature can potentially be used to avoid turbomachinery instabilities such as oil whirl, critical speeds, and cavitation (Ehrich, 1992; Maddox, 1994; Masser, 1996)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001390_robot.1997.606894-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001390_robot.1997.606894-Figure5-1.png",
        "caption": "Figure 5: A physical illustration of bouncing technique.",
        "texts": [
            " Furthermore, the product of l single Manhattan paths is a Manhattan path of order e . It is clear that all valid Manhattan paths of order k can be represented by a vector 2 E but not all 2 E Rn*\u2018 represent a valid Manhattan Path, since Ai E y k could easily violate a kinematic constraint, either due to an obstacle or due to joint limit. The bouncing technique allows us to map an arbitrary Manhattan path into an admissible Manhattan path. The basic idea is to bounce 08 the obstacle and has been used in [BA+93, HFT941 (see Figure 5). Suppose a certain Ai leads to collision. As mentioned before, at the given configuration, a collisionfree interval [AT\u201d, Ay\u201c\u201d] can be easily obtained (as in [LP87]) such that every joint value within this interval is collision-free (see Figure 3). We can then map the original interval A; modulo the collision-free interval to within the collision-free interval [ATin, AT\u2018\u201c]. Physically speaking, it is as if the the robot lin& repeatedly bounces off the obstacles until the entire Ai is travelled"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003918_cdc.2006.376701-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003918_cdc.2006.376701-Figure1-1.png",
        "caption": "Fig. 1. Mechanical setup of the helicopter laboratory experiment.",
        "texts": [
            ". INTRODUCTION The 3DOF helicopter laboratory experiment [12] is an example of a so\u2013called underactuated mechanical system. As it can be seen in Fig. 1, the helicopter basically consists of three hinge\u2013mounted rigid body systems: the base, which can turn about the travel axis q1, carries the helicopter arm with its rotation about the elevation axis q2. One end of the arm is attached to a counterweight that tares the weight of the third mechanical subsystem, i.e. the helicopter body. The rotation of this body is described by the pitch angle q3. At the ends of the helicopter body two dc\u2013driven motors with propellers are installed. The thrusts Ff and Fb, which arise when applying the voltages Vf and Vb to the motors, serve as control inputs to the system",
            " Starting from this physics\u2013based model, Section III presents the feedforward control design under input constraints. The additional incorporation of the constraints for the pitch axis q3 is addressed in Section IV. In order to stabilize the system along the trajectories given by the feedforward control, a time\u2013varying LQ feedback controller is designed in Section V. Finally, measurement results show the quality of the proposed control concept in Section VI. The paper will close with a short conclusion in Section VII. A detailed mathematical model of the 3DOF helicopter laboratory experiment as depicted in Fig. 1 was derived by utilizing the concept of twists and wrenches [11] in combination with the Euler\u2013Lagrange formalism, see [9], [10] for more details on this topic. For the nonlinear controller design purpose, the model of the helicopter in Fig. 1 has to be simplified in such a way that the essential dynamics and nonlinearities are reproduced in the best way. Following the assumptions given in [9], it is possible to write the equations of motion in the form q\u03081 = b1 sin(q3) cos(q2)u1 (1a) q\u03082 = a1 sin(q2) + a2 cos(q2) + b2 cos(q3)u1 (1b) q\u03083 = a3 cos(q2) sin(q3) + b3u2 (1c) with the transformed inputs u1 = Fb+Ff and u2 = Fb\u2212Ff . Thereby, the friction in each axis is neglected and the mass\u2013 and geometry\u2013dependent parameters ai and bi, i = 1, 2, 3 are given in Table I",
            " Following the basic idea of the approach presented in [4], the solvability of the BVP requires 2 free parameters p = (p1, p2) in the setup functions for the output trajectories y\u2217 1(t) and y\u2217 2(t). Thereby, some freedom exists concerning how the free parameters are distributed over the two output functions. The factor tan(y\u2217 2) in the right\u2013hand side of (9) reveals that the internal dynamics is essentially influenced by the second output y\u2217 2 . This is also apparent from a physical point of view, since the acceleration \u03b7\u0308\u2217 = q\u22171 of the travel axis is directly linked to the pitch angle y\u2217 2 = q\u22173 of the body, see Fig. 1. Thus it is reasonable to provide both parameters p in a setup function \u03a52(t, p) for the second output y\u2217 2(t) = \u03a52(t, p), whereas the first output is given by a predefined setup function y\u2217 1(t) = \u03a51(t). The setup functions \u03a51(t) and \u03a52(t, p) can be constructed e.g. with polynomials or trigonometric functions and have to satisfy the BCs (7a) and (7b) for the outputs y\u2217 1 and y\u2217 2 , respectively. The solution of the resulting BVP with free parameters comprises the parameter set p as well as the trajectory \u03b7\u2217(t) of the travel axis of the helicopter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001438_978-3-642-59785-5-Figure25-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001438_978-3-642-59785-5-Figure25-1.png",
        "caption": "Fig 25 Cross-secTional arrangement of hub mechanism for v[Jrlable pitch-In-motlon axial flow fan (colIIPressed air operation)",
        "texts": [
            " These forces are usually resisted by anti-friction bearings 225 of the ball or roller type. Such bearings have a lower capacity under the virtually static conditions prevailing, and in the early days failure was not uncommon. With increasing experience, however, the problems have been overcome. Levers at the base of each blade convert the equal pitch angle adjustment into axial movement of a sliding member within the impeller hub. This may be controlled in a number of ways: a) By movement of pneumatic bellows against a spring as shown in Figure 25. The bellows are expanded by compressed air through a rotary air seal onto a shaft extension. b) By an actuator (either pneumatic or electric) giving axial movement through levers to the stationary race of a ball thrust bearing, the revolving race being coupled to the sliding actuator within the hub. In all cases, when the fan is running, a force must be applied to each blade to maintain the required pitch angle or it would rotate to a position near zero pitch angle where the centrifugal forces on it were in balance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003141_tsmc.1982.4308921-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003141_tsmc.1982.4308921-Figure5-1.png",
        "caption": "Fig. 5.",
        "texts": [
            " (51) 3 [2m3(11 + 12 COS 42)13 COS 4)3 + m3/3c 4)2 +J3ncOs02] 1 + (m3/3 + '3,n)43 + [m313 sin 0)3 cos )2(21/1 + (212 + 13 cos 43) cos 4)) 3313 sin 4)3 cos 0)3 + J3sn sin2 42 sin 03) cos 3 1 + [rm313 sin 43(212 + 13 cos 4))3- J3, sin 03 cos 03 02 - [4mr31312 COS 0)3 sin 4)2 + M331/ sin 4)2 + m332 sin 02cos 203 + J3n sin 02 -3sJ3 sin 4)2 cos 24)3]4l42 + mr3g13 sin 43 sin 02. (52) 885 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS, VOL. SMC-12, NO. 6, NOVEMBER/DECEMBER 1982 The three equations (50)-(52) represent the driving torques as functions of generalized coordinates, velocities, and accelerations. The differential equation model can be determined by inverting the positive definite GIM ('M) of the manipulator. Computation of Certain Typical Coefficients by Uicker's Method Uicker's method requires a particular system of body fixed coordinates (Fig. 5). The 4 x 4 transformation matrices Tj'_, for transformation from i th to i - I th body fixed system can be shown to be given by Cos 10I T- sin 4I cos'0 I - 0 cos (03 T3 = sin P3 O2 LO 0 0 1 0 O - sin 21, cos O cos 41 21, sin 1 0 0 O 0 1 sin 42 212 coS 02 - COS42 212 sin 02 o 0 0 1 sin43 0 213cos403 Cos 03 0 2l3 sin403 0 1 0 0 0 1 Let a, = 211 a2 = 212 a3 = 213 G= (0 0 -g 0)' '(-J2 + 2J2, + 2m2/2) 0 0 - -ma2 0 2 J2sI1 o _I 0 0 0 iJ2s 0 - I2a2 0 0 -J3s+ 2J3n + 2m33) 0 \u00b0 - IM3 3 0 0 0 O 0 :2>3s: \u00b0 0 0KJ3<s 0 L - 2m3aI 0 0 m3 The general algorithm for an industrial manipulator is then given by [12] n {kI ~ j"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003044_978-1-4613-2359-4_4-Figure37-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003044_978-1-4613-2359-4_4-Figure37-1.png",
        "caption": "Figure 37. The relative oxygen reduction rate versus the distance between the electrode and the enzyme: for laccase adsorbed (1) on soot; (2) on cholesterol with planar orientation; (3) on vertically oriented cholesterol; (4) on lecithin. The curves a and b are calculated for barrier heights of 4 and 5 eV, respectively.",
        "texts": [
            " Variation in the distance between the active center and the electroconductive substrate was achieved by inserting an intermediate monolayer of lipid molecules: flatly and vertically oriented cholesterol molecules and vertically oriented lecithin molecules (scheme in Figure 36). In this case, the conditions of obtaining compact lipid monolayers were fulfilled. The subsequent setting of laccase did not lead to their desorption. In this comparison, the value of electrocatalytic activity for all electrodes was normalized with respect to the rate of the model enzymatic reaction hydroquinone oxidation. The data obtained are shown in Figure 37. It is seen that a sharp reduction in the reaction rate is observed within a narrow range of distances, and rer amounts to about 20 A. The shaded area corresponds to calculated data for a parabolic barrier height of 4-5 eV and other simple but by no means explicit assumptions. Nonetheless, the concepts of tunneling for electron transfer are quite promising for the interpretation of certain effects of bioelectrocatalysis. The theory of bioelectrocatalysis is only making its initial progress; however, in the field of practical application we can already point out two areas in which the use of biocatalysts is likely to yield essentially new results"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003936_13506501jet75-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003936_13506501jet75-Figure1-1.png",
        "caption": "Fig. 1 Schematic view of twin-disc rolling contact machine",
        "texts": [
            " To verify the effects of water temperature on the adhesion coefficient obtained by theoretical investigation in references [1] and [5], a number of experiments have been conducted on a twin disc rolling contact machine under wet conditions at different water temperatures. The water temperature has been clarified to have a significant effect on the adhesion coefficient by the experiments, which is qualitatively consistent to the theoretical results. On the basis of the results in this paper, a method for raising the water temperature in the contact zone between wheel and rail is considered to improve the adhesion coefficient under wet conditions and to prevent the damages on wheel and rail surfaces due to the decrease in the adhesion force as a result. Figure 1 shows a twin-disc rolling contact machine [6] used for the experiments. The machine has two 150 kW DC motors to control a disc of 300 mm in diameter (termed a wheel disc) and another disc of 170 mm in diameter (termed a rail disc), respectively. The wheel disc was made of real wheel material in accordance with JIS (Japanese Industrial Standard), used in Japanese Railways, and the rail disc, cut from a real rail. Table 1 indicates material compositions and properties of the wheel and rail discs. Figure 2 details how the rail disc was cut from a real rail",
            " When the rotations of both discs were accelerated to a target value of the rolling speed, the water stored in the high-pressure tank would be sprayed onto the contact zone between the two discs. For a short time during water spraying, generally 4 or 5 s, using the ECB, braking torque was applied on the rail disc, and if the slip ratio had increased to exceed a pre-set value (usually set to be 10 per cent), the experiment would automatically stop. During the experiment, pulse signals detected by the rotary encoders (Fig. 1) were converted to the rolling speeds through a pulse converter. A strain amplifier estimated resistance torque arising on the wheel axle detected by the torque transducer (Fig. 1). Finally, those measured values were converted into digital data with an A/D converter and were displayed on a PC screen. On the basis of the measured values of rolling speeds of the two discs and resistance torque on the axle of the wheel disc, the relationship between the traction force and the slip ratio was estimated as follows: Supposing the resistance torque on the wheel disc is Tw, it can be expressed as Tw \u00bc F Rw vw Iw (1) where F is the traction force between the wheel and rail discs; Rw, vw, and Iw are the radius, rotational acceleration, and moment of inertia of the wheel disc, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000723_6.1993-1996-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000723_6.1993-1996-Figure4-1.png",
        "caption": "Figure 4 shows a sketch of the arrangement to impose a radial excursion of the seal into the runner during dynamic testing. In order to elininate or minimize any kTal load due to pressure on the teat rig spindle, two brush seals are",
        "texts": [],
        "surrounding_texts": [
            "Bristle Hysteres-\nFigure 1 shows the schematic diagram of a convrntional brush seal. When in operation, the differential pressure \u2018Ap\u2019 acts over the annular area between the retainiug plate i d . ID,\u2019 and the bristle i.d. ID;\u2019. This unbalanced axial force causes the bristle pack to load against tbe backing plate with a high mechanical contact pressure over the an-\nfree body diagram of the bristle pack. The resultant force due to the contact pressure as well as the frictional force are indicated on the figure. Contact forces are also generated at the bristle-to-bristle interfaces within the pack by varying degrees. These frictional forces give rise to bristlr \u201cbystercsis\u201c with any radial movement. For exaniplr, during a rotor excursion, the bristle pack is forced radially outward. Subsequently, when the rotor withdraws, thr bristles do not drop back down on the shaft, causing bristle \u201chang up\u201d, unless the applied pressure i i decreased to a low value. In fact, experiments indicate that even a few psid pressure\nFriction Force\nnular surface between \u2018D,\u2019 and \u2018Dh\u2019. Figure 2 presents the Pressure Differential act\nDi\nSeal\nFigure 2. Free Body Diagram of a Conventional Brush\nLJ\ndifferential across the seal prevents free radial movrinent of the bristle pack. This bristle \u201chysteresis\u201d leaves a large gap and hence, causes an appreciable increase in leakage after any transient differential movement of the runner mto the bristle pack. This has been experimentally demonstrated many times at EG&G FCTG R&D Laboratory. The leakage increase is also likely to be cummulative as the shaft excursions take place in different radial directions by different amounts, and along the entire circumferencr during rotor thermal or centrifugal growth.\nBristle Stiffening Effect\nAs mentioned earlier, another detrimental effm t of the contact pressure between the bristle pack and tlir hacking plate is to increase the bristle stiffness. This phenomenon is caused by the fact that the bristles are preventd froni moving freely in the radial direction by the frictional iorre, thereby reducing their effective free length.\nRetaining Plate\nBristles\nBack Plate\nI\n1 D; l i t - b,\nW Figure 1. Schematic Diagram of a Conventional Hrush\nSeal\n2\nT h e \u2018generalized bristle stiffness\u2019, \u2018 K ~ ; , u ~ \u2019 , is a fundaniental parameter to characterize a brush seal. This is defined as the pressure required at the bristle tips to displace thein radially by a unit magnitude. The following functional relationship can be written :\nKbist~. = f(d,Z,@,w,E,Ap) (1)\nFor a given design, however, it is a function of \u2018Ap\u2019 only and is denoted M \u2018K~; ,*R~(A~)\u2019 . Although \u2018Kh;.tl.(O)\u2019 can be Pstimated theoretically at the 5CIO pressure differential condition, its value for a certain \u2018Ap\u2019 is generally determined experimentally which is covered in a later section.\nL)\nFor a given radial interference of \u2018&\u2019, the mechanical contact pressure \u2018p,,.\u2019 at the bristle/runner interface can be estimated using the following relationship,\npmr = K b i d A p ) 6, (2)\nThe \u2018pmr\u2019 at the interface has a direct bearing on the wear rate of the bristles, the life of the runner surface and the amount of heat generated at the interface. A lower \u2018p-\u2019 would yield a lower wear rate and hence, a longer seal life.\nExperiments done at EG&G FCTG R&D Laboratory demonstrated that the \u2018Kk;.,l.\u2019 of a conventional brush seal appreciably increases with pressure. Typically, an order of magnitude increase in bristle stiffness WM measured with a differential pressure rise of 60 psid. Because of this bristle \u201cstiffming\u201d effect, any differential movement of the runner, e.g. radial excursion or growth into the bristle pack, will introduce very high \u2018p-\u2019 at the sliding interface, causing an accelerated wear of the bristlea and degradation oi the runner surface. Subsequently, when the runner withdraws to its normal position, it will leave a clearance resulting in an increased leakage as well.\nL/\nD ow\nnl oa\nde d\nby U\nN IV\nE R\nSI T\nY O\nF T\nE N\nN E\nSS E\nE o\nn M\nay 1\n9, 2\n01 6\n| h ttp\n:// ar\nc. ai\naa .o\nrg |\nD O\nI: 1\n0. 25\n14 /6\n.1 99\n3- 19\n96",
            "Experimental Procedure\nIn the tollowiug two sections, the experimental arrangem a t s to measure the bristle stiffness and to introduce radial excursions during dynamic testing are described. I/\nA schematic of the test apparatus is shown Figure 3. In this act-up, two identical seals with the same nominal \u2018Kki.~.\u2019 are mounted on a runner with a face-to-face arrangement. The cavity between the seals is pressurized to create a desired pressure differential across the seals. A certain amount of radial interference, typically 0.010 in, is maintained between the seals and the runner. Although, for the sake of clarity, the ruuner diameter is shown to be smaller than the seal i.d., it is actually slightly larger to provide for the necessary interference. The seala are secured in a seal holder which is moved up and down vertically with respect to the fixed, static runner, by turning the adjustment nut at the top. The force required to do so is measured with a load cell. The seal hdder is initially made concentric with the runner so that there is no net force coming from the bristle/runner interface, and the load cell registers only the known dead weight of Kal holder and seal assembly. As the holder is made eccentric with respect to the runner, the force on the load cell ~ C I C M C E . The radial eccentricity \u2018A,\u2019 is measured with a Bently proximity probe, targeting on a f l a t - f ad pin attached to the bottom of the seal holder. The\nAdjustment\nProbe\nforces at different radial eccentricities are measured during the ascending and descending travel of the seal holder. The initial slope of the ascending curve gives twice (since there are two identical seals) the seal stiffness \u2018K,eai\u2019 which can be related to the \u2018Kbr,,cir\u2019 as foflows :\nK...A = C Kbrwt~E (3)\nwhere, \u2018C\u2019 is the constant of proportionality which depeltds on the seal geometry only.\nThe cavity between the seals is pressurized to create a certain pressure differential across the seals, as desired. The above test is repeated for various pressure differentials. The d u e s of \u2018K=#t\u2019 at different \u2018Ap\u2019 are determined from the initial slopes of the corresponding load-eccentricity curves. The \u2018Kbr,.~.\u2019 values are next calculated using eqn (3).\nRadial Excursion - Dynamic Test\nD ow\nnl oa\nde d\nby U\nN IV\nE R\nSI T\nY O\nF T\nE N\nN E\nSS E\nE o\nn M\nay 1\n9, 2\n01 6\n| h ttp\n:// ar\nc. ai\naa .o\nrg |\nD O\nI: 1\n0. 25\n14 /6\n.1 99\n3- 19\n96",
            "mounted face-to-face in a movable seal holder. One seal is the actual \"test seal\" under evaluation and the other seal is the \"dunimy seal\" required to presnurize the chambpr. The movable holder is allowed to move along a vertical axis up to 0.032 inches away from the center. Vertical niuvemcnt is guided by two shafts, attached to the seal holder, one at the 12 o'clock and the other at the 6 o'clock positions. Each shaft extends through the pod to an air cylinder and guide mechanism, which is attached to the test rig housing. The force to move the holder is supplied by these two air cylinders and the magnitude of the force can be regulated by adjusting the air pressure to the cylinders. Trawl of the seal holder is controlled by an adjustable stop on each air cylinder.\nPressure is introduced into the seal chamber via flexible pipings which extend through the test pod and into the movable holder. Leakage through the \"test seal\" is measured with a flow meter in aeries with a pipe attaclird to a port on the end plate. --\nIn the following sections, the characteristics of ronveutional seals are compared with \"low hysteresis\" seals. Two seals of different designs in each of the above two categories have been chosen. These seals are denoted M 'Conwntional Seal 1, 2' and 'Low Hysteresis Seal 1, 2' respectively. The outer and inner diameters, D. and D;, of all the above seals are 6.414 and 5.375 inches respectively.\nFigure 5 oreseuts the stiffness ratio (R.\\ band of t,wo\nLeakaxe Hysteresis\nThe leakage \"hysteresis\" characteristics of the above seals have been demonstrated and evaluated with the following three types of dynamic tests.\nDynamic test with concentric rotor,\nDynamic test with eccentric rotor, and . Dynamic test with radial excursion.\nThese teats and the corresponding results are described in the following sections. v\nDynamic Test with Concentric Rotor - ~ .I\nconventional seals of different bristle stiffness Characteristics I,, tllis test, the rotor was very care(Le. different 'K~r..tl.(0)'s). The lower and upper lines cor- fully so as to minimize any dynamic runout. The seal cham- respond to the 'Conventional Seal 1 and 2'respectivrly. The ber is pressurized to the desired The speed in- 'Kk..a.' at a given 'Ap' is non-dimensionalized with respect creased from the static condition to 16,000 rpm, in steps to the correwnding Zero Pressure value e. B. ~ ~ b r d o ) . of 5,000 rpm and then hack to 0 rpm. the 5,000 and 10,000 rpm conditions, the seal was tested for 15 minutes As seen in Fig. 5 , the bristle stiffness of the conventional seals increases by more than an order of magnitude ovcr the each, and descending parts of the r a g e of pressure differential considered (ea. 80 psid). As cycle. At 16,000 rpm, the seal WM tested for 30 minutes. mentioned earlier, this phenomenon would Cause a <orre- The leakge wM continuous~y monitored during the cycle, spondingly higher mechanical contact pressure at the sfid- Steady state leakage at each operating point is reported\nhere.\nboth\ning interface, resulting in higher wear and shorter life.\nThe bottom curve in the figure shows the stiffness ratio curve of the 'Low Hysteresis Seal 1'. It is evident that the bristle stiffness does not incresae over ' K ~ ; , , ~ c ( 0 ) ' until a pressure threshold of 30 psid is reached. However, this threshold value beyond which the stiffness begins to increase, dependa on a particular design and can be extended by changing various geomterical design parameters. Obviously, this design would cause a lower 'pme' at the runner interface than a corresponding conventional seal and hence, has a potential of longer life. Leakage data is presented in terms of flow parameter 'e' which is defined ~d follows : (4) It may be noted that the flow parameter definition, adopted here, is slightly different from the ones used by other investigators\"s.\nD ow\nnl oa\nde d\nby U\nN IV\nE R\nSI T\nY O\nF T\nE N\nN E\nSS E\nE o\nn M\nay 1\n9, 2\n01 6\n| h ttp\n:// ar\nc. ai\naa .o\nrg |\nD O\nI: 1\n0. 25\n14 /6\n.1 99\n3- 19\n96"
        ]
    },
    {
        "image_filename": "designv11_24_0000181_1.2787261-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000181_1.2787261-Figure2-1.png",
        "caption": "Fig. 2 A single-rod system",
        "texts": [
            " It is convenient to refer to 0~ '\u00b0 , @o, and 0 ld0 as those three degrees-of-freedom. The rod is uniform and its length is 1 ~ = 0.508 m. The mass per unit length is 0.113 kg/m. The cross-sectional moments of inertia are lyy = 1521.10 -9 k g . m I~ = 95.1.10 _9 kg .m. The stiffnesses of the torsional springs at the root are k~ =k~ = 20N.m; k~ = 2 . 1 0 - 3 N . m . The initial conditions are 0~ '\u00b0 = 0~ '\u00b0 = 0~ '\u00b0 = 0 . An axial compressive concentrated force, P~ (t) , is applied at the tip of the rod (see Fig. 2) : - P sin 7r P~( t ) o ~ t' t --< 0.4sec I - P , t >-- 0.4 sec P~ - P~ = 0. If the applied force P~ is less than the value of the critical buckling force (in the present case (P~ = (ky/ l )) , the dynamic response of the system is zero. If I P.[ [ ~- P,, and a very small component of force in the z-direction is applied, the exact response of the rod includes only the angle 0~ \u00b0 . The influence of the disturbance force (in the z-direction) on the phenomenon is negligible. The (exact) equation of motion in this case becomes m ( l t ) 2 ~ , 0 + kl01 ,0 1 l I 1,o - - y ~ y -~ -P~(t)\" \" s i n O y . (38) 3 The exact expression for the lateral component of the constraint force at the rod root (in the Z-direction, see Fig. 2), F~, is m ( l l ) 2 l,o \"1,o 10 F~ = ~ [(0~'\u00b0)2.sin ey - ey .cos ey' ] (39) 2 The system response (0 j'\u00b0 and F~) will be calculated using y three different methods: 0. . .5 - o.o ~\" -0 .5 8 g - 1 . 0 -1 .5 - 2 . 0 , , 0,0 0.5 (A,B,P) I I 1.0 1.5 2,0 TIME(see) Fig. 3 A single rod system~the rotation 0~, ,\u00b0 as a function of time: \"Accura te , \" B - - B a u m g a r t a , P--Present method A w (a) Direct integration of Eq. (38) and substitution into Eq. (39) in order to calculate F~. This solution will be referred to as \"accurate\" and will be used to assess the accuracy of the other methods"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003824_1.2202875-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003824_1.2202875-Figure1-1.png",
        "caption": "Fig. 1 Relative screw motion between skew gears in: \u201ea\u2026 Euclidean space; \u201eb\u2026 dual space",
        "texts": [
            ", the spatial motion of the Euclidean space is transferred to and analyzed in dual space, in order to obtain an equivalent dual spherical motion, thus emulating the motion of bevel gears. Moreover, the Pl\u00fccker conoid, which is the geometric locus of the instant screw axis when the transmission ratio takes any real value, is obtained by analyzing a pair of bevel gears in dual space. The proposed algorithm has been implemented in Matlab code; several numerical results obtained with this code are reported and discussed herein. Referring to Fig. 1 a , the driving gear 2 is assumed to be rotating about the I2 axis, which is coincident with the Z axis of the fixed frame Fe OXYZ , while the position of the I3 axis of the driven gear 3 is given by angle 1 and distance a1 along the positive X axis. The instant screw axis I32, or ISA for brevity, of the relative motion can be determined by means of the AronholdKennedy theorem in three dimensions, first proposed by Joseph S. Beggs in his doctoral dissertation 36 . The same theorem was reported later by Phillips and Hunt 37 . In fact, all three axes I2, I3, and I32 share the X axis as common perpendicular, while angle 2 and the coordinate b2 determine the I32 axis. 06 by ASME Transactions of the ASME hx?url=/data/journals/jmdedb/27829/ on 06/12/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F An algebraic approach through dual algebra and the principle of transference is introduced in this paper, whereby the Euclidean spatial motion of Fig. 1 a is mapped onto the dual spherical motion of Fig. 1 b . ISAs I2, I3, and I32 are represented on the dual sphere S\u0302 by the dual points P\u03022, P\u03023, and P\u030232, as given by the dual unit vectors e\u03022, e\u03023, and e\u030232, respectively, while the dual angles \u03021= 1+ a1 and \u03022= 2+ b2 give the position of e\u03023 and e\u030232 in the dual frame O\u0302X\u0302Y\u0302Z\u0302, henceforth referred to as Fd. The dual unit satisfies the proprieties 0, 2=0. Thus, the relative screw motion between any pair of external and internal skew gears is analyzed in the dual space of Fig. 1 b , with the aim of simplifying the problem and then taking the results, upon expansion of the dual formulation, back to the Euclidean space of Fig. 1 a . The well-know relation of the relative screw motion is expressed in dual space by 3e\u03023 = \u030232e\u030232 + 2e\u03022 1 where the dual relative angular velocity \u030232 is represented as the sum of a primal part, which corresponds to the relative angular velocity 32, and a dual part, which corresponds to the relative sliding velocity V32. The dual unit vectors e\u03022, e\u03023, and e\u030232 of Eq. 1 are defined in the following: e\u03022 = k\u0302 e\u03023 = Q\u0302 \u03021 k\u0302 e\u030232 = Q\u0302 \u03022 k\u0302 2 where k\u0302 is the dual unit vector of the Z\u0302 axis of frame Fd in Fig. 1 b , while Q\u0302 \u03021 and Q\u0302 \u03022 are dual rotation matrices about the X\u0302 axis, which are given by Q\u0302 \u03021 = 1 0 0 0 cos \u03021 \u2212 sin \u03021 0 sin \u03021 cos \u03021 and Q\u0302 \u03022 = 1 0 0 0 cos \u03022 \u2212 sin \u03022 0 sin \u03022 cos \u03022 3 From Eqs. 2 and 3 , moreover, e\u03022 = 0 0 1 e\u03023 = 0 \u2212 sin \u03021 cos \u03021 e\u030232 = 0 \u2212 sin 2 cos \u03022 4 Upon substitution of Eq. 4 into Eq. 1 , one obtains \u03022 = 2 \u2212 2 3 2 cos \u03021 + 2 5 32 3 2 Journal of Mechanical Design rom: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess.as tan \u03022 = 3 sin \u03021 3 cos \u03021 \u2212 2 6 Thus, in the Euclidean space of Fig. 1 a , and taking into account that \u030232= 32+ V32, \u03021= 1+ a1, and \u03022= 2+ b2, Eq. 5 gives 32 and V32 in the forms 32 = \u00b1 3 2 \u2212 2 3 2 cos 1 + 2 2 V32 = 3 2a1 sin 1 32 7 Equation 6 , in turn, gives 2 and b2 in the forms tan 2 = 3 sin 1 3 cos 1 \u2212 2 b2 = 3 2 \u2212 3 2 cos 1 32 2 1 8 Moreover, Eq. 7 can be conveniently expressed as 32 = \u00b1 3 1 \u2212 2k cos 1 + k2 V32 = k 3a1 sin 1 \u00b1 1 \u2212 2k cos 1 + k2 9 Equations 8 , in turn, can be expressed as tan 2 = sin 1 cos 1 \u2212 k b2 = 1 \u2212 k cos 1 1 \u2212 2k cos 1 + k2a1 10 where k is the transmission ratio k= 2 / 3, which is negative for external gears and positive for internal gears",
            " At the reference configuration, namely, that at which all dis- placement variables vanish, the X\u03023 axis is assumed coincident with the X\u0302 axis of Fd. Thus, using Eqs. 15 \u2013 17 , the pitch surface Pd is expressed in line coordinates by s\u03023 = \u2212 sin sin \u2212 cos sin cos \u2212 d sin cos cos cos sin 18 where d=b2\u2212a1 and = 2\u2212 1. In point coordinates, one has r3 , = d cos \u2212 sin 0 + \u2212 sin sin \u2212 cos sin cos 19 which expresses the pitch surface P3 in frame F3, as considered in Euclidean space. Thus, in the Euclidean frame OXYZ of Fig. 1 a , henceforth referred to as Fe, 796 / Vol. 128, JULY 2006 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess.as r3 , Fe = d cos sin cos 1 \u2212 sin sin 1 \u2212 sin sin cos sin cos 1 \u2212 cos sin 1 cos sin sin 1 + cos cos 1 + a1 0 0 20 because of the translation a1 along the X axis and the rotation 1 about the Z axis. Therefore, Eqs. 14 and 20 represent in Euclidean space the hyperboloid pitch surfaces P2 and P3 of the driving and driven gears, respectively. Figures 3\u20135 are included as a means of validation of the proposed formulation",
            " The image on the dual sphere S\u0302 of the pitch surface P4 of the rack is a polode given by s\u03024 \u0302 = S\u0302T \u0302 Q\u0302 \u03022 \u2212 \u0302 k\u0302 29 where the dual rotation matrices S\u0302 \u0302 and Q\u0302 \u03022\u2212 \u0302 are given by S\u0302 \u0302 = cos \u0302 \u2212 sin \u0302 0 sin \u0302 cos \u0302 0 0 0 1 30 and 0 mm and for k varying in the range 10 with both hyperboloid pitch surfaces for k=\u22121 Transactions of the ASME hx?url=/data/journals/jmdedb/27829/ on 06/12/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F the dual angle \u0302= + z4 representing the rotation about the Z\u03024 axis of the crown-rack 4, as attached to the frame F4, and \u0302= + b2, with = 2+ /2 giving the position of the dual unit vector e\u03024 in dual space, as shown in Fig. 1 b . At the reference configuration, frame F4 is assumed with the X\u03024 axis coincident with the X\u0302 axis of Fd. Thus, substituting Eqs. 30 and 31 into Eq. 29 , and expanding the equation thus resulting, the pitch surface P4 of the rack can be expressed in line coordinates as Journal of Mechanical Design rom: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess.as s\u03024 = sin cos 0 + z4 cos \u2212 sin 0 32 where the primal part expresses the unit vector s4 , while the dual part its moment s40 with respect to the origin O4. In point coordinates, one has r4 , = 0 0 \u2212 z4 + sin cos 0 33 which expresses P4 in F4, as considered in the Euclidean space of Fig. 1 a . In frame Fe, Eq. 33 takes the form r4 , Fe = z4 0 sin \u2212 cos + sin cos cos cos sin + b2 0 0 34 because of the translation b2 along the X axis and the rotation about the Z axis. JULY 2006, Vol. 128 / 799 hx?url=/data/journals/jmdedb/27829/ on 06/12/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F Moreover, referring to the dual sphere S\u0302 of Fig. 1 b , the rota- tion \u0302 of the polode of the crown-rack 4, which is a circumference in dual space, can be expressed as a function of the rotation of the driving gear 2, namely, \u0302 = \u2212 sin \u03022 35 where the dual angle \u03022 gives the orientation of the ISA in dual space. Upon expansion, Eq. 35 yields = \u2212 sin 2 z4 = \u2212 b2 cos 2 36 which expresses the rotation and the translation z4 as functions of the rotation of the driving gear 2 in Euclidean space. Equations 34 and 36 give the helicoid pitch surface P4 of the rack for the relative screw motion between any pair of external or internal skew gears"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003386_physrevlett.94.224102-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003386_physrevlett.94.224102-Figure2-1.png",
        "caption": "FIG. 2. Sample trajectories of the particle with respect to the motion of the cell for (a) the parabola driven at a frequency of 5.4 Hz, (b) the wedge at 6.6 Hz, (c) the hyperbola at 4.5 Hz, and (d) the hyperbola at 5.8 Hz.",
        "texts": [
            " We can then use this energy to calculate a maximum possible value for the height of the collision ymax, if all of the energy were potential energy, and a maximum possible tangential component of the velocity vmax t , for the particle if all of the energy were kinetic: ymax E mg v2 2g y (1) vmax t 2E m s v2 2gy q : (2) Note that this phase space projection must lie under the envelope given by plotting y=ymax as a function of v=vmax, where v is the total velocity of the particle after the collision. It is helpful to decompose the velocity into normal and tangential components relative to the local surface where the collision occurs. A completely stable period-one orbit for a symmetric boundary would have a zero tangential velocity component, each collision occurring normal to the local surface. Figure 2 shows sample trajectories of the particle\u2019s motion within a particular boundary. The trajectories shown here depict the motion of the free particle relative to the motion of the cell. Those portions of the trajectories where the slope of the ballistic motion changes while the free particle is in flight correspond to moments where the velocity of the cell changes direction. Figure 2(a) demonstrates the characteristic stable motion of the particle within the parabola driven at 5.4 Hz. As the driving frequency (and therefore energy) is increased or decreased, the average orbit moves up or down, respectively, within the parabola. The inelasticity and surface roughness allow the particle to move from one nearby stable orbit to another over long periods of time at fixed driving. Figure 2(b) shows a sample trajectory of the particle within the wedge when driven at a frequency of 6.6 Hz. The motion of an elastic billiard within a wedge is dependent upon the half vertex angle of the wedge. For half angles below 45 degrees, coexisting stable and unstable motion can occur [2,4]. For our half angle of 28.5 degrees, we observe this unstable motion as the inelastic particle is repeatedly driven toward the top of the boundary. In Fig. 2(c), we present a sample trajectory of the particle contained within the hyperbolic boundary when driven at a frequency of 4.5 Hz. Interestingly, the particle\u2019s motion is not stable, and the particle explores the phase space over longer periods of time. Figure 2(d) shows a trajectory of the particle within the hyperbola when the frequency has been increased to 5.8 Hz. The times of flight 2-2 between collisions are approximately 0.041 and 0.122 s for a half driving period of 0.086 s, indicative of a period-two orbit over brief time periods. However, the noise present in the system, combined with the inelasticity of the particle, causes the particle to quickly transition to unstable behavior and to be driven to the top of the hyperbola, similar to the case of the wedge"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000016_s0003-2670(99)00414-6-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000016_s0003-2670(99)00414-6-Figure3-1.png",
        "caption": "Fig. 3. Schematic representation of the sensing mechanism for polymer stabilized emulsion systems. s represents the plasticizer droplets containing the chloride-selective ionophore (I). {I\u00b7Cl}\u2212 represents the ionophore/chloride complex in the plasticizer.",
        "texts": [
            " Due to its nitrile-containing hard blocks the hydrogel is capable of stabilizing the resulting plasticizer droplets without the need for adding an emulsifier. The plasticizer droplets were estimated to have an average diameter of about 1 mm measured by an optical microscope. Another parameter to be considered is the hydrophilicity\u2013lipophilicity balance (HLB) of the sensor membrane and the dye contained in it. If the dye is too hydrophilic it leaches out of the hydrogel, if too lipophilic, the dye is mainly located in the plasticizer and no co-extraction can occur. The response mechanism is schematically illustrated in Fig. 3. The hydrogel surrounds the lipophilic plasticizer droplets containing the chloride-selective ionophore. The dye (D+) is positively charged and solvatochromic. Both the fluorescence intensity and the maxima of excitation and emission are affected by changes in polarity. If the membrane is exposed to chloride, it will be selectively extracted into the plasticizer droplets to form a complex with the ionophore. Simultaneously, the dye is co-extracted from the hydrogel into the lipophilic plasticizer in order to warrant electroneutrality"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000286_1.2834124-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000286_1.2834124-Figure1-1.png",
        "caption": "Fig. 1 Equivalent geometry",
        "texts": [
            " The accuracy were analyzed by comparisons with numerical results of an evaluation set and CDDT's expressions under pure rolling and/ or sliding condition. The results showed that the new expres sions have satisfactory accuracy and potential application to engineering analysis and design. 2 Theory 2.1 Geometry. In some mechanical transmission sys tems, such as angular contact bearing and variable-speed trac tion drive system, the two mating surfaces can be represented or simplified as a plane and an equivalent ellipsoid having prin cipal radii R^,, Ry, (Fig. 1). The principal axes of the contact ellipse for dry contact can be determined by Hertzian expres sions. b = (6\u00a3_FR/nkE')'\" (1) where R is given by the relative curvature sum of the principal radii of the equivalent ellipsoid. i -_L _L R ~ R, R,. (2) and (\u0302 is the complete elliptic integral of the second kind repre sented by. \u2014 ) sin^ 0 d4> (3) where k is the normal ellipticity ratio given by the approximate expression, ' \u0302 iff If the lubricant entrainment velocity at the center of contact ellipse is inclined at an angle 9 to the minor axis of the contact ellipse, it is convenient to portray solutions in terms of the curvatures of the surface of the equivalent ellipsoid in the en training direction 1 /R,, and side-leakage direction 1 //"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000920_s1474-6670(17)48874-4-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000920_s1474-6670(17)48874-4-Figure1-1.png",
        "caption": "Figure 1: CA RIN A re-entry capsule",
        "texts": [
            " Then the closed loop system exhibits stable behaviour and insensi tivity with respect to disturbances and variations of the satellite parameters avoiding the drawbacks of high gain systems such as peaking phenomena that, due to the control limit.ations described above, are not admissible for the spacecraft actuators. More over, the system state is in a prescribed neighbour hood of the sliding manifold at any time. The pro posed control algorithm is then applied to a possible configuration of the CARINA satellite. CARINA (see Fig. 1) is a new retrievable unmanned capsule developed by ALENIA SPAZIO under ASI contract for micro-gravity experiments. Its operative phase has a nominal duration of five days, with the cap sule in a circular Low Earth Orbit (300 km) nearly equatorial (inclination 2.9\u00b0). The attitude control is devoted to communication link purposes and to put the capsule nose in upwind direction as to obtain a stabilizing effect from the aerodynamic torques due to the capsule shape. Simulations are performed by using the ESA-I\\1IDAS dynamic simulator in pres ence of athmospheric disturbances and corrupted Earth-magnetic field measures"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001302_jmor.1052070111-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001302_jmor.1052070111-Figure6-1.png",
        "caption": "Fig. 6. Graphs showing direction of elongation of free margins. The abscissa is the value L and the ordinate is the ratio L to D measured as illustrated in the diagram at upper right (6. Fig. 5). A Idealized bilaterally symmetric free margins. Free margins with uniform curvature are plotted in relation to a solid curve of equation 3. Ones elongated perpendicular to the boundary l i e are shown above the curve and ones inflated parallel to it are shown below it. B, C: Free margin values for representative gastropods in relation to curve of equation 3. Free margins of some genera are depicted. B Prosobranchs of group 1. 1, Lunella; 2, Vittim; 3,",
        "texts": [
            " The axis of L is running normally from the midpoint of the boundary line ( M P ) , and the value D is equal to the radius of the circle (DJ. Thus, D: = (L - DJ2 + B2 (1) where B is the half length of the boundary line. The ratio L to D is obtained by substituting equation 1 into the value D. (2) When we use the value B as a unit length in the measurement, equation 2 is rewritten as a function of the value L. (3) Uniformly curved free margins follow this equa- L/D = (2L2)/(L2 + B2) L/D = (zL~) / (L~ + 1) tion. Equation 3 is graphed as a solid line asymptotically approaching the value L/D = 2 in Figure 6A-C. Since the unit length is the half length of the boundary line, the value L increases as the overlap zone decreases. In the infinitesimal overlap zone, L/D = 2 because the free margin becomes a circle. A free margin elongated normally to the boundary line has a value D less than D, (e.g., D, in Fig. 5) and L/D > equation 3. On the contrary, a free margin inflated parallel to the boundary line has a larger value D (e.g., D, in Fig. 5) and L/D < equation 3. Therefore, the L/D values can be used as a criterion of the direction of the free margin elongation",
            " C : Pulmonates of group 1.1, Satsuma; 2, Planorbis; 3, Camenella; 4, Ariuntu; 5 , Polymita; 6, Phuenicobius; 7, Plectotropos; 8, Hens: 9, Leucochrou; 10, E ~ h u i l ~ ; 11, Pupuina; 12, Fruticicolu; 13, Anguispiru; 14, Ryssotu; 15, Pedinogyru; 16, Polygyru. ary line. However, the free margins of all samples are obviously not so inflated that the criterion L/D cannot be applied in the meaning stated above, and furthermore almost all free margins have the value L/D higher than those of equation 3 (Fig. 6B,C). This indicates that their outlines are elongated in the direction opposite to the overlap zone. In other words, both sides of free margins are flatter than their middle portions. The only exception is for the genus Heris, for which the L/D value is located below the curve of equation 3. However, the shape of its outer lip is neither elongated parallel to the overlap zone nor uniformly curved. The less symmetric shape of its free margin may be a reason why its ratio is located below the curve"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000761_s0890-6955(97)00059-x-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000761_s0890-6955(97)00059-x-Figure5-1.png",
        "caption": "Fig. 5. Drive and the counterweights using result 9.",
        "texts": [],
        "surrounding_texts": [
            "The optimum balance of the drag-link drive with adding disk counterweights for minimizing the shaking force and shaking moment is studied in this paper. For the multi-objective optimization, the two-phase optimization technique is proposed. Excepting the balancing effects, their effects on the flywheel and brake of using the balancing designs are also evaluated. Based on the results, the following points are concluded. 1. The two-phase optimization technique starts with an initial estimate, but generates a few feasible designs, and it is quite easy to use. It is also shown that the results obtained with the technique are all better than those using the design criterion (CV) as the objective function in phase one, which is the way that the traditional technique is used. 2. When adding disk counterweights on links 2 and 4, the total balancing effect of result 12 shows that CV is reduced from 4 to 2.0231 and there is a 49.4% reduction; however the maximum difference of the kinetic energy is increased 14.4%, the maximum kinetic energy is increased 18.9%. 3. Comparing the results of with and without the tangent constraints, the balancing effects have only small differences, but the counterweights of those with the constraints are smaller, thereby they are better. 4. Comparing the results of adding counterweights on: (1) link 2, (2) links 2 and 4, and (3) links 2, 4 and 5, the CV values are reduced 25.2%, 49.4% and 51.2% respectively. If the amounts of added mass are considered, then result 12 obtained in case (2) has the greatest effect/mass ratio and it is the most cost-effective design. Acknowledgement\u2014The authors are thankful to the National Science Council of the Republic of China for supporting this research under grant NSC 82-0401-E006-450."
        ]
    },
    {
        "image_filename": "designv11_24_0002864_0301-679x(87)90042-9-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002864_0301-679x(87)90042-9-Figure3-1.png",
        "caption": "Fig 3 Computed pressure and displacement distribution",
        "texts": [
            " The matched steady state solutions for nodal pressures, obtained for the modified film geometry, were used to determine the static and dynamic performance characteristics 5 . Results and discussions To check the validity of the computer program and solution algorithm, performance characteristics were computed for a three-lobe journal bearing, taking the deformation coefficient ~ as zero. The static and dynamic performance characteristics obtained for Vp = 0.5, e-c = 0.3 and ~ = 0, were compared with published results 8'9. These results compare well. Fig 3 shows the computed displacements of the interface of the fluid film and bearing liner and corresponding pressure distributions for deformation coefficients f = 0.1 and = 0.5 and e-c = 0.3. The pressure curves in each lobe indicate that peak pressure decreases with increase in deformation coefficient, and the positive pressure zone increases at low deformation coefficients. However, at the large deformation coefficient the positive pressure zone is reduced. A similar trend was observed by Carl 1\u00b0 in his experimental investigations for circular journal bearings"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000539_bf00239872-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000539_bf00239872-Figure2-1.png",
        "caption": "Fig. 2. Musculo-skeletal model of the ankle extensor muscle. Me, External torque; F1 x d, internal torque; F, equivalent extensor force; ~b, articular angle;/3, angle made by the lever arm (length d) and Achilles tendon; \u00a9, centre of rotation of the ankle",
        "texts": [
            " 6 describe adequately the behaviour of the experimental B factor determined for each muscle group, the af parameter was determined by fitting the theoretical equation with the experimental B factor values from Eq. 13. isometric actions, and 1-min rest period between each isokinetic action. The ambient nature was kept constant during all experiments (19 \u00b0 C). Biomechanical analysbs. To determine F and V from torque and angular velocity, it was necessary to use a musculo-skeletal model. For the ankle architecture, the model considered the plantar arch as a rigid element the front end of which was connected to the Achilles tendon (Martin et al. 1993) (Fig. 2). The tendon transmitted effort to extend the mobilized segment around an axis that ran through the medial maUeous. The force IF(x, v)] de- F igure 4 represen ts the theore t ica l va r ia t ion of B* factor as a func t ion of V*, according to Eq. 7. Several curves are ob t a ined by varying the af p a r a m e t e r between 0.1 and 0.6 with i nc remen t s of 0.1. F o r all relat ionships, the B* factor decreases as the rate of shorten ing increases, and the grea ter the af the lower are bo th the slope of the curve and B* at a given shor tening velocity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002472_robot.2002.1014811-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002472_robot.2002.1014811-Figure8-1.png",
        "caption": "Figure 8: Structure of gripper.",
        "texts": [
            " Therefore, our problem can be summarized as follows: minimize z = ll+ll, subject to C f i k 2 m I I f i k I I - 1 (i = 3\u20194; k = l , . . . ,4) There are several algorithms to solve a nonlinear programming problem under certain constraints. Among them, we take the recursive quadratic programming approach[2]. The detail of the algorithm is omitted due to the space limitation. 4.4 Grasping force Since our humanoid hand has the 1-DOF gripper, we must take a special care when determining the joint torque of the hand. Suppose force f and moment n are applying to the hand. As shown in Figure 8, let f be decomposed into the axial component f, and other components perpendicular to it fz and f y . Moment n can be decomposed into nz, ny and n, in the same way. Considering the structure of the hand, the hand should exert the following torque to balance each component o f f and n: a a (34) (35) (36) Th1 = alfacl+ ;In& Th2 = aIfyl+ ;lnzl, alfzl I.& \u2019 7h3 = - (37) Pa where a denotes the radius of the gripper, b denotes the width of the gripper, and fia = P a / S is the maximum static friction coefficient at the gripper with an appropriate safety margin S (> 1)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002157_027836498900800302-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002157_027836498900800302-Figure5-1.png",
        "caption": "Fig. 5. A series of workstation coordinate frames.",
        "texts": [
            " Kinematics , To generate a robot program, we must find the tool position and orientation at each point along the weld seam trajectory. Mathematically stated, we wish to at UNIVERSITE DE MONTREAL on June 20, 2015ijr.sagepub.comDownloaded from 37 find the homogeneous coordinate frame F~ of the tool relative to and projected onto the robot base coordinate frame FR . The frame F~ is defined by the homogeneous coordinate transformation HAG which takes us from Fg to F~ . We define the following homogeneous coordinate frames (see Fig. 5): 1. FR, the robot base frame 2. FT, the positioning table frame 3. FB, the workpiece frame 4. Fc, the weld seam frame 5. FG, the tool frame The intermediate homogeneous transformations H,~,T, HT,B, HB,~, He,G can be determined. We can then find the net transformation HR,G as a product of these intermediate transformations, Let us consider the positioning table to be a kinematic chain with n links connected by joints. We can define the transformation Hi-I,; from link i - 1 to link i of the table using the Denavit-Hartenberg (1955) matrix, which is a function of known link parameters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003135_1.2389233-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003135_1.2389233-Figure7-1.png",
        "caption": "Fig. 7 Free body diagram of driver belt element",
        "texts": [
            " 5 Free body diagram of driver band pack Transactions of the ASME 28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use s t a b f l t a f t d i r m J Downloaded Fr equently gives rise to variations in the band pack tensile force T , as illustrated in Fig. 5. As the belt traverses the pulley wraps, he compressive force Q between the elements builds up. In ddition to the normal and friction forces from the band pack, the elt element is also subjected to the normal and frictional forces rom the pulley, as depicted in Fig. 7. Since the belt slips along the ine AD refer to Fig. 4 , the friction force acts along this line and hus is composed of two components one in the axial direction nd the other in the rotational plane ABE . In addition to the orces acting on the belt, Figs. 6 and 7 highlight the forces and orques acting on the pulley. Similar free-body analysis can be one on a belt segment engaged with driven pulley under the nfluence of load torque, l. The constraint of inextensibility of the belt implies that the time ate of change of length of any infinitesimal element of belt s ust be zero, i",
            "org/ on 01/ Now, summation of forces in the normal and tangential directions, n , , refer to Fig. 5 for the band pack yields the following equations respectively: Fn: \u2192 \u2212 dF + Td = bds a\u0304 . n F : \u2192 adF \u2212 dT = bds a\u0304 . Using A1 , A2 , and 11 , for an infinitesimal time step, the above equations for band pack can be simplified to obtain: Fn: \u2192 T \u2212 F\u0307 cos r\u0307 = b \u2212 r\u0308 \u2212 r\u03072 cos + 2r\u0307\u0307 + r\u0308 sin F : \u2192 aF\u0307 \u2212 T\u0307 = br\u0307 r\u0308 \u2212 r\u03072 tan + 2r\u0307\u0307 + r\u0308 A5 Similarly, summation of forces in the tangential and normal directions refer to Fig. 7 for the belt element yields the following quations respectively: Fn: \u2192 \u2212 Q + cos r\u0307 F\u0307 \u2212 2N\u0307 sin cos \u2212 b cos s cos + = e \u2212 r\u0308 \u2212 r\u03072 cos + 2r\u0307\u0307 + r\u0308 sin F : \u2192 Q\u0307 \u2212 aF\u0307 + 2N\u0307 sin sin \u2212 b cos s sin + = er\u0307 r\u0308 \u2212 r\u03072 tan + 2r\u0307\u0307 + r\u0308 A6 t is to be noted in the above equations that the acceleration of the elt element is same as that of the band pack as their center of asses are assumed to coincide. Neglecting the dynamics due to sheave inertial effects and suming the forces on the movable pulley sheave in the axial direcion results in the following equation: Fz = 0 dN cos + b sin s A7 umming all the moments acting on the driver pulley yields, M0: \u2192 I\u0307 = in + 0 2 br cos s sin dN A8 Except for a few equations, the governing equations of motion f the driven system are similar to the equations of driver system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003854_tmech.2005.852450-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003854_tmech.2005.852450-Figure1-1.png",
        "caption": "Fig. 1. Analytical model.",
        "texts": [
            " On the other hand, some of authors propose a control method for an underactuated two-link manipulator without state feedback of the free joint using the nonlinear characteristics of the bifurcations produced in the free link under the high-frequency excitations [12]. The proposed method is a unified strategy based on the concept of bifurcation control [13], [14] and can easily be modified to the motion control method of the free link for positions other than the upright position. The underactuated manipulator and control strategy in the previous study are shown in more detail as follows. The system is a two-link underactuated manipulator similar to that in the present study as shown in Fig. 1 (only the gravity effect is different between the previous and present manipulators: the present manipulator can be moved on the vertical plane, but the previous manipulator can be moved on the plane inclined from the horizontal plane with a small angle). The first link is attached to the first joint with an actuator and the angle \u03b81 is be set as the control as \u03b81 = a\u03b81 cos \u03c9t + \u03b81off , where the first term is 1083-4435/$20.00 \u00a9 2005 IEEE a measure of the high-frequency excitation to the second link and the second term expresses the configuration of the first link with respect to the direction of gravity (hereafter, \u03c9 and \u03b81off are called \u201cexcitation frequency\u201d and \u201coffset of the excitation\u201d, respectively)",
            " The sets of the stable equilibrium points construct surfaces in the parameter space of the excitation frequency and the offset of the excitation. Besides the discussion on a method to put the state of the free link on the surfaces, we clarify the reachable and stabilizable area of the free link without state feedback of the free joint. Furthermore, compared with experimental results, the validity of the theoretically obtained stabilizable and reachable area is confirmed. We consider a two-link underactuated manipulator as shown in Fig. 1. The manipulator moves on the vertical plane. The active (first) joint has an actuator which can provide torque \u03c4 for the first link and control the position of the first link easily. On the other hand, the free link (second link) cannot be controlled directly because the free joint (second joint) lacks not only an actuator but also a sensor. In such a circumstance of the second joint, we cannot utilize the state feedback of the second joint for the motion control of the second link. Therefore, according to the method proposed in the previous study [12], we perform the motion control of the free link based on the actuation of the perturbation of the bifurcations in the free link which is produced under high-frequency excitation",
            " We can numerically obtain the equilibrium points of the tip of the free link from (8) for combinations of \u03c3 and \u03b81off . Furthermore, their stabilities are examined by (7). For the excitation frequency range between 0 and \u221e, all stable equilibrium points are plotted as Fig. 10, where \u03b81off is changed in the range from 0 to \u03c0. The reachable and stabilizable area in this figure expresses one of the cases when we rotate the active (first) link counterclockwise. The origin of this figure is the origin O in Fig. 1. This area and the reachable and stabilizable area for the case when we rotate the active link clockwise, i.e., for the range of \u03b81off from 0 to \u2212\u03c0, are symmetric with respect to the x-axis. As a result, the union of these areas is the reachable and stabilizable area of the tip of the free link. Furthermore, taking into account the limitation of the power of the motor used in the subsequent experiment, i.e., the limitation of the excitation frequency in the subsequent experiment (the highest excitation frequency is \u03c9max/(2\u03c0) = 50 Hz), the reachable and stabilizable areas are modified as Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003135_1.2389233-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003135_1.2389233-Figure6-1.png",
        "caption": "Fig. 6 Forces of belt element on driver pulley sheave",
        "texts": [],
        "surrounding_texts": [
            "om: http://computationalnonlinear.asmedigitalcollection.asme.org/ on 01/ pulley deformation. The following equations describe the pulley deformation effects as introduced by the model in Fig. 3 = 0 + 2 sin \u2212 + 2 R tan = r tan 0 \u2212 tan \u2212 0 1 It is to be noted that although the amplitude of the variation in the pulley groove angle is small, it is not constant during shifting transients. Sferra et al. 17 proposed the following correlations for the variation and the center of the pulley wedge expansion, , Fig. 5 Free body diagram of driver band pack Transactions of the ASME 28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use s t a b f l t a f t d i r m J Downloaded Fr equently gives rise to variations in the band pack tensile force T , as illustrated in Fig. 5. As the belt traverses the pulley wraps, he compressive force Q between the elements builds up. In ddition to the normal and friction forces from the band pack, the elt element is also subjected to the normal and frictional forces rom the pulley, as depicted in Fig. 7. Since the belt slips along the ine AD refer to Fig. 4 , the friction force acts along this line and hus is composed of two components one in the axial direction nd the other in the rotational plane ABE . In addition to the orces acting on the belt, Figs. 6 and 7 highlight the forces and orques acting on the pulley. Similar free-body analysis can be one on a belt segment engaged with driven pulley under the nfluence of load torque, l. The constraint of inextensibility of the belt implies that the time ate of change of length of any infinitesimal element of belt s ust be zero, i.e., d dt s = 0 i . e. ournal of Computational and Nonlinear Dynamics om: http://computationalnonlinear.asmedigitalcollection.asme.org/ on 01/ d dt r cos = 0 3 Further simplification of 3 yields, r\u0307 r + \u0307 tan + 1 d dt = 0 4 Now, for an infinitesimal time step, introducing tangent approximation further reduces Eq. 4 as, r\u0307 r + \u0307 tan + 1 d dt = 0 r\u0307 r + \u0307 tan + \u0308 \u0307 = 0 5 Also, for an infinitesimal time step, tan r\u0307 r\u0307 6 Incorporating 6 into the final equation of 5 results into the following constraint equation for belt inextensibility: r\u0307 \u0307 + \u0307 + r\u0308 = 0. 7 Since the belt is treated as an inextensible strip, the total length of the belt refer to Fig. 9 must be constant. The constraint of constant belt length L can be mathematically expressed as dL dt = 0, where L = 0 rd cos + 0 r d cos + 2d cos = sin\u22121 r \u2212 r d 8 The constraint equation 8 kinematically couples the driver and driven systems to each other. Since the flexural effects of the metal belt are assumed to be negligible, it is reasonable to assume that the belt always exits and enters the pulley tangentially. Using this, the wrap angles can be found to be = \u2212 2 sin\u22121 r \u2212 r d = + 2 sin\u22121 r \u2212 r d 9 The relative velocity between a belt element and the pulley can be readily obtained as, v\u0304rel = r\u0307er + r se s = \u0307 \u2212 Also, tan = r s r\u0307 10 It is to be noted that the relative velocity, v\u0304rel, as given by Eq. 10 is not the actual sliding velocity of the belt element. It only rep- JANUARY 2007, Vol. 2 / 89 28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use r l s s p T o t I s d I t r p s e t t Q S n o M w f 9 Downloaded Fr esents the relative velocity between the belt element and the puley in the rotational plane ABE refer to Fig. 4 . Since the belt lides on the sliding plane refer to Fig. 4 , the actual or true liding relative velocity, vs, between the belt element and the ulley is, in fact, given by, vs = r\u0307 sec2 + tan2 , tan s = tan cos he absolute acceleration of the belt element, a\u0304, can be easily btained from the absolute velocity v\u0304 of the belt element, and is hus expressed as a\u0304 = dv\u0304 dt = r\u0308 \u2212 r\u03072 er + r\u0308 + 2r\u0307\u0307 e 11 n addition to the aforementioned assumptions, the following asumptions are also made in the analysis to aid the solution proceure: \u2022 Uniform pressure distribution dN /rd between the belt and the pulley; \u2022 Assume is negligible and \u0307 \u0307. t is reasonable to assume to be a small quantity as it implies hat the rate at which belt pitch radius changes is smaller than the ate at which belt traverses around the pulley. Moreover, it is lausible that the rate at which the slope angle changes is maller than the rate at which the angular position of the belt lement changes. Under all these assumptions, the following equations refer to he Appendix for detail describe the dynamic interactions beween the belt element and the driver pulley: Kinematics r\u0307 r\u0307 \u0308 = \u2212 r\u0307\u0307 r 12 Driver band pack T\u0307 = aF\u0307 \u2212 br\u0307r\u0308 T\u0307 \u2212 F\u0307 = b \u2212 rr\u0308\u0307 + r2\u03073 + r\u03072\u0307 13 Driver belt element \u02d9 \u2212 aF\u0307 + 2N\u0307 sin \u2212 b cos s sin \u2212 b cos s cos = er\u0307r\u0308 \u2212 Q\u0307 + F\u0307 \u2212 2N\u0307 sin \u2212 b cos s cos + b cos s sin = e \u2212 rr\u0308\u0307 + r2\u03073 + r\u03072\u0307 14 Driver pulley axial force Fz = N\u0307 \u0307 cos + b sin s 15 ince the driver pulley runs at a constant angular speed, the pulley ormal force N can be obtained by summing the torques acting n the driver pulley, thereby, yielding, N\u0307 = \u2212 in\u0307 2 br cos s sin 16 oreover, the constraint of the constant belt length, i.e., Eq. 8 , hich couples the driver to the driven system, reduces to the ollowing form: 0 / Vol. 2, JANUARY 2007 om: http://computationalnonlinear.asmedigitalcollection.asme.org/ on 01/ r\u0307 + r\u0307 = 0 17 Similar analysis of a belt element engaged with driven pulley under load torque conditions yields the equations for the driven system dynamics refer to the Appendix . The pulley flexibility causes the belt pitch radius to change refer to Fig. 3 , which is accounted for by introducing the following equations: = 0 + 2 sin \u2212 + 2 R tan = r tan 0 \u2212 tan \u2212 0 R\u0307 R = r\u0307 r \u2212 \u0307 sec2 \u2212 0 tan 0 \u2212 tan \u2212 0 \u2212 \u0307 sec2 tan \u0307 = \u0307 2 sin \u2212 + 2 + 2 \u0307 \u2212 \u0307 cos \u2212 + 2 18 The time rates of change of amplitude, , and of the center of wedge expansion, , can be obtained from Eq. 2 . There are 14 primary unknowns seven each for driver and driven in the CVT model, as R , ,T ,Q ,F ,N , . Since the driver pulley speed is maintained as a constant, the driver system has only six unknowns. Equations 12 \u2013 14 and 16 can be solved simultaneously to obtain the time histories of the six unknown driver system parameters. Later, appropriate modifications are introduced in the form of pulley bending equations to take flexural effects into account. Knowing the driver system parameters, the driven system solution procedure can be initiated using the constraint Eq. 17 . Almost all the models, except a few, mentioned in the literature use the classical Coulomb-Amonton friction law to model friction between the contacting surfaces of a CVT. The friction phenomenon described by this law is inherently discontinuous in nature. It is a common engineering practice to introduce a smoothening function to represent the set-valued friction law. However, certain friction-related phenomena like chaos, limit-cycles, hysteresis, etc., are neither easy to detect nor easy to explain on the basis of classical Coulomb-Amonton friction theory. It is also quite feasible to have a lubricated contact Stribeck-type friction characteristic in a belt CVT in order to reduce the losses due to wear and thermal effects. Since it is difficult to monitor friction experimentally during the running conditions of a complex nonlinear system e.g., a CVT , mathematical models of friction give insight into the different dynamic maneuvers that a system can undergo. With the aim to understand friction-related dynamics, two different mathematical models of friction were incorporated to describe friction between the belt element and the pulley. Figure 10 depicts the friction characteristics described by these mathematical models. The coefficient of friction between the belt element and the pulley is governed by the following relationship: Case 1: b = a + bo \u2212 a 1 \u2212 e\u2212 vs /b Case 2: b = bo 1 \u2212 e\u2212\u0304 vs 1 + fr \u2212 1 e\u2212\u0304 vs 19 The coefficient of friction mentioned in case 1 describes the classical Coulomb-Amonton friction law which aptly captures the dynamics associated with kinetic friction and is most commonly referenced in the literature. However, the coefficient of friction in case 2 is more detailed as it not only captures the dynamics associated with kinetic friction, but also captures the dynamics associated with stiction- and Stribeck-effects which are prominent under dry and lubricated contact conditions, respectively ."
        ]
    },
    {
        "image_filename": "designv11_24_0003122_acc.2003.1239789-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003122_acc.2003.1239789-Figure2-1.png",
        "caption": "Figure 2: The mechanical subsystem of a S-cam air brake system",
        "texts": [
            " The pneumatic subsystem includes the compressor, the storage reservoirs, the brake lines, the treadle valve and terminates at the brake chamber. The compressor charges up the storage reservoirs and the application of the treadle valve modulates the amount of air provided to the brake chambersthrough two circuits - the primary circuit and the secondary circuit. The advantage of such an.arrangement is that partial braking is possible in the case of failure of one of the two circuits. The ,nwr PrnUdD\" FlgUre 1: A general layout of the air brakc system in trucks mechanical subsystem, illustrated in Figure 2, starts from the brake chamber and includes the push rod, the slack adjuster, the S-cam and the brake pads. Compressed air acts on the brake chamber diaphragm providing a mechanical force that is transmitted to the brake pads through the push rod and the S-cam. 3 The Experimental Setup The experimental test bench at Texas A&M University is essentially the front axle of a tractor. Compressed air is supplied by a compressor and a pressure regulator is used to modulate the pressure ofthe air being supplied to the treadle valve"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000695_7.366334-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000695_7.366334-Figure1-1.png",
        "caption": "Fig. 1. Three-dimensional pursuit situation.",
        "texts": [
            "ig. 1. values, and \u00afis are weighting factors with P \u00afi = 1, reflecting the likelihood of \u00b0 taking on a particular set of values. Let us consider an example, where parametric uncertainty is present in the A matrix of the model A= 26664 0:5 \u00a10:7 0:7 0 0 0:8 0:6\u00b0 0 \u00a11 0 0 0:1 0 0 \u00a1\u00b0 0:4 37775 , B1 = 26664 0:5 0 0 0 0 0 0 0:5 37775 , B2 = 26664 0 0 1 0 0 1 0 0 37775 , C = 2640 0 1 0 0 1 0 0 0 0 0 1 375 , D = 2640 0:2 0 0:3 0 0:3 375 and \u00b0 2 [0:1 0:2]. Since the range of \u00b0 is not particularly large, the augmented Y can take the following form when s= 1 Y = \u00b7 C 0 0 \u00a1D 0 CAc CB1 CA CLD \u00a1D \u00b8 where A= dA(\u00b0)=d\u00b0 at \u00b0 = 0:15. The optimal designs for the 4\u00a3 3 matrix L and the 6\u00a3p matrix [v1 \u00a2 \u00a2 \u00a2vp] are carried out for each p, p= 1,2,3,4,5, where p is the dimension of the parity space P. The bound on the magnitude of the residual, given by the sum of the squares of the p smallest singular values of Y(L), is plotted against p in Fig. 1. It is clear that parity checks on the filtered measurements are more robust. REMARKS Although our method involves a full-order observer, it does not directly relate to another popular failure detection method called the detection filter method. It is conceivable however, if sensitizing residuals to failures [3] is also required by our design criterion, the part of effort toward this goal by our filter should be consistent with the effort made by a detection filter. N. EVA WU Department of Electrical Engineering Binghamton University Binghamton, NY 13902-6000 YUE Y"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001262_0045-7906(93)90039-t-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001262_0045-7906(93)90039-t-Figure7-1.png",
        "caption": "Fig. 7. The 3-D neural network, NBN for task scheduling.",
        "texts": [],
        "surrounding_texts": [
            "Following the derivation of the cost functions for TSP and MTSP in the previous section, we will formulate the cost function for the NBN, such that the lowest cost state of the network corresponds to the best schedule. The function consists of two parts: the physical objective function and the constraint functions. We will select the minimum time as our object function. The following lists all the energy terms of the network. The Et, the objective function, which minimizes the time required to complete all the jobs, is given by: E ~ = ~ vo, l + . (22) \"= i = l l = l C k The energy functions for row and column constraints are given by: \"i \u00b1i vol(vq, i + vol, + v~, 4 ), (23) El = ~i=~11=lj=t/,=l j,=l / I # l /I \u00a2 J . = ~ vijtvi,j,, (24) E~ 2j=l l=, i=Jq=l i I ~ i E3= v~t-n , (25) ~ \\ i = l j = l l = l 1 m E4 = ~j=~Z ~ H ( \u00a3 ) , (26) d l 0 0 0 0 0 0 J2 1 0 0 0 0 0 J3 0 0 0 1 0 0 J4 0 0 0 0 0 0 M a c h i n e 1 s c h e d u l e J1 0 0 1 0 0 0 J2 0 0 0 0 0 0 J 3 0 0 0 0 0 0 'J l 4 1 0 0 0 0 0 M a c h i n e 2 s c h e d u l e i, j, 1, i~, Jr, l~, l 2 are indices. Ck is a constant for scaling; v0~ is the output of the neuron, m: is the operation rate of the j th machine. Li is the ith job length. T o is the time required by thej th machine to complete the ith job. di is the deadline of the ith job. H ( f ) is the Heaviside function with a value equal to one if f > 0; otherwise it is zero. For the projected gradient method, we need to approximate H( f ) , which also needs to be differentiable. We use a high-gain sigmoid function approximation. This approximation is shown in Fig. 9, and it is computed by: where y is a constant. The constraints (23), (24), (25) and (26) are required to form m permutation matrices. They ensure that each job is only assigned to one machine and every machine at least does one job in the whole schedule sequence. Constraint (27) ensures that every machine needs to be assigned one job at time 0. Constraint (28) is to enforce the deadline requirements. Constraint (29) ensures that if the ith job is assigned to the j th machine at time l, then no other job is assigned to the machine until after l + T 0, and also job i I th cannot be assigned before l 2 -1- Ti,j. Again, the constrained optimization problem is converted to an unconstrained one by introducing Lagrange multipliers 2~. As suggested in the MTSP [12] solution, if we also let 2= be the state of an additional seven neurons, then the object is to minimize the total cost function: 7 E = Et + ~ 2~E~. (31) Applying the gradient technique, we can obtain a system of ordinary differential equations: duot [OE, dEe \\ (32) where f , giit, - E ~ , V ~ = l , 2 . . . . . 7. (35) dt By differentiating E, and E , , . . . , ET, w e obtain the neuron differential equations: k duOt=dt not / ' + T 0 - 1 - 2 ' r ~ ~ (vo, t+vot ,+vo, h ) - ) ' 2 ~ vi,j, ? ~k j, = I I, = ] i, = I JU =~J I I # I i I # i 23 ~ v,,j.i,--n + 2 4 [ \u00a3 H ( \u00a3 ) + g H ( f j ) f ) A e -aj)] i t = 1 J l = 1 / I = I - - 2 5 ( i 1 ~ ' ~ 1Jl = 1 ~'iljl l - - m ) 6 ( l - - 1 ) - - ; % H ( g o t ) g 2 l --)'7 h~H(h,) ~ v ,o , ,+h]H(h2) ~ v,,jt 2 , i I = I I L = I 12 i i \u00a2 i 12 # (36) d2~ - E ~ , Vc~=1,2, dt ., 7, (37) T 0, h~ and h2 are defined before and 1 I tanh(U\u00b0/~l, rot = ~ 1 + \\Uo/_J 6 ( / _ 1 ) = { 1 0 l = 1, otherwise. Here the connections between the neurons are not symmetric as in the Hopfield network. So the global convergence is not guaranteed; however, convergence to any suboptimal valid solution is also acceptable for practical purposes. d2~ - E~, V c ~ = l , 2 . . . . . 7. (33) dt"
        ]
    },
    {
        "image_filename": "designv11_24_0002472_robot.2002.1014811-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002472_robot.2002.1014811-Figure3-1.png",
        "caption": "Figure 3: Hand and foot.",
        "texts": [
            " To simplify the problem, we will set the following assumptions: 0 All of links including the torso, arms, and legs are rigid bodies. 0 Each arm has seven degrees of freedom (DOF) (three for shoulder, one for elbow, and three for wrist), whereas each leg has six DOF (two for hip, one for knee, and two for ankle). 0 When focusing only on motions in saggital plane, DOF of arms and legs can be simplified to three (each DOF for shoulder, elbow, and wrist as well as for hip, knee, and ankle). 0 The end-effector of each arm is a one-DOF openclose type hand as shown in Figure 3(a). A single motor simultaneously drives three joints so that the robot can grasp a bar or grip in the environment. When the hand is gripping a bar, grip or any other cylindrical object fixed to the environment, the hand can exert force and moment to any direction within the joint torque limitation and the static friction limitation. 0 The bottom shape of the foot is flat and rectangular as shown in Figure 3@). Reaction forces from the environment can be summarized to four force vectors at the vertices of the foot. The foot slips when none of these forces is within the friction cones. 0 Motions are quasi-static and dynamics is not considered. As shown in Figure 2, a body coordinate frame Cg is attached to the center of gravity of the main body (torso). For notational convention, we assign a number to each limb, i.e., i = 1,2,3,4 for left arm, right arm, left leg, and right leg, respectively. We also assign a number to each joint from the body base to the limb end",
            " Finally we can normalize r by a matrix T, as follows: + = T,T (25) = T,JT (G'tg + (I - G+G)z ) . (26) Matrix T, could be a diagonal matrix each of which diagonal element is the inverse of the maximum joint torque of the corresponding joint. Optimization of joint torque can be realized by changing the internal force component x in eq.(26). 4.2 Friction constraint and joint torque limit Supporting force/moment at each foot, f and n i (i = 3,4), are the summation of reaction forces at the vertices of the foot as shown in Figure 3(b). They can be related as follows: T r = J f e , (i = 3,4) where f ik (k = 1, . . ,4) denote reaction forces at the kth vertex of the left (i = 3)/right (i = 4) foot as shown in Figure 3(b). Skew-symmetric matrices P i k (k = 1, - * ,4) in eq.(28) can be defined similarly to P i in eq.(20). When optimizing the joint torque, friction limit constraint must be satisfied. Friction constraint at feet can be described by the following equation: (30) where e i k denotes a unit vector along with the contact normal of the k-th vertex of the left (i = 3)/right (i = 4) foot, and fir = p f / S is the maximum static friction coefficient with an appropriate safety margin S (> 1). To check the friction constraint given by eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002397_cdc.2001.981134-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002397_cdc.2001.981134-Figure1-1.png",
        "caption": "Figure 1: Dead-zone Model",
        "texts": [
            " Without constructing an inverse dead-zone nonlinearity to minimize the effects of dead-zone, the new approach can be employed to control a class of nonlinear systems preceded by an unknown dead-zone (section 3). The new control law ensures a global stability of the entire adaptive system and achieves both stabilization and strict tracking precision (section 4). Computer simulations were carried out to illustrate the effectiveness of our method. o-7~o3-7o~i-9/oi/sio.oo Q 2001 IEEE 1627 2 Dead-zone Model and Its Intuitive Properties The dead-zone with input v( t ) and output w(t ) is shown in Fig.1 and described by: mT(v(t) - b,) for v ( t ) 2 b, ml(v(t) - br) for v ( t ) 5 br w ( t ) = D(v( t ) ) = 0 for b! < v ( t ) < b, (1) { As stated in [ll], this dead-zone model is a static simplification of diverse physical phenomena with negligible fast dynamics. Equation (1) is a good model for a hydraulic servo valve or a servo motor. The key features of the dead-zone in the control problems investigated in this paper are: (Al) The dead-zone output w( t ) is not available for measurement. (A2) The dead-zone slopes in positive and negative re gion are same, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002067_978-1-4684-8667-4_5-Figure11-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002067_978-1-4684-8667-4_5-Figure11-1.png",
        "caption": "Figure 11. Polarization curves for sulfur dioxide oxida tion on (1) carbon AG-3, (2) graphite TO, and (3) carbon black PM-lOO in 0.5 M H 2S04 \u2022",
        "texts": [
            "j can be represented as follows: A detailed study of the mechanism of sulfur dioxide electrooxida tion was carried out on a pyrographite electrode143 and on a thin floating electrode made of the activated carbon AG-3 and other carbon materials with equally accessible surface.144 The effective value of the standard potential in 0.5 M H2S04 at a pressure PS02 = 98 kPa is -0.65 V on pyrographite and 0.35 to 0.40 Von the activated carbon. Electrocatalytic activity of carbon materials in the reaction of sulfur dioxide oxidation decreases in the series: activated carbon> graphite> carbon blacks> pyrographite (Fig. 11). The anchoring of the acidic oxides on the surface of carbon materials decreases the reaction rate. The reaction order of electrochemical oxidation in the sulfur dioxide concentration depends on the solution composition, being in all cases less than 1. This may be due to adsorption effects or to the fact that adsorbed sulfur-containing particles are subjected Electrocatalytic Properties of Carbon Materials 331 to oxidation. At low concentrations of sulfur dioxide, the coverage is low (OS02\u00ab 1) and the reaction rate is proportional to the con centration in the bulk of the solution"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001274_0005-1098(92)90008-4-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001274_0005-1098(92)90008-4-Figure1-1.png",
        "caption": "FIG. 1. Clockwise (a) and counterclockwise (b) curves in t o.",
        "texts": [
            " For the sake of simplicity, we will assume that ~( t ) exists ~\u00a2t e (t., to), i.e. the denominator of (2) never vanishes in that interval. The curve is said to satisfy the clockwise property in to if cO(t0) < 0. (3) Conversely, the curve is counterclockwise in to if 0 < c\u00a2(to). If (3) holds '\u00a2to ~ ( t , , tb) then we say that F is a clockwise curve. Geometrically, condition (3) means that the center of the curvature is on the right side of ~(t0), the tangent vector to F in F(to)--(X( to) , Y( to) ) , or, equivalently, that the vector ~(t0) rotates clockwise (see Fig. 1). In fact, denoting by W( t )= arctg(YffXt) the phase of ?(t), we have xtY,, - x . E Wt = X2t + y2 ' (4) and the clockwise property (3) amounts to Wt(to) < 0. (5) Given a change of parameter t=t(r) ~\u2022[lr~,rb] such that t ( . ) \u2022 C 2 and t~>0, then it can be verified that c\u00a2(t(r)) = c\u00a2(r), (6) i.e. the definition of curvature does not depend on the parameterization of F. Before ending this section, we provide a global property of clockwise curves which will be exploited in the sequel. Given a value to ~ (ta, tb), let us split the clockwise curve F as follows (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003472_robot.2005.1570310-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003472_robot.2005.1570310-Figure1-1.png",
        "caption": "Fig. 1. Horizontal transport of suspended object",
        "texts": [
            " Since the impulse sequence that cancels the oscillation at each end of the motion consists of impulses spaced at half-period intervals, the impulse sequences may be \u201coverlapped\u201d and convolution of the nominal trajectory with such an impulse sequence will produce non-smooth motions. This is shown in the following example. 1) Example: The experimental setup for this work is the transport of a simply-suspended rigid body with a radius of gyration l = 0.3982 m. This body is moved through a horizontal translation of 1 m in a time duration of 2 s. Fig. 1 shows a schematic of the suspended object. The translational robot and suspended object are identical to a gantry crane. For small \u03b8, the period of oscillation of this suspended object is given by T = 2\u03c0 \u221a g/l = 1.266 s, (1) and this period is longer than half the duration of the motion. If the nominal trajectory for x(t) is a cubic polynomial, convolution of this trajectory with the threeimpulse ZVD impulse sequence [4] yields the velocity input x\u0307(t) shown in Fig. 2. The unshaped velocity input is shown for comparison",
            " To ensure capturing the residual oscillation they used the cumulative objective function in the two load line rotation angles J = \u222b tf +\u2206 tf [ \u03b82 1(t) + \u03b82 2(t) ] dt (3) Time increment \u2206 = 2 sec. The endpoint velocity constraints \u03b8\u03071(tf ) = 0 and \u03b8\u03072(tf ) = 0 were enforced using an equality constraint. Minimization of J using recursive quadratic programming revealed that \u201cthe time required for a solution of this gradient-based approach was dependent on the quality of the initial guess\u201d [19]. 1) Convexity of objective function: It is illustrative to examine the behavior of the quadratic objective function J vs the basis function parameters of Fig. 4 for the system of Fig. 1. With the fixed final time symmetric acceleration profile, the single variable parameter can be considered to be the duration of the acceleration/deceleration pulse tA; trajectory parameters A, tA, tf and motion endpoint conditions x(0), x\u0307(0), x(tf ), x\u0307(tf ) are related by six constraints. The equation of motion for Fig. 1 is \u03b8\u0308 + g l sin \u03b8 = \u2212 1 l x\u0308 cos \u03b8. (4) Using the same numerical values as in Section IIA, the objective function J of (2) was evaluated for a range of acceleration durations tA. The result is shown in Fig. 5. The nonconvexity of J is apparent. A closeup around the global minimum is shown in Fig. 6. Similar behavior was seen for the cumulative objective function of (3). Our own experience confirmed the difficulty in obtaining an optimal result; the numerous local minima in J required a very accurate initial estimate of the trajectory parameters to obtain convergence to the global minmum; this parameter estimate may often be elusive"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003361_j.jmatprotec.2004.12.017-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003361_j.jmatprotec.2004.12.017-Figure3-1.png",
        "caption": "Fig. 3. Tooling arrangement used in flange forming, 1\u2014casing; 2,3\u2014bearing; 4\u2014bolt; 5\u2014pin; 6\u2014shank; 7\u2014weld; 8\u2014ball; 9\u2014specimen; 10\u20143-jaw chuck; 11\u2014plug; 12\u2014tool post; 13\u2014shank; 14\u2014plate; 15,16,17\u2014starin gauges; 18\u2014lathe jaw chuck.",
        "texts": [
            " Commercial purity Aluminum (in the asreceived condition) was used originally received in form of seamless tubes, 23 mm outer diameter and 10 mm inner diameter. Fixed specimen rotating speed (500 rpm) and outward radial tool feed (0.314 mm/rev) were chosen optimized from a recent publication of the authors [7] to get the best surface quality. Specimens having a fixed inner diameter (13 mm) and varying tube initial thickness (t0) of 2, 2.5, 3.0 and 3.5 mm were prepared on a center lathe and finished using a sand p a A v e t f is shown in Fig. 3. The set up is similar to that described in detail in Ref. [6]. The shank carrying the ball-shaped tool was shortened as possible to avoid bending. Self-adjusting was assured using a dial gage to ensure the coaxiality. Strain gage bridge was used to measure the radial force. Fig. 4a gives the maximum radial force values in flanging for different t0 and Ta values. It is clear that the measured flanging load increases as the t0 and Ta increase. This increase is referred to the increasing volume which should be displaced by the tool in this case"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001455_50006-1-Figure5.61-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001455_50006-1-Figure5.61-1.png",
        "caption": "FIGURE 5.61 A MEMS actuator: (a) top view; and (b) side view [30].",
        "texts": [
            " The fabrication process for this structure is shown in Fig. 5.60a-e [30]. The operation of the actuator is as follows: When a uniform field Hex t is applied, it induces a magnetization in the plate and a magnetic torque develops that acts to rotate the plate up, away from the substrate. This rotation is resisted by a restoring torque that results from the torsion of the support beam. The plate rotates to an equilibrium deflection angle ~b where the magnetic and restoring torques are in balance (Fig. 5.61b). To determine ~b we need to compare the two torques. We consider the restoring torque first. This is due to the torsion of the support beam. Since the midportion of the beam is attached to the plate, it does not twist. Therefore, the restoring torque is due to the torsion of the two end portions of the beam (between the plate and the anchor points). Each of these can be considered as a separate beam with length l and cross-sectional dimensions w and t. We assume that both 460 CHAPTER 5 Electromechanical Devices beams obey Hooke's law Tm (~b) = ks~b, where T m is the mechanical restoring torque and k s is the torsional stiffness"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003266_1.2179462-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003266_1.2179462-Figure4-1.png",
        "caption": "Fig. 4 Defining margin against slip",
        "texts": [
            " Physically this value could indicate how far the chosen solution is from the nearest possible solution that will make a foot slip boundary of the friction cone , thus can be used to represent a solution\u2019s robustness against disturbances and as a measure for choosing the optimal solution. We define the margin against slip NCi as the ratio of the smallest angle between the chosen force solution vector and the friction cone Ci\u2212 Ci * , over the angle between the friction cone and its center axis Ci where, for contact point Ci, these are defined by Ci = tan\u22121 Ci 12 and Ci * t = cos\u22121 u\u0304Ni \u00b7 F\u0304Ci t u\u0304Ni F\u0304Ci t 13 as shown in Fig. 4. Thus, for contact point Ci, the margin against slip NCi is represented by NCi t = 1 \u2212 Ci * t Ci 14 By definition, a margin against slip can only have a value between 0 and 1. A margin against slip of 1 indicates that the force solution vector coincides with the center axis of the friction cone or the surface normal vector Ci * =0 , thus the contact force at this case is pure normal force with no friction force components. A Transactions of the ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F margin against slip of 0 indicates that the chosen force solution vector is at the boundary of the friction cone Ci * = Ci and thus is at the verge of slipping"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002688_ic00182a014-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002688_ic00182a014-Figure1-1.png",
        "caption": "Figure 1. Diagram of the cell used for far-infrared spectroelectrochemical studies.",
        "texts": [
            " Solutions used for electrochemical studies were either 0.2 N LiC10, in methanol, saturated NEt4BF4 in methanol, or 0.3 N NBu4BF4 or LiBF4 in tetrahydrofuran. The THF solutions were stored over sodium amalgam prior to use. SCE, SSCE, or Ag/AgCI reference electrodes were used with a platinum-wire counterelectrode and ferrocene as an internal standard. Silicon, carbon-disk (IBM), or platinum-disk (IBM) electrodes were used as working electrodes. Far-infrared sptroelectrochemical measurements were performed by using a cell whose design is shown in Figure 1. The cell fits into a standard IR cell holder with an extended V-shaped trough. The infrared light beam passes through two windows, one a standard IR-transparent material such as a KBr disk and the other a working (6) A report on a SnOz electrode modified with a molybdenum dinitrogen complex containing two diphosphine ligands has appeared, but protonation of the soluble analogue of this complex does not result in the formation of ammonia: Leigh, G. J.; Pickett, C. J. J. Chem. Soc., Dalton Trans"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001632_j.1460-2687.2000.00055.x-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001632_j.1460-2687.2000.00055.x-Figure1-1.png",
        "caption": "Figure 1 Coordinate system.",
        "texts": [
            " 3 The ball and the club head are made of linear elastic material, although the ball is actually made of viscoelastic material. This assumption is considered to satisfactorily model the characteristics of the club head. 4 The club head moves horizontally before impact because only the impact phenomenon is analysed. 5 Coulomb's friction law applies on the contact surface between the ball and the club head because the exact mechanism is not known. The software LUSAS ver.11 was used for the analysis of impact between the ball and the club head. Figure 1 shows the co-ordinate system used in the analysis. The origin o is the position of the centre of gravity of the ball before impact. The y-axis corresponds to the direction of club head motion before impact. The x-axis is perpendicular to the y-axis, while the z-axis completes a right-handed co-ordinate system. Calculation of release velocity and spin rate The \u00afight distance and direction of the \u00afying ball are the indices used to estimate the performance of 196 Sports Engineering (2000) 3, 195\u00b1204 \u00b7 \u00d3 2000 Blackwell Science Ltd the club head"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002006_978-3-662-09769-4-Figure4.21-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002006_978-3-662-09769-4-Figure4.21-1.png",
        "caption": "Figure 4.21: Representation of the system",
        "texts": [
            " Centrifugal terms: The first component of ( 4.255) includes the standard centrifugal term due to the distance of the reference point P from the center of mass C. The second component includes two terms which are contributed by the term ((1 ) of (4.254b) and by the term (K:2 ) of (4.253d). 4.6.4 Technical realizations of the above mechanism Three technical realizations which are associated with the above model equa tions are collected in Figure 4.20. 4.6.5 DE model derived from the Newton-Euler approach The vehicle model of the Figure 4.21a includes a rigid body which rotates around the point C in the x-z plane. The body-fixed point C is attached to the base by a revolute-translational link with a translational DOF in the z-direction. As a consequence, the point C can only move in the z-direction. Let m be the mass of the body, C its center of mass, and Je its moment of inertia with respect to C. The body is further attached to the base by two translational springs which are placed in the horizontal distances L 1 and L 2 200 4. Planar models of a rigid body under absolute constraints Figure 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003010_1.2149394-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003010_1.2149394-Figure1-1.png",
        "caption": "Fig. 1 Model of the rotor sup",
        "texts": [
            " This paper presents a new model to calculate the fluid-film forces under the Reynolds boundary condition and applies this model to investigate the nonlinear dynamics of a rigid rotor in the elliptical bearing support. Both balanced and unbalanced rotors are considered herein. Hopf bifurcation of the balanced rotor; synchronous and periodic, quasi-periodic, and chaotic motions of the unbalance rotor are also shown. Poincar\u00e9 maps, bifurcation diagram and frequency spectra are selected as diagnostic tools. Figure 1 shows a rigid journal rotating in a fixed elliptical bearing housing which consists of two 150 deg arch pads. Oj is the geometric center of the journal, Ob is the geometric center of the bearing; and Ob\u2212xy is the fixed Cartesian coordinates system. FEBRUARY 2006, Vol. 128 / 3506 by ASME 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use po Downloaded F To simplify the analysis, only the parallel radial motion of rotor is considered. The equations of the motion of journal center Oj can be written as mX = FX X,Y,X ,Y + me 2 cos t mY = FY X,Y,X ,Y + me 2 sin t \u2212 mg 1 Equation 1 has the following dimensionless form: mC 2x\u0308 = 6 Rb 4 C2 fx x,y, x\u0307, y\u0307 + me 2 cos mC 2y\u0308 = 6 Rb 4 C2 fy x,y, x\u0307, y\u0307 + me 2 sin \u2212 mg 2 Introducing the dimensionless rotating speed = e /g, eccentricity to clearance ratio =e /C and combined parameter =6 Rb 4 /mC3 \u00b7 e /g, Eq",
            " Thus, the solution of r can be obtained directly. If the solution gives an 0, then cavitation appears. In the cavitation case, should be modified and a is recalculated iteratively until an=0. The fluid-film forces of one pad in local coordinates can be obtained by fu fv = \u2212 \u2212 g d 0 r cos sin d = \u2212 c3 b1 Ta b2 Ta 28 Transforming the forces to global coordinates and summing for all of the pads gives the bearing forces fx and fy In this paper, both rigid balanced and unbalanced rotors in elliptical bearing supports are investigated Fig. 1 . The value of the parameters for the example are Rj =0.1 m , m=100 kg , =0.02 Pa\u00b7s , C /Rj =0.003, Cmin/C=0.5, and =1.0. Since the fluid-film forces are calculated pad by pad, the present method is effective not only on cylindrical bearings, but also on multilobe bearings, including the elliptical form. Because the accuracy of the fluid-film force will subsequently change the numerical values of the nonlinear rotor simulation, a validation for the proposed method is conducted. The fluid-film forces of the elliptical bearings are obtained by setting up C /Rj =0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000035_1.555338-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000035_1.555338-Figure1-1.png",
        "caption": "Fig. 1 Journal bearing configuration",
        "texts": [
            "org/about-asme/terms-of-use Downl m# is assumed to be Vogel\u2019s formula: m# 5 C1 expC2/~T# 1 C3! (9) C 1, C 2, and C 3 are the temperature-viscosity coefficients. The ISOADI thermal boundary conditions are used. The groove temperature is obtained by the overall energy balance on the groove (Zhang et al., 1998a). The journal is at a uniform temperature and its steady-state temperature can be obtained by the pseudo-transient heat balance (Zhang et al., 1998a). A contact model developed by Lee and Ree (1996) is used here to calculate the asperity contact pressure. Referring to Fig. 1, the equation of motion for journal is: Me\u0308X,Y 5 FoilX,Y 1 FeX,Y 1 FcX,Y (10) The basic equations above are for a power law fluid. For the upper convected Maxwell fluid with the viscosity, m*, treated as a function of the second invariant of strain rate, its momentum equations are (Paranjpe, 1992): p9 x 5  y m* u y and p9 z 5  y m* w y (11) where p9 5 p 1 kp/t. Hence, its basic equations are in the same form as the equations above, expect that the variable film pressure is E(p9) 5 E(p#) 1 vkE(p#)/t# instead of E(p#)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002387_robot.1997.619348-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002387_robot.1997.619348-Figure2-1.png",
        "caption": "Figure 2: A four-joint planar manipulator",
        "texts": [
            " , n- 1) does not affect the end-effector motion. On the other hand, when a = 0, the endeffector motion is changed by the virtual external force applied to the whole arm as well as the end-effector. In addition to the end-effector impedance control, the relative motion between the manipulator and its environment can be considered through the virtual impedance M F ) , BPI, K:) using the non-contact impedance control. 4 Computer Simulation Computer simulation using a four-joint planar manipulator shown in Fig. 2 was carried out. The parameters of each link of the manipulator are as follows: the length is 0.4 m, the mass 3.75 kg, the moment of inertia 0.8 kgm\u2019, and the center of mass of each link is at its middle point. The end-effector impedance kg, Be = diag.[20, 201 Nm/s, K , = diag.[100, diag.[ll 100 I1 of the manipulator is determined as Me = Njm, and the desired end-effector position, i.e. the equilibrium position, is simply chosen as its initial position, where the initial posture of the manipulator is Let us consider the manipulator close to the object. By using the conventional impedance control only, the ~ ( 0 ) [ E - X -I -KIT rad. 2 \u2019 43 4 \u2019 4 the NCIC the NCIC manipulator cannot take any action for avoiding the object without the interaction force. As an example of the non-contact impedance control, ei ht virtual circles are used ( n = 8) as shown in Fig. 2 fb), where the centers of the circles are located at the middle point of each link and each joint except for the first joint. Figures 3 and 4 show the change of the arm posture for the moving object. The radius of each circle is di) = 0.1 m and the virtual impedance are Mi.\u201c) = diag.[2, 21 kg, B?) = diag.[40,40:1 Ns/m, K?) = diag.[200,200] are used. Also the desired joint impedance in (7) are chosen as Mj = diag.[O.Ol, 0.01, 0.01, 0.011 kgm\u2019, Bj = diag.[0.2, 0.2, 0.2, 0.21 Nm/(rad/s), Kj = diag"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002567_acc.1994.751797-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002567_acc.1994.751797-Figure1-1.png",
        "caption": "Fig. 1: Cross-sectional view of t,he mechanical apparatus",
        "texts": [
            " The bearing load is applied by tightening a nut to prestress tlie ring. The load-cell readings are stored in a computer-assisted data acquisition system. Any desired time-variable motion of the shaft can be generated with sufficient accuracy by a computer controlled D.C. servo motor. The experimeiita.1 test system comprises a mechanical test a.pparatus, a persona.1 computer, a data acquisition and control interface board, a digital strain indicator a.nd analog signal amplifiers and D.C. power supplies. The mecha.nica.1 test appa.ratus, Fig. 1, contains a ma.in support fra.me, shaft-bea.riiig assembly, bearing loading assembly, D.C. servo-motor, tachometer (calibrated D.C. generator), strain gage mounting strips and a. 1ubrica.tion system. Design features of the mechanical t,est appa.ratus are explained with the aid of Fig. 1. The test-shaft (C) is supported by two ball bearings (A) a.tta.ched to tlie main support frame (B). There are four brass sleeve test-bearings (H). The inner diameter of each bea.ring, d, is 25.4 inm and its length is 19 min. The ratio between the diameter clearance, Ad, and clhineter is commonly, Ad/d = 0.001, so in the test-bearing Ad = 25pm. The a.djusta.ble load is applied by tightening the nut (PI on bolt (R). This applies internal force between the inner and outer housings (N) and (IC) and causes the two iiiiier bearings and the two outer bearings to be loaded equally and in opposite directions, thereby applying equal load to each bearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003766_0278364906061159-Figure14-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003766_0278364906061159-Figure14-1.png",
        "caption": "Fig. 14. Inner mechanisms of the hermetic wheel case.",
        "texts": [],
        "surrounding_texts": [
            "As shown in Figures 14 and 15, the hermetic case is composed of the following: 1. a winch; 2. a slip ring; 3. an air tank (hermetic case); 4. lock mechanism. The winch winds up the tube and wire simultaneously. The slip ring allows the supply of electricity to the outside through the wire wound up around the winch. The air tank contains the air supplied from the air compressor. The amount of tube expansion is controlled by the handle and lock mechanism. This hermetic wheel case can wind up to 10 m of tube. Since the wire is inside the tube and will be wound up along with the tube, the wire will twist if no measure is taken. The slip ring prevents this twist. In the next section we explain the handle lock mechanism. When air pressure is applied, the tube will expand in a forward direction. Accordingly, it will continue expanding unless the expansion is stopped. In rescue operations, however, some- at Virginia Tech on March 14, 2015ijr.sagepub.comDownloaded from times it is necessary to stop the tube expansion and search a certain area for a while. Therefore, the device controls the expansion amount by locking the handle to stop the tube expansion. Figures 16 and 17 show the actual handle lock mechanism. The Slime Scope controls the tube expansion by locking and releasing the handle. 5. Test Machine Figure 18 shows our test machine. We used this test machine to confirm that the DETube can travel in rubble. Table 3 shows its specifications."
        ]
    },
    {
        "image_filename": "designv11_24_0002383_robot.1996.506891-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002383_robot.1996.506891-Figure4-1.png",
        "caption": "Figure 4: Cylindrical contact with a cylindrical joint kinematic model.",
        "texts": [],
        "surrounding_texts": [
            "J c , =\n- - - 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0\n0 0 0 0 0 1 0 0 1 Gc, = 0 0 1 0 \u2018 (10) 0 1 - - 0 0 0 0 -\nr is the peg radius. s, and c, are, respectively, the sine and cosine of a, the angle between the axis of the peg and the contact normal (Fig. 1). This contact situation has two identifiable geometrical uncertainty parameters: the rotation angle 19 of the peg about its own axis, and the angle a between the peg axis and the contact normal.\n3.3 Three point contact\nThere are three distinct contacts:\n1. surf: the contact between the outer surface of the peg and the rim of the hole.\n2. riml and rim2 the two contacts between the bottom rim of the peg and the rim of the hole. These two contacts are positioned symmetrically with respect to the plane through the peg\u2019s axis and through surf.\nEach of the three point contacts is modelled by means of a five degrees-of-freedom virtual manipulator [5]\n(Figs. 2 and 3). These manipulators form three parallel connections between the hole and the peg, and constrain the peg\u2019s motion freedom in the same way as the contacts. This means that the total number of degrees of freedom of the peg with respect to the hole is reduced to three:\n1. Slip: rotation of the peg about its own axis.\n2. Slide: rotation of the peg about the hole\u2019s axis.\n3. Align: rotation of the peg about the tangent to the hole\u2019s rim, at the contact point.\nFor a detailed description of the alignment motion and the twist and wrench Jacobians see Bruyninckx et al. [6]. The three point contact has two identifiable geometrical uncertainty parameters: the alignment error (i.e. the angle between the axes of peg and hole), and the rotation angle about the peg axis.\nThis contact situation has no identifiable geometrical uncertainty parameters.",
            "4 Experimental Results\n4.1 Test Setup\nThe test setup consists of an industrial KUKA IR 361/8 robot equipped with a six component flexible force/torque sensor of which the deformations are measured. Its end effector holds a peg with radius r = 100mm. The experiment is executed without contact model but with a task frame based compliant motion robot controller [7]. The insertion strategy is as explained in Section 3. The measured twists and wrenches are stored during execution and are used afterwards for off-line identification and monitoring of the different contact situations. The measurements are filtered by a low pass filter with a cut-off frequency of 3 Hz.\n4.2 Identification\nThis section shows the results of the off-line identification of uncertainties in the different contact situations. As mentioned in Section 3, only the curve-face and the three point contact have identifiable uncertainty parameters. Fig. 5 shows the result of the identification of geometrical uncertainty parameters in the curve-face contact. The angle between the peg's axis and the contact normal remains constant, about 0.85 rad; whereas the rotation angle of the peg about its own axis is small. This means that the contact point belongs to the Y-2 plane (Fig. 1). Fig. 6 shows the identified uncertainty parameters of the three point contact. Due to friction disturbancies on the forces measurements, only the kinetic energy error term of (4) is minimized. In the top figure the identified alignment error (full line) is compared with the specification (dashed line). When the alignment error is small, the insertion can start. The rotation angle about the peg axis (bottom figure) is small. This means that the surfcontact belongs to the Y-2 plane (Fig. 2).\n4.3 Monitoring The detection of the transitions between the different contact situations is based on the total energy error function of the expected model. Jumps in Ea are detected with the Page-Hinckley test. Fig. 7 shows the total energy error for the successive contact situations. The insertion starts in free space. After 16 seconds a jump in the energy error is detected which means that the transition to the curve-face contact takes place. From now on, the model of the curve-face contact is valid. The energy error is low until t = 30 sec. Then a jump in the total energy error occurs, which means that the curve-face contact is no more valid. The peg has fallen into the hole and the controller is asked to",
            "generate a three point contact which is established at t = 47 sec. The contacts during this transition are not modelled. The alignment then starts, and ends when the identified alignment error is small, i.e. at t = 56 sec. In the completely aligned configuration the three point contact is not stable. Hence the insertion starts is started already at an alignment error of 0.1 rad ( t = 55.5 sec on Fig. 6). From now on, the cylindrical contact situation is valid. At t = 59 sec E A increases which means that the peg contacts the bottom of the hole. Then the peg is pulled out of the hole.\n5 Conclusions A new method has been presented to identify geometrical uncertainty parameters in a kinematic contact model for constrained motion, and to monitor the correctness of the model. Uncertainties are identified by looking for the minimum in the total energy error function, whereas the correctness of the contact model is validated by observing jumps in only one signal, the same total energy error. This energy error corresponds to that part of the measured twists and wrenches that cannot be explained by the contact model. The presented methods are invariant with respect to changes in the mathematical representations. Experimental results of a complete insertion of a peg into a hole have been presented. They confirm the theoretical methods.\nAcknowledgments This work was sponsored by the Belgian Programme on Interuniversity Attraction poles initiated by the Belgian State -Prime Minister\u2019s Office- Science Policy Programming (IUAP-50). The scientific responsibility is assumed by its authors. H. Bruyninckx is PostDoctoral Researcher with the Belgian National Fund for Scientific Research (NFWO).\nReferences [l] M Basseville. Detecting changes in signals and\nsystems-a survey. Automutica, 24(3):309-326, 1988.\n[2] A. Bicchi, K. Salisbury, and D. L. Brock. Contact sensing from force measurements. The Int. J. Rob. Research, 12 (3) :249-262, 1993.\n[3] M. Blauer and P. R. B6langer. State and parameter stimation for robotic manipulators using force measurements. IEEE Trans. Aut. Control, AC32(12):1055-1066,1987.\n[4] H. Bruyninckx, J. De Schutter, and S. Dutr6. The \u201creciprocity\u201d an \u201cconsistency7\u2019 based approaches to uncertainty identification for compliant motions. In Proc IEEE Int. Conf. Rob. Automation, pages 349-354, Atlanta, GA, 1993.\n[5] H. Bruyninckx, S. Demey, S. Dutr6, and J. De Schutter. Kinematic models for model based compliant motion in the presence of uncertainty. Int. J. Rob. Research, 14(5):465-482, 1995.\n[6] H. Bruyninckx, S. Dutr6, and J. De Schutter. Pegon-hole: A model based solution to peg and hole alignment. In Proc. IEEE Int. Conf. Rob. Automation, pages 1919-1924, Nagoya, Japan, 1995.\n[7] J . De Schutter and H. Van Brussel. Compliant robot motion 1-11. A formalism for specifying compliant motion tasks. Int. J. Rob. Research, 7(4):3- 33, 1988.\n[8] S. Dutr6. Calculating the derivative of a Jacobian for serial and parallel manipulators. Internal report 95R49, 1995.\n[9] B. Eberman and J. K. Salisbury. Detection to dynamic contact sensing. Int. J. Rob. Research, 13(5):369-394, 1994.\n[lo] B. J. McCarragher and H. Asada. Qualitative template matching using dynamic process models for state transition recognition of robotic assembly. Trans. ASME, J . Dyn. Syst., Measurement, and Control, 115:261-269, 1993.\n[ll] F. C. Park. Distance metrics on the rigid-body motions with applications to mechanism design. Truns. ASME, J . Mech. Design, 117:48-54, 1995.\n[12] T. Yoshikawa and A. Sudou. Dynamic hybrid position/force control of robot manipulators -on-line estimation of unknown constraint. IEEE Trans. Rob. Automation, 9(2):220-226, 1993."
        ]
    },
    {
        "image_filename": "designv11_24_0002815_bf01896173-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002815_bf01896173-Figure8-1.png",
        "caption": "Fig. 8. Fig.9.",
        "texts": [
            " From (1.7) we know that c=0 as h=0 , so (4.3), duce to U = (1 - - g h ) [ (a--b)cos=O+b] OU ---- --2gas[ (a--b)cos~V+ b] Og,, g;~' = +, In the discussion below we suppose (4.5) , (1.2) , (4.6) now re- (3 3) (3.4) (3.5) ( 3 . 6 ) C > B > A (3 .T) In this case we have: for r o o= r-~-(C-A)>O, i.e. anda>b b-~ ~(C--B)>0, ~>b>0 t . for q~ for Po As regards the position of o= q-~-~ (B-C)<O b=--~(B--a)>O b>O~>o -~-- (A--B) < o a ~ a n d a > b b=;2~ - (A--C) <0 O~a>'b P0, q0 and ro in the sphere /~ , see Fig.8. (~.8, (3.9) (3.1o) In the following we study the properties of the set of steady motion r 0 The properties of the sets of steady motion q~ and P0 can be acquired simultaneously. It is pointed out that for r o we have a>b>o Hence from (3.3) and (3.4) we obtain 0 as gs~ = I (Um,x)m~x-~o as gas=0, 0----0, n U= (U,..,,)=.,=b a s g~,=O. O=-f, - { - 0 as g~,=--I ( <0 as 0<g,s~.<l o U_ ( =0 as O,,=0 Ogs~ i i>0 as -- l<~g.<0 k (3,1 1) (3.12~ 874 On Global S tab i l i t y of Rotational Motion If we cut the sphere k along any shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003768_j.mechmachtheory.2005.10.010-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003768_j.mechmachtheory.2005.10.010-Figure1-1.png",
        "caption": "Fig. 1. The toroidal drive.",
        "texts": [
            " Based on the geometrical analysis and mathematical modeling [15], this paper investigates the effect of these rollers on the meshing characteristics of the toroidal drive, characterizes the toroidal drive properties with different shapes of rollers and develops the mathematical models of the contact curve, the meshing surface, undercutting and meshing limit curves and the induced normal curvature based on different rollers. The paper provides a comparative study of meshing properties with different rollers including their effects on contact stress and tooth profile machining. The toroidal drive in Fig. 1 is a specific type of an epicyclic gear train with a stationary internal toroidal gear and is driven by a sun-worm with angular speed x1 transmitted through planet worm-gears to the output motion of the planet carrier with angular speed of xp. It consists of three components including the sun-worm, planet worm-gears and the stationary internal toroidal gear. The meshing rollers are media in the meshing contact of these components. A planet carrier is the output of the drive. Focusing on the meshing characteristics between a planet worm-gear and the sun-worm, the meshing properties between the planet worm-gear and the stationary internal gear can be revealed by setting up relevant coordinate systems between a planet worm-gear and the sun-worm and between a planet worm-gear and the stationary internal gear as in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000017_s0043-1648(99)00148-9-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000017_s0043-1648(99)00148-9-Figure1-1.png",
        "caption": "Fig. 1. Elastohydrodynamic film and corresponding grid.",
        "texts": [
            " The limiting shear stress t or t , as well as theE 1 non-Newtonian exponent n, are derived through experiw x w xments at discs test rigs 5 or other devices 6 . In the following analysis the exponential model was selected in first approach, due to the simplification of the mathematical procedure: 1yn Eu dt t Eu sA q 2\u017d . E y d t h E y Furthermore the elasticity term can be neglected for the \u017d .working conditions under consideration, thus Eq. 2 reduces to: ny1 Eu Eu tsh 3\u017d . E y E y The line contact considered is shown in Fig. 1. The fully developed lubricating film totally separates the two bodies. The two mating surfaces are considered ideally smooth. The motion of a lubricant element in the film is described by the Navier\u2013Stokes equations. A series of sim- plifying assumptions are commonly made without serious accuracy losses. Given that in line contacts the contact width is orders of magnitude smaller than the face width, the motion along the z direction can be neglected. Likewise the motion along the height direction y can also be neglected",
            " Having determined pressure distribution and film thickness, velocity and temperature fields can be calculated by solving the motion and energy equations with the above mentioned boundary conditions. In this way the time consuming solution of continuity equation and the prerequisite determination of the elastic deformations, can be avoided. In order to solve numerically the above mentioned set of equations, the finite difference method is applied. For this purpose a uniform mesh is used as shown in Fig. 1. Replacing the derivatives with the finite difference ratios the equations of motion and energy can be written: h yhi , jq1 i , jy1 n u yu\u017d .i , jq1 i , jy1nq12D y\u017d . ny1 h yh\u017d .i , jq1 i , jy1 qh n u y2u qu\u017d .i , j i , jq1 i , j i , jy1nq1ny12 D y\u017d . p ypi iy1 y s0 18\u017d . D x l q y2q qq\u017d .i , jq1 i , j i , jy12 D y nq1u yui , jq1 i , jy1 qh s0 19\u017d .i , j \u017e /2D y Following the determination of velocities and temperatures at every node, the shear stresses at the surfaces can be calculated: n nu yu u yui ,2 i ,1 i ,m i ,my1 t sh and t shi ,1 i ,1 i ,m i ,m D y D y 20a,b\u017d "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003141_tsmc.1982.4308921-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003141_tsmc.1982.4308921-Figure3-1.png",
        "caption": "Fig. 3.",
        "texts": [],
        "surrounding_texts": [
            "IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS, VOL. SMC-12, NO 6, NOVEMBER/DECEMBER 1982\n'i'\nFig. 2.\nzo\nYo\nFig. 1.\nB. Assumptions\nIn order to develop the modeling procedure certain assumptions will be made. 1) Each link is assumed to be symmetrical about its longitudinal axis. 2) One of the principal axes of inertia of each link lies along its longitudinal axis. 3) The center of gravity of each link coincides with its middle point. 4) A displacement in a translatory joint does not displace the center of gravity of any link in its body-fixed coordinate system. As a large number of mechanisms are constructed of symmetrical members, the above assumptions are fairly representative of physical systems. The simplicity obtained in the modeling procedure is considerable at no great cost in accuracy.\nC. The Coordinate Systems\nThe development of the mathematical model requires the precise definition of the system of coordinate axes. These are chosen as follows.\nzi - Parallel to the axis of joint i and passing through the center of gravity of link i (sense arbitrary). If the joint i is rotary (revolute), then zi is parallel to the axis of rotation. If prismatic (translatory), then zi is parallel to the direction of linear motion. zo passes through joint 1 and points vertically upwards. xi -The common perpendicular directed (in the positive sense) from the axis of joint i to zi and passing through the center of gravity of link i. When the joint axis itself passes through the center of gravity\nxi is arbitrary, subject only to the condition zi xi = 0. x0 is defined arbitrarily subject to the condition zo x0 =0.\nYi, zi x xx, i = 0, 1,2,* *, n.\nThus an orthonormal coordinate system (xi, yi, zi) fixed in link i, i = 0, 1, 2,-*-*, n is defined (Fig. 2). A displacement in a translatory joint displaces all vectors (towards the open end) parallel to themselves; their direction of orientation is not affected. A displacement in a rotary joint changes the direction of orientation of all vectors towards the open end. The new position r' of any vector (r) can be calculated by the use of Rodrigue's formula [19] after rotation (i in a joint i:\nr' = rcos i + (1-cosi)(ei ri)ei + ei x risin(i. (1)\nThe points of application of all vectors towards the open end of a displacement (in rotary or translatory joint) are not altered in body-fixed systems but are displaced in inertial coordinates.\nD. Kinetic Energy\nConsider the open-loop kinematic chain in an arbitrary position at any time t. The position vector of the center of mass of link i (Figs. 1 and 3) is\nr, = Rlj + a,(je, + Rji + rJ + (1-a)ryi. (2)\nIt is assumed that the mass centers of all members towards the open end of a translatory joint are displaced equally by the displacement in that particular joint. The partial differential of the distance vector ri can then be written [13]\nd= aje1 + (1 - )ej X rji- (3)\nThe velocity of the center of mass of member i\nd = dti\ncan be expressed in terms of the generalized velocity vector + as\nV = [pd,ri d\u00bdri d . ri o. (4)\n878\ne;\nI",
            "MAHIL: DESCRIPTION OF DYNAMIC SYSTEMS\nThe total kinetic energy of member i is then given by\ni= 2VT(\"M)$ where\nliM = I'iM + 12iM\nand\nMjK = i [aj K (ej eK)\n+aj (1 - CJK)ej * eK X rKi\nThe kinetic energy due to translational motion of member i is then\nTiose iVi * Vi\nor in terms of the generalized velocity vector [ 17] Tt = 1T(IM)+ (5)\nwhere\nIliMjK = dr, dra ojaO\n(6)\nSubstituting for the partial differentials of vector ri from (3)\nMjK mMi[{ajK + (1 -aj )(l - aK)( ri * rKi))(ej * ek)\n+'7j( - OK)ej * eK X rKi\n+coK(I - aj)eK- ej X rji\n-(1 - aj)(l -aK)(ej. rKi)(eK - r.)] (7) The angular velocity wi of any member i in terms of generalized velocity vector is given by [13]\nwi [(1 al)el (1 -a2)e2 (1 -ai)eei o... o]$\n(8) The angular momentum of a symmetrical member i (having a cylindrical shape) about its mass center can be written as [17], [20]\nHi = J +1 ( qil)qil (9) and hence the kinetic energy due to angular motion of member i is\nTr = i * Hi\n2 Jin ( \u00b0i Xi ) + 2 Jisn( Xi qi l) * (1l ) Substituting for wi in terms of the generalized velocity vector it can be shown [13], [17] that\nTr = l$T(I2iM) (11)\nwhere\nMK = (1 - a )(1 - ak)[Jin(ej ek) +JS(ee qil) ( ek * qj1)]. (12)\n+ K( 1-- j) eK * ej X rji] + (1- aj)(l - UK)[Jif(ej - eK)\n+ Ji,sn(ej * qil )(eK * qil )\n+mi{(ej * eK)(rji * rKi) - (ej * rKi)(eK -rji). ] (15)\nAs up and (1 - ap) cannot both be nonzero simultaneously, the above expression for 'iMjK is considerably simpler to determine than appears at first sight.\nE. The Generalized Inertia Matrix\nThe matrix llM is called the generalized inertia matrix of member i [13], [14] and plays a role similar to that of inertia tensor of a rigid body. There are some dissimilarities also [13]. The element (j, K) of the GIM of member i depends upon the types of jointsj and K. Thus\n1) j, K are rotary joints\nMjK = {Jin + mi ( ri * rKi))(ej * eK)\n-m1n(ej qril)(eK qil)\n-mi(ej *rKi)(eK rji ... j < K 1i(6) 2) K is a rotary joint, j is a translatory joint.\nMjK = mi(ej - eK X rKi) ... j < K < i.\n3) j is a rotary joint, K is a translatory joint.\n'iMjK = mi (eK * eJ X rji) ... j < K < i.\n4) j, K are translatory joints.\n'iMjK = Mi(ej * --K) .. j < K < i\n5) j, K are translatory or rotary joints.\niMjK = O jorK> i,\niMKj MjK, j, K i.\n(17)\n(18)\n(19)\n(20)\n(21) While the symmetricity of the matrix 1iM is obvious, it is not normally appreciated that none of the scalar (or triple scalar) products in the above expressions for element (j, K) can depend upon the generalized coordinates Oi, 'k2, .. I*'% Consequently for the determination of any element K in jth row (K > j) the (translational or angular) displacements in joints 1, 2, , j can be ignored. The significance of this property of the GIM of member i is not obvious at\n(13)\n(14)\n879",
            "IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS, VOL. SMC-12, NO. 6, NOVEMBER/DECEMBER 1982\nfirst sight: after all, the displacements have to be considered in all but the first joint to compute the elements in the first row of the GIM of any member i.\nLagrange's method involves partial differentials, and owing to the above property the partial differentials of the elements of the GIM have to be calculated for a far less number of cases than seems obvious. This fact considerably reduces the effort involved in the dynamic modeling of open-loop kinematic chains and can be exploited to considerably reduce the computational effort in automated model-formhtion algorithms. It can be immediately seen that the (i, i)th element of the GIM of any member i is a constant. The symmetricity of the matrix \"M also aids in considerably reducing the computational burden. The total kinetic energy of the open-loop kinematic chain is a summation of the kinetic energies of the individual links.\nT= 14T(IM)$ (22)\nwhere n\nIM= E Iim i=1\n(23)\nThe matrix 'M is called the generalized inertia matrix of the whole open-loop kinematic chain and plays a role similar to the inertia tensor. As the kinetic energy of a system is necessarily positive the GIM ('M) is a positive definite symmetric matrix. By virtue of the property of the GIM's of individual members the (j, k)th elements (j < k) of the GIM ('M) is independent of the generalized coordinates 1,2.2,*.. Consequently its (n, n)th element is a constant. The GIM's of individual links and hence of the whole open-loop kinematic chain have been formulated in closed form in terms of certain physical vectors. The elimination of redundant computations in this formulation makes the determination of kinetic energy simpler than by determining velocities first. Moreover the formulation of kinetic energy in (22) is particularly suited to the application of Lagrange's method as will be demonstrated below.\nF. Partial Differentials\nApplication of Lagrange's method requires the partial differentials of the GIM and the distance vectors. The GIM is symmetrical and hence the partial differentials are required only for its (1, m)th elements for m > 1. Differentiation of the relationships given in (16)-(21), and algebraic manipulations of the results obtained lead to simple relationships for the partial differentials of the GIM. Depending upon the types of joints the partial differentials involve ten different types of relationships, some of which are trivial.\n1) 1, m, p are rotary or translatory joints\ndp=0 ~P 1 < m < (24)\nThis is an obvious result of the independence of the element \"IMIm (1 < m) of the generalized coordinates (1'P02''\n2) 1, m, p are rotary joints.\nI1 Ml', = 2mi(rli * ep x rp,) + 2J,,,(el ep x qil)(e, qil)\n1= m <p < i\n= [ Ji; + m, ( r1i * rmi)] (el * e, X em) + mi [(el em)(RI, * ep, X rmi.) - (em - r1i)(el . ep X rmi) - (e, - rmi)(RIp - e, X em)] +Jisn(em * qil)(el, ep x qil),\n= mi[(el- em)(R,p * ep X rmi)\n- (em - r,i)(el ep X rmi)]\n+Jisn(em * qil)(el - ep X qil), = mi(e1 em)(R1p + Rmp)\n-mi[(em - r1i)(el ep x rpi) + (e, i rmi)(em * ep X rpi)] +Jisn[(em * qil)(el ep x qiz)\nl<p < m < i\n1 <p = m < i\n+ (e, * qil)(em. ep,x qi)], l < m <p < i.\n3) 1, m are rotary joints, p is translatory joint. Unit vectors change neither in magnitude nor in direction by displacement in a translatory joint. Only vector r1i is altered by translatory displacement in joint p forp > 1. In this case\nalMim =mi [(el em)(ep rmi) - (el rmi)(em ep)], <p <m i\n= mi(el- em)ep * (rmi + r1i)\n-mi[(e, * ep)(em * r1i) + (el * rmi)(em ep) m < p < i. (26)\n4) 1, p are rotary joints, m is a translatory joint. In this case the rotary displacement in joint p influences vectors em (for p < m) and r1i (for 1 < p < i). Hence\nad m = mi(el * ep)(em * RIP) + mi[(em * ep)(el * rpi)\n- (e1. em)(ep * rjj)], I<p < m < i\n= mi[(em. ep)(e,. ri)\n- (e, ep)(em * rJi], I < m<p< i. (27) 5) 1 is rotary joint, m and p are translatory joints.\nSubstituting a ,i ep in the partial differential of the\nelement ilMim,\na1lm Mi(em * e, x ep), I < m < < p < i, p m m\n(28)\n(25)\n880\n-2mi(el, ep -',( rpi)(el, r1i),\n= 0. 1 < m,<, i,p = M."
        ]
    },
    {
        "image_filename": "designv11_24_0002994_tmag.2004.824591-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002994_tmag.2004.824591-Figure1-1.png",
        "caption": "Fig. 1. Geometry of Bessho actuator with dimensions in millimeters.",
        "texts": [
            " A formula [3] for the wavefront derived for a field switched between and is here altered to account for a field switched from 0 to by an applied (1) where (2) These two formulas are here applied to determine magnetic diffusion time. Since the current is a step applied at time zero, is also a step and, thus, the left-hand side of (1) has its integral over time replaced by . The value of is zero, since when . Thus, (1) becomes (3) giving (4) The magnetic actuator analyzed here was originally analyzed by Bessho et al. [4]. As shown in Fig. 1, it is axisymmetric of axial length 270 mm. The radius of its cylindrical plunger and of its cylindrical stopper is 20 mm. The diffusion time of (4) can be evaluated for the nominal applied current A in the 3300 turn coil [2] as follows. The applied needed in (4) is found from (5) where . The path length is assumed to be the 250-mm axial length of the coil window, meaning that the cylin- 0018-9464/04$20.00 \u00a9 2004 IEEE drical core of radius 20 mm drops all ampere-turns (the outer yoke is assumed to have negligible MMF drop)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002676_j.scriptamat.2005.11.010-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002676_j.scriptamat.2005.11.010-Figure7-1.png",
        "caption": "Fig. 7. Liquidus projection surface for Ni rich region of Ni\u2013Al\u2013Mo system [14].",
        "texts": [
            " A reduction in the extent of solute enrichment in the solid dendrite or interdendritic liquid, which would depend on the value of k under normal casting conditions, could result in a significant difference between the as-solidified microstructure of the cast alloy and that observed in the weldmetal. In the present work, such microstructural differences included interdendritic microconstituents containing a mixture of c, c 0 and a Mo rich phase in the weld fusion zone, which was not present in the base alloy. This could be related to the modification of the primary solidification path resulting from an alteration in the degree of solute partitioning, as would be discussed subsequently. The ternary Ni\u2013Al\u2013Mo liquidus projection, proposed by Nash et al. [14] and re-drawn in Fig. 7, provides a basis for developing a qualitative understanding of microstructural evolution during solidification of the alloy IC6. The three primary phase fields in the Ni\u2013Al\u2013Mo system that are of interest in the present work are c, c 0 and a, while b, d (NiMo) phase fields that exist at higher concentration of Al and Mo, respectively, are not of interest. It should, however, be noted that carefully designed systematic experimental investigations of Ni\u2013Al\u2013Mo system containing mixtures of Ni-rich face-centered cubic c and bodycentered cubic a have shown that the a phase which forms at high temperatures in these alloys becomes unstable at lower temperatures [15,16]. It transforms during cooling by an invariant peritecto-eutectoid type reaction c + a ! c 0 + d (NiMo) at around 1130 C [15]. Using the projection of the liquidus valleys, shown in Fig. 7, to qualitatively describe the solidification reaction sequence in alloy IC6 at the initiation of solidification, the first solid to form will be c dendrites. During their continued formation, the liquid will be enriched, depleted or almost retain its initial nominal composition of Al and Mo, depending on the nature of solute partitioning during cooling. On further cooling, depending on the prevalent solidification condition, the liquid composition could intersect the line of twofold saturation between c and c 0 or that between c and a. At this stage (represented by points P and R, respectively, in Fig. 7) the solubility limit of the primary solidification phase, c matrix, is exceeded, and secondary solidification constituents c + c 0 or c + a would form simultaneously from the liquid by a eutectic-type reaction, L ! c + c 0 or L ! c + a, respectively. The liquid will continue to be consumed through this reaction as its composition varies along the monovariant line of twofold saturation. Final solidification could occur by either of the two monovariant eutectic-type reactions or by a ternary eutectic-type reaction L "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000476_s0045-7949(99)00201-1-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000476_s0045-7949(99)00201-1-Figure4-1.png",
        "caption": "Fig. 4. A close-up view of the laminated sti ener: (a) discretization of the cross-sectional pro\u00aele of the sti ener into Kb segments; and (b) detailed view of the ith segment in a local coordinate system.",
        "texts": [
            " Each layer is assumed to be homogeneous, elastic, and orthotropic with elastic moduli, E1 and E2; shear modulus, G12; and Poisson's ratio, n12. The subscripts ``1'' and ``2'' specify the longitudinal and transverse directions relative to the \u00aebers in the layer. Also, the pos- ition of each ply with respect to the element mid-plane is denoted by the local coordinate z-. As in the case of the shell component, the sti ener is also made of layered composite materials. The cross section of the sti ener can be arbitrary, both in lamination and geometry, as illustrated in Fig. 4. In order to perform integrations over the cross-sectional area of the sti ener, the area is \u00aerst discretized into a \u00aenite number of segments, as shown in Fig. 4(a). Each segment is then assigned a local coordinate system with the horizontal axis parallel and the vertical axis perpendicular to the layers stacked on this segment. This is illustrated in Fig. 4(b) for the ith segment. Each layer in the ith segment is identi\u00aeed by thickness, width, and layered material properties with respect to the assigned local coordinate system. The layered properties de\u00aened with respect to the ith local coordinate system permit the integrations to be performed. The integration procedure described above for the ith segment can be repeated for all segments to complete the full integration across the cross-sectional area of the sti ener. Considering the geometrical and material properties for both components of the sti ened shell element as described above, the terms belonging to the shell element in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001412_ias.2000.882068-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001412_ias.2000.882068-Figure1-1.png",
        "caption": "Fig. 1: Combustion engine with adaptive starter generator control for damping of toque pulsation",
        "texts": [
            " The reciprocating energy flow can be buffered in a capacitor. An overview of the proposed adaptive damping concept is followed by the discussion of opportunities and inherent boundaries of this approach. 11. ADAPTIVE DAMPING CONCEPT To provide optimal damping, the torque pulsation produced by the combustion engine has to be identified online and separated from other effects such as acceleration or load variation. For this task, an algorithm employing a Harmonic Activation Neural Network' ( H A \" ) including signal conditioning as shown in Fig. 1 has been designed. After an initial adaptation period, it provides a good estimate of the torque pulsation to calculate the appropriate compensation torque even at transient engine operation. A. Combustion Engine Torque Pulsation The torque pulsation of a combustion engine correlates to the crank angle p and can hence be represented by a periodic signal, which consists of the combustion frequency and its harmonics. The Fourier transform, for example, provides a compact representation of a periodic torque Ten&), using a specific set of even and odd coefficients eAk and &k respectively: K Teng (q) = + (9,4k cos(k'"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001329_robot.1991.131580-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001329_robot.1991.131580-Figure1-1.png",
        "caption": "Fig. 1 Four-Legged Walking Vehicle",
        "texts": [],
        "surrounding_texts": [
            "A Four-Legged Walking Machine The first numerical example is intended to show that a) discontinuities will occur in the solution produced by eqs.(4a) to (4c), even when no collision occurs during the change in topology of the system, and b) the techniques presented can be used t o smooth these discontinuities. The four-legged walking machine shown in Figure l a is supported by three of its legs while its center of mass moves forward as shown in Figure 2a; its fourth leg is lowered to contact the ground at t = 0.5 s. with zero contact velocity. The inertia of the legs is assumed t o be negligible, allowing us to write the dynamical equations for the body of the machine as follows: 1 mo(ao + g ) where f, is the %dimensional vector of foot contact forcesi.e., we assume that moments cannot be generated at the foot/ground contact. Matrix A1 will therefore undergo a discontinuous change at t = 0.5 s as follows where the matrices Ci are defined by eq.(lc) with the ci vectors defined as follows: c1 = [ -0.5 ] , c2 = [ 0.5 ] 1.5 - cm 1.5 - x C ~ -0.7 -1.0 - X c m - X c m c3 = [ c4 = [ !f7] The objective function given by eqs.(l4a) and (14b) was minimized with c = 0, W = 1 and W = pl-i.e., placing a weight of p on the continuity of the contact forces. Contact constraints are imposed on the system t o ensure nonnegativity of the normal contact forces between the feet and the ground, and foot friction forces within the friction pyramid with a coefficient of friction ,U = 0.5 [8]. Furthermore, the inequality constraints given by eq.(8c) are included to limit all contact force discontinuities t o A, = . . . = Aq = A Newtons per time step of 10 ms. Three cases were investigated: a) no effort is made to smooth the solution t o the optimization problem ( p = 0, A = 00); b) inequality constraints are used t o limit the rate of change of each contact force t o 20 N/step ( p = 0, A = 20); and c) a penalty is imposed on discontinuities in the contact forces through the objective function ( p = 10, T = 0.5 s, A = 00). Figures 2b, c and d show the resulting norm of the contact forces at each of the four feet (all forces a t foot #1 are zero until t = 0.5 s). Both of the proposed techniques have resulted in considerably smoother force time histories of the foot contact forces. h 24 1 Two Manipulators Handling a Common Object The second example is intended to show the behavior of the proposed smoothing techniques for a collision during which there is no change in topology. Two Puma 560 manipulators rotate a payload, as shown in Figure 6a. The payload, initially at an angle of 45\u2019 counterclockwise from the horizontal, is rotated through 90\u2019 clockwise in two seconds, as shown in Figure 6b. The Hartenberg-Denavit parameters and inertia properties of the Puma 560 were taken from [ll]. The payload was a 1 m long solid aluminum bar with a rectangular crosssection 5 cm high and 10 cm deep. Its mass was therefore 13.5 kg and its moment of inertia about the relevant horizontal axis through its center of mass was 1.128 kg-m2. At t = 1.0 s, a sudden external force is imposed in the xdirection of fz = lOON a t the center of mass of the payload (i.e., ce = 0 ) , thereby simulating a collision between it and the environment. The objective function given by eqs.(l4a) and (18) was minimized with c = 0, W = 1 and W = pl-i.e., placing a weight of p on the continuity of the actuator torques. The only inequality constraints included in this problem are those given by eqs.(ba), (8b) and (11) to limit all actuator torque discontinuities to A,, = ... = Apr = A N-m per time step of 10 ms. Once again, three cases were investigated: a) no effort is made to smooth the solution to the optimization problem ( p = 0, A = 00); b) inequality constraints are used to limit the rate of change of each actuator torque to 11 N-m/step ( p = 0, A = 11); and c) a penalty is imposed on discontinuities in the actuator torques through the objective function ( p = 10, T = 1.0 s, A = 00). The resulting actuator torques for manipulator #1 (on the left in Figure sa) for case (a) are shown in Figure 3 . (The results are not shown for the second manipulator due to their similarity to those shown.) Since the maneuver takes place in a plane, two of the wrist actuators (#4 and #6) are not active. When the actuator torques are smoothed using inequality constraints-case (b) as shown in Figure 4-these same two actuators remain inactive. The discontinuity in actuator # 3 is reduced, while that in actuators # 2 and 5 is increased (n.b., the plot scales are different for the various actuators). In effect, the inequality constraints have distributed the discontinuity more evenly over the active actuators, thereby decreasing the largest discontinuity. This is desirable, assuming that all the actuators are equally able to withstand discontinuities. If they are not, the A,\u2019s can be made more restrictive for the more sensitive actuators. When the actuator torques are smoothed using the new objective function, the two previously-inactive actuators become active (see Figure 5). This time, the discontinuities in actuators # 1 and 3 are reduced, while those in actuators # 2, 4, 5 and 6 are increased. Once again, the largest discontinuity has been decreased by distributing the shock more evenly, this time over all the actuators. If the actuators were not all equally able to withstand discontinuities, the weighing matrix W could be modified to penalize discontinuities in the more sensitive actuators more heavily. h h Conclusions vary discontinuously when the kinematic structure changes. These discontinuous changes were traced to two independent causes (yet which often occur simultaneously), namely a) changes in the topology of the system and b) discontinuous changes in the motion of the system due to shocks. Two techniques have been proposed to smooth the force discontinuities by modifying the optimization problem which is normally formulated to solve the inverse dynamics of redundantly-actuated systems. The first technique imposes new inequality constraints to limit the difference in the force solution between two instants in time, and yields smooth linear force time histories with a small increase in CPU time, assuming it need not be applied iteratively. The second, preferred technique alters the objective function to penalize large differences in the force solution between two instants in time. This technique is not expected to increase the CPU time required to find a solution. Acknowledge me nt s The work reported here was completed with the support of the Natural Sciences and Engineering Research Council of Canada (NSERC Research Grant #A-4532), the Fonds pour la formation de chercheurs et l\u2019aide k la recherche, of QuCbec (FCAR Research Grant #88AS2517) and the Institute for Robotics and Intelligent Systems (IRIS). References [l] Orin, D. E., and Oh, S . Y., \u2018Control of Force Distribu- tion in Robotic Mechanisms Containing Closed Kinematic Chains\u2019, Trans. of the ASME Journal of Dynamic Systems , Measurement and Control, Vol. 103, No. 2, 1981, pp. 134-141. [2] Kerr, J., and Roth, B., \u2018Analysis of Multifingered Hands\u2019, International Journal of Robotics Research, Vol. 4, No. 4, Winter 1986, pp. 3-17. [3] Nakamura, Y., Nagai, K., and Yoshikawa, T., 1987, \u2018Dynamics and Stability in Coordination of Multiple Robotic Mechanisms\u2019, International Journal of Robotics Research, Vol. 8, No. 2, Apr. 1989, pp. 44-61. [4] Zheng, Y. F., and Luh, J. Y. S., \u2018Optimal Load Distribution for Two Industrial Robots Handling a Single Object\u2019, Proceedingsof the 1988 IEEE Int. Conf. on Rob. and Aut., Philadelphia, pp. 344-349. [5] Klein, C. A., and Kittivatcharapong, S., \u2018Optimal Force Distribution for the Legs of a Walking Machine With Friction Cone Constraints\u2019, IEEE Trans. on Rob. and Aut., 1\u201901. [6] Klein, C. A., and Chung, T.-S., 1987, \u2018ForceInteractionand Allocation for the Legs of a Walking Vehicle\u2019, IEEE Journal of Rob. and Aut., Vol. RA-3, No. 6, 1987, pp. 546-555. [7] Danowski, P., \u2018Dynamics of the Walking Stick Insect\u2019, (in German), Masters Thesis, Technical University of Munich, 1989. [SI Nahon, M., \u2018Optimization of Force Distribution In Redundantly-Actuated Robotic Systems\u2019, Doctoral Thesis, McGill University, Feb. 1991. [9] Zheng, Y. F., \u2018Collision Effects on Two Coordinating Robots in Assembly and the Effect Minimization\u2019, IEEE Trans. on Systems, Man, and Cybernetics, Vol. SRIC-17, [lo] Goldfarb, D., and Idnani, A., \u2018A Numerically Stable Dual Method for Solving Strictly Convex Quadratic Programs\u2019, Math. Prog., Vol. 27, 1983, pp. 1-33. [ll] Armstrong, B., Khatib, O., and Burdick, J., \u2018The Explicit Dynamic Model and Inertial Parameters of the Puma 560 Arm\u2019, Proceedingsof the 1986 IEEE Int. Conf. on Rob. and Aut., San Fransisco, pp. 510-518. 6, NO. 1, 1990, pp. 73-85. NO. 1, 1987, pp. 108-116. The dynamic equations of motion of systems with timevarying kinematic structure have coefficients which may"
        ]
    },
    {
        "image_filename": "designv11_24_0002619_095440605x31481-Figure13-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002619_095440605x31481-Figure13-1.png",
        "caption": "Fig. 13 Cutting geometry of a CC2-gear in two singleindexing cycles using two cutter heads with round-nosed tools having the same radius to the \u2018finishing point\u2019, N \u00bc 24, x \u00bc \u00fe0.7, f \u00bc 208, and R/m \u00bc 10",
        "texts": [
            " Regardless of the earlier facts, Sidorenko et al. [49] suggested a method of generating what is termed here CC2-gears. Two cutter heads with roundnosed cutters \u2013 rather than pointed styli \u2013 finish the gear in two single-indexing cycles. The cutter nose centre, in the midplane, is fed tangentially to the base circle, and the radius to the \u2018supposedly fixed\u2019 working point is made equal to R in both cases. The original drawings in reference [49] are too short of doing justice to the idea. Instead, Fig. 13 is drawn to depict two independent, momentary positions of the cutter heads superimposed; the outside cutter on its way down (position 1) and the inside cutter on its way up (position 3) the respective flank in the midplane. The two flanks are being generated by a torus each, of a tube radius equal to the tool nose radius rt. Here, a further error is introduced, as these tori will not even generate rack tooth flanks correctly; a torus neither fits inside nor around an (inclined) elliptic cylinder in line contact. The imagination, that it will be precisely one point on the tool nose edge that finish-cuts across the facewidth, is false, but again, the deviation from exact ellipticity of the rack tooth flanks is small with the \u2018usual\u2019 pressure angle of 208 and with small ratios of the torus tube radius to the torus mean radius. The cutter head feed must be stopped where the tool nose reaches the root circle in the midplane, from either direction, positions (1) and (2) in Fig. 13. In the side planes, position (2) could \u2013 incidentally \u2013 also depict the tool nose of the outside cutter, when at its midplane stop (1), while position (4) is that of the inside cutter, when at its stop (2). Therefore, the outside cutter could (be made to) generate almost the same whole depth across the face, but the inside cutter must either dig shallower in the side planes as shown, or, with a little further feed down, deeper in the midplane. At these positions the cutting point must have generated the profile to below the form circle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001914_rob.10048-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001914_rob.10048-Figure8-1.png",
        "caption": "Figure 8. Schematic diagram of the hexaglide mechanism.",
        "texts": [],
        "surrounding_texts": [
            "Based on the two-stage algorithmpresented in the last section, a computer program for solving the direct kinematics problem of the two LAP types is developed. The program is written in Fortran 77 and executed on a 650MHz Pentium III personal computer. Two numerical examples are presented in this section todemonstrate the characteristics of theproposed method. The manipulators used for the examples are the general Stewart platform and the Hexaglide, as shown in Figures 7 and 8, respectively. The geometric dimensions of the two manipulators are given in Tables I and II. The dimensions of the general Stewart platform are identical to those presented by Innocenti and Parenti-Castelli.5 Example 1. To demonstrate the efficiency and stability of the proposed method, 100 sets of driving joint variables, randomly generated within the workspace of the robots, were given the program to solve for the corresponding configuration of the moving platform. The initial approximation of PC and [R] for all of the problems was assigned to: PC = 0 and [R] =  0 0 1 1 0 0 0 1 0   where 0 is a null vector. The convergence criterion is designated to \u03b5 = 10\u22128. It turned out that all of the problems were solved without any difficulty. The average computation time for solving one problem is about 0.36 second for the general Stewart platform, and about 0.37 second for the Hexaglide. To illustrate the typical convergence property of the method, the objective function value versus the iteration steps of an arbitrarily selected problem of the general Stewart platform is plotted in Figure 9 by using linear and logarithmic scales. The figure indicates that when the feasible configuration search algorithm tends to slow down as it approaches the solution, the NR algorithm takes over and gives the quadratic convergence rate. Example 2. This example demonstrates the ability of the proposedmethod for findingmultiple direct kinematic solutions. The values of the driving joint vari- ables for the general Stewart platform are given as Qd = [7.141, 7.348, 7.141, 6.403, 9.165, 5.000]t, and for the Hexaglide are given as Qd = [9.5, 12.0, 9.5, \u22129.5, \u221212.0, \u22129.5]t. To find the multiple solutions, the programwas executed recursively 100 times, and the initial approximations of PC and [R] were randomly assigned for each execution. The convergence criterion is alsodesignated to \u03b5 = 10\u22128. The total execution time for the case of the general Stewart platform is about 27 seconds, and that of the Hexaglide is about 81 seconds. Table III shows the six distinct real solutions found for the general Stewart platform, which are exactly the same solutions reported by Innocenti and Parenti-Castelli.5 For the Hexaglide, a total of 12 distinct real solutions were found. These solutions were distributed symmetrically above and below the base plane. The six solutions that are above the base plane are given in Table IV."
        ]
    },
    {
        "image_filename": "designv11_24_0001455_50006-1-Figure5.59-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001455_50006-1-Figure5.59-1.png",
        "caption": "FIGURE 5.59 Magnetic MEMS actuator.",
        "texts": [
            " There has also been recent progress towards the commercialization of such devices [32]. However, most of these devices are not fabricated in a purely batch mode. Instead, they typically require a modest amount of manual assembly. It is likely that magnetic microactuators will gain in importance as methods for depositing rare-earth materials such as NdFeB onto microstructures improve. In the remainder of this section we discuss the operation of a batch-fabricated magnetic microactuator. A batch-fabricated magnetic microactuator is shown in Fig. 5.59. It consists of a soft magnetic (NiFe) plate supported on one side by a narrow torsion beam that is anchored at either end to a silicon substrate. The fabrication process for this structure is shown in Fig. 5.60a-e [30]. The operation of the actuator is as follows: When a uniform field Hex t is applied, it induces a magnetization in the plate and a magnetic torque develops that acts to rotate the plate up, away from the substrate. This rotation is resisted by a restoring torque that results from the torsion of the support beam"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001455_50006-1-Figure5.28-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001455_50006-1-Figure5.28-1.png",
        "caption": "FIGURE 5.28 Cross section of a rotary bias field actuator.",
        "texts": [
            "10 RESONANT ACTUATORS 405 406 CHAPTER 5 Electromechanical Devices Magnetooptical (M-O) recording was discussed in Section 4.10. The basic elements of an M-O system are shown in Fig. 5.27. Recall that M-O systems require oppositely oriented bias fields for the recording and erasure processes [13-15]. In this section we discuss an actuator that serves the dual function of providing the bias field and implementing the bias field reversal. Specifically, we analyze the rotary permanent magnet actuator shown in Fig. 5.28. This actuator consists of a cylindrical bipolar bias magnet (Fig. 5.29), surrounded by a stationary concentric conductive shell and a drive coil. When the coil is energized it rotates the magnet to one of two equilibrium positions, thereby producing a bias field of desired polarity across the recording media. Rotation of the magnet gives rise to eddy currents in the conductive shell that impart a drag torque and reduce oscillations of the magnet about its equilibrium positions. We develop a model for this actuator in the following example [16,171. 5.11 MAGNETOOPTICAL BIAS FIELD ACTUATOR 407 408 CHAPTER 5 Electromechanical Devices EXAMPLE 5.11.1 Set up the equations of motion for the rotary bias actuator shown in Fig. 5.28. The magnet has a radius a and length h, with a << h. The coil has n turns and has a length l c. SOLUTION 5.11.1 This is a moving magnet actuator and is governed by the equations for rotational motion (5.87), which we repeat here for convenience: _ _ [ cgA(i, 0) ] di(t) _ 1 Vs(t ) _ i(t)(R + R~oil) - - - - c o ( t ) dt L ~0 dog(t) 1 = T(i,O, co) dt Ym dO(t) dt - - = co(t). (5.207) These equations contain nonlinear terms and can be solved numerically once expressions for L, c~A(i, 0)/00, and T(i, 0,09) have been determined"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000878_s0167-8922(08)70451-6-FigureI-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000878_s0167-8922(08)70451-6-FigureI-1.png",
        "caption": "Figure I: Plain radial lip seal for rotating shafs",
        "texts": [],
        "surrounding_texts": [
            "Radial lip seals, also called rotating shaft seals, are very widely used machine elements, providing good performance at relatively low costs. They are employed to seal rotating and reciprocating shafts. They prevent (1) leakage of a fluid under low static pressure or that is splashed at the shaft, and (2) entrance of dust, dirt, etc., into the sealed fluid. The plain rotating shaft seal is the most interesting of the two, since the operational principles are still unclear. Figure 1 shows the confguration of a rotating shaft seal. The contact width is very narrow and of the order of 0.1 mm. The design of this modern lip seal is more than 60 years old. In the ideal case, the geometry of a shaft seal is rotationally symmetric. Reynolds' equation explains that there is no reason why a continuous fluid film should develop, because it would be parallel. There is no entrainment action. Nevertheless, since 40 years researchers generally agree on the existence of a coherent fluid film, after Jagger (1957) concluded that the measured film thickness is of the order of 1 pm. More support for full film lubrication conditions stems from the exceptional low seal wear, after a run in period. During this run in period, which may take a few 100 hours, a wear track is formed. The surface roughness of this track is vital to the sealing properties (Horve 1991, 1992). The lubrication mechanism is not obvious and has not found general agreement yet. If the existence of a full film is accepted, leakage would be expected. Fortunately, a properly operating plain lip seal does not leak after running in. Experienced seal designers know that a lip seal can pump fluid from the air side to the oil side, even 220 against a pressure head. This upstream pumping ability allows leakage free operation of the seal. The sealing mechanism is not obvious and still being disputed. It is clear that experiments play an important role in the quest for the physical explanation of the lubrication and sealing mechanism. Most of the experimental studies on radial lip seals that have been published concern global quantities like friction torque, radial load, or leakage. As part of the solution lies in the surface roughness, these global measurements cannot solve the problem. Local measurements are needed to generate ideas for the understanding of the operating principles. This paper reports on local measurements of tangential deforniations and of film thickness in the contact between shaft and seal, to provide more support for some recent theoretical models. A brief review of theories and experiments will be given first."
        ]
    },
    {
        "image_filename": "designv11_24_0001361_s0021-9290(02)00029-5-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001361_s0021-9290(02)00029-5-Figure7-1.png",
        "caption": "Fig. 7. (A, B) Map of the correction term DL of the hammer throw distance L computed for calmness (A) and an east-wind with a speed of 2 m=s (B) for a stadium at the latitude of Sodankyl.a (j \u00bc 67:51) if the reference stadium is at the latitude of Athens (j \u00bc 381) where the reference release direction is North (b \u00bc 01). The border lines of the alternating grey and white zones represent different DL values changing between the numerical values given at the margins of the annular maps with a step of DL \u00bc 2 cm (A) and 8 cm (B). Every point of the map gives the numerical value of distance DL; by which the hammer thrown in Sodankyl.a would fly further or closer in comparison with an imaginary hammer thrown northward in the reference stadium in Athens on horizontal ground with the same initial (release) and environmental conditions T \u00bc 201C; p \u00bc 101 325 Pa; H \u00bc 0 m: The inner black circle in the annular maps represents the male world record Lr \u00bc 86:74 m achieved in 1986. (C, D) Change of DL computed for the male world-record range Lr of the hammer throw as a function of release direction b:",
        "texts": [
            " In these angular coordinate systems the range is measured radially, and the angle measured from North is the release direction. As a demonstration for using the correction maps in practice, consider the following example: In an athletic competition in Sodankyl.a a male hammer thrower reached a range of 70 m with an eastward release direction. His trainer (or the spectators, or officials) would like to know how great would be his range in the reference stadium in Athens. One first selects the corresponding correction map (Fig. 7A) then the eastward direction (b \u00bc 2701) and measures a section, corresponding to the range L \u00bc 70 m; from the centre of the map. Thereafter the value of the correction term DL is read on the map. Finally, adding the correction term to the range L \u00bc 70 m; the corrected range is obtained. The correction maps in Figs. 7\u201310B are asymmetric. One of the reasons for this is the non-linear effect of the wind. As we have seen above (Fig. 3), a head wind with a given speed decreases the range to a greater extent than the enhancement of the throw distance due to a tail wind with the same speed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002326_dac-34138-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002326_dac-34138-Figure6-1.png",
        "caption": "Figure 6. Uniform and Non-uniform Layer",
        "texts": [
            " Since the multi-axis slicing algorithm is adopted, non-uniform layers may appear during deposition. The building process of non-uniform layers requires cooperation between LM and machining. The purpose of integrating two processes is to improve overall efficiency and accuracy of the whole system. The sequence of two processes also needs to be decided. In the deposition process, each layer consists of two slices upper slice and lower slice. The thickness of the traditional slicing layer is uniform; however, in LAMP, the thickness in one layer may not be uniform. In Figure 6, two types of slicing layers are shown. For one non-uniform layer, the distance between the upper slice and lower slice varies from point to point. Due to the difficulty of the deposition thickness control, currently the laser deposition process can only build the layer with uniform thickness. In order to build a non-uniform layer, a uniform (thickness) layer is deposited and then the machining process is carried on to craft the shape of a non- 44 aded From: http://proceedings.asmedigitalcollection"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002064_3-540-36224-x_1-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002064_3-540-36224-x_1-Figure3-1.png",
        "caption": "Fig. 3. Configuration space potential field generated by each obstacle point Pi.",
        "texts": [
            " Each obstacle point Pi detected by the on-board sensors ot the robot produces a potential field in the plane defined as follows. If M is a point in the plane at distance d from Pi, ui(M) = 1 (d+d0)2 \u2212 1 (d1+d0)2 if 0 \u2264 d \u2264 d1 ui(M) = 0 if d > d1 d0 < d1 are constant distances. Let fi(M) = \u2212\u2207ui(M) be the force in the plane deriving from this potential. Let R and T be the closest points to Pi on the robot and on the trailer. The configuration space potential field implied by Pi is defined by evaluating the plane potential field at R and T (Figure 3): Ui(q) = ui(R)+ui(T ) (16) If Pi is inside the robot or inside the trailer the corresponding term in Ui is set to 0. The configuration space potential field is defined as the sum of the potential fields relative to each obstacle point: U(q) = \u2211 i Ui(q) The gradient of the potential field is obtained by differentiating (16) w.r.t. the configuration variables (x, y, \u03b8, \u03d5). \u2202Ui \u2202q (q) = \u2207ui(R) \u2202R \u2202q +\u2207ui(T ) \u2202T \u2202q = \u2212fr \u2202R \u2202q \u2212 ft \u2202T \u2202q where fr = fi(R) and ft = fi(T ) are the values of the plane force field induced by ui at R and at T "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001967_910017-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001967_910017-Figure7-1.png",
        "caption": "Fig. 7 \"Three-Axis Theorem\" in a three dimensional suspension",
        "texts": [
            " Hence, we are naturally ready to consider a screw axis to replace the roll axis since a roll axis is a purely two dimensional product made with purely two dimensional geometry of suspensions. Let us consider an expansion of the Kennedy Theorem in three dimensional space. Beggs (8) called the expanded theorem the \"Space Dual\" of the Kennedy-Aronhold Theorem in Plane Motion\", and Suh (9) called it simply the \"Kennedy Theorem in Space\" or \"Three-Axis Theorem.\" We shall call it here the ThreeAxis Theorem.\" Compare the line passing through the three points G. E and F in Fig. I 149 in two dimensional space with the line passing through the three points G, E and F in Fig. 7 in three dimensional space. The instant screw axis of F is the screw axis of the suspension with respect to the chassis, the instant screw axis of E is the screw axis of the tire with respect to the ground, and the instant screw axis of G is the screw axis of the chassis with respect to the ground, The Three-Axis Theorem states that the line GEF in three dimensional space intersects all of the three instant screw axes with perpendicularity. Since a vehicle, assumed as a rigid body in three dimensional space, should have one instant screw axis with respect to the ground at any instant, we use this Three-Axis Theorem four times; once for each of the four independent suspensions, to establish the vehicle's screw axis for the instantaneous motion with respect to the ground"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000194_1.2832445-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000194_1.2832445-Figure1-1.png",
        "caption": "Fig. 1 A schematic diagram of a rolling element bearing",
        "texts": [
            " Each of these stiff nesses is nonlinear in nature and has to be considered separately. This is what is done in the present work. In this section, a model for analysis of the structural vibration in rolling element bearings is developed. First the expressions for kinetic and potential energies are formulated. Using these expressions the equations of motion are derived utilizing La- grange's equation. These equations are then normalized to ob tain a comprehensive form. 2.1 Kinetic and Potential Energy Expressions. A sche matic of rolling element bearing is shown in Fig. 1. Figure 2 illustrates the mathematical model wherein the rolling element bearing is represented by a mass-spring system. Since the Hert zian forces arise only when there is contact deformation, the springs are required to act only in compression. In other words the respective spring force comes into play when the instanta neous spring length is shorter than its unstressed length; other wise separation between ball and race will take place and the resulting force is set to zero. A number of assumptions are made in the development of the mathematical model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003529_gt2004-53611-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003529_gt2004-53611-Figure1-1.png",
        "caption": "Fig. 1 Bump-type gas foil bearing",
        "texts": [
            " Foil bearings (FBs) fulfill most of the requirements of novel oil-free turbomachinery by increasing tenfold their reliability in comparison to rolling elements bearings, for example [1]. Foil bearings are made of one or om: http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ashx?u more compliant surfaces of corrugated sheet metal and one or more layers of top foil surfaces. The compliant surface provides bearing structural stiffness and comes in several configurations such as a bump-type (see Figure 1), leaf-type and tape-type, among others. Due to the hydrodynamic film created by rotor spinning, the top foil and elastic structure retract resulting in a larger film thickness than with rigid wall bearings [2, 3], thus enabling high speed operation and larger load capacity [1], including a tolerance for shaft misalignment. The underlying compliant structure (bumps) provides a tunable structural stiffness source [4, 5, 6], and damping of Coulomb type arises due to the relative motion between the bumps and the top foil, and between the bumps and the bearing wall [7, 8]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003463_cdc.2006.377242-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003463_cdc.2006.377242-Figure2-1.png",
        "caption": "Fig. 2. Scheme of the controlled surfaces.",
        "texts": [
            " Assuming airfoil profiles with small Reynolds numbers and with reasonably small angles of attack, we make use of the following expressions CL = KLp CD = KDp2 with p the angle of attack with respect to relative wind and KL, KD constant coefficients collecting other geometric parameters. Similar arguments could be used to model ducted fan thrust T and resistance torque Q as T = KT w2 e Q = KQw2 e (4) with KT and KQ constant coefficients. Output velocity of the air generated by the main rotor, denoted by Ve, is assumed to be proportional to angular fan velocity we. In our model air velocity Ve represents also the relative wind velocity to calculate forces generated by each active flap using (3). To model those forces we refer to our design configuration shown in figure 2. First we will consider singularly all forces generated by each active flap and then we will consider the resultant contributions that affect the rigid body dynamics. Geometric pitch of each active flap is obtained as the sum of two different control inputs. The first one, denoted with c, is the same for all four surfaces and represent the control action able to generate the anti-torque necessary to counteract engine one and to obtain controllability of \u03c8 dynamics. Second one, a or b dependently on which flap is considered, is used to obtain two different forces directed respectively along x and y axis. These forces are used to govern both \u0398 and, by propeller thrust projection, lateral/longitudinal dynamics. Since all four surfaces are equivalent, we denote with KFL and KFD respectively the constant lift and drag coefficients of each flap. With an eye to figure 2, by means of equations (3) and (4), the expressions of the modules of lift forces F i L and drag forces F i D associated to each flap are given by F 1 L = KFL w2 e (c + b) F 2 L = KFL w2 e (c \u2212 b) F 3 L = KFL w2 e (c + a) F 4 L = KFL w2 e (c \u2212 a) F 1 D = KFD w2 e (c + b) 2 F 2 D = KFD w2 e (c \u2212 b) 2 F 3 D = KFD w2 e (c + a) 2 F 4 D = KFD w2 e (c \u2212 a) 2 whereas the direction of each F i L and F i D is shown in Figure 2. Consider first the overall effects of the lift forces and observe that the module of each F i L is a linear function of the control inputs a, b and c, i.e. we could consider separately the effects of each control inputs in the overall dynamics. Since the centers of pressure of any two opposite surfaces are at distance dT , by means of control input c we obtain a resultant torque QF directed along z axis and given by QF = \u22122KFL dT w2 ec whereas inputs a and b are in charge of generating a couple of forces directed respectively along the body x and y axis and given by Fx = 2KFL w2 ea Fy = 2KFL w2 eb "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001026_tt.3020010103-Figure10-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001026_tt.3020010103-Figure10-1.png",
        "caption": "Figure 10 Variations of inlet and exit angles with h\",",
        "texts": [
            " It is further assumed that any negative pressure excursions (also observed by other^'^^\"^'^^'^) just before cavitation are negligible in magnitude compared with the average positive pressure. The subambient pressure loop in some experimental pressure traces is associated with electrical effects (as fully discussed in ref. 32). Tribotest journnl 1-1, September 1994. (71 44 1354-4063 $6.00 + $2.50 Measuring Contact Pressure Distributions under Elastohydrodynamic Point Contacts 45 The local inlet and outlet positions are determined in terms of a pair of characteristic angles 7c - \u20acIi and 8, - n, tabulated by Tipei\u201d and illustrated by Figure 10 (see overleaf). The local exit positions found form symmetrical straight lines on either side of the x-axis. The conjugate inlet positions also form symmetrical lines about the same axis. The inlet boundary thus found is for just fully flooded conditions as described by Tipei\u201d and is not used as the reference in this analysis. The exit zero pressures of experimental traces at each cross-section are positioned along the outlet boundary found and the trace bases are extended parallel to the x-axis in order to determine the inlet boundary which corresponds to the experimental meniscus"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003917_0278364905058242-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003917_0278364905058242-Figure4-1.png",
        "caption": "Fig. 4. The minimal disk containing three footholds when is (a) an acute and (b) an obtuse triangle.",
        "texts": [
            " The PCG algorithm described below approximates the feasible three-limb postures by cubes. The approximation requires an explicit formula for the reachable set which we now describe. The following is an equivalent formulation for Rijk Rijk = { (s1, s2, s3) \u2208 Ii \u00d7 Ij \u00d7 Ik : rmin(s1, s2, s3) \u2264 R } , where rmin(s1, s2, s3) is the radius of the minimal disk containing the foothold positions x(s1), x(s2), and x(s3). Let be the triangle generated by these three points. Then the formula for rmin(s1, s2, s3) is divided into two cases (Figure 4). When is an acute triangle (i.e., with angles less than 90\u25e6), rmin(s1, s2, s3) is the radius of the disk passing through the three points, given by rmin(s1, s2, s3) = \u2016x(s1)\u2212 x(s2)\u2016 \u00b7 \u2016x(s2)\u2212 x(s3)\u2016 \u00b7 \u2016x(s3)\u2212 x(s1)\u2016 2\u2016x(s1)\u00d7 x(s2)+ x(s2)\u00d7 x(s3)+ x(s3)\u00d7 x(s1)\u2016 , where u\u00d7 v is the scalar obtained by taking the determinant of the 2 \u00d7 2 matrix [u v]. When is an obtuse triangle, rmin(s1, s2, s3) is simply the half-length of the longest edge of : rmin(s1, s2, s3) = 1 2 max 1\u2264p,q\u22643 {\u2016x(sp)\u2212 x(sq)\u2016}. The two-part formula for rmin(s1, s2, s3) reveals that the set Rijk is bounded by quadratic surfaces in contact c-space"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002942_6.2004-5008-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002942_6.2004-5008-Figure8-1.png",
        "caption": "Figure 8: The NASA Flying Test Platform.",
        "texts": [
            " This perturbed dynamical system can be viewed as an linear parameter varying (LPV) system for control law design wherein the scheduled parameters may include the trim parameters such as attitude and translational velocity. This viewpoint is particularly attractive because the control law analysis and synthesis is well understood and technologically viable (see for example [11],[12],[13],[14]). For further details on both control law approaches, see [8]. The attitude control approach described above is tested using the vehicle pictured in Figure 8 as a CAD model. The vehicle is a platform levitated by four ducted fans arranged symmetrically about the z-body axis. Each fan duct is equipped with a parallel pair of thrust vectoring vanes, downstream from its fan. Each fan and pair of vanes is individually commanded by the control system. The z-body axis angular momentum bias is provided by a momentum wheel, powered separately from the levitation fans, and can be seen in the Figure at the center of the platform. Although the simplest and lightest momentum biasing mechanism is provided by augmenting the z-body axis moment of inertia of the propulsion system, momentum wheel is separately mechnized in order to facilitate tests in which different magnitudes of momentum bias are explored"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002566_s0022-0728(83)80533-6-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002566_s0022-0728(83)80533-6-Figure5-1.png",
        "caption": "Fig. 5. Absorption spectra of the oxidized forms of TPPD in CH3CN. (I, 2) Spectra obtained from a Pt electrode modulated with a 30 Hz square wave, pulse amplitude equal to 0.50 and 1.0 V respectively from the base line at 0.0 V for a 1.7x 10 4 M solution of TPPD; (1', 2'): conventional spectra of solutions 2.8 \u00d7 10 -4 M in TPPD \u00f7\" and TPPD 2+ respectively.",
        "texts": [
            " increased at the level of the first anodic peak but a further slow-increase was observed till the beginning of the reduction of TAP 2+ where a faster increase of (AR/R)43o occurred. With the potential at the level of the TAP 2 +//TAP +\" couple, the light beam was integrating the total spatial concentration distribution of TAP +. as it was formed following reaction (3) from TAP 2+ moving into the bulk of the solution and encountering TAP diffusing towards the electrode. (AR/R)59o for TA P 2+ did not increase unt i l the onset of the second oxidat ion step (a small signal due to the spectral overlap of Figure 5 shows the spectra obta ined from T P P D in CH3CN dur ing DPSC with pulses either into the first wave or spann ing both waves. The posi t ions and the relative intensit ies of the bands of T P P D +\" and T P P D 2+ are in good agreement with the corresponding values of the convent ional spectra of these species in bulk solution. The transients AR/R = f(t) were obta ined by moni to r ing T P P D +\" at 825 n m and T P P D 2+ at 550 nm. The (AR/R)82s-t 1/2 plot was not l inear for the whole of the anodic pulse at the level of the first wave and the ratio [ A ( 2 t a ) - A ( t a ) ] / A ( t a ) was higher than the theoretical value for a pure diffusion control led process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001382_robot.2000.844729-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001382_robot.2000.844729-Figure2-1.png",
        "caption": "Figure 2: External Forces",
        "texts": [
            " In addition, we define the unit vector n, pointing in the direction of the center of path curvature (not necessarily tangent to the surface), and I C , fixed to the inertial frame opposite of the gravity force. The projections of the unit vectors k and n on the vehicle fixed frame are denoted by subscript of the respective unit vector. For example, kt denotes a projection of k on t . The external forces acting on the vehicle consist of the friction force F (the sum of all the horizontal tire forces), the normal force R (the sum of all normal tire forces) applied by ground on the vehicle in the I- direction, and the gravity force - m g k , as shown in Figure 2. The equation of motion of the vehicle are written in the vehicle fixed frame in terms of the tangential speed B and the tangential acceleration I [ l l ] : ft = m g k t + m s (7) f, = m g k , + m m , S 2 (8) R = m g k r + m n n r B 2 (9) where ft and f, are the components of the friction force tangent and normal to the path, R is the normal force (the sum of all normal tire forces), n = l / p , and p is the path curvature. The moment of the friction force around the center of mass is missing from the equations of motion; it is considered later when we account for the tipover constraint"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002619_095440605x31481-Figure14-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002619_095440605x31481-Figure14-1.png",
        "caption": "Fig. 14 Cutting geometry of a CC3-gear in a singleindexing cycle with one cutter head; one torus for both flanks, N \u00bc 20, f \u00bc 208, x \u00bc \u00fe0.784, rt/m \u00bc 0.47, and b/m \u00bc 1.254",
        "texts": [
            " It can be shown that these conditions are realizable only when the base circle is appropriately smaller than the root circle. A schematic of a CC2-gear generator according to the previous method is included in reference [49]. The headstock is guided to move along a straight rail that could be tilted to the cutter head plane by the pressure angle in either direction. Generating this form is similar to the previous one except for using only one cutter head with one set of round-nosed tools for both flanks (Fig. 14). By implication, the teeth are crowned and they will have point contact. Cutting is done in a single-indexing cycle with two different outward or inward feeds of the tool-nose centre tangentially to the base circle, in the same phase setting. Needless to mention that devising a mechanism for such a feed cycle requires special attention. The deepest point lies on the \u2018vertical\u2019 common line of symmetry of tooth space/ cutter in the midplane, where a continuous root fillet or bottom land is produced",
            " rt m \u00bc 0:25p cosf x sinf (6) In constrast, the root radius plus the tool-nose radius must equal the standard (uncorrected) pitch radius, which gives b m \u00bc rt m \u00fe x (7) Equations (6) and (7) define the design space in Fig. 15. It is used to specify sets of parameters that just fit CC3-gears, and proves that, in the practical range of dedendum and pressure angle, only substantially profile-shifted gears are feasible. Worth mentioning is that the number of teeth to be cut has no influence, perhaps against initial expectation. The example indicated by the arrows in Fig. 15 is that of the gear in Fig. 14, for cross-reference purposes. Similar conditions pertain to CC2-gears; the reason why Figs 13 and 14 depict notably profile-shifted gears. It is also evident from Fig. 15 that rt/m would not exceed 0.5 m, which makes the (implicit) difference Rcav2 Rvex 4 m, versus a half-pitch in the case of CV2-gears. Hence, the inevitable crowning of CC3-gears is more reasonable. The idea of generating CC3-gears was introduced by Sidorenko et al. [50], and it is worth mentioning that both the pseudo-involute CC2- and CC3-gears are \u2018all-Russian\u2019 inventions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002326_dac-34138-Figure10-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002326_dac-34138-Figure10-1.png",
        "caption": "Figure 10 Machining tool-path for upper slice",
        "texts": [
            " Given a direction D ur , it is easy to find the maximum and minimum projection of the outermost plane, 55 nloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 01/28/2016 Terms o denoted as maxT and minT . The stepover distance of toolpath is dependent on the cutting tool diameter, denoted as S . A small increment \u03b4 is added to maxT and minT . The number of passes required to cover the whole area of the upper slice is given by max min 2 1 T T N S \u03b4\u2212 + = +     (9) The start and end points can be decided by the intersection of the cutting plane and the outermost loop, shown in Figure 10. The orientation of the machining tool is the same as the normal of the upper slice. Actually CC points are CL (cutting location) points. The next step is to machine out the side shape of the non-uniform layer. Since the thickness of one non-uniform layer is very small, one-pass multi-axis sculpting will achieve the goal. With sufficient resolution, the STL model can represent the actual model well. Points for edges in loops on the lower slice can be used as CC points. CL points can be obtained by ipCL CCp p rV= + r (10) where r is the radius of the machining tool"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000878_s0167-8922(08)70451-6-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000878_s0167-8922(08)70451-6-Figure6-1.png",
        "caption": "Figure 6: Photograph of RLS 2 test rig forjl in thickness nieasurenients (the test seal is removed). See text.",
        "texts": [
            " Test rig RLS2 Test rig RLS2 is a new apparatus, especially designed for film thickness determination in radial lip seals through fes detection. 3.3.1. Description The RLS2 apparatus consists of a hollow steel shaft, which holds a lens system and electronics, and is supported in two precision angle contact bearings. At one end a hollow glass sleeve is glued on this shaft. At the other side a pulley is mounted, which is driven by a toothed belt. The maximum shaft speed is 600 mid\u2019 and is closed loop controlled. Two seals are mounted in tandem geometry in a small housing, that can move axially with respect to the shaft. 226 Figure 6 shows the RLS2 test rig with the housing disassembled. The seal housing is mounted on a base plate with elastic pivots, allowing very small motions in two perpendicular directions. These motions are realised by means of two micrometers. At present. i t is not possible to measure friction on this apparatus. The hollow sleeve is made of duran glass with a refraction index n, = 1.477. It is glued on the steel shaft. I t has an outer diameter of 70h7 mm, and the thickness is 2.0 mm. The original sleeve had a radial runout of +/- 2 pm, but this one cracked (see under 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003965_bit.260221212-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003965_bit.260221212-Figure3-1.png",
        "caption": "Fig. 3. Lineweaver-Burk plot of the hollow-fiber enzyme reactor. PVA-B; F = lo-\u2019 ml/sec; [a = 5 unit/ml.",
        "texts": [
            " [El have a slope of k3a2 ln[(a + bYa1 and a Y intercept of Km/~,Eliq cyl The amount of product in the fractionated effluent (not total) increased and leveled off several hours after the introduction of the enzyme solution into the hollow fiber as is shown in Figure 2, where the abscissa is the time after the introduction of enzyme solution and the ordinate is the amount of hydrochloric acid used for titration of the fractionated effluent. The plateau value gave us the apparent reaction velocity v under equilibrium conditions. From the Lineweaver-Burkplot [eq. ( I ) ] with this velocity, which is shown in Figure 3, the apparent Michaelis-Menten constant K,(app) of this enzyme reactor systems was estimated. The Km(app) for various enzyme concentrations for several kinds of hollow fibers at F = ml/sec are shown in Figure 4, whose abscissa is the amount of the enzyme in unit/ml of the introduced enzyme solution and whose ordinate is the apparent Michaelis-Menten constant Km(app). From the figure, it is obvious that: 1) K,(app) increased with enzyme concentration. 2) The larger an activity of enzyme (unitlmg), the smaller the value of K,(app)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003549_rissp.2003.1285572-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003549_rissp.2003.1285572-Figure3-1.png",
        "caption": "Fig. 3: Friction Constraint for Contact Forces",
        "texts": [
            "2 Statics in the humanoid robot is'giveu by , .' By using eq.(3), the relationship of the force acting aP/aO. f B , n B , ~ H i , T L j f H i , fLi,andPdenotethe total force acting on the origin of the body coordinate, the total moment, the joint driving torque of the hand i, that of the leg j , the contact force vector of the hand i, that of the leg j , and the potential energy, respectively. 4 Manipulation In this section, we focus on the 2D motion of a hu- manoid robot within the sagittal plane as shown in Fig.3. Let us consider the case where a humanoid robot applies a contact force f H onto an object. If the contact force in the horizontal direction; f H z =I1 ,e: f )I becomes larger than the friction force between the object and floor f , = po 11 eff, -,mag 11, the object will begin to move on the floor. Thus, we consider how a humanoid robot can effectively apply f H s by using the whole body. For this purpose, we focus on the whole body internal force acting among the contact points. 4.1 Whole Body Internal Force Solving eq",
            " Now, we redefine the internal force for whole body manipulation as follows: Definition 1 (Whole Body Internal Force) Assume that a humanoid is standing on a floor and that the hands are contacting with an object. We define the internal force acting among the contact points and realizing the manipulation of an object as the \"Whole Body Internal Force\". Then, we consider two problems regarding the whole body internal force, i.e., 1) Can a humanoid robot apply the whole body internal force large enough onto the object? 2) If not, how is the whole body internal force limited? As shown in Fig. 3, the friction cone constraint for the contact force is defined as f = V A , x 2 0 , (8) where : 1 , v = .[ 0 0 WL11 WL12 0 wH1 w H 2 0 0 0 0 0 0 0 WL21 W L 2 2 T = [ AH1 A H 2 k . 1 1 XLlZ XL21 XLZZ ] , w ~ j and W L ; ~ denote the unit vector expressing the edge of the friction cone, and X H ~ and XL;~ denote the magnitude of the contact force along the edge of the friction cone. Substituting eq.(S) into eq.(6), the friction cone constraint for the whole body internal force is expressed as Nk=G+mg+VX X > O , (9) ' where we implicitly assumed that the total force / moment acting on the body balances ( t B = 0)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003880_ssp.116-117.534-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003880_ssp.116-117.534-Figure1-1.png",
        "caption": "Figure 1. Schematic representation of new type injection machine for test.",
        "texts": [
            " To avoid these problems, we propose to manufacture magnesium alloy component by using new type semi-solid injection machine [3]. This machine has advantages such as environmental friendliness and energy saving, because this machine without using CO2 and SF6 gases. Those gases have highly persistent greenhouse effects and contribute to global climate change [4]. And low yield of gating system compare with products is attainable. The aim of this paper is to investigated the fluidity in a permanent mold and the microstructures for the different fraction solid of AZ 91 D manufactured by new type injection machine. Figure 1 shows schematically new type injection machine for test only, not for production. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, www.ttp.net. (ID: 129.78.32.97, University of California, San Diego, La Jolla, United States of America-15/03/13,05:40:50) To ensure good casting products, uniform temperature distribution was required inside injection cylinder. Therefore, the injection cylinder was divided with six zones and covered with six heating elements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003294_detc2005-85275-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003294_detc2005-85275-Figure1-1.png",
        "caption": "Figure 1. Schematic for combined spindle-holdertool system. The frequency response function, G11(\u03c9), is the response to a harmonic force F1(\u03c9) at the tool tip, in the direction of the X1 axis.",
        "texts": [
            "org/about-asme/terms-of-use Do Here, blim is the limiting depth of cut, Ks is the specific cutting energy, z is the average number of teeth in the cut (this depends upon the number of teeth on the cutter and the selected radial immersion), and Gor(\u03c9) is the oriented toolpoint frequency response function (FRF) [5]. A simple relationship converts spindle speed \u2126 (usually given in revolutions per minute) into circular frequency \u03c9 . Generically, Gor(\u03c9) can be expressed as the product of a directional orientation factor, that depends on the radial immersion and force angle, and the tool-point FRF, in the case where a single flexible direction is considered. Figure 1 identifies the tool-point FRF, which is also called the direct receptance of the system at X1 [6], ( ) ( ) ( ) . 1 1 11 \u03c9 \u03c9\u03c9 F Examination of Eq. (1) indicates that the limiting depth of cut blim is controlled by the negative regions of the real part of the FRF. Furthermore, it follows from the formula that, as the absolute value of the negative real part of the FRF becomes smaller, the magnitude of the limiting depth of cut increases. Thus, if one could develop techniques for adjusting the minima of the real part of G11(\u03c9) (assuming that the directional orientation factor is constant), and for shifting the frequencies at which these minima occur, a method would be available for optimizing the material removal rate (MRR) in a given machining operation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001455_50006-1-Figure5.29-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001455_50006-1-Figure5.29-1.png",
        "caption": "FIGURE 5.29 Cylindrical bipolar bias magnet.",
        "texts": [
            "10 RESONANT ACTUATORS 405 406 CHAPTER 5 Electromechanical Devices Magnetooptical (M-O) recording was discussed in Section 4.10. The basic elements of an M-O system are shown in Fig. 5.27. Recall that M-O systems require oppositely oriented bias fields for the recording and erasure processes [13-15]. In this section we discuss an actuator that serves the dual function of providing the bias field and implementing the bias field reversal. Specifically, we analyze the rotary permanent magnet actuator shown in Fig. 5.28. This actuator consists of a cylindrical bipolar bias magnet (Fig. 5.29), surrounded by a stationary concentric conductive shell and a drive coil. When the coil is energized it rotates the magnet to one of two equilibrium positions, thereby producing a bias field of desired polarity across the recording media. Rotation of the magnet gives rise to eddy currents in the conductive shell that impart a drag torque and reduce oscillations of the magnet about its equilibrium positions. We develop a model for this actuator in the following example [16,171. 5.11 MAGNETOOPTICAL BIAS FIELD ACTUATOR 407 408 CHAPTER 5 Electromechanical Devices EXAMPLE 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003861_msf.505-507.949-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003861_msf.505-507.949-Figure2-1.png",
        "caption": "Fig. 2. Coordinate systems of internal gear meshing.",
        "texts": [
            " (3) Then, the transmission ration i of the nutation drive can be given as, 21 1 sinsin sin2 \u03b4\u03b4 \u03b4 \u03c8 \u03c0 \u2212 ==i (4) Coordinate system and coordinate transformation matrix in nutation drive Coordinate systems and their transformation are fundamental for meshing analysis and modeling. In the nutation drive, in order to obtain the meshing equations and the tooth surface equations, the meshing between the external and internal gear is discussed by introducing the crown gear. The coordinate system between the meshing of the internal gear and the crown gear is shown in Fig. 2. The Fig.1. Sketch of nutation drive. fixed coordinate system 0 0 0 0( )S , ,i j k is fixed at the point of the pitch cone of the crown gear. A body-fixed rotatable coordinate system ( )p p p pS , ,i j k is rigidly connected to the crown gear and rotates with the crown gear at angular speed of c\u03c9 about axis pk . The initial orientation of location of crown gear rotatable coordinate system pS is the same as the fixed coordinate system of 0S . The rotation movement of the crown gear is represented by the angle c\u03d5 in the meshing process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001533_robot.1989.100101-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001533_robot.1989.100101-Figure4-1.png",
        "caption": "Figure 4: IntersecCion of three dimensional friction cones with plane through contact points.",
        "texts": [
            "1 holds for any ci(p) = c i ( e (p ) ) which is monotone as a function of 6\u2019. Assuming that the coeficients of friction at the contact points are the same, it seems natural to define the functions ci(p) in such a way that, when they are equal, the resulting angles between finger forces and normals are equal. (The normals are 3-dimensional vectors.) We proceed as follows. Let ni be the unit normal at the contact point pi. (Unless otherwise stated i ranges from 1 to 3.) Let wi be the angle between ni and the plane M that contains the points pi (see Figure 4). Notice that w; does not depend on p. Define tan2(ei(p)) + sin2(wi) COSZ(Wi) ci(p) = where &(p) is defined as before. Since Ci(p) = tan(ang(p - p i , ni)), this definition achieves the desired result. Now assume c1@) = cz (p ) = c3(p) = k. Then, tan(O,(p)) = f ~ c o s ~ ( w i ) k Z - sin2(wi). Let us set, pj (k ) = -tan(Oi(p)). Equation 6 now becomes ( P - pi)*(Pi(k)ni + ti) = 0, (11) which in turn can be transformed into (see Equation 8) References (111 - D(k)X)P = 0 (12) [l] J . Demmel and B"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002815_bf01896173-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002815_bf01896173-Figure3-1.png",
        "caption": "Fig. 3",
        "texts": [
            " If the angular velocity vector of liquid-filled-cavity body rotating about 0 is ~ , its projections on the axes of Ox~x~x] are p, q, r respectively, then the Euler dynamic [2] equations are A~t =(B--C)qr+Mghg2~ dq B - ~ - = ( C - - A ) r p - - M ghg~ (2. l) dr C - ~ - = (A--B) pq \\, O' h x<' 2 represents the rotation about positive semiaxis of Ox~ (0' is above 0), the latter represents the rotation about negative semi-axis of Ox~ (0' is below 0). We designate the-former as r~ , the latter as r~ In the following we shall discuss three possible cases. l. a>b>c>O It was already studied in [i] that in this case U (\") (the extreme value curve of U given by (4.6) lies in the upper semisphere of A\" (Fig.3).. Besides, from (4.3) we can calculate U= and from (4.5) we get oU O g g., 0 (Ll m~,) ~,~ = ( l -- : ) (o - -c ] >O r )(b-c)>O (U~,,}~,~ = ( I - b - - 4 C >0 as -- l~.g33<.g33 =h as g33--g 'm -<,~ as 9~T' <.q3~-<< + I as 933----+I as 933=9~ ~ , as gs3=g~' , as 9s8=--I 2'2 (2.4) (2.5) Therefore, if we cut the sphere K along any @ -direction, we may obtaln the U--g3~ curve as shown in Fig.4. It should be noted that Fig.4 and Fig.5 both are the expansion planes of the sphere K , hence the g33=--I on the left and that on the right are actually the same point. If we look upon the sphere K as the earth, then gu:,=+] corresponds to the Arctic Pole, g33-------] the Antarctic Pole. Considering Fig.3, Fig.4, utilizing the formulas (I.i), (3.22), (3.23), (1.5) and then making use of the same argument as that for Theorem 1 in [I], we get Theorem i. For o>b>c>O if: 9 ( c )(b--c) , then the dis- (l) the initial disturbed energy Vo~(Um,x)m*, = I--i, turbed motion of liquid-filled-cavity body will asymptotically approach r~ as (.q~), 0 (~ ; 6Fend r; as (g~', 8 (~ EF (2) the initial disturbed energy V0>(Um~)mjn=(,--~)(b--c ) then the disturbed motion of liquid-filled-cavity body will asymptotically approach either r0 + or r7 From this we know that r0* and r7 are both stable nodes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003209_1.2061007-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003209_1.2061007-Figure3-1.png",
        "caption": "Fig. 3 Dimension and structure of grooves",
        "texts": [
            " The joint strength experiments were performed using a MTS 880 testing machine by straining the joints at a set rate while recording the load. The pullout force F was determined when there was initial slippage of the joint. Experimental Results. In order to investigate the effect of geometry of circumferential grooves on the attachment of joints, a series of specimens with different groove widths, locations, depths, and spacings were fabricated. The dimension and the structure of the circumferential grooves are shown in Fig. 3. Influence of one geometric parameter on the connection strength was studied; the other ones remained fixed. A total of 63 joints were tested, and the results are shown in Figs. 4\u20137. The relationship between pullout force and groove width based on experimental results is plotted in Fig. 4. It can be seen from this plot that the best result for carbon steel is obtained when the groove width ranges from 7.5 to 10 mm. Figure 5 indicates that, for maximum pullout strength, the groove should be located at a Table 1 Dimensions of the tube and tubesheet Tube Tubesheet Nominal outside diameter mm 25 100 Nominal thickness mm 2 50 Nominal hole diameter mm 25"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001381_1.1287239-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001381_1.1287239-Figure1-1.png",
        "caption": "Fig. 1 Schematic of the FMR noncontacting mechanical seal assembly",
        "texts": [
            " The present work provides important theoretical insight into the rotordynamics of the noncontacting FMR mechanical face seal utilizing closed-form solutions to assist the strategy of contact elimination. First, the parametric analysis by Zou et al. @18# is applied to the present seal, which affirmatively concludes that contact can be eliminated through variation of the seal clearance. Finally, the feasibility of the proposed contact elimination is investigated experimentally. Seal Angular Response. The test rig subject for this study is shown in Fig. 1 and is discussed in the next section. The analysis and notation that pertain to the current work are consistent with both the theoretical work of Green @7,8# and the experimental work utilizing the test rig. For conciseness this is not repeated. Only the final results necessary for the current study are summarized below. In FMR seals the stator misalignment, gs , and the initial rotor misalignment, gri , always exist due to assembly and manufacturing tolerances, or will eventually develop in time because of shaft deflection and machine deterioration",
            " Studying the effects of different input variables on the total normalized relative misalignment may suggest possible control parameters for a contact elimination strategy. The parameters of Eqs. ~1!\u2013~3! are affected by two kinds of basic physical variables: seal geometry, e.g., seal inside and outside diameters and conning angle; and operational variables, such as sealed fluid ~lubricant! viscosity, sealed pressure, shaft speed, and clearance. The results of this research are applied to the seal test rig ~Fig. 1! with fixed seal size and sealed pressurized water. In particular, the effects of two parameters are actually tested on the rig and are presented here. The first is the clearance\u2014an operating variable, which has been sought as the variable to be adjusted. The second is the seal coning angle\u2014a geometrical variable that always exists in practical mechanical seals, which strongly affects the rotordynamic coefficients and, therefore, the clearance. The effects of other parameters have been studied elsewhere @18#",
            " Particularly, when intermittent face contact occurs the assumption and analysis of a \u2018\u2018noncontacting\u2019\u2019 seal become irrelevant. The only analysis of intermittent seal face contact has been performed by Lee and Green @9# who observed higher harmonic oscillations ~HHO!, and offered a contact model based on a Fourier series expansion. Therefore, when it comes to actual diagnostics a phenomenological approach for contact detection is more appropriate, and indeed such an approach is adopted here. Seal Test Rig. The noncontacting FMR mechanical face seal test rig used in this study ~Fig. 1! is essentially identical to that in Lee and Green @9\u201311#, equipped, however, with the more advanced real-time data acquisition and analysis system introduced by Zou and Green @12,13#. Other significant modifications include now the stator, which is made entirely of carbon graphite, and the rotor, which is made entirely of AISI 440C stainless steel. Both have been fabricated and lapped to industry standards by seal manufacturers. All these modifications facilitate more reliable measurement and determination of the relative position between rotor and stator"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002121_an9881301057-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002121_an9881301057-Figure4-1.png",
        "caption": "Fig. 4. Influence of pH on absorbance readings. Sample volume, 85 pl; flow-rate, 0.74 ml min-1; other conditions as in Fig. 2. (1 Periodate; (2) chromate; (3) vanadate; and (4) hexacyanoferrate(III]",
        "texts": [
            "85 -1.99 0.98 1.92 -1.71 0.79 -1.96 0.00 -1.90 -1.90 Table 3. Determination of chromium and vanadium in steels Mean value Relative Certified value obtained in standard and range, this work, deviation, Sample YO % % Max-Planck Institut 1/832 . . . . . . Cr 4.026 k 0.025 4.037 0.161 V 2.51540.029 2.583 0.203 yAceroF-553 . . Cr 4.223 4.147 0.393 V 1.077 1.101 0.691 Instituto Hierro 5 min - T 40 I\"' 50 .O A Time -3 pH had a decisive influence on the reaction development and, hence, on the absorbance. Fig. 4 shows that a pH range of 4.5-5.5 is suitable for obtaining maximum signals with all analytes. The results of the determination of the chosen substances are summarised in Table 1. There was a linear response of the absorbance (A) vs. the concentration ( C ) of the analyte over Sample Proposed method ICP Crackedfueloil . . . . 249.0 252 Heavyfueloil . . . . 167.4 168 Crudepetroleum . . . . 228.8 228 about one decade. The limit of determination is defined here as the analyte concentration for which the absorbance was ten times the peak to peak noise"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000263_0096-3003(94)00111-g-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000263_0096-3003(94)00111-g-Figure3-1.png",
        "caption": "FIG. 3. Stability boundary in /(3, K4 control parameter space for K1 > 3 and /(2 > 0. The whole area above the hyperbola is the stable domain of the linear system following from the conditions (12). The restriction below the straight line follows from the nonlinear condition (38).",
        "texts": [
            " (3s) Kl((32K4 + 13K1 - 208) 2 + (52K2 - 8/(3) 2 + 2082) Since the denominator (the determinant of M given by (31)) after canceling of K1 is positive for all control parameters the inequality reduces to - 104K2 + (K1 - 3)K3 + 16K2(2 + / ( 4 ) < 0. (39) Condition (39) in addition to conditions (12) following from the linearized stability analysis define now the stability region for the control parameters. We follow now the representation given in [1]. There, for fixed values K1 > 3 and K2 > 0 the stability conditions (12) are plotted in the K3, K4 parameter plane. The result is shown in Figure 3 where the stable region for the linear problem is above the hyperbola. However, the nonlinear stability condition in addition reduces the domain from an unlimited one to a finite one. This is a very important result from a practical point of view because it shows that too large values /(3,/(4 to effect v~ and 0 r in the linearized control problem will have a destabilizing effect on the out of plane motion. This research project has been supported by the Austrian Science Foundation ( FWF) under the project P07003"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002211_bf01560628-Figure11-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002211_bf01560628-Figure11-1.png",
        "caption": "Fig. 11.",
        "texts": [
            "_ 1 + h - h + 2 b i s en arcos - 2 p x/l i-1 2bih from which a i + b i are determined by subsequent approximation, being a i + b i = L/2. Let at tention be given now to kinematic chain P of fig. 10 which is presumed to be on a horizontal plain. I f the coupling in A i and B i of its elements are obtained by means of joints that allow also the coupling of rods perpendicular to the plain, it becomes possible to place in A i and B i (i = 1, 2, 3, . . . , N) points A 1 and B 1 of N kinematic chains, all equal, which get arranged according to a parabola, of a given parameter on plains perpendicular to the one of fig. 11 (fig. 12 ) (4). Each an every vertical parabola therefore is set o n a parallel plain, has the axis parallel to the one of the parabola of fig. 10 and the vertex on the parabola itself. The expanded surface is then a paraboloid, either elliptic, if the opening of the horizontal and vertical parabolae have a common direction, or hyperbolic, if they have an opposite direction. t I s + 9t = 92 + 92 = L (1.13) By pin-joining second element X 2 to the first X l, so that A ' 1 = A 2 and B' 1 = B 2 (fig. 11), condition (1.13) expresses the capability of the chain consti tuted by two elements to be closed (3). As co-ordinates X/l, Y/ll are known, to haveA ' 2 of the pa- rabola it must be: (2) Elements X i of the second quadrant are equal to those of the first one, yet symmetric to them as regards axis y. (3) As A~ coincides with Ai+ 1 and B~ withBi+ 1, one may generally speak of points A i or of points B i. (4) Lr of the vertical elements X r must be equal to L 0 of the horizontal elements X 0 for the grid to undergo compaction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002233_j.physleta.2003.10.027-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002233_j.physleta.2003.10.027-Figure2-1.png",
        "caption": "Fig. 2. Interlocking arrangement of buckyballs associated with the fifth order symmetry axes: (a) arrangement of the decagonal middle sections of the buckyballs with the arrows showing the directions of movement of the decagon\u2019s sides when the section moves upwards (indicative of the inclinations of the contacting faces), (b) a fragment of interlocking assembly. The buckyballs contact each other on their hexagonal faces.",
        "texts": [
            " It is proven in Appendix A that an element is (translationally) locked if, and only if, by continuously shifting the section plane in either direction normal to the middle section, the corresponding polygon eventually degenerates to a segment of a straight line or to a point. The above-mentioned principles will now be used to explain the interlocking arrangements of buckyballs. Consider the assembly of buckyballs in a layer perpendicular to a fifth order symmetry axis. A middle section normal to this axis is a decagon with the side length 3a/2, where a is the edge length of a buckyball. An arrangement of decagons on a plane that ensures interlocking of buckyballs is shown in Fig. 2(a). Traces of the faces of the reference buckyball in contact with its neighbours and the corresponding arrows are marked by letters c, d, . . . , h placed outside the buckyball section. At first glance it appears that the reference buckyball can be removed by displacement, for example, in the direction of arrows c and f . This is, however, not the case, since, as shown in Appendix B, by progressive shifting of the section plane, the corresponding polygon will eventually degenerate. In the arrangement considered the buckyballs are situated at the nodes of a deformed hexagonal lattice and contact their neighbours on their hexagonal faces. The deformed hexagonal lattice is characterized by two distances, d(1)5,6 and d (2) 5,6, between the decagon centres as well as by the angles \u03d5 and \u03c8 , Fig. 2(a). These parameters are d (1) 5,6 = 3a 2 \u221a 5 + 2 \u221a 5, d (2) 5,6 = 3a 4 \u221a 26 + 6 \u221a 5, (1)\u03d5 = cos\u22121 ( d (1) 5,6 2d(2)5,6 ) , \u03c8 = \u03c0 \u2212 2\u03d5. Here the first index in d refers to the symmetry axis the layer is normal to and the second one refers to the contacting faces, the hexagons in this case. A fragment of the assembly of this type is shown in Fig. 2(b). Consider now the assemblies of buckyballs in a layer perpendicular to a third order symmetry axis. A middle section normal to a third order axis is an 18-gon in which the sides are grouped in six triplets; all six together form a hexagon-like figure, as seen in Figs. 3(a) and 4(a). The middle side in each triplet has the length of a( \u221a 5 + 1)/4. It passes through a pentagonal face of the buckyball. Two other sides of a triplet have the length of a \u221a 3/2 and pass through hexagonal faces of the buckyball",
            " Therefore, the contacting faces of the polyhedron are parallel to what can be called the cone of permitted directions of movement. This cone is not empty if, and only if, the continuations of contacting faces of the polyhedron form an unbounded region. Furthermore, the boundness of this region is equivalent to the following. A polygonal section of the polyhedron formed by a plane parallel to the middle plane of the assembly degenerates to a straight segment or a point as the secant plane shifts away from the middle plane. Suppose the section in Fig. 2(a) moves with a constant velocity in the direction normal to the plane of drawing such that the sides of the polygon in the section move in the directions indicated by the arrows. Due to the buckyball symmetry the polygon sides will move in these directions with a constant velocity v. Consider the common point of intersection of the continuations of sides e and g with the broken line perpendicular to side c. This point will move in the direction of arrow c with velocity v/ sin\u03d5e, where \u03d5e is the angle between the broken line and sides e and g",
            " These two spheres do not coincide. No movement of P can displace the centre of the first sphere down or that of the second sphere up, otherwise the spacing between them would change (which is prohibited, since rigid body motion preserves distances.) The movements of the sphere centres consistent with rigid body motion are precisely those movements that are blocked by the neighbouring elements. Therefore, P is locked, and so is the element containing P , which completes the proof. Consider now the assembly presented by Fig. 2. The general statement cannot be used here because condition (1) is violated since, for example, amongst faces c, e, and g that ensure the upward interlocking, faces e and g form a sharp angle with the middle plane, while face c forms an obtuse angle. Firstly we note that hereafter we only have to consider rotations about axes parallel to the middle cross-section since all rotations in this plane are obviously blocked. Then we note that for the assembly in Fig. 2 a rotation of the reference buckyball about an axis R normal to line cf is blocked. Indeed, the plane contact areas at faces c and f prevent the rotation, since each of them contains the base of normal drawn from the centre of the reference buckyball. Now suppose that there is an axis about which rotation is admissible. Then, because the arrangement possesses a plane of mirror symmetry passing through cf, there must be another axis of admissible rotation oriented symmetrically. If we perform two successive infinitesimal rotations, \u03c91 and \u03c92, about these axes, we will obtain an admissible rotation, \u03c91 + \u03c92. However, due to the symmetry this sum is an infinitesimal rotation about R, which was shown to be blocked. Therefore, the buckyballs shown in Fig. 2 are rotationally and hence fully interlocked. Since a buckyball is a truncated icosahedron, this proof is applicable to the arrangements of interlocked icosahedra as well. For the assembly shown on Fig. 4 the general statement does not work since condition (2) is violated. We note, however, that rotations about an axis R parallel to the faces contacting neighbours 1 and 4 are blocked by other neighbours. Suppose there is an axis about which a rotation is admissible. Because of the symmetry of 3rd order, there must exist another axis of admissible rotation, at an angle of 2\u03c0/3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002619_095440605x31481-Figure11-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002619_095440605x31481-Figure11-1.png",
        "caption": "Fig. 11 Flank geometry of a CC1-rack, f \u00bc 208",
        "texts": [
            " Thus, the tool rake face maintains a fixed attitude relative to the gear blank (Fig. 10). This is achieved by either of the two methods: (a) the individual cutters are made to rotate about their own shank axes at the same rate and in the opposite sense of cutter head rotation; (b) a cutter (for one tooth space) or a cutting rack (for a few teeth) is imparted an oscillatory, parallel, arcuate motion in a plane tangent to the gear pitch cylinder; viz. an arcuate gear planer. The outside- and inside-cutting straight edges sweep out each of an oblique cylinder as shown in Fig. 11. The resulting tooth traces are identical circular arcs, the transverse tooth thickness and space are equal, and meshing gears have line contact. The oblique cylinder is an inclined slice of an elliptic cylinder of semi-major axis R in the gear lengthwise direction and of semi-minor axis R cos f normal to the rack tooth flank in the midplane. The axes of the two cylinders are inclined at +f to the normal to the rack pitch surface. These cylinders intersect all transverse planes of the generating rack in straight lines of the same slopes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000944_s0094-114x(96)00075-4-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000944_s0094-114x(96)00075-4-Figure2-1.png",
        "caption": "Fig. 2.",
        "texts": [
            " The superscript (m) or subscript m indicates that a vector or a parameter belongs to ~'~m and also the superscript (f) or subscript f indicates that the vector or parameter belongs to El. Now we take the fixed axode Ef as an original ruled surface, and examine the path of a fixed point A of moving body Em in the fixed reference frame Of- idfkf. At any instant, the point A is adjoint to the ruling Sr(~ f)) (or generator) of El, so that the trajectory of point A is an adjoint curve of the fixed axode Y~r, shown in Fig. 2. Thus, the vector equation of FA is given by FA: RA = rf + xIE(I fj q- x2E~2 f) --~ x3 Eft) (8) where (xl, x2, x3) are the coordinates of point A in the Frenet frame (rf, ~f~, ~f~, ~f)), which shows FA in the fixed reference frame Of- idfkf by the orthogonal system (~f), ~rl, ~3\"). Although (~f), ~f~, ~r~) varies with different ruling of El, the relationship between the two orthogonal systems {~r~, ~f~, ~f)} and ifjfkf can be determined by the second expression of equations (7) and (2). Then, by equation (3), the first derivative of RA with respect to af is - \\~-~f - x2 + c~f Eyt ~ + x~ daf - tifx3 E~"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002692_1.2074117-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002692_1.2074117-Figure1-1.png",
        "caption": "Fig. 1. Physical pendulum.",
        "texts": [
            " The frequency\u2013response curve is obtained for periodic motion with small amplitude. Theoretical and experimental results are in good agreement with each other. The plane oscillations of a physical pendulum about the lower vertical position with the periodically varying * Institute of Mechanics, Moscow State University, Michurinski\u0153 pr. 1, Moscow, 119192 Russia e-mail: seyran@imec.msu.ru ** Institute of Engineering Mechanics and Systems, University of Tsukuba, Tsukuba, Japan 1028-3358/05/5009- $26.00 0467 displacement of the suspension point and viscous damping (see Fig. 1) are governed by the equation (1) Here, I and m are the moment of inertia and the mass of the pendulum, respectively; \u03b8 is the angle measured from the lower vertical position; c is the viscous-friction coefficient; r is the distance between the suspension point and the center of gravity of the pendulum; g is the acceleration of gravity; z is the vertical displacement of the suspension point; and the dot stands for differentiation with respect to time t. It is assumed that the displacement of the suspension point of the pendulum is governed by the law (2) where a and \u2126 are the excitation amplitude and frequency, respectively, and \u03c6(\u03c4) is an arbitrary smooth I \u03b8\u0307\u0307 c\u03b8\u0307 mr g z\u0307\u0307\u2013( ) \u03b8sin+ + 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003766_0278364906061159-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003766_0278364906061159-Figure1-1.png",
        "caption": "Fig. 1. Slime Scope.",
        "texts": [
            " We think that an efficient rescue operation is achieved when many people can work using the rescue tools at the same time. Therefore, we believe that rescue tools are more important than expensive and specialized robots. If we want people without any specific skills or training to be able to use rescue tools, the tools should be very simple, easy to use and have a power source. Moreover, these tools should be easy to transport, maintenance-free and low cost. In this paper we report on the pneumatic drive expandable arm \u201cSlime Scope\u201d (Figure 1), which has a search tool, such as a CCD camera, at the end of the pneumatically controlled expandable arm. The first step of a rescue operation in the rubble is to identify the location of survivors. Conventionally, such searches mostly depend on hearing survivors, with the occasional use of rescue dogs. However, noise from survivors is often drowned out by the noise of earthmoving machines and helicopters, which significantly reduces the efficiency of rescue operation (Rescue Robot Equipment Study Group 1997)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001897_robot.1997.614281-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001897_robot.1997.614281-Figure6-1.png",
        "caption": "Figure 6: A joint evolution of asymptotic trajectory",
        "texts": [
            " The length L of the sole to execute the ballistic trajectory must be not less than 4 cm. 5. The reference trajectory We use the ballistic motion of the robot as a candidate to define a reference trajectory because we believe that in the nature, locomotion consists of parts which are near ballistic. 5.1. Difference with asymptotic trajectory The velocity around the impact with the ground is chosen in order to minimize the energy needed to accomplish the asymptotic trajectory. The schematic evolution of one joint variable for the asymptotic trajectory is drawn in fig. 6. Impulsive torques are required and cannot be produced on a real prototype. So, it is necessary to modify the trajectory around the impact with the ground in order to have a feasible motion with finite torques. With the control law defined in section 3, it is possible to join a desired trajectory even if an initial velocity error exists. Assuming that after the impact with the groupd the configuration is the desired one and the velocity is x+, it is possible with the dynamic control law to join the ballistic trajectory"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002008_.2001.980449-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002008_.2001.980449-Figure1-1.png",
        "caption": "Figure 1: The Inertia Wheel Pendulum",
        "texts": [
            "roceedings of the 40th IEEE Conference on Decision and Control Orlando, Florida USA, k e m k r 2001 FrAOl-3 Global Stabilization of a Flat Underactuated System: the Inertia Wheel Pendulum Reza Olfati-Saber California Institute df Technology Control and Dynamical Systems 107-81 Pasadena, CA 91125 olfati@cds.caltech.edu Abst rac t Inertial Wheel Pendulum (IWP) is a planar pendulum with a revolving wheel (that has a uniform mass distribution) a t the end. The pendulum is unactuated and the wheel is actuated. Our main result is to address global asymptotic stabilization of the inertia wheel pendulum around its up-right position. Simulation results are provided for parameters taken from a real-life model of the IWP. 1 Introduct ion Inertia Wheel Pendulum, depicted in Fig. 1, is a planar inverted pendulum with a revolving wheel at the end. The wheel is actuated and the joint of the pendulum at the base is unactuated. The inertial wheel pendulum was first introduced by Spong et al. in 131 where a supervisory hybrid/switching control strategy is applied to asymptotic stabilization of the IWP around its upright equilibrium point. Here. we show that based on a recent result of the author in [l], the dynamics of the inertia wheel pendulum can be transformed into a cascade nonlinear system in strict feedback form using a global change of coordinates in an explicit form"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003814_12.601652-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003814_12.601652-Figure8-1.png",
        "caption": "Figure 8. Multiple Sensor Layout. Top View.",
        "texts": [
            " This will require quantitative understanding of the relationship between independent process parameters (laser power speed, powder deposition rate etc.), dimension, cooling rate, microstructure and properties by developing fundamental understanding of the associated transport phenomena. Strategies for on-line process control will also be required to achieve the desired melt pool volume and cooling rate. One can either use one sensor or multiple sensors for close-loop feedback control of the deposit height. Multiple sensors will overcome any problem related to the field of view with respect to the cladding direction for a single sensor. Fig. 8 shows a top view of the ideal layout of the three sensors, which are spaced equally 120 degrees apart. For the actual layout of the sensors for this study, the second sensor was only 90 degrees from the first sensor. This uneven spacing did not cause any problems since the sensors are effective up to 180 degrees. Since two or more sensors were added to the system, the signal processor also had to be modified. In order to input one signal into the processor, the three sensor signals were combined through several logic gates before they were sent to the processor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001679_095965180321700606-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001679_095965180321700606-Figure2-1.png",
        "caption": "Fig. 2 Journal\u2013back-up bearing contact model",
        "texts": [
            " Moreover, N cbi , T cbi and T mi are the force or torque also associated with the contact force, which will be addressed in the next section. In addition, for a back-up bearing with a hard support, eqution (19) may be ignored. For a back-up bearing with a rotationally constrained inner race (or solid bush), equation (20) may also be ignored. Back-up bearings are the security components that supply the AMB rotor with additional support and hence protect the rotor from direct contact with other parts of the stator or the stators of the magnetic bearings themselves. Figure 2 shows a cross-section of the rotor\u2013 back-up bearing contact model [2 ], which represents the back-up bearing at the ith position (i=p or q). The inner radius of the back-up bearing is R bi , while the radius of I07902 \u00a9 IMechE 2003 Proc. Instn Mech. Engrs Vol. 217 Part I: J. Systems and Control Engineering the back-up contact journal is Rsi . The contact sti ness is kc, which is calculated from Hertzian contact theory. The contact damping is cc. With the de nition above, the contact force Nci at contact point C is Nci =Gk c d +c c db d>0 0 d \u00e50 (21) where d i is the penetration of the back-up contact journal into the bearing, which is expressed as d i =|r i r bi | R bi +R si (22) and db i = [(rb i rb bi) \u00d7conj (r i r bi) +(r i r bi) \u00d7conj (rb i rbbi)] /( |r i rbi |) (23) where conj ( ) denotes the conjugation of the complex in the brackets"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003814_12.601652-Figure17-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003814_12.601652-Figure17-1.png",
        "caption": "Figure 17. Conventional straight line cooling channel and conformal cooling channels used for the \u201cfuse cover die\u201d Saving in cooling time: 26 %",
        "texts": [],
        "surrounding_texts": [
            "Our initial work on the development of the DMD process was driven by industrial needs. The main foci were: (a) to provide aluminum components with low enough oxidation that it retains mechanical properties [95] and (b) to provide mechanically sound H13 tool steel components. The emphasis is the demonstration of the strength of the DMD technique. Both were successfully demonstrated [1, 96, 97]. Mechanical properties of aluminum and H13 tool steel components fabricated by DMD were found to be almost the same as the wrought materials [1, 95]. The cooling rate can be varied by varying deposition layer thickness and adjusted specific energy [2]. Control of cooling rates enables one to control the dendrite arm spacing and microstructure refinement. Within the power, velocity and powder mass flow rate study, the wall profile roughness averages were found to vary between 13 and 51 microns, while the wall maximum peak to valley distances ranged from 75 to 275 microns [2]. These roughness were found to both be directly related to the layer thickness. The wall roughness can be reduced significantly by making the deposition layers thinner. The reason the wall surface gets rougher as the layer thickness increases is due to the beam diameter variation due to defocusing. As the layers become thicker, the beam diameter has a longer distance to diverge. Therefore, the width of cladding is larger at the bottom of the cladding pass in comparison to the top of the cladding pass. By reducing the layer thickness, this beam diameter variation is also reduced and therefore the specimen wall roughness is minimized. In cases with higher deposition velocities, there was a problem with wall quality. With higher velocities, the cladding at the sample edges sometimes was not able to catch as much powder as the internal sample cladding. Eventually, the cladding was unable to build up fast enough to compensate for this condition, creating gaps in the cladding passes at the sample edges. By reducing the traverse speed of the deposition around the outline of the part, there is enough time for the clad to build to the required height eliminating any defects. The three sensor systems proved to be effective in reducing the surface roughness average of the fabricated parts by approximately 14 percent. In other words, from an average of 7 different specimen sets (5 different build patterns and 2 more with higher pass overlap), the three sensor configurations reduced the profile roughness average from 44 microns to 38 microns. And at the same time reduced the average maximum profile roughness height from 270 microns to 210 microns, or a 22 percent improvement. As was stated before, the maximum profile roughness height is the maximum surface peak to valley measurement. It has been demonstrated that a wide range of deposition rate and geometrical resolution may be possible by DMD by controlling the laser power and beam quality. With CO2 laser lateral resolution of 500 micrometer and vertical resolution of 25 micrometer have been achieved. Fig. 13 shows an IMS-Tl sample fabricated with H13 tool steel using DMD. This is a benchmark design used to validate any rapid prototyping process. Interfacing of DMD laser systems with CAD/CAM systems for one material or two materials in sequence e.g., copper cooling channels and heat sinks in injection molding die in Fig. 14 has also been demonstrated. As shown in Fig. 14, conformal cooling channel, along with copper heat sink has the Figure 13. IMS-T1 sample process parameters IMS-T1 Sample Process parameters: Material: H13 Laser power: ~1000W Deposition rate: ~5 gr/min Slice thickness: 0.01\u201d Total height: ~2.93\u201d (293 slices) Traveling speed: ~30\u201d/min Real laser-on processing time: ~50 hrs Total processing time: ~100 hrs Stress relieving time: ~24 hrs (6 x 4 hrs) Total time:~124 hrs Proc. of SPIE Vol. 5706 51 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/12/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx potential for improved thermal management and theoretical calculation shows that the time cycle can be reduced considerably. used for the \"fuse cover die\". Theoretical calculation shows potential time savings of 26%. A benchmark experiment carried out by one of the users showed 9% saving without any optimization of the flow. Potential time saving increases with the complication of the shape as shown in Table 4. This type of macrostructure design has already attracted considerable industrial interest. The Closed Loop DMD opens up a new horizon of designed materials when integrated with \u201cHomogenization Design Method\u201d and Heterogeneous CAD. This methodology of producing performance based \u201cDesigned Materials\u201d has the potential to change the manufacturing paradigms. This methodology will provide materials with properties that do not occur in Mother Nature. Fig. 18a shows an example of a designed material with negative co-efficient of expansion using Homogenization Design Method (HDM) [76]. Fig.18b shows the component fabricated by homogenization DMD technique using a combination of Nickel and Cycle Time\u2026. Injection time Packing time Freezing time Clamp Open time Up to 75% Cooling Time Cooling time = Freezing time + Packing time (Injection time \u2013 Time to reach the node) Figure 16. In an injection-molding die, 75% of the cycle time is devoted to cooling. 52 Proc. of SPIE Vol. 5706 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/12/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx Chromium. Fig.19 shows a designed component similar to a turbine blade that has 50% less mass but has the similar mechanical strength when compared to conventional blade designs. Fig.20 shows creep test data for a component fabricated with Inconel 738. Implication of 50% reduction in mass in a turbine is proportional reduction in fuel lost. Integrated Design and manufacturing: Imagine the impact of \u201cDesigned Materials\u201d on society and in the environment. On can foresee is new paradigm of manufacturing where it is driven by customer\u2019s desire instead of the best available practice. Fig. 21 illustrates the synergy this methodology can create compared to present day practice. Remote Manufacturing: Modern communication methods are improving the Internet\u2019s capability to transfer large volume of data in a relatively short time. Mathematical and optical methods of data compression are enhancing this capability even further. This will enable seamless communication between design and manufacturing teams in industry. It is conceivable that a design team can send their design data electronically and observe the fabrication from a remote site and even edit it on line [99]. Of course, to Proc. of SPIE Vol. 5706 53 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/12/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx realize this scenario, synthesis and enhancement of various technologies are needed. Fig. 22 shows the process already made possible at POM Group Inc. This has the potential for becoming a global manufacturing platform. An advantage for such platform will be paperless technology transfer across the globe. At the same time it will protect the intellectual property of the inventor by reducing paper trail. Electronic data transfer can be encrypted and thus reduce the potential for exposure to unwanted eyes. 54 Proc. of SPIE Vol. 5706 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/12/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx"
        ]
    },
    {
        "image_filename": "designv11_24_0001135_10402009208982101-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001135_10402009208982101-Figure2-1.png",
        "caption": "Fig. 2-Groove geometry.",
        "texts": [
            " The width of this groove also varies linearly with P. The equation of the groove in the 0-P plane is NO - 2Ua(+- I)/(?o- 1 ) = constant, [241 Once 11 is specified as an explicit function of P and 0, where the parameter a is a measure of the slope of the D ow nl oa de d by [ Y or k U ni ve rs ity L ib ra ri es ] at 2 3: 16 1 3 N ov em be r 20 14 The Effects of Shallow Groove Patterns on Mechanical Seal Leakage groove. Positive values of a yield grooves which have a positive slope in the direction of motion of the mating face as shown in Fig. 2. For spiral grooves, the film thickness profile is expressed as, The phase of the cosine function in this expression varies with the log of P, thereby defining a spiral groove. The width of this groove varies linearly with P. Such a groove is also illustrated in Fig. 2. RESULTS In order to compare the leakage rate, IS, of the grooved seal to that (&) of an equivalent plain-faced seal (without grooves) with the same minimum film thickness, it is useful to express results in terms of a leakage rate ratio, Q,, Gf is computed using the following film thickness profile: where hl and h2 take the values appropriate to the corresponding grooved seal. Values of Q, less than 1.0 indicate lower leakage rates than the plain-faced seal, while values greater than 1.0 indicate higher leakage rates"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003266_1.2179462-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003266_1.2179462-Figure1-1.png",
        "caption": "Fig. 1 The force system",
        "texts": [
            " The unit surface normal direction vectors uN1, uN2 and uN3 are given as \u00af uN1 = \u2212 0.577,\u2212 0.577,0.577 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/27/201 u\u0304N2 = 0.667,\u2212 0.333,0.667 u\u0304N3 = 0.000,0.707,0.707 2 and their corresponding friction coefficients C1, C2 and C3 are C1 = 0.2, C2 = 0.32, C3 = 0.15 3 The known external force FO and the known external moment MO expressed in the body coordinate frame and acting on the origin O are F\u0304O = 0.0,0.1,\u2212 8.0 , M\u0304O = 2.0,0.1,0.0 4 This example system is represented in Fig. 1 with the friction cones shown at each contact point. 3.2 Solution Space and Force Space Graph. As the first step, the solution space and its force space graph must be found using the strategy introduced in Hong and Cipra 16\u201318 . Among the nine unknown foot contact force components, three of them are explicitly found the e component forces FC1 , FC2 and FC3 by summing the moments about e , e and e unit force component vectors. For the example system these are found as FC1 = 1.901, FC2 = 1.876, FC3 = 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002783_s0007-8506(07)61886-1-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002783_s0007-8506(07)61886-1-Figure1-1.png",
        "caption": "FIGURE 1",
        "texts": [
            " F o r a d e f l e c t i o n beyond t h e p l a y t h e b e a r i n g h a s a s t i f f n e s s c o r r e s p o n d i n g to h a l f of t h e b a l l s b e i n a i n c o n t a c t . Thus c o n s i d e r a b l e i n c r e a s e i n s t i f f n e s s is o b s e r v e d . An e x p e r i m e n t was a r r a n q e d i n which t h e load - d e f l e c t i o n c h a r a c t e r i s t i c w a s measured on t h e SDind le o f t h e S u n d s t r a n d O n n i m i l l 20 mach in ing center . T h i s machine i s e q u i p p e d w i t h b e a r i n g s as i n FiG 1. The measurement was done close t o t h e f r o n t b e a r i n g , a t d i f f e r e n t amounts of p r e l o a d as e x p r e s s e d i n i t - l b t o r q u e a p p l i e d t o t h e n u t e x e r t i n g t h e a x i a l p r e l o a d . The r e s u l t s a r e p r e s e n t e d i n FIG 3 f o r p r e l o a d s 0: 5 , 5 0 , 1 5 0 and 350 f t - l b . I t i s seen t h a t f o r l a r g e de - f l e c t i o n s a l l t h e f o u r c u r v e s have t h e same slone o f a b o u t k2 = 9 x 105 l b / i n ",
            " Obvious ly a s t i l l b e t t e r match c o u l d be a c h i e v e d by a s t i l l lower s o f t e n i n q r a t i o and some i n c r e a s e of damplnq w i t h d i s p l a c e m e n t . However, i t is v c r y c l e a r l y i l l u s t r a t e d t h a t t h e T g i s i s t h e 1 1 +lo- ' iullb - 2 , . 2 I i a) Im I 0- - 2 I 0 b) Re 1 b -;;A -1 -1 ! 1 d) Im t FIGURE 6 distortions in the measured TF's as they increase with the increase of the excitation impact are due to the softening spring of the preloaded roller bearing of the spindle. The second spindle systcm is the one of FIG 1 and actually the one for which the static characteristics of FIG 3 were obtained. The TF's measured on this spindle are presented in FIG 8. The impact values and the initial displacements of the f o u r cases were: x in) max Fmax (lb) a) 400 0.2 b) 650 0.35 C) 1100 0.9 d) 3200 1.9 The force range in these measurements was 400/3200 = 1/8. The TF's contain several modes of which the highest one marked as feature B is a mode in which the bearings strongly participate as springs. The preload of the bearings during these measurements was set at 200 ft-lb torque tightening the nut"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002571_bfb0035233-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002571_bfb0035233-Figure1-1.png",
        "caption": "Figure 1 An example of a spaceborne long-reach manipulator system: The Canadian SPDM and SSRMS [1]",
        "texts": [
            ". I n t r o d u c t i o n Robotic systems supported by flexible long-reach deployable structures have been proposed for future space projects. The Special Purpose Dexterous Manipulator (SPDM) mounted on the Space Station Remote Manipulator System (SSRMS) (Figure 1) [1] and the Japanese Experiment Module Remote Manipulator System (JEMRMS) proposed by the Japan's NASDA [2], are examples of long-reach space manipulator systems now being developed. While promising, the development of long reach space manipulator systems requires the solution of fundamental technical problems. A key problem is dynamic coupling between the manipulator and its flexible supporting structure. This causes uncontrolled motion of the manipulator supporting structure when the manipulator performs a task"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003411_ip-rsn:20041177-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003411_ip-rsn:20041177-Figure1-1.png",
        "caption": "Fig. 1 Two-axis Gimballed seeker configuration",
        "texts": [
            " It has a similar structure to that of the conventional Kalman filter, and the steady-state robust filter gain can easily be obtained by solving the algebraic Riccati equation. Since it is easy to design and implement the proposed filter for real-time applications, and thus it is a practical result. A numerical example is given to show the estimation performance and the robustness of the proposed LOS rate estimator. A commonly used configuration for seeker systems suspended by a two-axis gimbal system is illustrated in Fig. 1. It is assumed that a generic LOS angle tracking loop (depicted in Fig. 2 [1]) is constructed in the yaw gimbal plane. Also, it is assumed that only the angle position controller is available in the pitch gimbal plane. The yaw q IEE, 2005 IEE Proceedings online no. 20041177 doi: 10.1049/ip-rsn:20041177 The authors are with Guidance and Control Department 3-1-3, Agency for Defense Development, P.O. Box 35-3, Taejon 305-600, Korea Paper first received 30th June 2003 and in revised form 1st September 2004"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002175_1.1515333-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002175_1.1515333-Figure6-1.png",
        "caption": "Fig. 6 Free body diagram for the free end of the tine",
        "texts": [
            " Taking any random element i within the tine, the governing equations for the tine deflection may be derived. Resolving the vertical and horizontal forces and taking moments about the mid point; Transactions of the ASME 7 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F mRiv 21lx~ i11 !2lxi50 (6) ly~ i11 !2lyi50 (7) Ti2T ~ i11 !2~lxi1lx~ i11 !! l 2 sin u i2~lyi1ly~ i11 !! l 2 cos u i50 (8) where Ti5k~u i2u i21! (9) The free end of the tine, element n, experiences no reaction at the tine end, Fig. 6, and therefore the following set of equations may be derived. mRnv22lxn50 (10) Ft2lyn50 (11) And; Tn5k~un2un21!5Ftl cos un1mRnv2 l 2 sin un (12) At the constrained end of the tine, n51, the connecting spring cannot do any work. To overcome this a \u2018\u2018pseudo-link\u2019\u2019 is introduced such that this link deflects a negative amount from the steady state position, Fig. 7a. In order for the constraint to undertake zero work the negative work undertaken by the constraint must be equal to the positive amount of work done"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003693_1.2208910-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003693_1.2208910-Figure1-1.png",
        "caption": "Figure 1. Cylindrical column used to polarize activated carbon for hemosorption: 1\u20134 self-tightening current leads; 5\u20137 stainless steel wire meshes.",
        "texts": [
            " Constant compression was achieved by using a threaded top cover, which applied pressure to the granules through a spiral spring and a Teflon perforated diaphragm. The silver/silver chloride reference electrode was placed into a small PVC pipe, which was filled with saline and hermetically connected with the Teflon cylinder via a lateral connecting tube. A cylindrical hemosorption column was used for the study of platelet count changes when blood came into contact with different types of activated carbon Fig. 1 . Blood was perfused through the column by a peristaltic pump with a volumetric flow rate of blood of 100 mL/min. Platelet counts were taken before and after perfusing Table I. Regions of normal values of surface charge densities and electrophoretic motilities of blood cells calculated from data in Ref. 21 and 22. Blood cell Electrophoretic mobility, /cm2 V s Charge density C/cm2 Erythrocytes 1.1\u20131.3 \u22121.12 to \u22121.21 Leukocytes 120\u2013130 \u22120.83 to \u22120.85 Platelets 53,000\u201358,000 \u22122.45a a Data from Slayman",
            " However, difficulties arise due to the necessity of providing equipotential conditions for all carbon granules during the polarization process: high electrical resistance of the bulk of the granulated carbon is observed due to the poor electrical contact between granules. If granule compression is increased, there is a danger of pulverizing the granules because of their low mechanical durability. Therefore, a different path of polarization is desired. The alternative suggestion is to polarize carbon by shifting its initial potential by prior chemical or electrochemical treatment, which would modify the compounds on the surface of activated carbon. Direct polarization was realized in a special electrochemical column Fig. 1 . Stainless steel current leads 1\u20134 were placed into the column packed with granular activated carbon. Stainless steel wire meshes 5\u20137 with thickness of 2 mm were placed into the column in order to reduce the electrical resistance of the bulk of carbon from 1500 no meshes to 300 6 meshes . Such a design enabled the polarization of activated carbon in 0.9% NaCl solution or in blood with currents less than 10 mA that shifted the initial carbon potential to 0.5 V. Stainless steel self-packing rods tightened by a nut were used as current-carrying devices",
            " This observation suggests that stationary potential is an important intrinsic characteristic of activated carbon. In order to effectively use this parameter, it is necessary to elucidate the effect of stationary potential of activated carbon on properties of the activated carbon/blood system or activated carbon/physiologic saline system. So, the investigation of the dependence of hematological indexes on stationary potential of activated carbon during its contact with blood was the next step. Blood was perfused through a cylindrical column packed with granulated activated carbon Fig. 1 . For study of the effect of carbon potential, activated carbon was polarized by an external dc power supply in order to shift the stationary potential toward more negative values compared to the initial potential. The data obtained are shown in Table III. As can be seen from these data, unfavorable changes of blood cells and hemoglobin occur on certain activated carbons. The higher positive values of carbon potential applied, the more significant changes of blood composition occur. Indeed, abrupt changes were observed on the initial sample of SIT-1 at a potential of E = 0",
            " Potential of modified activated carbon depends on the electrochemical or chemical reactions occurring on the carbon surface during the modification process, so changes in composition of the surface compounds of modified activated carbon are quite probable. Direct polarization of activated carbon in a nonfaradaic process would elucidate the effect of carbon potential itself on the interaction with blood. There are data regarding destructive effects of faradaic processes on blood when electric current is passed through it.63 Polarization of activated carbon in blood in a nonfaradaic regime was realized by using a special electrochemical hemosorption column Fig. 1 . Some hematological indexes were measured subsequent to perfusion of blood through the column packed with unmodified SKT-6A E = 0.18 V and externally polarized SKT-6A E = \u22120.2 V . Currents through the 450 mL of blood passing through the column were below 1.5 mA or 5 10\u22129 A/m2, which indicates a nonfaradaic process. The data collected is summarized in Table VII. The comparison of the data in Table VII with the data shown in Tables IV-VI lead to the conclusion that only the potential of carbon adsorbent, but not the method of polarization, affects the interaction between carbon and blood"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000662_027836499201100502-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000662_027836499201100502-Figure2-1.png",
        "caption": "Fig. 2. Hand and finger configuration for a part-pair",
        "texts": [
            " The robots are American Cimflex Merlin models with six degrees of freedom and kinematically similar to PUMAS. The advertised repeatability is 0.001 inches with a 20-pound payload and a maximum reach of about 1 m. Each robot has a Monforte Robotics parallel-jaw servoed pneumatic gripper. This device has a total throw of about 95 mm, with about 250 steps across the opening range. The robots are equipped with different style fingers to permit cooperative grasps and entry into different kinds of spaces. A typical grasp configuration is shown in Figure 2. One robot has long slim fingers that can reach horizontally into narrow holes, and the other has wider fingers suitable for vertical approaches into vertically oriented holes. Typically a part is pulled vertically up, although the roles are reversed when necessary. The hands and fingers are sensorless, as feedback is not necessary for reliable Duplo disassembly. The system is constructed to be simple and coarse enough so that primitive operations are reliable, and no error detection is required",
            " At each point, the system estimates which (or both or neither) of the configurations will not break the cables to the gripper. These are unified and one is chosen or, if a single one is impossible, failure is reported, and the high-level planner must try something else. 9.2. Grasp Planning The fundamental grasp is one gripper grasping a set of parts at a single Duplo Z level and the other gripper grasping a set of parts connected immediately above (or below). No grasp points are specified, but rather just the parts to be held, with a list of other attached parts that will be moving during the separation. Figure 2 shows the basic grasp-pair configuration. The robot with the longer fingers is always below the other. This first robot can reach into horizontal holes and the second into vertical ones. This is the only grasp-pair configuration used, as few others are possible with these hands because of hand or arm conflicts. A secondary operation is to do similar planning for only one robot for operations such as repositions. While this section describes grasp-pair planning, the same planner is used for single-robot grasps"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000944_s0094-114x(96)00075-4-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000944_s0094-114x(96)00075-4-Figure7-1.png",
        "caption": "Fig. 7.",
        "texts": [
            " In the case, we rewrite the former two expressions of equation (25) as r2(fl*~ *' - ~*fl*\" + fl*Zx3) + c\u00a2*(~*x3 + fl*]lmX3 \"3 I- f l * X l X 2 ) -~- 0 -~*x2 +/~'2r2 + p*(x , x3 - x 2 ~ ) k = R2r Substituting equation (26) into the above equations, we have r[r(o(*/fl*)\" + r 2 sin 0 + ~*De sin(0 + 0e)] = 0 (31) k = r - D ecos(0 + 0e) r 2 + (~,/fl,)2 (32) Another two expressions of equation (32) are derived by replacing curvature k with curvature radius p: p[r - De cos(0 + 0e) ] = r 2 + (a , / f l , )2 (33) 1 + 1 _ p (34) r p - r (0(*/fl*) 2 + p D e cos(0 + 0g) Equations (32)-(34) are called the Euler-Savary analogues of a point trajectory in spatial motion. Equation (33) can be expressed by A0A AJA = AP~, + (~,//~,)2 (35) where A is the tracing point on a moving body, 0A is the curvature center of the trajectory FA, PA is the intersection point of the principle normal n of FA and axis of E~I f) while JA is the intersection point of n and the geodesic inflection circle, which is on the plane perpendicular to axis of ~f~ and passing through point A(xi, x2, x3), shown in Fig. 7. Obviously, it is not any point in moving a body that can trace a trajectory which holds the above Euler-Savary analogue until the point is on the surface determined by equation (31) in the moving body at an instant. In other words, there exists a geodesic Euler-Savary analogue for any point trajectory in spatial motion, but a Euler-Savary analogue for some point trajectories. In particular, the point A in a moving body must be on the intersection curve of the geodesic Kinematic differential geometry--I 429 inflection surface and the surface determined by equation (31) if the geodesic curvature kg and normal curvature k"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002451_bit.260360809-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002451_bit.260360809-Figure1-1.png",
        "caption": "Figure 1. Schematic diagram of glucose sensor",
        "texts": [
            " Similar coupling procedures were performed with various amounts of CMC, glucose oxidase concentrations, and reaction time periods, respectively. The enzyme membrane was soaked further in acetate buffer, pH 5.6, and was used for the preparation of biosensors. Glucose Oxidase Sensor The procedure for the preparation of the enzyme electrode was as follows. The immobilized glucose oxidase membrane was mounted on the surface of the dissolved oxygen electrode and secured with a nylon net and 0 ring (Fig. 1). Then the electrode was stored in acetate buffer, 0.05M, pH 5.6, at 30\u00b0C. The electrode response time was proportional to the amount of glucose oxidase on the electrode surface. When the dissolved oxygen was at a constant level, the sample solution (5000 ppm glucose solution, 0.4 mL) was added to 9.6 mL buffer and the initial rate of change in dissolved oxygen of buffer was recorded as activity (Fig. 2). The activity of free glucose oxidase was measured by the same method as the immobilized glucose oxidase"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001743_0167-2789(91)90188-f-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001743_0167-2789(91)90188-f-Figure8-1.png",
        "caption": "Fig. 8. Aspect ratio of small double spirals ~ = a/b. The distance between the cores is denoted by d.",
        "texts": [
            " 4b realized 13 cycles of self-reproduction. Therefore, three wave fronts around the double spiral center are left, as seen in fig. 4b. Second, the distance between the cores of the spiral centers grows in the course of time. Simultaneously the frequency decreases until it reaches the characteristic value for a single spiral in the medium considered. During the growth process of the double spiral the aspect ratio K = a/b was found to change from K = 1.22 at the moment of appearance to K ~ 1.36 at t o + 35 rain (compare fig. 8). For wave propagation in the presence of obstacles the evolution of breaks in a wave front (or of remaining front pieces) depends very sensitively on the size of the breaks (respective pieces) and on the excitability of the medium [10, 11]. This will be discussed in greater detail in a forthcoming paper [12]. Here we only briefly summarize preliminary observations. Three critical values, 11, 12, 13, for the size of the segment of the front determine the final outcome of its evolution. For I < 11 it disappears in the course of time"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003343_ac040032v-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003343_ac040032v-Figure1-1.png",
        "caption": "Figure 1. New experimental setup for the OW studies including a CW argon ion laser (1), a pair of two plane mirrors (2), a mechanical chopper (3), a plane mirror (4), a holder (5) that accommodates a disk and a piezoelectric ring, an adjustable sleeve (6), a housing (7), and the power detector (8).",
        "texts": [
            " At 502 nm \u03b5502 ) 3150 dL g-1 cm-1 for lycopene, whereas \u00e2-carotene was estimated from A471 with \u03b5475 ) 2049 dL g-1 cm-1. After extraction, an almost colorless (beige to light orange) fluffy solid residue remained, whereas the polar layer was light yellow. All manipulations were performed under dim lighting conditions. Each product was analyzed at least in triplicate. Determination of Lycopene by the Optothermal Window Method. The exploded view of the new, improved experimental setup for the OW studies is shown in Figure 1. It consists of the radiation source, a number of plane reflecting mirrors, the modulator, and a massive platform carrying the x-y translation stage that accommodates the OW cell held in a gimbal mount. All these components were mounted on a granite table. The present construction enables the easy and precise alignment of the entire setup. The 502-nm radiation was provided by a Lexel 851 CW argon ion laser (1). The laser beam reflected at two plane mirrors (2) was mechanically modulated (25 Hz) by means of a chopper (3) (16) Heinonen, M"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003505_robot.2006.1642018-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003505_robot.2006.1642018-Figure5-1.png",
        "caption": "Fig. 5. Comparison of the initial posture with that after 3.0s.",
        "texts": [],
        "surrounding_texts": [
            "OF 3-D OBJECT GRASPING As shown in Figs.2 to 4, denote the position of object mass center Oc.m. by x = (x, y, z)T on the basis of the cartesian coordinates O-xyz at the fixed coordinates. Define the Y Z-plane so that it is in parallel with two parallel surfaces of the parallelepiped rigid object and define the Xaxis so that it is orthogonal to the Y Z-plane (see Fig.4). It is well known that the overall motion of a rigid body can be expressed by the translational velocity vector of its mass center v(t) = (vx, vy, vz)T and the three unit vectors rX , rY , rZ corresponding to three mutually orthogonal axes X, Y, Z that can be recast into an orthogonal matrix R(t) = (rX , rY , rZ)T (1) Since R(t) belongs to SO (3), the 3 \u00d7 3 matrix \u03a9(t) defined as ( d dt R(t) ) R(t)\u22121 = \u03a9(t) (2) becomes skew-symmetric [16]. Hence, \u03a9(t) can be expressed as \u03a9(t) = \u239b \u239d 0 \u2212\u03c9Z \u03c9Y \u03c9Z 0 \u2212\u03c9X \u2212\u03c9Y \u03c9X 0 \u239e \u23a0 (3) and thereby the instantaneous axis of rotation of the object can be expressed by \u03c9 = (\u03c9X , \u03c9Y , \u03c9Z)T. Since in this paper we assume that there does not arise any spinning motion around the X-axis, it is possible to assume \u03c9X = 0. Next, denote the centers of hemi-spherical finger ends by x0i = (x0i, y0i, z0i)T and the contact points between finger-ends and parallel surfaces of the object by xi = (xi, yi, zi)T for i = 1, 2. Then, it is obvious to see that xi = x0i \u2212 (\u22121)irirX . Since these two contact points can be expressed as ((\u22121)ili, Yi, Zi) from the local frame Oc.m. - XY Z attached to the object (see Fig.4), it follows that x = x0i \u2212 (\u22121)i(ri + li)rX \u2212 YirY \u2212 ZirZ (4) The two contact constraints between finger-ends and object surfaces can be expressed as Qi = \u2212(ri + li) \u2212 (\u22121)i(x \u2212 x0i)TrX = 0, i = 1, 2 (5) which is obtained by taking an inner product between (4) and rX . The rolling constraints between finger-ends and object surfaces can be expressed by equalities of two contact point velocities expressed by spherical coordinates of finger-ends relative to local coordinates of the object. In fact, the rolling constraints can be expressed as ri d\u03c6i dt = \u2212 d dt Yi, i = 1, 2 (6) ri d dt \u03b7i = \u2212 d dt (Zi cos\u03c6i), i = 1, 2 (7) where (\u03c6i, \u03b7i) denotes the contact points between finger-ends and object surfaces expressed in spherical coordinates (\u03c6, \u03b7) as shown in Fig.3. These four equalities expressing rolling contact constraints seem to be non-holonomic, but they are integrable in time t, which results in RY i = ri\u03c6i + Yi + c0i = 0, i = 1, 2 (8) RZi = ri\u03b7i + Zi cos\u03c6i + d0i = 0, i = 1, 2 (9) where \u03c6i = \u03c0 \u2212 (\u22121)i\u03b8 \u2212 qT i ei, i = 1, 2 (10) \u03b71 = \u03c8, \u03b72 = \u2212\u03c8 \u2212 q20 (11) and \u03b8 denotes the indefinite integral of \u03c9Z and \u03c8 that of \u03c9Y , or \u03b8\u0307 = \u03c9Z and \u03c8\u0307 = \u03c9Y . In (10), e1 = (1, 1, 1)T, e2 = (0, 1, 1)T and qi = (qi1, qi2, qi3)T (i = 1, 2) and in (8) and (9) c0i and d0i are an integral constant. Then, it is reasonable to introduce Lagrange\u2019s multipliers fi for (3), \u03bbY i for (6), and \u03bbZi for (7) and define Q = \u2211 i=1,2 fiQi, R = \u2211 i=1,2 (\u03bbY iRY i + \u03bbZiRZi) (12) The Lagrangian for the overall fingers-object system can now be expressed by the scalar quantity L = K \u2212 P + Q + R (13) where K denotes the total kinetic energy expressed as K = 1 2 \u2211 i=1,2 q\u0307T i Hi(qi)q\u0307i + 1 2 M(x\u03072 + y\u03072 + z\u03072) + 1 2 (\u03b8\u0307, \u03c8\u0307)TH0(\u03b8\u0307, \u03c8\u0307) (14) and P denotes the total potential energy expressed as P = P (q1) + P (q2) \u2212 Mgy (15) where Hi(qi) stands for the 3 \u00d7 3 inertia matrix for finger i, M the mass of the object, H0 the 2 \u00d7 2 inertia matrix of the object rotating around Y -axis and Z-axis, P (qi) the potential energy of finger i, g the gravity constant. Now, it is possible to calculate the gradients of Qi, RY i, and RZi in qi for i = 1, 2, which leads to( \u2202Q \u2202qi )T = fi ( \u2202Qi \u2202qi ) = (\u22121)ifiJ T i (qi)rX , i = 1, 2 (16) ( \u2202R \u2202q1 )T = \u03bbY 1 { JT 1 (q1)rY \u2212 r1e1 } + \u03bbZ1 { JT 1 (q1)rZ cos\u03c61 + Z1e1 sin \u03c61 } (17)( \u2202R \u2202q2 )T = \u03bbY 2 { JT 2 (q2)rY \u2212 r2e2 } + \u03bbZ2 { JT 2 (q2)rZ cos\u03c62\u2212r2e0+Z2e2 sin \u03c62 } (18) where e0 = (1, 0, 0)T. In this calculation, the following relations that are obtained by inner products between (4) and rY , rZ , are referred to: Yi = \u2212(x \u2212 x0i)TrY , i = 1, 2 (19) Zi = \u2212(x \u2212 x0i)TrZ , i = 1, 2 (20) and, by taking differences between Y1 and Y2, Z1 and Z2, Y1 \u2212 Y2 = (x01 \u2212 x02)TrY (21) Z1 \u2212 Z2 = (x01 \u2212 x02)TrZ (22) In the same say, it follows that( \u2202Q \u2202x )T = (f1 \u2212 f2)rX (23) ( \u2202R \u2202x )T = \u2212(\u03bbY 1 + \u03bbY 2)rY \u2212(\u03bbZ1 cos\u03c61 + \u03bbZ2 cos\u03c62)rZ (24) The details of derivation of derivatives of Q and R in \u03b8 or \u03c6 will be given in Appendix (Due to space limitation, Appendix will be omitted in this article). Thus we obtain Hi(qi)q\u0308i + { 1 2 H\u0307i(qi) + Si(qi, q\u0307i) } q\u0307i \u2212(\u22121)ifiJ T i (qi)rX \u2212 \u03bbY i ( \u2202 \u2202qi RY i )T \u2212\u03bbZi ( \u2202 \u2202qi RZi )T + gi(qi) = ui i = 1, 2 (25) M x\u0308 \u2212 (f1 \u2212 f2)rX \u2212 \u2211 i=1,2 \u03bbY i ( \u2202 \u2202x RY i )T \u2212 \u2211 i=1,2 \u03bbZi ( \u2202 \u2202x RZi )T \u2212 Mg \u239b \u239d 0 1 0 \u239e \u23a0 = 0 (26) IZ \u03b8\u0308 + IZY \u03c8\u0308 \u2212 (f1Y1 \u2212 f2Y2) \u2212 \u2211 i=1,2 ( \u03bbY i \u2202 \u2202\u03b8 RY i + \u03bbZi \u2202 \u2202\u03b8 RZi ) = 0 (27) IY \u03c8\u0308 + IZY \u03b8\u0308 + (f1Z1 \u2212 f2Z2) \u2212 \u2211 i=1,2 ( \u03bbY i \u2202 \u2202\u03c8 RY i + \u03bbZi \u2202 \u2202\u03c8 RZi ) = 0 (28)"
        ]
    },
    {
        "image_filename": "designv11_24_0003886_095440705x34937-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003886_095440705x34937-Figure2-1.png",
        "caption": "Fig. 2 Discretized boundary element model of a driveshaft and the virtual microphones surrounding it",
        "texts": [
            " Owing to the lash minimum desired frequency (wavelength) to bezones and the variable number of gear tooth pairs captured, which was set to 680 Hz, a value that wasthat are in contact simultaneously, the equations also defined on the basis of vehicle tests. Therefore,of motion become strongly non-linear and can the distance from the source is calculated asbe solved using piece wise linear elements with time-dependent coefficients [20]. l= 343 (m/s) 680 (Hz) =0.5 (m)Since the response of the dynamic system is calcu- lated for the period of interest, the reactions at the driveshaft extremities are obtained with respect to Figure 2 shows the discretized model of a tube and time. These data are used as an input for a transient the virtual microphones surrounding it. analysis with the finite element analysis (FEA) models The propagation of small-amplitude waves can of the tubes. Then, the surface velocities of the shaft be represented by Helmholtz\u2019s equation in the wall nodes are computed for every time step. These frequency domain eventually become the initial conditions for the (V2+k2)p=0 (2)acoustic analysis. By using these historical data and applying the indirect boundary element method, the wheresound pressure fields in the exterior domain can be obtained in a natural way, having previously simuV2= q2 q2x + q2 q2y + q2 q2zlated the in-service events of interest"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003282_j.jmatprotec.2004.04.404-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003282_j.jmatprotec.2004.04.404-Figure5-1.png",
        "caption": "Fig. 5. Meteorological control by: (a) 3D-scanning of RT die inserts; (b) 3D-plot of scanning lines passing through the geometry points cloud.",
        "texts": [
            " The most significant material properties of bronze-based sintered powder and the manufacturing time and cost of RT-DMLS inserts are in Table 1. A sample made of sintered nickel\u2013bronze powder infiltrated with epoxy resin (extract from the DMLS tool insert) has a fractography from scanning electron microscopy (SEM) shown in Fig. 4. The dimensional control of RT die inserts is required in order to verify if the dimensional accuracy is in accordance with nominal CAD data [19]. This geometry control is rapidly made by laser triangulation [20] with a non-contact 3D-scanner system, at Laboratory of Modelling Prototypes (LMP), Fig. 5(a). The 3D-scanning system gives a cloud of coordinate points of the tool surface. A 3D-plot from the geometry digital data scanned is shown in Fig. 5(b). To estimate the capabilities of different rapid tooling processes in the manufacture of inserts for sand casting die-plates four pairs of RT-models (DMLS/SL/LOM/SLS-P) have been measured at LMP. After measurements the di- mensional analysis has permitted to plot the error distribution function (EDF) for each RT-model, Fig. 6. For each pair of RT-models have been registered 118 measurements per bin. Upon analysis of each EDF histogram it is recognised that for the RT-models the X\u2013Y\u2013Z dimensions peaks within the tolerance \u00b10"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003625_1-84628-269-1_7-Figure7.6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003625_1-84628-269-1_7-Figure7.6-1.png",
        "caption": "Figure 7.6. Bearing test bed II (left) and an FE model of the bearing structure (right)",
        "texts": [
            " Through such an iterative process, sensor locations with the relatively largest EfI values will form the largest possible FIM determinant [7.32], and the candidate sensor location set will contain only a relatively small number of sensor locations, compared with the original set. To guarantee that a critical sensor location is not incorrectly eliminated, only one sensor location can be removed at each time during the iteration process. The performance of an EfI-based sensor location selection approach was evaluated on bearing test bed II, as shown on the left-hand side in Figure 7.6, whereas a geometry-true finite element model of the bearing housing is shown on the righthand side. The nodal displacements of the bearing were obtained through a transient solution of the finite element model. To reduce computational load, coupling between the DC motor and the shaft through a universal joint, as well as between the hydraulic cylinder and the bearing housing, were not directly included in the model, but modeled as a noise load (Fa) and a static force load (Ps), respectively. Input to the test bed, a bearing defect-induced vibration, was modeled as a transient dynamic force (Fb) of 2,860 N (10% of the bearing\u2019s dynamic load rating) with 1 ms duration, and is applied radially to the test bearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003325_j.mechmachtheory.2006.09.008-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003325_j.mechmachtheory.2006.09.008-Figure3-1.png",
        "caption": "Fig. 3. The transmission error curve.",
        "texts": [],
        "surrounding_texts": [
            "An example of hypoid gear drive designed by the modified pitch cone method is considered in this section, and the meshing behavior, the tooth surface contact stress, the maximum tensile bending stress and the maximum compressive bending stress are studied by using the tooth contact analysis, loaded tooth contact analysis and finite element method [16\u201318]."
        ]
    },
    {
        "image_filename": "designv11_24_0002006_978-3-662-09769-4-Figure7.4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002006_978-3-662-09769-4-Figure7.4-1.png",
        "caption": "Figure 7.4: Drawing, vector and orientation diagram of the mechanism",
        "texts": [
            "88e) The equations (7.88) provide the well known model equations of the planar rotor (see Section 4.3) (7.89) 7.3 Rigid body attached to the base by a universal joint (two rot. DOFs) In this section the spatial model equations of a rigid body, which is fixed to the base by a universal joint, will be derived. This will be clone on the basis of the constraint equations of a universal joint which connects two rigid hoclies of Section 5.2.2.4 of (1]). The underlying drawing of this mechanism is shown in Figure 7.4 (see also Figure 5.28 of [1]). To use these constraint equations for the above mechanism, the body i will be identified with the base. The inertial frame R with the origin 0 is fixed on the base. 7.3.1 Model equations in DAE form Choosing the vector of the Cartesian coordinates (7.90a) with (7.90b) the constraint position equations of the universal joint are (see (5.45) of Section 5.2.2.4 of [1]): T QO - T PO - . T QP 3 ( R R ARL L ) (0 ) g(p) = P;!(x) \u00b7 ARL \u00b7 Pr(Y) = 0 (7.91a) with the projectors 7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002117_rob.10031-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002117_rob.10031-Figure6-1.png",
        "caption": "Figure 6. Directional stiffness of two-link elastic-joint manipulator.",
        "texts": [
            " Suppose that an infinitesimal displacement \u03b4DP of the end-effector occurs along the direction \u03b1D; then, it can be expressed as \u03b4DP = { \u03b4DxP \u03b4DyP } = { cos\u03b1D sin\u03b1D } \u03b4DP (22) The corresponding active force \u03b4fP can be obtained from the stiffness matrix SP f , that is, \u03b4fP = { \u03b4 fxP \u03b4 fyP } = [ sP11 sP12 sP21 sP22 ]{ cos\u03b1D sin\u03b1D } \u03b4DP (23) where \u03b4DP is the amplitude of the displacement. Let \u03b4fP be the amplitude of the force, and let KPd = \u03b4fP \u03b4DP = ( \u03b4 f 2xP + \u03b4 f 2yP )1/2 \u03b4DP = ( cos2 \u03b1D ( s2P f 11 + s2P f 21 ) + 2 sin\u03b1D cos\u03b1D(sP f 11sP f 12 + sP f 21sP f 22) + sin2 \u03b1D ( s2P f 12 + s2P f 22 ))1/2 (24) be defined as the directional stiffness of the point P with respect to the displacement direction \u03b1D; then KPd indicates the stiffness along the direction \u03b1D. A curve of KPd with respect to \u03b1D is plotted on a polar coordinate system in Figure 6, with \u03b8s1 at 0.6 rad (correspondingly, \u03b81 at 0.25 rad and \u03b82 at \u22121.05 rad), and with the manipulator parameters the same as when calculating the stiffness matrix in Section 5. Similarly, twomore curves can be plottedwith \u03b8s1 at 1.0 rad (correspondingly, \u03b81 at 0.69 rad, \u03b82 at \u22121.49 rad), and with \u03b8s1 at 1.4 rad (correspondingly, \u03b81 at 1.17 rad and \u03b82 at \u22121.74 rad), with the remaining parameters the same as in the previous case. The polar map of the change in directional stiffness with respect to the displacement direction produces a twin circle. The intersection of the twin circles represents the smallest stiffness, and the line passing through the origin perpendicular to that intersection line indicates the largest stiffness. The directions with the smallest and largest stiffnesses vary with the change of themanipulator configuration. The three twin circles in Figure 6 illustrate the changed directional stiffness when the manipulator configuration changes. The displacement directions with the largest and smallest directional stiffnesses can also be obtained directly from Eq. (24). A trajectory map of the end-effector has been proposed that relates the reachable trajectory to the stiffness ratio of the active and passive joints. This map is generated in position and force analysis by implementing the Taylor series and solution range analyses in solving a transcendental equation set"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003258_detc2005-84712-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003258_detc2005-84712-Figure2-1.png",
        "caption": "Figure 2. Planar 5-bar mechanism in a singular configuration q0.",
        "texts": [
            " In q0 the kinematic tangent space Tq0 V ( IK ) \u2261 K1 q0 V ( IK ) is two-dimensional. Embedded in it is the kine- matic tangent cone Cq0 V ( IK ) = C\u2032 q0 V ( IK ) \u222a C\u2032\u2032 q0 V ( IK ) , which is the union of the tangent spaces to the manifolds U (q0)\u2229V \u2032\\ {q0} and U (q0)\u2229V \u2032\u2032\\ {q0}. V can be partitioned in the 0-dimensional manifold of singular points \u03a3 \u2261 \u03a31 and the manifold M1 \u2261 V \\\u03a3 of regular points. Points in M1 have degree 0, i.e. P \u2261 P 0 \u2261 M1. The connected submanifolds of M1 constitute the modi of the mechanism. In all points \u03b4loc (qi) = dimCqi V ( IK ) = 1, i = 0, 1, 2. Figure 2 shows a planar 5-bar mechanism with L > 0 in its reference configuration q0 = 0. I. Kinematic tangent cone to V : In q0 is dim D (q0) = 2. The filtration terminates after \u03ba = 2 steps with the constraint algebra D(2) (q0) , se (2). It holds Cq0 V ( IK ) = K2 q0 V ( IK ) . The first and second order cone is K1 q0 V ( IK ) = { (u, v \u2212 2u \u2212 w, u \u2212 2v, v, w) ; u, v, w \u2208 R } K2 q0 V ( IK ) = { x \u2208 R5| ( x2 )2 + ( x3 )2 + x5 ( x4\u2212x3 ) = 0 } II. I-tangent cone to V : It holds Cq0 V ( IK ) \u223d Cq0 V ( I ) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000371_20.717855-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000371_20.717855-Figure2-1.png",
        "caption": "Fig. 2 Part of thle band with distorted elements",
        "texts": [
            " The explicit formula has been used to solve the mechanical equations [6] I One of the most important problems in the analysis of machine dynamics is the representation of motional effects. The author has tested two methods: (a) the method similar to the moving band method for 2D problems (MBM), and (b) the 3D representation of band interpolation technique (BIT) [7]. Here, the algorithn) with the moving band method is considered. The circular band of llength I is placed inside the air gap; where I is the distance between the boundary surfaces z=O, z=I (cp(z=O)=O, cp(z=Z)=$). The band is subdivided into layers of thickness AZ, - sde Fig. 2. In the presented example each layer is composed Iof 9-edge regular prisms. The trace of the prisms in the r,yplIane is a grid with triangles of identical angular length of base p. At each time of the rotor displacement the elements of the band are distorted or, if a=$ (i=1,2,3 ,... ), the band is rkmeshed. The electromagnetic tckque is calculated from the formula which is obtained by thb finite difference approximation of the magnetic energy dekvative versus the virtual moving. The approximation gives I I T(a> = { W(a - PI - W(a + P)} / (2P) 9 ( 5 ) where W(afP) is the magnetic energy for rotor position a$ and for cp=cp(a), i.e. q(a) w a f P I = S((a f PI, cpw) d c p . ~ ( a P) = 05i[cp(a)IT[~(a * ~>]cp(a> . (6) 0 For the linear magnetic system this integral gives I (7) The magnetic energy has been expressed as a sum of 3 components: (a) energy stored in the stator region, i.e. for r>r,, (b) magnetic energy W, stored in the rotor region, i.e. for r<r,., and (c) magnetic energy wb stored in the band, i.e. for r, >r> r, - see Fig. 2~. It can be seen that, if moving band method is applied, Ws(p+p)= W,(a-p)= W,(a), W,.(a+P)= = Wr(a-P)= Wr(a), and ,the matrices S(afp) differ from S(a) in distribution of nqn-zero elements only. As a result of the displacement of an le P these elements change their position. This change c n be described by the conversion matrix k 171. Thus, the dffference of magnetic energy can be W s t 0 Ss,r ( k T - .I][:; 1 ( 8 ) = \u2019[\u201d 2 \u201c [ ( k - ,kT)S$, 0 expressed as follows w(a-p) - w(a+pj = &(a-p) - wb(a+p) = 3622 and T = 9sTSs , r (kT-k )cp ,K2P) 9 (9) where cps is the vector of edge values of A on the boundary between the band and stator region, 9, relates to the other edges of the band (see Fig. 2), and Ss,T is the submatrix of S(a) which describes the interconnections between the edges of potentials cp, and other edges of the band. It can be proved that if the rotor region is empty, i.e. V=VO, J=O, and subdivided into bands of regular elements, similar to the moving band, the torque calculated from (9) is exactly equal to zero, i.e. (9) gives a faultless result. This is the most advantageous property of the presented formula. IV. EXAMPLE Transients in a drive with a 4-pole permanent magnet motor are analysed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003486_iros.2003.1248890-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003486_iros.2003.1248890-Figure1-1.png",
        "caption": "Fig. 1. Direction definitions",
        "texts": [
            " The fuzzy navigation strategy combines the repelling influence, which is related to the distance and angle between the robot and the detected obstacles (also referred to as the obstacle-avoidance behavior), with the attracting influence produced by the angular difference (target angle) between the robot heading direction and the final goal position (also referred to as the goal-seeking behavior). The definition of the direction used in a mobile robot navigation system is usually in the form illustrated in Figure 1. Since a computer is normally used in mobile robot control systems, it is efficient and helpful to select a discrete universe of discourse X. In onr application, X is defined as X : [-lSO\", 180\"] The robot heading direction is always taken as the 0\" direction, with negative on its left and positive on its right. Because piecewise linear functions are evaluated faster and more efficiently by computers and microcontrollers used in embedded applications, the membership functions used in a fuzzy-logic navigation system of a mobile robot take on triangular and trapezoidal shapes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003824_1.2202875-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003824_1.2202875-Figure4-1.png",
        "caption": "Fig. 4 Hyperboloid pitch surfaces for a1=100 mm, 1=90 deg, and k=\u22122",
        "texts": [],
        "surrounding_texts": [
            "Developing the second equation of Eq. 10 with respect to the transmission ratio k, one obtains a second-order algebraic equation, namely, b2k2 + a1 \u2212 2b2 cos 1k \u2212 a1 \u2212 b2 = 0 21 with solutions k = 1 2b2 \u2212 a1 \u2212 2b2 cos 1 \u00b1 a1 \u2212 2b2 2 cos2 1 + 4b2 a1 \u2212 b2 . 22 When the relative position of the skew axes of rotation I2 and I3 is given via the distance a1 and angle 1, the position of the instantaneous screw-axis I32 for the relative motion between the skew gears, which is given by distance b2 and angle 2, changes according to the variation of the transmission ratio k in the range + , \u2212 . During the variation of its position, I32 remains perpen- Journal of Mechanical Design rom: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess.as dicular to the common normal between I2 and I3, according to the Aronhold-Kennedy theorem, and traces a ruled surface that is termed the cylindroid or Pl\u00fccker\u2019s conoid 37,38 . In other words, even if k varies in the range + , \u2212 , the locus described by the instantaneous screw axis I32 is represented by a bounded ruled surface. Thus, in general, not all kinds of internal and external gears can always be obtained, as we prove below. In fact, the limits of the Pl\u00fccker conoid can be determined by equating to zero the discriminant of Eq. 22 , i.e., = a1 \u2212 2b2 2 cos2 1 + 4b2 a1 \u2212 b2 = 0 23 Thus, solving Eq. 23 , for b2, b2 * = a1 2 1 \u00b1 1 sin 1 24 which gives two extreme positions of I32 on the Pl\u00fccker conoid. In particular, when 1=0, which means spur gears, one obtains from Eq. 24 that b2 can take on any value in the range + , \u2212 . In this case, there is no limit on the Pl\u00fccker conoid, which becomes a plane containing the two axes of rotation I2 and I3. When 1 =90 deg, one realizes from Eq. 24 that b2 can vary in the range 0, a1 . These results are depicted in the plot of Fig. 6, displaying the two extreme values of b2 versus 1, for a1=100 mm. As shown in Fig. 6, when 1 90 deg, internal gears can be obtained because the I32 axis intersects the common perpendicular at both axes of rotation I2 and I3 at a point which can fall outside the internal segment that is perpendicular to both axes I2 and I3. Moreover, substituting Eq. 24 into Eq. 22 for =0, one has k* = cos 1 1 \u2212 sin 1 sin 1 \u00b1 1 25 which allows the determination of the transmission ratio k* for the extreme positions of I32 on the Pl\u00fccker conoid. Consequently, substituting k* of Eq. 25 into the first equation of Eq. 10 , one has tan 2 * = sin 1 \u00b1 1 cos 1 26 which gives the angular coefficients, in the YZ plane, of both extreme axes of the Pl\u00fccker conoid. These axes are always mutually orthogonal because the product of their angular coefficients is equal to \u22121. Referring to the sketch of Fig. 7, the equation of the Pl\u00fccker conoid can be obtained by considering a pair of bevel gears in dual space as the dual representation of a pair of skew gears. In fact, when both axes I2 and I3 are represented in dual space through the points P\u03022 and P\u03023, respectively, the image of the Pl\u00fccker conoid in dual space is given by the circle C\u0302, which is traced by point P\u030232 of the dual unit vector e\u030232 during the variation of the transmission ratio k in the range + , \u2212 . Circle C\u0302 corresponds to a ruled surface of revolution in Euclidean space, which is the Pl\u00fccker conoid. Thus, expanding the third equation of Eq. 4 , which expresses e\u030232 as a function of the dual angle \u03022, one obtains the equation of the circle C\u0302 in line coordinates: e\u030232 2,b2 = 0 \u2212 sin 2 cos 2 \u2212 b2 0 cos 2 sin 2 27 One has, in turn, the equation of the Pl\u00fccker conoid in point coordinates in Euclidean space, namely, rc 2,b2, = b2 0 0 + 0 \u2212 sin 2 cos 2 28 where the bounds of can be chosen arbitrarily, because they define only the extension of the Pl\u00fccker conoid, while the param- JULY 2006, Vol. 128 / 797 hx?url=/data/journals/jmdedb/27829/ on 06/12/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F eters 2 and b2 are obtained from Eq. 10 when the transmission ratio k varies in the range + ,\u2212 . For instance, the bounds of can be chosen equal to the thickness of the pitch surfaces P2 and P3. Some numerical results are shown in Figs. 8\u201310 where the Pl\u00fccker conoid PC is shown along with both hyperboloid pitch surfaces P2 and P3. In particular, Fig. 8 shows an example for a1=100 mm and 1=90 deg, where P2 and P3 are obtained for k=\u22121. According to the diagram of Fig. 6, and from Eq. 24 for 1=90 deg, Fig. 8 shows a ruled surface PC, where b2 varies in the range 0, a1 . Of course, the Pl\u00fccker conoid is the same for the example of Fig. 9, where only P2 and P3 change, because k=\u22122. Figure 10 shows, in turn, the case for a1=100 mm and 1 =30 deg, where P2 and P3 are obtained for k=k*=1.732, which has been derived from Eq. 25 in order to find one extreme position of I32. Moreover, according again with the diagram of Fig. 6 and from Eq. 24 , a pair of internal gears is obtained because 1 90 deg. Some particular results can be obtained from the first of equation Eq. 13 when k=cos 1 because the second term becomes infinite. Two examples are reported for a1=100 mm: 798 / Vol. 128, JULY 2006 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess.as Figure 11 shows the case for 1=90 deg and k=0, while Fig. 12 shows the case for 1=45 deg and k=0.707. A singularity occurs when 1=0 and k=1 because a pair of coincident internal cylindrical gears cannot be obtained."
        ]
    },
    {
        "image_filename": "designv11_24_0003638_j.electacta.2006.03.085-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003638_j.electacta.2006.03.085-Figure2-1.png",
        "caption": "Fig. 2. Cyclic voltammograms of 1.0 mmol/l SPQ and MPQ at pH 2.15 using GCE. Scan rate = 0.1 V/s.",
        "texts": [
            "1 V/s the oxidation wave is irreversible with anodic peak potenial (Ep,a) = 0.654 V. The scan rate variation from 0.05 to 2.0 V/s auses increase in the height of the oxidation wave and Ep,a s shifted towards positive potential. The relationship between nodic current values (Ip,a) and \u03bd1/2 is linear, indicating that the lectrodic reaction was controlled by diffusion, confirming preious results [1\u20133]. SPQ and MPQ prodrugs display the same voltmmetric behavor of primaquine. Both compounds showed one irreversible xidation wave also controlled by diffusion. Fig. 2 shows the yclic voltammograms of MPQ and SPQ in acidic medium. n this experimental condition, a quasi-reversible redox couple peaks 1 and 2) was recorded at less positive potential in the everse scan. These results indicate a new species was formed n the first anodic peak, being more easily oxidized than the 8- minoquinolines derivatives themselves. This quasi-reversible ave was shifted to negative potential region as pH increases. his behavior is completely in accordance with the results preiously registered to primaquine [1]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000332_s0094-114x(96)00076-6-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000332_s0094-114x(96)00076-6-Figure2-1.png",
        "caption": "Fig. 2.",
        "texts": [
            " [1] for a rigid body in spatial motion, the Frenet frames {rf, E~I l), E~2 0, E~3 0} of Y-f and {rm, ~m), ~m), E~3m)} of E~ are established in that paper, and they are coincident with each other at any instantaneous screw axis (ISA). Now, we take the moving axode Y'm and the fixed axode Zf as an original ruled surface respectively for examining a line trajectory. A line trajectory E~ in the fixed frame Or-idfkr traced by a line L fixed in the moving body, which passes through a point A fixed in a moving body, can be regarded as an adjoint ruled surface of the fixed axode Zf, shown in Fig. 2 and its vector equation can be written as ~i: Rl0(o'b/2) = RA + /gl (7) where or, is the spherical image curve's arc-length of unit vector ! of the line L and 1 = l , ~ f~ + l,E~,_ ~ + 13E[ ~, l~ + l~ + l~ = 1 RA = rf + xIE~ f~ + .x'2E~2 n + x3ff30 (8) while (ll, 6, 13) are the components of the unit vector ! of line L in the Frenet flame {rf, ~n, 40, ~ } respectively, and rf is the vector of the original point of the Frenet frame, or the striction point of the fixed axode Zf and RA is the vector from the origin of the fixed reference Or-idrkf to the point A in the moving body",
            " Differentiating I with respect to a, which is denoted by a prime, we have r = (l( - h ) ~ ~ + (i, + / ; - /~fh)E 'a + (M: + tg)~ ~ (9) where a is the spherical image curve's arc-length of the unit vector of ISA and a = af = Om [1]. The first and the second derivatives of a letter with respect to a are denoted by the letter with a prime and two primes respectively in the paper. R;, has been revealed in Ref. [1]. Meanwhile, the fixed line L passing through a fixed point A in the moving body is adjoint to ISA at any instant, so that it has a trajectory )'~m) examined in the moving reference system 0m-inffmkm fixed with the moving axode Y~m, which can be regarded as an adjoint ruled surface of Em shown in Fig. 2, and its vector equation is ~'~,Im): Rlm}(cr/,/a) = R~A ~1 +/.tl ~m' (10) where R~A ~ is the vector from the reference point 0m to the point A in a moving body, whose vector equation is the same as that in equation (10) in Ref. [1]. l (m) is the unit vector of the line L in the reference frame 0m-inffmkm and its components in the Frenet frame {r~, ~ml, ~m/ ff3m~} are (l~, 6,/3) correspondingly, or 1 ~J = l,~m~ + /_,~m~ + /3~mL Since {~m), ~m~, ~ml} are coincident with { ~ , ~ , ~ ) , the component of "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003766_0278364906061159-Figure17-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003766_0278364906061159-Figure17-1.png",
        "caption": "Fig. 17. Lock mechanism.",
        "texts": [],
        "surrounding_texts": [
            "Table 2. Head unit specifications\nDiameter 90 (mm) Weight 400 (g)\nFig. 13. Head unit.\nextra wire will pile up at the end. To make the head unit follow the tube, it is necessary to wind up the excessive wire length. Therefore, we added a wire-rewinding device to the head unit (Figure 12).\nThe head unit has a CCD camera. The specifications of the head unit are shown in Table 2.\nAs shown in Figures 14 and 15, the hermetic case is composed of the following:\n1. a winch;\n2. a slip ring;\n3. an air tank (hermetic case);\n4. lock mechanism.\nThe winch winds up the tube and wire simultaneously. The slip ring allows the supply of electricity to the outside through the wire wound up around the winch. The air tank contains the air supplied from the air compressor. The amount of tube expansion is controlled by the handle and lock mechanism.\nThis hermetic wheel case can wind up to 10 m of tube. Since the wire is inside the tube and will be wound up along with the tube, the wire will twist if no measure is taken. The slip ring prevents this twist.\nIn the next section we explain the handle lock mechanism. When air pressure is applied, the tube will expand in a forward direction. Accordingly, it will continue expanding unless the expansion is stopped. In rescue operations, however, some-\nat Virginia Tech on March 14, 2015ijr.sagepub.comDownloaded from",
            "times it is necessary to stop the tube expansion and search a certain area for a while. Therefore, the device controls the expansion amount by locking the handle to stop the tube expansion. Figures 16 and 17 show the actual handle lock mechanism. The Slime Scope controls the tube expansion by locking and releasing the handle.\n5. Test Machine\nFigure 18 shows our test machine. We used this test machine to confirm that the DETube can travel in rubble. Table 3 shows its specifications.\nIn the following, the DETube\u2019s holding power is the power needed to maintain the tube\u2019s expansion against the propelling force at the head of the DETube, with the propelling force being caused by the inside pressure. Assuming that the propelling force produced by the DETube is FT , the holding power is Fk, the force that holds the tube from outside is Ff and the loss is FL, the relationship between these can be expressed as\nFT = Fk + Ff + FL. (1)\nThe retracted tube is wrinkled since it has the same diameter as the external tube, causing friction, resulting in loss, etc.\nAs the DETube\u2019s propulsion principle is the same as the principle of a pulley, the following equation is established:\nFk = Ff . (2)\nSubstituting eq. (2) into eq. (1) yields the following equation:\nFT = 2Fk + FL. (3)\nHere FT is the product of the pressure inside the tube and the stress area, so if the holding force Fk is determined, the impact of the loss in propelling force can be calculated from eq. (3). In other words, determining the holding power is considered to be important to know the characteristics of the DETube.\nat Virginia Tech on March 14, 2015ijr.sagepub.comDownloaded from",
            "Therefore, we calculated the loss in propelling force by measuring the holding power Fk using the experiment device shown in Figure 19. Figure 20 shows the result.\nThe experiment demonstrated that the holding power was not the same as the propelling power. This discrepancy results from the friction loss, possibly because higher pressure increases the friction resistance inside the tube and thus increases the loss.\nIn addition, Figure 20 shows that the holding power remains almost the same regardless of the expansion amount. In other words, the impact of the loss is independent of the expansion amount. However, in theory, as the expansion amount becomes larger, the contact area between the external tube and retracted tube (i.e., the area where there is loss from friction resistance) will increase. As a result, the loss must be larger. However, this does not appear clearly in the experiments, since the expansion amount was small, thus resulting in a small friction resistance.\nIn the previous experiment, we studied the impact from the loss by measuring the holding power when the DETube went straight forward. However, in actual search operations in rubble, the DETube will often need to bend to go through, rather than go straight forward. Accordingly, we studied the changes of the loss when the DETube bends, using the experiment of apparatus shown in Figure 21. Figure 22 shows the result.\nFigure 22 shows that the holding power decreases as the bending angle increases. This would suggest that increasing the bending angle results in an increased loss.\nThen we studied the loss. When the DETube is bent, the contact area between the external tube and retracted tube will increase and the area affected by sliding friction will increase. Therefore, it is considered that the loss will increase.\nTo study the impact of the friction loss, we repeated the previous experiment once again after applying grease inside the tube for lubrication. Figure 23 shows the result.\nat Virginia Tech on March 14, 2015ijr.sagepub.comDownloaded from"
        ]
    },
    {
        "image_filename": "designv11_24_0003996_tase.2005.846289-Figure9-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003996_tase.2005.846289-Figure9-1.png",
        "caption": "Fig. 9. Model to be processed.",
        "texts": [
            " the GA module calculates according to the mapping relationship listed in Table I for all facets in the STL model. Apply them to the objective function and the fitness value (i.e., the error, as defined in (10), can be obtained for . Evolving after several generations, when the termination condition specified by the user is satisfied, this algorithm terminates and the best genome is thus output. The GA parameters used here are: crossover 0.9, mutation 0.02, population 200, and generation 750. A part with free surfaces shown in Fig. 9 has been tested with this algorithm. We also implemented the orientation optimization under the single-direction deposition system for the minimal slicing error. A comparison of the optimization process for the two methods is shown in Fig. 10 and the error value is given in Table II. As can be seen in Table II and Fig. 10, the final optimized direction is nearly the same under the two optimization criteria if they are presented in the spherical coordination system, but the final error values for the orthogonal method was nearly reduced by 30%",
            " Otherwise, when the deposition directions are not perpendicular to each other, some special processing steps are needed to avoid the problem of staircase interaction: in Qian and Dutta\u2019s work [28], feature interaction volume (FIV) (shown in Fig. 12) was used to act as a bridge between different features, and the refined feature volumes (RFVs) are then obtained by subtracting the FIV from different feature volumes. The computation of FIV and RFV is quite complicated, while in the proposed orthogonal LM system there is no staircase interaction by nature or the FIV is degenerated into the interface plane. Shown in Fig. 13 is the result of volume decomposition for the part in Fig. 9, the interface between the flat volume and the rest of the part is a horizontal plane, hence the computation is significantly simplified in this condition. The processing techniques for slicing and path generation in the conventional LM process planning can also be applied in this method. The only difference is that the slicing will be in the horizontal direction for the flat volume. As shown in Fig. 14, the part was separated into two parts: the flat volume and the steep volume. The flat volume was sliced along the horizontal direction and the steep volume was sliced along the vertical direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003240_1.1688379-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003240_1.1688379-Figure6-1.png",
        "caption": "Fig. 6 The overall deformed shapes and distributions of the effective strain in cold forward extrusion of a spur gear with the \u201ea\u2026 7 and \u201eb\u2026 18 teeth number",
        "texts": [
            " The forming load increased almost linearly with the number of total teeth according to Fig. 5~b!. Table 2 Comparison of average forming pressures between FE simulation and experimental results Extrusion without mandrel FE Simulation Experiment @10# Friction condition 0.06 0.08 0.12 Average pressure ~MPa! 290.06 313.2 365.7 317.5 Extrusion with mandrel FESimulation Experiment @11# Friction condition 0.12 0.17 0.20 Average pressure ~MPa! 522.9 608.6 670.9 617.9 258 \u00d5 Vol. 126, MAY 2004 rom: http://manufacturingscience.asmedigitalcollection.asme.org/ on 01/2 Figure 6 shows the deformed shapes and distributions of effective strain for the cases of 7 and 18 teeth. The central free end surface of the deformed workpiece was formed to be rounded. Such a roundedness was formed due to the difference of material flow between the center and tooth regions of the gear. Because of the friction effect, the material flow was slower in the tooth die cavity region compared to the central region of the gear. Because of such a difference in material flow, complete filling in the tooth die cavity region was not guaranteed for all cases"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002230_s0003-3472(05)80722-5-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002230_s0003-3472(05)80722-5-Figure1-1.png",
        "caption": "Figure 1. Typical l-rain samples of swimming tracks for Polyphemus (a) and Bosmina (b). Labels indicate the time in seconds since the start of the sample.",
        "texts": [
            " A measure of the ground covered during the l-rain swimming period was obtained by first calculating the coordinates for each sampling position relative to an X-axis joining the first and last positions, with an origin at its mid-point. Then the interquartile ranges for all the X-axis coordinates and for all the Y-axis coordinates were used as the long and short axes respectively of an ellipse, representing a core area for the track, which we have called the 'groundcovered ellipse'. The tortuosity of the track was estimated by the turning rate per mm swum; this is the meander rate as defined by Bell et al. (1986). Figure 1 shows typical tracks for Polyphemus and for Bosmina. In both cases there was a tendency for straight track segments to alternate with large turns, often approaching 180 ~ . Because of the presence of long parallel sections Polyphemus tracks typically had a bimodal distribution of track segment headings (Fig. 2a). Each of our Polyphemus tracks produced a statistically significant heading distribution (P < 0-005, Rayleigh test). Moreover, the mean vectors of these heading distributions for different individuals clustered closely together (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003285_0021-9797(81)90136-3-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003285_0021-9797(81)90136-3-Figure1-1.png",
        "caption": "FIG. 1. Bell jar glow discharge system.",
        "texts": [
            " We have reported (11, 12) both perpendicular and parallel alignment of nematic liquid crystals on a variety of plasma-polymerized films which exhibited a wide range of polar and dispersive components of surface energy. The purpose of this study is to determine the role played by the chemical nature and the surface energy of the plasmapolymerized surfaces in liquid crystal orientation. E X P E R I M E N T A L The plasma-polymerized films described in this paper were deposited in a laboratory (46 \u00d7 76-cm) vacuum system shown in Fig. 1. This system is a small plasma discharge reactor utilizing a continuous flow of the reacting gases and parallel screen electrodes with 30% open structure. The electrodes are supported by magnetron structures to confine the primary glow to a race track on the screen surface. Journal of Colloid and Interface Science, Vol. 82, No. 1, July 1981 The gases to be reacted in the glow discharge (precursors) were introduced at the top of the bell jar. This avoided gas-phase polymerization, which can occur if the precursor is introduced in the vicinity of the electrodes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000476_s0045-7949(99)00201-1-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000476_s0045-7949(99)00201-1-Figure2-1.png",
        "caption": "Fig. 2. Geometric description of the sti ened shell element: (a) the reference plane; and (b) the cross section.",
        "texts": [
            ", 0esL, 0ebL, d0esN, and d0ebN are grouped on the left-hand-side of the equation; the right-hand-side of the equation, however, contains only the terms that involve traction forces and internal forces, which are known from the previous time step. Eq. (10) forms a basis for the derivation of the \u00aenite element equations of equilibrium for the sti ened shell element. The subsequent sections will, therefore, focus on the \u00aenite element implementation of Eq. (10) and the development of the sti ened shell element from its components, shallow shell and shallow beam (sti ener) elements. The geometric description of the sti ened shell element is depicted in Fig. 2. As shown in Fig. 2(a), two Cartesian coordinate systems are used to de\u00aene the kinematics of the sti ened shell element and to derive the element matrices and vectors associated with this element. The element matrices and vectors belonging to the shell element are derived with respect to the (x, y, z ) element coordinate system. In order to carry out integrations of matrices belonging to the beam element, a local coordinate system situated on the reference surface of the shell element is utilized. This coordinate system is established by projecting the longitudinal axis of the beam element to the reference plane",
            " Hence, a simple plane transformation is su cient to transform variables between these two coordinate systems. The zand the z '-axes of these two coordinate systems are parallel to each other. Thus, the same vertical axis can be used to de\u00aene the mid-heights and the transverse displacements in both elements. The position and the orientation of the local coordinate system (x ', y ', z ') are identi\u00aeed by the vector rb and the angle fb between the x '- and x-axes, respectively. The height of the shell from the reference surface is denoted by hs (see Fig. 2(b)). The distance between the neutral axis of the beam and the shell mid-surface is indicated by the eccentricity parameters z 0ec: The positive directions of displacement and rotation \u00aeeld in both elements are shown in Fig. 2(a). They will be discussed later in this section. The material lay-ups for both the shell and the stiffener components are illustrated in Figs. 3 and 4, respectively. As shown in Fig. 3, the shallow shell element is made of a layered composite laminate. Each layer is assumed to be homogeneous, elastic, and orthotropic with elastic moduli, E1 and E2; shear modulus, G12; and Poisson's ratio, n12. The subscripts ``1'' and ``2'' specify the longitudinal and transverse directions relative to the \u00aebers in the layer",
            " (10) lead to 0As XKs k 1 zk zk\u00ff1 d0eT sLQs 0esL d z d0As 0l XKb i 1 A i b d0eT bLQb 0ebL dA i b d0x 0 0As XKs k 1 zk zk\u00ff1 d0eT sN t 0ss d z d0As 0l XKb i 1 A i b d0eT bN t 0sb dA i b d0x 0 dWe \u00ff 0As XKs k 1 zk zk\u00ff1 d0eT sL t 0ss d z d0As \u00ff 0l XKb i 1 A i b d0eT bL t 0sb dA i b d0x 0 11 In accordance with Mindlin's theory [17], the incremental displacement components of the shell element, u, v, and w in the x-, y-, and z--directions, are expressed as us x, y, z us0 x, y zysy x, y 12a vs x, y, z vs0 x, y zysx x, y 12b ws x, y, z ws0 x, y 12c The functions u0 and v0 represent the in-plane displacements and w0 the out-of-plane displacements on the mid-surface of the shell element. The bending (normal) rotations about the x- and y-axes are denoted by yx and yy, respectively. The element coordinate system is chosen such that the positive x-axis points in the direction from node 1 to node 2 of the element. As shown in Fig. 3, the element reference plane coincides with the (x\u00b1y ) plane. The components of the incremental displacements and bending rotations at each node of the element, with positive sign conventions, are shown in Fig. 2(a). The variable z- is de\u00aened as z z\u00ff h x, y 13 where h(x, y ) describes the shallow mid-surface of the shell element. For the beam element, the displacements at a point are expressed based on the Timoshenko beam theory, which assumes constant transverse shear deformations across the thickness of the beam. Considering the interaction between the shell and the sti ener, it is also assumed that the in-plane shear and in-plane bending sti nesses of the shell element are much higher than those of the beam element",
            " Thus, the slope of the beam element associated with the in-plane bending deformations of the shell element (the drilling rotation) can be disregarded. The resulting expressions for the displacements at a point in the sti ener can be written as u 0b x 0, y 0, z 0 u 0b0 x 0 z 0y 0by x 0 14a v 0b x 0, y 0, z 0 v 0b0 x 0 \u00ff z 0y 0bx x 0 14b w 0b x 0, y 0, z 0 w 0b0 x 0 y 0y 0bx x 0 14c where u 0b0, v 0 b0, and w 0b0 are the displacements de\u00aened along the longitudinal axis of the beam and y 0bx and y 0by represent the rotations about the x '- and y '-axes, respectively. The sign conventions for the displacements and rotations are illustrated in Fig. 2(a). In Eqs. (14a)\u00b1(14c), z-' is obtained from z 0 z\u00ff h 0b with h 0b x 0 denoting the height of the neutral (curvilinear) axes of the beam measured from the reference plane. The height function, h 0b x 0 , is related to the shell height function, h(x, y ), as h 0b x 0 h x x 0, 0 , y x 0, 0 z 0ec 15 where z 0ec is the eccentricity of the beam (Fig. 2(b)). The coordinates x(x ', 0) and y(x ', 0) in Eq. (15) are obtained from the coordinate transformation between (x '\u00b1y ') and (x\u00b1y ) planes, i.e., x x 0, y 0 y x 0, y 0 cos fb \u00ffsin fb sin fb cos fb x 0 y 0 rbx rby 16 At y '=0, the coordinates x and y de\u00aene a line passing through the x '-axis: x x 0, 0 cos fbx 0 rbx 17a y x 0, 0 sin fbx 0 rby 17b The linear part of the Green's strain tensor is based on the de\u00aenitions given by Reissner [24] and Mindlin [17], combined with the shallow shell theory introduced by Marguerre [16]",
            " This approach requires that the cross section of the beam and the section of the shell before deformation remain co-planar after deformation (i.e., the cross section of the beam lies on the same plane as that of the shell after deformation), thus leading to constraint equations between the displacement and rotation \u00aeelds of these elements. Based on this approach, the following constraint conditions are, therefore, introduced: y 0bx \u00ff y 0 sx 33a y 0by y 0 sy 33b w 0b0 w 0s0 33c in which w 0b0 is the transverse displacement and y 0bx and y 0by are the slopes of the beam in the primed coordinate system. As shown in Fig. 2(b), the corresponding transverse displacement, w 0s0, and the slopes, y 0 sx and y 0 sy, belonging to the shell element are de\u00aened as functions of x ' 2. Utilizing the constraint conditions in Eqs. (33a) and (33b), two additional constraint equations can be obtained by relating the displacements of the beam element in terms of the displacements and rotations of the shell element as u 0b0 u 0s0 z 0ec y 0 sy 34a v 0b0 v 0s0 z 0ec y 0 sx 34b where u 0b0 and v 0b0 are the displacement components of the beam element in x '- and y '-directions, respectively",
            " The tangential direction, s, points from node 1 to node 2 for k = 1, node 2 to node 3 for k = 2, and node 3 to node 1 of the element for k = 3. The displacement components tangent and normal to the kth edge of the element are denoted by u k s s and v k n s , respectively. Similarly, the out-of-plane rotations about s- and the opposite ndirections are denoted by y k s and y k n on the kth edge, respectively. These displacements and rotations are related to those de\u00aened with respect to the element coordinates (see Fig. 2) through appropriate transformations. Imposing the constraints given by Eq. (39) along the edge of the element leads to the following transformation between intra-edge displacements and corner displacements: v b Lbv with b u, v, w 40 or v Lv 41 where LT LT u LT v LT w and v T v T u v T v v T w 42 with v T u fu 04, . . . , u 09g v T v fv 04, . . . , v 09g v T w fw 04, w 05, w 06g The explicit forms of the transformation matrices Lb (b=u, v, w ) are the same as those given by Tessler [30]. These matrices are presented in Appendix A for completeness"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003960_detc2005-84728-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003960_detc2005-84728-Figure8-1.png",
        "caption": "Fig. 8 GSAM predicted contact patterns and load distribution for single pinion cases (a) 1-GA (b) 1-GB (c) 1-GC (d) 1-GB-R",
        "texts": [
            " In case1-GA, the pinion is supported by rigid bearings and so the generated bearing moments do not result in any bearing tilt. In the absence of other factors that may cause misalignments, the resulting contact pattern is well centered. The values of Mx-PIN and My-PIN are close to their theoretical values of 0 and 264 Nm, respectively. The values of Zs and Zr that would cause the small deviations from theoretical value of the moments are -0.03 and 0.56 mm respectively. The values of Zs and Zr are strictly true for the mesh position under consideration and will vary to a limited extent as the gears roll through mesh. Figure 8 (a) shows the corresponding GSAM predicted contact pattern and the load distribution for the mesh position under consideration. In case 1-GB the pinion is supported by a bearing of intermediate stiffness causing moderate shifts in contact pattern. In case1-GC the pinion is supported by a flexible bearing and the resulting bearing tilt pushes the contact pattern towards the ends of the facewidth. The theoretical prediction was a contact pattern shift as in Table 8, Case D. The effect of the contact pattern shift (from Table 8) is to slightly change Mx-PIN and significantly reduce My-PIN",
            " The final load distribution depends upon these deflections along with the rigid body movements (and other sources of misalignments) and tooth flank modifications (lead crowns and lead tapers). Case 1-GB-R has the same bearing stiffness as case 1-GB, but the modulus of elasticity of the gear material was assumed to be 10 times that of steel. This was done to illustrate the influence of gear tooth deformation due to tooth bending and surface contact. In this case, the neutralizing influence of the deflections is greatly reduced and the contact shifts significantly more than in case 1-GB. Figure 8 (d) shows the GSAM predicted contact pattern. The interactions between the load distribution, bearing tilts and body deformations cannot be predicted without considering a full system level model of the gear-bearing system. Next the following double pinion cases were analyzed. \u2022 Case 2B-GA Rigid bearing support \u2022 Case 2B-GB Normal bearing support The bearing stiffnesses were same as those used in the corresponding single pinion planetary cases. The moments causing line of action misalignment were extracted from the GSAM runs and are shown in Table 11"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003104_bfb0036160-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003104_bfb0036160-Figure2-1.png",
        "caption": "Figure 2(a) illustrates the motion in the lateral plane by using the inverted pendulum model. This figure shows the transition from k-1 th step to k th step. The leg-length r, rk and rk+, represent the length of the leg which was projected on the lateral plane. The leg-length can be adjusted by the bending angle of the knee joint. At first, the system is being supported by the left leg (actually by both of the fore and hind legs) in k-1 th step. The landing occurs after shortening the right leg by Uk-1 (the leg-length changes from r to rk). Secondly, the shortened right leg is extended up to. the initiM leg-length r just after the leg-support-exchange (r~ --+ r). In k th step, the left leg is shortened by uk similarly. Then, the supporting leg is exchanged again.",
        "texts": [
            " D i sc re t e - t ime M o d e l 2.1 C o m p e n s a t i o n of A n g u l a r M o m e n t u m In the stepping motion, the exchange of the Supporting point causes a loss in an angular momentum about tile roll axis. Therefore, unless the lost angular momentum is compensated in aIW way, the angular momentum of the system is attenuated so that tile continuation of the stepping motion will be impossible. In this section, an indirect and efficient compensation method which utilizes an gravity effect is discussed by using Fig.2. Figure 2(b) shows the trajectory of the center of gravity in k th step. The center of gravity transfers in tim order of 1, 2, 3 and 4 according to the arrows in the figure. The number 1 indicates the position of the center of gravity just after the leg-supportexchange. As seen from the figalre, since the period (3 --4 4) When the inverted pendulum undergoes the positive moment caused by the gravity effect (the positive moment is defined as the moment which affects in the direction of rotation) is longer than the period (2 --+ 3) when it undergoes the negative moment, the lost angular momentum is compensated",
            " In this study, we assumed that this motion completes instantaneously because the behavior of the inverted pendulum is not greatly affected by the speed of the motion. In this case, according to the law of the conservation of angular momentum, the following equation holds - - k-I Step ,,I,~ k Step 1 ', / \\~ /,,~\\ ;rk.V I ,' ',rl \\', // I k ~/ Ir / \"i .... \u00b0/ -\" I . (a) Motion in the laterM plane C\u00a2)kl ~ Supporting ! \\r.\\l Swing /I \\ \\ ,//r \\ ' _\u00a3___:g_ Ok+1 Ok .. ~l\" (b) Trajectory of center of u ~ S gravity (c) Leg-support-exchange model Fig.2 Inverted pendulum model T 2 k w ~ k , = ~ k ( 1 ) where Wk is the angular velocity before extending the supporting leg (namely just after the leg-support-exchm,ge), and wk, is the angular velocity after extending. Upon the leg-support-exchange which happens at the position 4, the loss of the angular velocity (loss of the angular momentum) takes place as follows: T COS ~k+l 0~k+t - ~ k 2 (2 ) rk+l where wk2 is the angular velocity just before the leg-support-exchange. Figure 2@) shows a model of the leg-support-exchange. In this figure, sk+l is a stance, 8k+l and ~k+t are the configuration angles of the model. When ut~ slightly changed aromid equitibrimn state u, small variations Ark+l, Ask+l, ~XOk+l arid A(k+l in the vicinity of the equilibrium state are expressed as follows respectively: Ark+l = a l ~ U k A s k + l = a 2 t u k AOk+i = aaAuk /k~k+l = a4Auk (3) The sun, of kinetic and potential energies which the inverted pendulum model is located at the position 2 and that at the position 4 are equal due to the law of the energy conservation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001388_icsmc.1997.633290-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001388_icsmc.1997.633290-Figure7-1.png",
        "caption": "Fig. 7. Forces due to the contact.",
        "texts": [],
        "surrounding_texts": [
            "\\Ye searcli [.lie joint. traject,ories which minimize a.n energet,ic crit.erion X subject. to a constraint. C(y ) > 0. Forces and t,orques a.re calculat,ed using t,lie dynamic model of t.he robot. A. Dynaniic model on the model of our biped robot see [3]. The model used is given in Eq.(l). For more details r , , ( q ) = A ( q ) i i + H ( q , i ) + r F + r G + J T F , x i (1) \\v 11 ere r,(y) : Motfor torque, A ( q ) i : Torque due t.o inertia, H ( q , q ) : Torque due to centrifugal and Coriolis r F : Torque due to dry and viscous friction, r(;(q) : Torque due to gravity, J ( q ) : Jacobian matrix computed at the Fezt : Force on mobile foot due to the . forces, a.pplica.tion point of the force FeZt . contact with the floor. B. Oplimzzatzon criterion Rather than optimizing the energy consuniption during a step which is highly dependent on the shape of the floor, we have chosen to minimize the sum of mechanical losses, r$j, and motor Joule losses, Consequently, we use the following cost function A. m;f, FM. When Fext exists, its contribution is taken into account via r M . C. Constraint During a step the mobile foot must be above the floor. This yields to the calculation of the kinematic"
        ]
    },
    {
        "image_filename": "designv11_24_0000856_81.852953-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000856_81.852953-Figure1-1.png",
        "caption": "Fig. 1. The circuit network.",
        "texts": [
            " When x 2 E00, it is obvious that k1(\"0 \"00) k1\"0: (34) From (28), (31), and (34) we obtain dV (x; t) dt >(x; t)Q (x; t) + ( ~ )>~ = >(x; t)Q (x; t) ~ >~ + >~ >(x; t)Q (x; t) 1 2 ~ >~ + 1 2 > min(Q) >(x; t) (x; t) 1 2 ~ >~ + 1 2 > J (Ex(t)) 1 2 k1 ~ >~ + 1 2 k1\"0 > + J (Ex(t)) k0V + 1 2 k1\"0 > + J (Ex(t)) (35) where k 0 = minf2; k1 g maxf2; max( 1)g = \"0 \" 0 0 > 0: By integrating (35) we can establish that V (x; t) e k t V (t = 0) + 1 e k t k0 1 2 k1\"0 > + J (Ex(t)) which implies that the parameter estimation error ~ converges exponentially to the residual set D = ~ : ~ >~ < 1 k0 min( 1) 1 2 k1\"0 > + J (Ex(t)) 1 min( 1) J (Ex(t)) : If we properly choose and k1 such that k0 1, then the residual set becomes D = ~ : ~ >~ < 1 2 min( 1) k1\"0 > : (36) V. SIMULATION STUDY Application of singular systems to circuit network theory can be found in many publications (see [12]\u2013[14], for example). In this section, we use a similar circuit network model as in [13] to demonstrate the effectiveness of our control design. Using a simplified model for a transistor in the circuit of Fig. 1 yields the circuit equation c1 _uc = ie (37) y(t) = R2ic (38) ie ic = ib (39) u(t) + n(t) +R1ib + uc = 0 (40) wheren(t) = 0:23x1 0:36x2+0:015 sin(x1x2)u(t) represents input perturbations. Our control problem is to find a control voltage u(t) for output voltage y(t) to track the desired trajectory yd(x; t) = 0:5x1. Assuming R1; R2; and c1 all have values of one and the current gain be an unknown constant, we describe the system (37)\u2013(40) in the form of (2): E dx dt = f(x; t) +B(x; t)f[I +4B(x;p; t)]u(t) + g(x;p; t) +4g(x;p; "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003861_msf.505-507.949-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003861_msf.505-507.949-Figure4-1.png",
        "caption": "Fig. 4. Schematic of normal tooth profile of internal bevel gear.",
        "texts": [
            " The transformation matrix from the crown gear rotatable coordinate system pS to internal bevel gear rotatable coordinate system 2S can be obtained and denoted as { } { } { } { } { } { } { } { }2 2 0 0 M M M M m p m p = , and the detail is given as, { } { } 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 cos cos sin sin sin cos sin sin sin cos sin cos 0 cos sin sin cos sin cos cos cos 0 M cos sin cos cos sin 0 0 0 0 1 c c c c c c p c c \u03d5 \u03d5 \u03d5 \u03b4 \u03d5 \u03d5 \u03d5 \u03d5 \u03b4 \u03d5 \u03d5 \u03b4 \u03d5 \u03b4 \u03d5 \u03d5 \u03b4 \u03d5 \u03d5 \u03b4 \u03d5 \u03d5 \u03b4 \u03d5 \u03b4 \u2212 \u2212 \u2212 + \u2212   \u2212 \u2212 =  \u2212 \u2212     . (5) From the above mentioned, to avoid the second undercutting in machining process, the double circular arc profile shown in Fig. 3 is proposed in nutation drive and the normal section of circular arc helical tooth profile in crown gear rotatable coordinate system pS is presented in Fig. 4. Here, \u03c1\u2032 is the polar radius of point nO at actual gear alignment curve of the tooth surface obtained by moving the common symmetry center gear alignment curve in the normal direction with equivalent distance. The amount of this movement is equal to the half width of tooth thickness or space width, the common symmetry center gear alignment curve is a loxodrome with equivalent helical angle \u03b2 and can be denoted as cote\u03b8 \u03b2\u22c5 ; \u03b8 is the rotating angle representing the tooth parameter. A whole gear tooth profile consists of four circular arcs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003945_s0956792505006170-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003945_s0956792505006170-Figure4-1.png",
        "caption": "Figure 4. A diagram of the shearing problem.",
        "texts": [
            " For a material where \u03b1, \u03b2, A and B are given then the initial order of the material is the only parameter that influences the position of the maximum, whereas the initial entanglement affects the magnitude of the resistive force linearly since the height of the maximum is Fmax = B\u03ba0\u03c1 2 0U l(0) ( 3 + \u03b1 (1 \u2212 A/B)(1 \u2212 \u03c60)(3 + \u03b1+ \u03b2) ) 3+\u03b1 \u03b2 ( \u03b2 3 + \u03b1+ \u03b2 ) . The qualitative comparison between experiment and mathematical simulation are good. We have simply chosen \u03b1 = \u03b2 = \u03ba0 = 1 and B to match the greatest force magnitudes in corresponding mathematical and experimental results, however one could use more detailed experimental studies to estimate the parameters \u03b1, \u03b2, A, B and \u03ba0 for a chosen material. We continue testing the mathematical model by considering a shearing problem (see Figure 4). The material is now sheared by two parallel solid boundaries. In the experiment two hooked carding surfaces were used to produce a shear stress across the tuft, one moving the other stationary. The force was measured as the moving surface travelled at uniform velocity. One method of modelling the \u201cshear force\u201d experiment is to consider the hooks as a body force Fi, and this is similar to ideas used by Ockendon & Terrill [21] for a viscosity dominated Newtonian fluid moving through an array of long tethered fibres"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001837_095441003770887359-Figure16-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001837_095441003770887359-Figure16-1.png",
        "caption": "Fig. 16 Canard activity with a modi\u00aeed classical design",
        "texts": [
            " Because of the control allocation of equation (18), the \u00afaperon time history is essentially the negative of that of the canard and is not shown. The airspeed and thrust time histories are essentially unaffected by the failure. The pitch\u00b1 attitude pilot/vehicle tracking for the classical design indicated that almost immediately after the damage the system becomes unstable. The comparisons between the SMC and classical designs clearly demonstrate the superiority of the SMC design as regards stability and performance robustness. Figure 16 shows the canard time history when the modi\u00aeed form of the classical design, as de\u00aened in section 3.5.5, was used with no damage but with the aft c.g. position. An examination of the canard-de\u00afection rate showed the surface to be in rate saturation for nearly the entire time history. This performance problem was attributable to the effect of the additional 0.015 s of unmodelled measurement time delay. Figure 17 shows the pitch\u00b1attitude pilot/vehicle tracking performance for the SMC design for damage condition 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003621_1-4020-4533-6_19-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003621_1-4020-4533-6_19-Figure1-1.png",
        "caption": "Figure 1. Piston ring reciprocating liner test rig.",
        "texts": [
            " The mixed lubrication model of Zhao and Sadeghi [15] has been extended to include rough surfaces in a transient elliptical contact 272 typical of the current test rig. Details of the mixed contact region are used to predict the frictional losses throughout the stroke for correlation with experimental findings. The contacts are examined in detail for the portion of the stroke near bottom dead center (BDC). Surface modifications are imposed upon the rough surface and their effects are discussed. Figure 1 illustrates the bench-scale Piston Ring Reciprocating Liner (PRRL) test rig designed, developed and constructed for this study. The test rig was designed to have the cylinder liner reciprocate while keeping the piston ring stationary and can accommodate a wide range of loads, speeds, and lubricant conditions at the PRCL interface. Details of the apparatus and experimental procedure are available in Bolander et al. [11]. The piston rings considered in this study are symmetrically crowned and typically have a negatively skewed, pitted surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003077_iembs.2006.259841-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003077_iembs.2006.259841-Figure1-1.png",
        "caption": "Fig. 1. Conceptual drawing of the hybrid swimming robot; robot body bonded to the propulsive element. Inset: magnified image of the propulsive element: An array of bacteria attached to a polymer micro-disk.",
        "texts": [
            " Moreover, simple nutrient such as glucose is provided and ATP or ion gradients are generated by the cell. Most importantly, sensors are already present in the cell and integrated with the motor. Lastly, more complex organelles can be used hence more sophisticated motions can be produced [2], [3]. Therefore, in this research, we use flagellar motor inside the intact cell. Here, we propose a hybrid swimming microrobot which is propelled by helical flagella - only about 20 nanometers in diameter - of the bacteria attached to an inorganic robot body. Conceptual drawing of the robot is depicted in Fig. 1. The advantages of the hybrid robots include: (i) They run on a small amount of nutrient for an extended period of time (miniature and efficient), (ii) Components of the propulsive element, i.e. bacteria, self-replicate; therefore no microfabrication is required. However, there are numerous challenges associated with realization and characterization of these robots. Some of them are: (i) Repeatability and yield, B. Behkam is with Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA behkam@cmu"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003162_iros.2005.1545603-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003162_iros.2005.1545603-Figure4-1.png",
        "caption": "Fig. 4. Illustrations of the four ranges for a compliant section. P is shown in dark gray, O in light gray, obstacles are black. The ranges show the possible placements of the center of P . (a) The free push range FPR, these are all push positions for which the pusher is collision free. (b) The push range PR consists of all push positions that result in a motion of O in the desired direction (shown as the dotted arrow). (c) The valid push range VPR = PR \u2229 FPR. (d) The reachable valid push range RVPR; the part of VPR that is actually reachable for P from its current position by a contact transit.",
        "texts": [
            "3 (push position). At position s on the path, the position of P is denoted by \u03c3(s). \u03c3(s) is an angle relative to the center of O. At position s, the world coordinates of P are: \u03c4(s) + ( cos(\u03c3(s)) sin(\u03c3(s)) ) (ro + rp). For the desired object path \u03c4 our goal is to calculate a corresponding push plan \u03c3 such that if P complies to this path, it pushes the object along \u03c4 . Definition II.4 (free push range). The free push range FPR(\u03c4(s)) is the set of push positions that do not collide with any l \u2208 L (see Fig. 4a). Definition II.5 (push range). For every \u03c4(s) a set of push positions PR(\u03c4(s)) is specified, called the push range. PR(\u03c4(s)) is defined such that if P pushes O while \u03c3(s) \u2208 PR(\u03c4(s)) then O follows \u03c4 . The push range is a continuous set of angles from PRb(\u03c4(s)) to PRe(\u03c4(s)). The position of the pusher \u03c3(s) \u2208 PR(\u03c4(s)) iff \u03c3(s) is in the interval of the smallest rotation between PRb(\u03c4(s)) and PRe(\u03c4(s)). If i \u2208 I is a compliant section (see Fig. 4b) then: \u2022 PRb(\u03c4(s)) = arctan(\u03c4 \u2032(s)) + \u03c0. \u2022 PRe(\u03c4(s)) = arctan(\u03c4 \u2032(s)) + \u03c0 2 . This also holds for circular compliant sections. If \u03c3(s) \u2208 PR(\u03c4(s)), O slides along the compliant edge or rotates about a vertex. If i is noncompliant then: \u2022 PRb(\u03c4(s)) = arctan(\u03c4 \u2032(s)) + \u03c0. \u2022 PRe(\u03c4(s)) =PRb(\u03c4(s)). This definition shows that for a noncompliant section, there is only one push position such that O is pushed along the desired path section. Depending on the direction of \u03c4(s) it may be necessary to subtract \u03c0 from both PRb(\u03c4(s)) and PRe(\u03c4(s)). For a compliant section, the position of PRb(\u03c4(s)) always moves toward \u03c4(s) while the position of PRe(\u03c4(s)) maintains a distance of ro + rp from \u03c4(s). Definition II.6 (valid push range). The valid push range (Fig. 4c) consists of those push positions that are both free and within the push range: VPR(\u03c4(s)) = FPR(\u03c4(s)) \u2229 PR(\u03c4(s)) VPR(\u03c4(s)) may consist of multiple intervals, split up by obstacles if I(s) is a compliant section. At most one of these intervals is reachable for P from its current position. Therefore we define the reachable valid push range. Definition II.7 (reachable valid push range). The reachable valid push range (Fig. 4d), RVPR(\u03c4(s), \u03c3(s)) is the set of push positions that is reachable for the pusher from its current position \u03c3(s) and object position \u03c4(s) using a contact transit. B. Problem statement Using the definitions of the previous section, we formally define our problem: Given a collision free desired path \u03c4 for O consisting of k sections, that are allowed to be compliant, amidst a collection of disjoint obstacle line segments L, create a push plan \u03c3 for P such that if P complies to this plan, it pushes O along \u03c4 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000419_ecc.1999.7099923-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000419_ecc.1999.7099923-Figure5-1.png",
        "caption": "Fig. 5: Regularized 3-sliding controller",
        "texts": [
            " The task is to steer the car from a given initial position to the trajectory y = g(x), while x, y and \u03d5 are assumed to be measured in real time. Define \u03c3 = y - g(x), Let v = const = 10 m/s, l = 5 m, g(x) = 10 sin(0.05x) + 5, x = y = \u03d5 = \u03b4 = 0 at t = 0. The relative degree of the system is 3 and both 3-sliding controller N\u00b03 and its regularized form (8) may be applied here. It was taken \u03b1 = 20. The corresponding trajectories are the same, but the performance is different. The trajectory and function y = g(x) with measurement step \u03c4 = 2\u22c510 -4 are shown in Fig. 4. Graphs of \u03c3, \u03c3 , \u03c3 are shown in Fig. 5, 6 for regularized and not regularized controllers respectively. 4-sliding control. Consider a model example of a tracking system. Let input z(t) and the control system satisfy equations z (4) + 3 + 2z = 0, x (4) = u. The task is to track z by x, \u03c3 = x - z, the 4-th controller with \u03b1 = 40 is used. Initial conditions for z and x at time t = 0 are = 0, (0) = 0, (0) = 2, (0) = 0; x(0) = 1, (0) = 1, (0) = 1, (0) = 1. A mutual graph of x and z with \u03c4 = 0.01 is shown in Fig. 7. A mutual graph of and with \u03c4 = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003687_bf01516929-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003687_bf01516929-Figure2-1.png",
        "caption": "Fig. 2. Simple shear flow in rotating frame of reference",
        "texts": [
            " The Jaumann's derivative ~ / ~ t describes the rate of change of the components of a tensor in a coordinate system attached to a liquid particle. In order to clarify its meaning in an arbitrary (x, y, z) system, it will be shown that the same values of normal stresses as in eq. [6] are obtained for an ordinary partial derivative with t he stress components given in a system (x ~, yx, z a) attached to a fluid particle and rotating with it. In simple shear flow (eq. [5]) each particle rotates around the z-axis in the negative sense with an angular velocity co, given by (see fig. 2) 1 (~?u g v ) ~; [10] c o = T 0y ~x = T ' The stress components in the xy-system are Sxx, Sxy and Syy. According to the rules of transformation we have for a tensor T: T'= RTR*, [11] where R is the matrix of rotation, and R* its transpose. For the present two-dimensional case of simple shear (negative direction): [coscot - s i n c o t ] Rij = . [12] ksin cot cos cot_l Effecting the transformation according to [11] and differentiating with respect to time, we find that in the xl, Y~ system: 0 S -~ -~m =-2coS~ys in2co t + co(S"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003139_12.539578-Figure10-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003139_12.539578-Figure10-1.png",
        "caption": "Figure 10. RF powered wireless temperature sensor using a Colpitts Oscillator",
        "texts": [
            " Once the frequency operation was established, appropriate values for the other components shown in Figure 9 were chosen according to the design equations given by [12],[14]. The feedback factor is given by: 2 S 21 1 C C CC C = + =\u03b2 (6) The amplifier gain must satisfy: S 2 V C C A \u2265 (7) From the operating frequency of 1.2 MHz and the inductance value for L, a relationship for the values of the sensing capacitances can be obtained from: L\u03c9 1 C 2S = (8) The other components, R1, R2, CB and RE in the final circuit shown in figure 9, assure that the device is properly biased and were chosen to obtain an emitter current of 1mA. Figure 10 shows the sensor circuit constructed. It can be observed that the oscillator components responsible for amplifying the signal were placed and the sensing capacitors were placed in different board. In this way the sensing elements can be attached to the measurement point without increasing the temperature of the active and passive components of the circuit. 372 Proc. of SPIE Vol. 5391 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/18/2016 Terms of Use: http://spiedigitallibrary"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002495_6.2003-608-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002495_6.2003-608-Figure3-1.png",
        "caption": "Fig. 3 Induced drag for a three-dimensional wing.",
        "texts": [
            " It is also assumed that induced drag is the most variable and the only significant drag term (within the context of this simulation), that vorticity is shed purely along the x axis (an adequate approximation if the bird\u2019s velocity is mostly forward), does not decay and always consists of straight filaments that remain bound to the bird\u2019s wings, and that all birds have identical, constant physical parameters. In classic aeronautical fashion, each boid is modeled as a discrete vortex system, with the wake assumed to lie in the horizontal plane (see Fig. 2). Induced drag (Fig. 3) on a wing in the presence of a vortex is known to vary proportionally to the strength and distribution of the downwash induced by the vortex, and the total drag may be obtained by integrating the effect of every vortex in the system over the span of the wing. A more 3 of 9 American Institute of Aeronautics and Astronautics Paper 2003\u20130608 comprehensive discussion of discrete vortex theory and induced drag is given in Ref. 18. where A = \u221a (Px \u2212Qx)2 + (Py \u2212 yq + yp \u2212Qy)2 + (Pz \u2212Qz) 2 and that the vertical component of the downwash at the same point, due to a bound vortex of strength \u0393 stretching between y1 and y2 on the same wing originating at Q is: w = \u0393 (\u2212Px + Qx) (B1 + B2) 4\u03c0 ( (Px \u2212Qx)2 + (Pz \u2212Qz) 2 ) (6) where B1 = Py \u2212 y1 + yp \u2212Qy\u221a (Px \u2212Qx)2 + (Py \u2212 y1 + yp \u2212Qy)2 + (Pz \u2212Qz) 2 and B2 = \u2212Py + y2 \u2212 yp + Qy\u221a (Px \u2212Qx)2 + (Py \u2212 y2 + yp \u2212Qy)2 + (Pz \u2212Qz) 2 Note that when computing downwash, points P and Q are constrained to a grid of spacing \u2206y, which corresponds to the distance between vortex filaments"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003836_icems.2005.202684-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003836_icems.2005.202684-Figure1-1.png",
        "caption": "Fig. 1. Wind driven DFIG with slip energy recovery scheme.",
        "texts": [
            " Variable speed slip-energy recovery scheme enables induction generators to operate at continuously variable speeds efficiently and economically and is able to maintain maximum power transfer conditions for shaft speed variations over a wide range of wind speed. Slip power is frequency converted and consumed (or returned) from (or to) the grid depending on the sub-synchronous or supersynchronous operation of the generator. One scheme for wound rotor induction machine used as a variable speed generator is shown in Fig. 1. In this scheme, a converter cascade is used between the slip-ring terminals and the utility grid to control the rotor power. This scheme is called the doubly fed induction generator (DFIG) scheme, because the power output is tapped from both the stator and the rotor circuits. Therefore, the DFIG is the only known scheme in which the generator gives more than its rated power without being overheated and the power generation can be realized in a wide range ofwind. Field orientation control, also known as vector control [2,3], of an induction machine achieves decoupled torque and flux dynamics leading to independent control of the torque and flux",
            " In both the motor and Vds, Vqs Vdr, Vqr ids, iqs idr, iqr Ads, Aqs 2dr, Aqr Rs,Rr Lss Lr Lsl, Lrl V ds =Rs id +- I Xdqs1 d dtw0 dt 1 dA v =R i + qs+ A'sqs s qs dt0 dt v R i + (d 1d- ]-w )2Adr r dr mt d qr 0 dt 1 dA v RR i + qr +( _)Ad, qr r qr dt dr 0 t generator cases the controller was of the conventional PI type with fixed gains. In this paper, the two-axis (d- and q-axis) machine model is chosen to model the wind driven doubly-fed induction generator due to the dynamic nature of the application. This model is discussed in details in the dynamic machine model section. This model is used to build the wind driven slip energy recovery system shown in Fig. 1. A vector control scheme is implemented to control the rotor-side PWM voltage source inverter (VSI). Usually vector control schemes employ a conventional PI controller with a fixed proportional and integral gain which gives a pre-determined response and can't be changed. In this paper, a simple yet efficient way by which the controller can change the system behavior is proposed. This is achieved by allowing the controller to schedule its parameters depending on the set values and the operating conditions",
            " The forth order characteristics are expressed by: Kp i = a5 le (t )4 +b5 le (t)1 +c5 le (t )| (17 +d5 le(t)l +f5 where a5, b5, c5, d5, f5 are the coefficients of the fourth order characteristics. The coefficients used in the above functions were selected such that, for the proportional gain (Kp), a fast dynamic response, less overshoot and small settling time is desired. While for the integral gain (K1), it is required to reduce the overshoot and to eliminate the steady state error. The system considered is a grid connected doubly-fed induction generator with the rotor circuit connected to the grid through back-to-back PWM voltage source converters in a configuration shown in Fig. 1. The wind turbine considered has a power rating of 40kW. The turbine output power changes as a function of the wind speed as shown in Fig. 4. The wind speed is measured in order to determine the set values for both the 7) maximum output power and the corresponding generator speed in order to track the maximum power curve as shown in Fig. 4. These set values are then used to calculate the error signal which is the set value minus its corresponding measured actual value (Fig. 3). The absolute value of the error signal is used to calculate the scheduled proportional and integral gains depending on the chosen characteristics (linear, exponential, etc)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003956_tia.2005.863899-Figure20-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003956_tia.2005.863899-Figure20-1.png",
        "caption": "Fig. 20. Flux distribution of synchRel under the full-load condition (with flux barriers).",
        "texts": [
            " The motor current and the rotor position were set according to the loading conditions. The effect of the flux barriers was almost negligible under the no-load condition. Under this condition, the flux lines were almost symmetrically distributed over the pole arc of the machine as shown in Figs. 17 and 18. The reduction of the d-pole arc under the loaded condition can be clearly observed in Figs. 19 and 20. The flux lines are even more concentrated near the end of the Y-shaped flux barriers as can be seen in Fig. 20. In order to consider the effect of flux barriers and effective reduction in pole arc under loaded condition, the pole arc of the simulated machine was reduced by 6.8\u25e6 (mechanical), and the interpolar arc was increased by the same magnitude. The model was stable at full load with the changed polar arcs. The value of 6.8\u25e6 was obtained by trial and error. The transient stator current and speed of the synchRel during starting with the changed pole arc are shown in Figs. 21 and 22, respectively. The value of the moment of inertia (J) used for simulations in Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000975_iros.1994.407615-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000975_iros.1994.407615-Figure5-1.png",
        "caption": "Figure 5: The robot rests in the initial position of a path transporting a small workpiece from one tool machine into another. The ceilings, walls, and bodies of the machines are obstacles which are to be avoided. The motion which is shown through its tool-center-point track has been generated automatically and contains an obviously supeduous detour.",
        "texts": [],
        "surrounding_texts": [
            "not all locations of a and b may produce a collision-free polygon; therefore, a clever strategy is needed to compute the optimal locations. The most likely c88e - if there are obstacles in the nearer neighbourhood - is that the polygon goes around an obstacle. Hence the optimal strategy to find a and b should start at U and w and then move step by step in direction of U. This results in the following algorithm, that should be used iteratively:\n/* area test * / for i := 1 to (n - 2)\na := zi-1 b := zi+l A := 0 while no direct connection from a to b possible\nand 11 b - a II> E*;,,\na := z;-l+ X(Z; - zi-1) (*) b := Z;+I + X(Z; - .;+I) (**I X : = X + & (***) endwhile if direct connection from a to b possible\nz, : = a insert vertex b at index i + 1 in the polygon\nendif endfor\nThe disadvantage of this algorithm is - in the worst case - the examination of the whole triangle with the sides (u,v), ( v , w ) , and (w,u) for collision. But since the test for collision is the most expensive operation, no two-dimensional (or higher dimensional) space should be tested. Therefore, a better strategy is needed to find a and b. A simple change of the marked lines [(*). . .(***)I of the algorithm solves the problem: the idea is to separate the lines (U, U) and (w, U) by a bisection.\n/* bisection test */ a := z; - (.; - z;4)/2X b := zi - (z; - ~;+1)/2' X : = A + l\nGiven a polygon in an obstacle-free space, the algorithm using an area test for collision would converge to a straight line from start to end point. The algorithm using a bisection test for collision converges to a parabolic function. This means that the resulting polygon is not shortened most because it does not converge to a straight line. Yet the main result is that the smoothness of the polygon is improved. If a value X for cutting off the triangle is found, a possibility of controlling the properties of the resulting polygon is to use a value (A - g) instead of A where g is a real number between 0 and 1. Using 0, the algorithm\nworks like normal bisection, using 1, the algorithm creates a polygon smoother and having a greater distance to obstacles. That is the nearer g is at 1 the nearer the resulting polygon takes a course at the starting polygon.\n4.3 Retraction of Vertices This algorithm only modifies the polygon by changing the location of single vertices. This proceeding requires a starting polygon that has a minimum density of vertices, which means that the distance between two adjacent vertices should not be too large. If there are only few vertices in a polygon with a complex spatial location, it is impos sible to get good results without insertion. Therefore, the following algorithm presupposes a incoming polygon having.a lot of vertices with nearly equal distance (this can be reached by interpolating some vertices).\nFigure 3 shows how the algorithm works. Watching the vertex v one can see, that the smoothness of the polygon would be improved, if the angle between (U, U ) and ( v , w ) would be more obtuse. But how to reach it, without changing U and w? (One of our premises was that only local changes should be done, because of the cost risk of calculating a large part of the polygon.) The canonical way of doing it, is to retract v in direction of a imaginary point a, which is in the middle of the line (U, w ) . Letting v be equal to a, the result would be a straight line, which is by definition the most smooth polygon. If there are obstacles in the way between U and w , that means, v cannot be retracted to a, v should be retracted to that point b on the line (U, a), that lies next to a, but fulfils the condition that (U, b ) and ( b , w ) is collision-free. The move of vertex v in direction of a could be made in a step-by-step matter shown above or using a bisection of the line (v,a). The following algorithm should be iteratively used:",
            "for i := 1 to (n - 1) U := ( ~ i + l - t i-1)/2 A := 1 while (COLLISION(zi-1, b )\nor COLLISION(b, zi+l))\nand 11 b - t i [ I > Emin b := zi - ( t i - 0)/2('-') X : = A + l\nendwhile if not COLLISION(zi-1, b )\nand not COLLISION(b, zi+l) := b\nendif endfor\nAlthough this algorithm converges in an obstacle-free space to a straight line, the converge is slow. Therefore, the retraction algorithm does not change the global location of a polygon very much, but it is suitable for a subsequent treatment of an optimized polygon. This requires a combination of the represented algorithms:\n4.4 Composition of Methods Each of the three algorithms shown here has its own advantages: only deleting vertices for example is well for shortening the polygon but cannot improve the smoothness, whereas the cutting off triangle corners is good for smoothing but not for a large changing of the global location of the polygon. This suggests a combination of these algorithm that makes use of the special advantages.\nIf, for example, one wants to compute the shortest path, one should iteratively make use of the deletion algorithm and the cutting algorithm (figure 4). The more often these algorithms are repeated the shorter the polygon becomes, though a very good result is computed already by two or three iterations.\nNevertheless, this is only a local optimum for two reasons: all algorithms shown here make only local changes that will not find a far away located better solution; secondly, all changes made here convert a convex polygon to a convex polygon; so if the optimum would be concave it cannot be reached. In addition to the control of the cutting algorithm the alternating use of the algorithms can be used to control the properties of the resulting polygon. A final deletion of vertices destroys the perfect smoothness but produces a very short polygon, while first using the deletion and afterwards the cutting algorithm produces a polygon that is short and smooth. If one primarily wants to get a very short path but smoothness is also desirable, one should first compute the shortest path and then smooth it by using the retraction algorithm.\n5 Experimental Results\nBecause of the relative simplicity of the algorithms we soon got a prototype running which is implemented in C on a Unix workstation. The results of the performed experiments with many different environments and tasks show that the polygonal optimizer is fast and efficient.\nWe tried simple scenes with primitive obstacles, tasks with holes for the robot to reach in (like the one in figures 5 to 8), and even very difficult environments with strong obstacle constraints and large bulky payloads (like the one in figure 9).\nThe results are best estimated through the figures themselves. Table 1 give additional information regarding path length and computation time.",
            "IV/ IIW I\nI I\nFigure 8: Leff: Another, different, automatically planned path. Right: The same path after optimization for smoothness. Note that here another local optimum than in figure 7 is obtained.\nFigure 9: A very difficult pick-and-place task. The large plate has to be moved from the shelf (visible on the left of the left picture) to the trestles (in front of the right picture). All six degrees of freedom must be taken into account because the payload is bulky and the environment is very tight. In both pictures the same optimized path is shown."
        ]
    },
    {
        "image_filename": "designv11_24_0000286_1.2834124-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000286_1.2834124-Figure2-1.png",
        "caption": "Fig. 2 Hertzian contact ellipse",
        "texts": [
            " \u2014 ) sin^ 0 d4> (3) where k is the normal ellipticity ratio given by the approximate expression, ' \u0302 iff If the lubricant entrainment velocity at the center of contact ellipse is inclined at an angle 9 to the minor axis of the contact ellipse, it is convenient to portray solutions in terms of the curvatures of the surface of the equivalent ellipsoid in the en training direction 1 /R,, and side-leakage direction 1 //?, by the expressions, K\" R. \"\u0302 Ry sin cos R. R. R, (5) (6) and the effective ellipticity ratio, k,, can be written as 2.2 Kinematics of the Surfaces. Suppose that the two contacting surfaces (A., B) have rolling velocities (UA, VA), (UJI, v\u201e) and spinning velocities UIA, UJB- In Fig. 2, let Mo = (M/I + Ui,)l2 vo = (VA + u\u00ab)/2 OJ = {iJA + uJn)l2 (8) then the entraining velocities at point {x, y) can be written as u = uo \u2014 yu) u = Do -I- .^w ( 9 ) Nomenclature a = semimajor axis of Contact el lipse h = semiminor axis of contact el lipse Bo = ratio of spinning to rolling, lujRJua d^, dy = dimensionless mesh size along jc-axis and y-axis on the coarsest grid E' = equivalent elastic constant F = normal load G = dimensionless material parame ter h = film thickness ha. Ho = constant H = dimensionless film thickness, hRe/h^ HMIN = dimensionless minimum film thickness HCEN = dimensionless central film thickness k = ellipticity ratio, alb kc = effective elliptical ratio p \u2014 pressure P = dimensionless pressure, plpi, R,"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000809_1.2826964-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000809_1.2826964-Figure6-1.png",
        "caption": "Fig. 6 (a) A Bendix wrist (b) canonical graph",
        "texts": [
            " Then kinematic properties of the secondary links are computed using the fundamental circuit equations and coaxial conditions. In the second step, the joint forces and moments are computed by using the Newton and Euler's equations of motion. The computation begins from the highest level primary links followed by the secondary links, one or two levels at a time working backwards toward the base. Finally, equivalent force systems are introduced for the evaluation of actual joint forces and moments among the coaxial Unks. Finally, we use the Bendix wrist as shown in Fig. 6 to illus trate the need of solving two levels of dynamical equations simultaneously. In the Bendix wrist, there are two transmission lines, 5-6-3 and 7-8-3, terminated at the end-effector. The evalu ation procedure is as follows. We first solve the dynamical equations of links 3 and 2 simultaneously, followed by links 6 and 8, and then links 1, 4, 5, and 7. Armstrong, W. M., 1979, \"Recursive Solution to the Equations of Motion of an N-linl< Manipulator,\" Proc. 5th World Congr., Machines and Mechanisms Theory, Vol"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002211_bf01560628-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002211_bf01560628-Figure6-1.png",
        "caption": "Fig. 6.",
        "texts": [
            " Radii p have a finite value and are all equal: points A 1 become then set along an arch of circumference and consequently are the polygonal line joining points A 1 gets its vertices lying on this arch. As h decreases, P decreases too, while the lenth of the arc increases up to a full circumference, whatever N be [ 12]. Fig. 3. \\k \\ \\ \\,.AglJ7 ~\" / 8 S \\ \\ x A \\ \\ / / ], \\ \\ [ \\ \\ \\ \\ \\ \\ \\ \" \\ \\ | ~ \\ ] AI l j ' ~ \"\" \"\" ~\" x 21 (1986) 107 108 the polygonal line and the given curve are lower than a pre-set value (fig. 5). In a reference system originating at A t and with element t X 1 set as in fig. 6 is taken, the co-ordinates of point A l are: XA, ~ = s sen a (1.6) YA'a = s COS O~ - - h If distance h is taken as a variable, the parametric equa- tions of point A'I are: (argos 2 b l h b~ + h2--a~ YA'~ = ~ h 2 b l h and for nth element x~ = xi_ 1 + ~ sen arcos cos X i -- 2 b l h + h2 -- a2 h I (# 2 b,h X i ] s e n Yi = Y i - 1 + ~ s e n a r c o s 2 bih + h cos X i 2 bih (1.7) (1.8) sen X i + with n . q~i = arctg tg 0 i / '/i+ 1 for ( 1.2), and being: 1 ~ = ~ (~i + ~i ) b7 + h2--a2i a. = arcos t 2 bih ~i = arcsen ~ en arcos a i 2 bih "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001531_robot.1995.525721-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001531_robot.1995.525721-Figure5-1.png",
        "caption": "Fig. 5 Collision free path obtained by proposed method",
        "texts": [
            " Let the inertia moment about the axis through the center of the gravity, I=4.167 x kg . m2, the mass, M=1.0 kg and a half length of the link, 1=0.1m for each link. And let each element of the term D which represents viscous friction be zero for simplicity. The limitations of the driving torques and the initial configuration are given in Table 1. The goal position of the endeffector is (0.4m, 0.lm). The centers of two obstacles are (0.3m, 0.4m) and (O.lm, -0.05m) and each radius is 0.05m. Fig. 4 shows a initial path obtained by the method in chapter 4. Fig. 5 shows the path obtained by applying the proposed algorithm for the initial path in Fig. 4. !\u2018 t I Fig. 3 Structure of manipulator - 3073 - This path not only avoids the obstacles but also shortens the travelling time. T in Figs. 4 and 5 show the minimum travelling times of its spatial paths obtained by means of the M T T P algorithm. The total computation time is about 1.5 minutes by using SUN S-4/CL work station. 8 Conclusions In this paper, a method using the potential function is proposed for the collision free trajectory planning problem of the manipulator"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000602_mssp.1997.0092-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000602_mssp.1997.0092-Figure8-1.png",
        "caption": "Figure 8. Rotating shaft with a flexible disc and an array of sensors to measure disc vibrations.",
        "texts": [
            " Pn (v, t) is the time\u2013frequency distribution associated with the n nodal diameter related motion. It can be shown (Appendix D) that the forward and backward time\u2013frequency distributions can be expressed in terms of the individual time\u2013frequency distributions (each sensor processed independently): forward whirl P+1(v, t)=S1(v, t)\u2212 iS2(v, t) (11a) backward whirl P\u22121(v, t)=S1(v, t)+ iS2(v, t) (11b) where Sk (v, t)= fa \u2212a sk (t)W(t\u2212 t) e\u2212ivt dt is the time\u2013frequency distribution measured from the kth sensor. A measurement system is depicted in Fig. 8 capable of separating flexible discs\u2019 vibration into different wave patterns (in fact, the method is applicable for any type of rotating structure and not only discs). A stationary sensor, sk , will measure the response which the disc experiences modulated by the rotating mode shapes, so that by using an array of sensors we are able to decompose the different wavelengths present. In this paper, most derivations assume that the sensors measuring the vibration signals on the surface are equally spaced (circumferentially, Du), but this is not a requirement. For non-equally spaced sensors, a general set of linear equations need to be solved [9] instead of using a standard DFT. In Fig. 8, a vector of measurements at time t, [s1(t) s2(t) \u00b7 \u00b7 \u00b7 sm (t)], is constructed from all m sensors. The decomposition of the different wavelengths necessitates the extraction of the coefficients in equation (5). Since the sensors are assumed to be spaced equally at an angle Du, the shortest wavelength that can be extracted, according to the Nyquist sampling criterion [10, 11], (expressed in terms of the equivalent number of nodal diameters) is: nnyq = p Du (12) For example, in the system depicted in Fig",
            " 9(b) provides the direction in addition and clearly separates the forward (positive frequency) and backward (negative frequency) components. It is clear that the proposed method provides much better separation and does not display the smearing effects due to the overlap of the two frequencies of (a). The separation into forward and backward components, apart from providing more information, also yields better resolution. 4.1.2. Example: rotating disc This example simulates an array of nine sensors, fixed in space, (as in Fig. 8) all positioned at the same radial location r= r0, but having different angular locations. The sensors are measuring the displacement of the disc in the axial direction. The disc is assumed to rotate at a constant speed V. The qth sensor is located at an angle uq = q \u00b7 12\u00b0, q=1 . . . 9; each sensor measures the following time function: sq (t)= s 4 n=1 Afn cos (n(uq \u22128f(t)))+Abn cos (n(uq +8f(t))) (24) where the forward amplitudes are: {Ab1, Ab2, Ab3, Ab4}= {0.0, 2.0, 0.0, 1.0} the backwards amplitudes are: {Af1, Af2, Af3, Af4}= {0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003270_1.2360598-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003270_1.2360598-Figure7-1.png",
        "caption": "Fig. 7 Static load deflection mechanism for full damper",
        "texts": [
            " Based on the desired stiffness value and maximum expected motion, the compliant bumps were made of 0.152-mm-thick Inconel foil. Figure 6 shows an unwrapped section of the full compliant foil journal bearing damper subassembly. Static Load Deflection Mechanism. In order to conduct a static load deflection test on the full damper once installed in the Transactions of the ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use w f b d n d t i i d a h d c a t d v d M l X 3 s o m F fl J Downloaded Fr eldment, a mechanism as shown in Fig. 7 was designed and abricated. This mechanism used two precision coil springs and a ar to apply a known load to the inner ring/disk assembly. The isplacement of the bump foil assembly, due to the applied exteral load, was measured using two high precision mechanical inicators precision as high as 50 m . Additionally, in various ests, an eddy current displacement sensor was used to measure nner ring motion to verify the readings taken with the dial ndicators. Previous testing of a smaller 150-mm-diameter compliant foil amper assembly was completed using a computer controlled and utomated load deflection tester as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000847_70.833184-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000847_70.833184-Figure8-1.png",
        "caption": "Fig. 8. Under the constraint of hand pose given by (37), the K-1207i was placed in worst-case and best-case configurations for a free-swinging failure of the first joint. Configurations before and after a failure are shown for both cases. The value of o\u0302 for the best case is 0.038 and for the worst case is 0.384.",
        "texts": [
            ") Since collision with any part of the arm is of concern, the objects are chosen to be the CAD models of the K-1207i links used to make the images of the robot for this article. All points on the arm are equally important, so the weighting function is chosen to be a constant, m . The values for the free-swinging joint error and its partial derivatives are calculated using the techniques given in [4]. For the hand pose given by (37) and link masses and centers of mass given in Table III, the worst-case and best-case configurations for tolerating a free-swinging failure of the first joint as found using the gradient-projection technique [25], [26] are shown in Fig. 8, both before and after a failure. With equal to 0.384, the motion for the worst-case configuration is kinematically equivalent to translating a 1-m cube by 62 cm. In contrast, with equal to 0.038, the motion for the best-case configuration is kinematically equivalent to translating a 1-m cube by 19 cm. It is clear from Fig. 8 that this reduced motion corresponds to a reduced likelihood of collision with the environment. Even for this case, which is made more difficult by its focus on free-swinging failures, optimizing the configuration does not require excessive computation time. For the RRC K-1207i with a focus on free-swinging failures, and can be calculated for all in less than 4 ms on a Sun Microsystems SPARC 10 workstation. This allows even the most general measures, including those incorporating all possible joint failures, to be minimized in real time"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003300_6.2004-6529-Figure10-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003300_6.2004-6529-Figure10-1.png",
        "caption": "Figure 10. Suitable path finding and modification",
        "texts": [
            " The dangerous priority of popup-threat could be higher than the original, in order to make its effect strong, since it didn\u2019t affect the initial potential field and path. The start node and end node are assumed as boundary condition of constant position. Then, if we solve the dynamic equation of the chained masses system in the section, the modified path can be derived as the details described in Ref. 2. 2. Suitable path finding and modification This strategy is used in order to find some paths avoiding the popup threat and approach the goal point. First of all, it is necessary to find point A, in Fig. 10, at a distance of determined value on the initial path. It is determined as a local goal point. The global goal point can be a local goal point in case the distance between current and global local point is shorter than value determined. Then one has to find some paths which approach the local goal point avoiding dangerous areas of pop-up threat. These paths can be found by examination through the scanning route. This scanning route is determined as follows; It turns to the left and right with minimum turn radius at current point and goes forward to escape from the dangerous area"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003959_iemdc.2005.195779-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003959_iemdc.2005.195779-Figure2-1.png",
        "caption": "Fig. 2. The relationship between flux and voltage space vectors.",
        "texts": [
            " IMMEDIATE FLUX CONTROL IFC and PTC algorithms are performed in DSP with a sampling interval T being much smaller than the other time constants. After converting basic stator voltage-flux differential equation dt diRv S SSS \u03bb r rr += , (1) into its discretized form, the flux at the end of the sampling interval can be written as ( ) ( ) ( ) ( ) '( 1) 1 S S S S S S n n n i n R T v n T \u03bb \u03bb \u03bb + + = \u2212 + r r r r r 14424443 (2) In a common three-phase inverter Svr is limited to seven (six \u201cactive\u201d and one zero) distinct space vectors. Fig. 2 shows the relationship between the space vectors. In general, the aim of IFC is to find a voltage space vector that will force )1(' +nS\u03bb r towards the reference flux )1(* +nS\u03bb r thus minimizing the final flux error )1( +nV\u03bb\u03b5 r . Note the difference between DTC and IFC: in IFC, the chosen voltage vector is the one belonging to the sextant in which the predicted flux error )1(0 +n\u03bb\u03b5 r as a difference ( ) ( )1'1* +\u2212+ nn SS \u03bb\u03bb rr is positioned! Since the only possible six inverter\u2019s voltage space vectors usually do not coincide with the desired trajectories of the flux error )1(0 +n\u03bb\u03b5 r , a certain final flux error can occur at the end of the switching interval",
            " The task of the second variant is to find the optimum application time (ton) for the active voltage vector within the sampling interval. For the remaining time, the zero vector is selected. The flux error at the end of the interval, during which an appropriate inverter voltage space vector Svr is impressed, is calculated as ,)()1(')1( )1()1()1( * * Tnvnn nnn SSS SSV rrr rrr \u2212+\u2212+= =+\u2212+=+ \u03bb\u03bb \u03bb\u03bb\u03b5 \u03bb (3) whereas the final error with an impressed zero vector only is ).1(')1()1( * 0 +\u2212+=+ nnn SS \u03bb\u03bb\u03b5\u03bb rrr (4) The application of an active voltage vector is justified if (Fig. 2) ,)1()1( 2 0 2 +<+ nnV \u03bb\u03bb \u03b5\u03b5 rr (5) where 2222 VbVaVV \u03bb\u03bb\u03bb\u03bb \u03b5\u03b5\u03b5\u03b5 +== r and 2 0 2 0 2 0 2 0 ba \u03bb\u03bb\u03bb\u03bb \u03b5\u03b5\u03b5\u03b5 +== r are calculated in a stationary reference frame. The squared errors have been chosen for their simpler calculation in a DSP. Considering , 3 2 2 22 \u239f \u23a0 \u239e \u239c \u239d \u239b=+ DCSbSa Vvv (6) the practical form of the criterion (5) becomes )()1()()1( 9 2 00 nKnnKnTV VbbVaaDC \u22c5++\u22c5+< \u03bb\u03bb \u03b5\u03b5 , (7) being KVa and KVb the components of a chosen inverter voltage vector (out of six possible) in a stationary reference frame ( ) ( ) ( ) ( ) ( ) ( ) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000041_1.1392031-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000041_1.1392031-Figure7-1.png",
        "caption": "Figure 7. Open view of the assembly of a sectioned electrode consisting of four graphite slices.",
        "texts": [
            "3, and the cross\u2013sectional surface area for electrolyte solution flow is 5.1 3 1024 m2. Two Journal of The Electrochemical Society, 146 (8) 2933-2939 (1999) 2935 S0013-4651(98)08-021-5 CCC: $7.00 \u00a9 The Electrochemical Society, Inc. 3 mm diam holes are positioned near the perimeter of each slice for alignment when mounting the cell. Insulation of the graphite slices from each other is achieved by intercalating thin porous Teflon mesh between consecutive slices. The Teflon mesh thickness (0.1 mm) is neglected for all calculations and graphical representations. Figure 7 represents an open view of the assembly of a sectioned electrode consisting of four graphite slices. To test the performance of the sectioned design, a model electro\u2013oxidation system involving the partial oxidation of the six\u2013carbon-molecule sodium gluconate to the corresponding five\u2013carbon sugar D\u2013arabinose has been chosen. The electrochemical oxidation can be written as follows 1 CO2 1 H1 1 Na1 1 2e2 [1] Chromatographic analysis (discussed later) indicates that the further oxidation of the arabinose produced to lower order sugars (such as the four\u2013carbon erythrose) is not significant under the conditions employed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003240_1.1688379-Figure10-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003240_1.1688379-Figure10-1.png",
        "caption": "Fig. 10 Distributions of the effective strain obtained from FE simulations with variations of the mandrel radius of \u201ea\u2026 20 mm, \u201eb\u2026 30 mm, and \u201ec\u2026 35 mm",
        "texts": [
            "org/about-asme/terms-of-use Downloaded F z coordinate. As can be seen in this figure, deformed shapes of the workpiece were almost similar irrespective of the initial billet radii. The predicted forming load was reduced to 8.1 MN in the current case from 17.4 MN for the case of the initial billet radius of 73.4 mm. Underfilling was not solved by decreasing the initial billet radius. 4.3.4 Effect of Mandrel Radius. As the final forming variable, the size of the mandrel was varied for the forward extrusion of a spur gear with 18 teeth as shown in Fig. 10. The simulations were conducted with the variation of the radius of a mandrel of 20 rom: http://manufacturingscience.asmedigitalcollection.asme.org/ on 01/2 mm, 30 mm, and 35 mm. Table 4 summarizes the punch stroke at the final step, required load calculated, and completeness of filling of a tooth obtained from the FE analyses. As shown in this table, it was found that forming load increased as the size of mandrel increased. Complete filling at the tip of a tooth cavity was achieved when the radius of the mandrel was 35 mm in which ART/G was 0.53. In other cases, underfilling occurred as shown in Fig. 10. Also, the level of underfilling decreased with the increase of the mandrel radius. Thus, prevention of material flow at the center region by the mandrel might lead to improvement of filling in a tooth die cavity. The distributions of the effective strain according to the variation of the mandrel radius are also shown in Fig. 10. As shown in this figure, maximum values of the effective strain were different due to the difference of punch stroke. However, higher levels of the effective strain concentrated on the roots of the teeth for all cases. 4.4 Determination of a Major Design Parameter. Through FE simulations, it was found that the geometry of a gear including the mandrel radius was most important in determining the filling status. Thus, the usefulness of area ratios of ART/G and ARG/R was investigated to predict the filling status of a gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002351_s0263574700006093-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002351_s0263574700006093-Figure3-1.png",
        "caption": "Fig. 3. Compensation of deviation of the ZMP position.",
        "texts": [
            " Then we can write1'9 s(ARc + ARB) = Mx = R Ay (38) dx ARA - d2(ARB + ARC) = My = RAx where ARA, ARB and ARC are deviations of the vertical reaction force components acting on the sensors A, B and C, respectively; R is the total vertical reaction force; AJC and Ay are the unknown displacement of the actual ZMP with respect to its nominal position. These displacements can be computed from (38) and used for an additional corrective control synthesis. Let consider the mechanism whose motion is such that the deviation of reaction force from its nominal position in the direction of axis X is Ax (Figure 3) and the overall system deviation is expressed by the moment Mu, Mu = R Ax. Further, let the correctional action is performed only at one joint, chosen in advance. Let this joint be An approach to biped control synthesis 237 joint O in Figure 3, and let all links above it can be considered as a rigid body of mass m, inertia moment around the axis X joint O, Jo, and the gravity centre at C. A basic assumption introduced for the sake of simplicity is that the action at joint O causes no motion at any of other joints, and the system behaves as two rigid bodies joined at O. In other words, the servosystems are supposed to be sufficiently stiff. The distance between the ground surface and O is denoted by L, and between C and O by /, where AMP denotes the compensating motor moment applied at joint O. At first, we should define the AMP which has to be applied to compensate the ZMP displacement. If we suppose that AMP induces only a change in accelerations of compensating link A0 and if we take into account only the tangential component of acceleration, then from the equilibrium equations for the mechanism part beneath 0 (Figure 3) we obtain (39) If AMP is known, it is possible to compute the control input which has to realize it. Let write the model of the DC motor which is used at the mechanism joint O (hence the subscript \"o\") Aqo Aq'o ts.iRo_ = 0 1 0 0 fl22 fl23 _0 a32 a33j + Aqo Aqo _AiRo_ h 0 APO + u 0 b3 (40) If we adopt that Aq = Aq At and AiR = (AiR/At), the correctional control can be written as A u _AiRo{(l/At)-a33)-(APJJo)At In this way, an additional feedback is introduced to maintain the ZMP position, what is of basic importance for stabiity of the mechanism as a whole. It is clear that the quality of tracking of the nominal trajectory at joint O will not be improved by the additional requirement of maintaining the ZMP position. However, the system overall stability is of greater importance than the behavior of one of its powered joints. Joint O can be chosen arbitrarily. In Figure 3, it corresponds to the hip joint, but any other joint (e.g. the ankle, or trunk joint) can be used instead. Moreover, more than one joint can be chosen, either at the same time, or successively. In the following section we describe the simulation of some of these cases. 5. SIMULATION RESULTS A software package, specially developed for locomotion mechanisms2'3 was used for all simulations. First, the nominal dynamics was synthesized by a prescribed synergy method and then simulation of the mechansism's behaviour at the level of perturbed regimes is performed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000555_s0890-6955(97)00031-x-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000555_s0890-6955(97)00031-x-Figure4-1.png",
        "caption": "Fig. 4. (a) Stress distribution on the rake face and flank. (b) Contact zone on the rake face.",
        "texts": [
            " Since the flank wear, VB, exists almost throughout the whole lifetime in machining, the contact length between tool and workpiece is approximately equal to the major flank wear land. In this work, linear and constant stress distribution models were adopted for their simplicity. The models for load distribution are also supported by other investigators. 6.1. Load on rake face Cutting loads are assumed to exist on all contact areas between tool and chip. The image in Fig. 3 shows the contact area between the chip and the tool on the rake face at different feed rates. The contact area on the rake face can be formed in the area ABCDE, as shown in Fig. 4(b). The contact area is determined by the depth of cut, contact length and angle, a2. The angle a2 is actually determined by the feed rate and the tool nose radius, which can be estimated from the following expression: a2 = ~ + arct~m (34) where s is the feed rate and r is the tool nose radius. When the depth of cut is greater than the tool nose radius, along the x-axis, the whole contact area on the rake face can 1700 J.M. Zhou et aL be divided into two areas: a rectangular area and a segment area, as shown in Fig. 4(b). Along the y-axis, the contact area between the chip and the rake face can be classified into two areas: seizure contact area and sliding contact area. Therefore, the whole contact area is divided into four subareas and the contact load on each subarea is different. 6.1.1. Normal load on rake face. Based on Zorev's work, the normal load was assumed to have a triangular distribution on the rake face in the presented model, as shown in Fig. 4(a), which means that the load has its maximum value on the cutting edge and decreases linearly to zero at the separation point of the chip and tool. In the nose area, the maximum load along the cutting edge will decrease linearly to zero with increasing angle 012. More specifically, as shown in Fig. 4(b), for the contact area r < x < b~ and 0 < y < l . , the normal load is calculated from the following equation: / c r - - Y ~rr](x,Y) - - - Pr (35) l . For the contact area 0 < x < r and 0 < p < r - / c r ( 0 1 2 - - 01 ) /012 , the normal load is calculated from the equation (p + lc, - r)(a2 - a) Orr2(P,01) = 1cr012 Pr (36) where Pr represents the maximum load along the cutting edge. Accordingly, the normal force on the rake face and the normal contact load on the rake face have the following relationship: Icr b l \u00b0t2 NT=ffO'r,(X,y) dxdy+f i o'~z(P,01)pdpd01 0 r 0 0 l 2 _ 01 r -- lcr 01 lcr b l \u00b0t2 0 r 0 012 - 01 r - ~ r - - 012 = (bl - r) - 1-~ 012(7lcr -- 25r) le~ r ( P + ~ r - - ~ ( 0 1 2 - - 01) 1~r012 PPr dp dot (37) 6.1.2. Shear load on rake face. The shear load on the rake face can be resolved into the load in the axial direction and the load in the radial direction. The distribution of the shear load on the rake face is different from that of the normal load, as shown in Fig. 4(a). In the seizure contact area, the shear load is distributed uniformly due to the seizure occurring between chip and tool materials under high normal stress, which makes the shear stress equal to the shear yield stress of the chip material. In the sliding contact area, however, the load is distributed linearly, due to the reduced normal load on the rake face in this region, which allows the chip to slide along the tool face. The shear load, therefore, is calculated with different distribution models in four different zones"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002057_iecon.1993.339076-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002057_iecon.1993.339076-Figure5-1.png",
        "caption": "Figure 5 : Fuzzy variable of the adjustment time",
        "texts": [
            " We formulate them following fuzzy label in figure 4, and reasoned acceleration time are shown in Table 1. The performance at the deceleration section is the inversion of the motion of the acceleration section. However, at the beginning of the deceleration section, there is a little swing. If we ignore it, the swing angle becomes sometimes large. So we should adjust the length of constant speed traveling section by fuzzy reasoning. The antecedent consists of the swing angle and the change of swing angle at the beginning of the deceleration section. We formulate them following fuzzy label in figure 5 , and reasoned adjustment time of the constant speed traveling section in Table 2 . 4 Result In order to investigate the usefulness of on control method, some numerical experiment are done. We calculated the swing angle, running distance, and the time to avoid the obstruction and rope length at the maximum traveling speed. The following parameters are used. Maximum traveling speed 2.5 [m/sec] Hoisting acceleration -0.5 [m/sec2] Maximum hoisting speed -1.0 [m/sec] Initial rope length Traveling distance 22 [ml Final rope length 23 [ml 20 bl Figure 6 shows the graphs of swing angle versus time using control rule2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002290_1.1538192-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002290_1.1538192-Figure7-1.png",
        "caption": "Fig. 7 Classical support ring",
        "texts": [
            " So far the paper presented the general formula that governs the spin motion on the contact between a cylinder and a ball. This formula can be particularized for different applications. In order to exemplify how to ameliorate the spin loss for a specific application the authors have chosen a traction drive with conical disks, balls and support ring. The Classical Support Ring. The CVTs with conical disks, balls and support ring are well known in CVT community. A schematic of this type of traction drive is seen in Fig. 7. The authors have chosen this type of traction drive because this device has a special contact that offers a great opportunity to evaluate the value of spin loss. The device has a special EHD contact formed Transactions of the ASME /data/journals/jotre9/28716/ on 07/10/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F by a ball and the supporting ring. This special EHD contact may be defined as passive contact because it does not transmit power. Since this contact doesn\u2019t transmit power the passive contact has negligible longitudinal slip",
            "asmedigitalcollection.asme.org/pdfaccess.ashx?url= the high value of the normal force acting onto this contact suggest that the contact would generate significant spin loss. Another advantage of using of this type of traction drive is provided by the fact that a change of the passive contact configuration may be done without modifying the other characteristics of the device. The value of angular spin velocity for the passive contact is determined by applying the Eq. ~9! to the configuration given by Fig. 7. As a result the magnitude of the angular spin velocity is given by the Eq. ~10!. vsp52v in5 ~11x cos a!sin a2~ tan21 b1x cos a!cos a ~ tan21 b1x sin a!sin b2~11x cos a!cos b \u2022cos~a1b! 1 j S 11 j 2 D cos b \u2022 cos a~sin a2cos a tan21 b! ~ tan21 b1x sin a!sin b2~11x cos a!cos b \u2022cos~a1b!6 (10) where x5R/R1 . For x50.5, v15100 s21, and j50.05 the variation of angular spin velocity is given in Fig. 8. The graph presents a wide variation of the angular spin velocity. Figure 8 shows that for some values of the contact angles (a545 deg and b545 deg) the spin value is zero but for lower values of the same angles the spin value increases dramatically"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003411_ip-rsn:20041177-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003411_ip-rsn:20041177-Figure4-1.png",
        "caption": "Fig. 4 Relation between inertial and LOS frames",
        "texts": [],
        "surrounding_texts": [
            "Most modern homing missiles make use of PN (proportional navigation) guidance law using LOS (line-of-sight) rates. In homing missiles with a seeker, the LOS rate can be estimated by a low-pass filter or Kalman filter using tracking error measurements of the seeker [1, 2]. It is well known that the conventional low-pass filter approach requires a more accurate seeker system than the Kalman filter approach. On the other hand, the LOS rate dynamics model is necessary for the Kalman filter approach [3]. Many ASM (anti-ship missile) systems adopt sea skimming technologies in the vertical plane to enhance survivability and ECCM (electronic counter countermeasure) capability. Since sea-skimming ASM systems are designed basically to fly maintaining a prescribed altitude, the homing guidance loop is constructed only in the horizontal plane [1]. Therefore, the seeker for ASM systems is often designed to aquire horizontal LOS rates only. In this case, the seeker takes advantage of saving key hardware components of the antenna control loop and makes no effort to obtain the vertical LOS rate information. The guidance algorithm for sea skimming missiles is conventionally implemented independently in the horizontal plane and in the vertical plane under the assumption that the pitch and yaw planes of the missile are coincident to the the vertical and horizontal planes, respectively. This implies that a roll stabilisation loop must be designed to keep the roll angle very small. Unfortunately, however, the roll stabilisation performance is degraded by various factors such as missile dynamics uncertainties, unexpected wind gusts, seeker control loop imperfection, and so on. The unexpected large roll motions produced by these uncertainties can generate poor LOS rate measurements through a roll coupling effect. Consequently, an LOS rate estimation scheme considering the roll motions is necessary to improve the guidance performance. In the previous work [3], the Kalman filter based on a simplified LOS dynamics model was set up to handle the measurement delay for the IR (infrared) seeker system. The simplified model does not fully include the roll coupling effect and the derivation of a more precise model for LOS angle behaviour remains as a further research topic. Besides the roll coupling effect, the nonlinear and timevarying nature of the seeker detection gain is a frequently encountered error source in RF (radio frequency) seeker systems [4]. Since the calculation of LOS tracking errors in the seeker system is influenced by detection gain variation, it may cause severe degradation of LOS rate estimates. In particular, the conventional low-pass filter approach may cause unreliable homing performance because it makes direct use of the tracking errors to estimate LOS rates. In this paper, a more precise LOS rate dynamics model reflecting the roll coupling effects for two-axis gimballed seeker systems is derived. The detection gain variation is considered as a norm-bounded parameter uncertainty. A robust LOS rate estimator to cope with both roll coupling and detection gain uncertainty is proposed by applying a new robust Kalman filter theory to the model. The proposed robust Kalman filter is the first attempt to extend the Krein space estimation theory [5, 6] to the robust filtering problem. It has a similar structure to that of the conventional Kalman filter, and the steady-state robust filter gain can easily be obtained by solving the algebraic Riccati equation. Since it is easy to design and implement the proposed filter for real-time applications, and thus it is a practical result. A numerical example is given to show the estimation performance and the robustness of the proposed LOS rate estimator."
        ]
    },
    {
        "image_filename": "designv11_24_0003960_detc2005-84728-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003960_detc2005-84728-Figure3-1.png",
        "caption": "Fig. 3 Case 1 : Forces acting on the pinion from the sun and ring meshes",
        "texts": [
            " Figure 2 shows the GSAM models for both cases and the orientation and spatial locations of the gears can be seen 2 Copyright \u00a9 2005 by ASME l=/data/conferences/idetc/cie2005/71315/ on 04/01/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Dow Table 1 Case 1: Single Pinion Planetary Gearset Sun Pinion Ring Number of teeth 35 26 86 Nor. module mm 1.59 Nor. pressure angle deg 20 Nor. helix angle deg 21 R 21 L 21 L Face width mm 32.35 29.00 32.00 Center distance mm 51.945 51.945 Input torque Nm 1378.7 input to sun Reaction member Carrier Number of pinions 3 First we will consider the calculations for bearing loads and moments for the single pinion planetary arrangement shown in Figure 2 (a). Figure 3 shows a plot of a pinion and the forces acting on it. The forces are assumed to be concentrated at the operating pitch point in the center of the facewidth of the pinion. This approximation is commonly done and gives the bearing loads and moments in the absence of a distributed load, or when the effective centroid of the distributed load (at a given point in time) coincides with the pitch point in the center of the pinion facewidth. For clarity, only two teeth are shown on the pinion \u2013 one at the sun mesh and one at the ring mesh. The coordinate axes are oriented such that the origin is at the center of the pinion, the radial mesh forces are along the X axis, the tangential forces are along the Y axis and the axial forces are along the Z axis. Centrifugal forces are omitted in this calculation but can be easily superimposed. Let, Fx, Fy and Fz Forces in the X, Y, Z direction (In figure 3 FyS, FyR, FxR, FzR are negative) RpS and RpR Operating pitch radius of the pinion at the sun and ring meshes RSUN Operating pitch radius of the sun gear nloaded From: http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ashx?url Fx-PIN, Fy- PIN, Fz- PIN Resultant forces on the pinion due to contact loads Mx-PIN, My-PIN, Mz-PIN Resultant moments on the pinion due to contact loads Force Balance X direction: Fx-PIN = FxS + FxR Y direction: Fy- PIN = FyS + FyR Z direction: Fz- PIN = FzS + FzR Moments \u2022 The forces in the X direction pass through the origin and cause no moments"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001864_bf02327567-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001864_bf02327567-Figure8-1.png",
        "caption": "Fig. 8--Definition of coordinates and number of forces for multipoint contact",
        "texts": [
            " The results of this integration were substituted into eq (4) to give (A,P+B,Q)} + (CtP+ D,Q)] = (~f %2 \" 2h \" (7) where A, , BI, C, and D, are constants determined from the integration of eq (5), and the subscript j indicates the point selected at position (xs, Zs) with a fringe order Ns. The equation contains the unknown forces P and Q associated with the asperity contact. Since we have J data points, where J is much larger than the number of unknowns, we solve for P and Q using an overdeterministic method.'9 146 9 June 1991 Data Analysis--Multiple Point Contact For multipoint contact the stresses at point .4 are due to all of the loads acting on the surface of the half plane as shown in Fig. 8. In this case eqs (5) and (6) are used with the appropriate choice of the origin and the stresses at A due to each force is obtained by superposition. The superposition expands the form of eq (7) and gives ( A 1 P , + B t Q 1 + 9 . . + A k P , + BhQ,)j2 9 . D 2 { N , f ' 1 2 + (C,P,+D, QI + . + C,P,+ ,Q,)j = \"2h \" (8) where k is the number of contact points for each experiment. A second modification was introduced in treating the data from the multiple-contact experiments. We noted in an examination of the fringe patterns for the 3 and 5 asperity experiments that residual stresses existed in the model in regions of critical interest"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003553_iecon.2004.1433434-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003553_iecon.2004.1433434-Figure3-1.png",
        "caption": "Fig. 3 Limit trajectories a) mi=0.907(cl) b) mi=O,9514(c2) c) mi=l (c3).",
        "texts": [
            " In this figure, the single pole double throw switches, Q, Qb, and Qc represent the legs of the voltage source inverter. The inverter conduction state can be represented by three logic variables, Sa, S,, and S,. A logic \u2018 1 \u2019 and logic \u20180\u2019 are assigned for each case of up side connection and lower side connection, respectively. The switching o f 8, a, and Qc results in 8 operation states for the inverter as shown in Fig. 2. 111. OVERMODULATION METHOD USING LIMIT TRAJECTORY There are three limit trajectories in PWM VSI [6] . The limit trajectories are represented in Fig. 3. One is the largest circular trajectory in the voltage space vector hexagon which is represented as c l , another is the voltage space vector hexagon trajectory represented as c2, and the other is discontinuous six-step trajectory represented as c3 in Fig. 3. Amplitude of the voltage vector at c 1 corresponds to v, When modulation index is defined as a ratio between the obtained fundamental amplitude of output voltage of a PWM inverter and that of six-step operation mode as follows: ?I the modulation index of c l is 0.907. From the definition of the modulation index, the modulation index of c2 is calculated as 0.9514, and the modulation index of c3 i s 1 . If voltage command is within the limit trajectory cl , amplitude of the output voltage of PWM inverter can be- zero sequence voltage can be obtained as made using CPWM or SVPWM regardless o f voltage angle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003924_13506501jet62-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003924_13506501jet62-Figure1-1.png",
        "caption": "Fig. 1 Model of a tailored boundary-slippage bearing",
        "texts": [
            " They showed that generic slider bearing performance can be improved by the slip/no-slip surface. Their numerical results also demonstrated the load capacity for parallel surfaces under their slip/noslip arrangement, but no further analyses were given. Their work is concentrated on improving the performance of a slider bearing by using a heterogeneous slip/no-slip surface, whereas in this article, the emphasis is on the generation of a hydrodynamic effect exclusively by tailored boundary slippage. Figure 1 gives the schematic illustration of a parallelsurface bearing with tailored boundary slippage on the stationary surface. The gap between bounding surfaces 1 and 2 is a constant h0. Surface 1 and part BC of surface 2 are fully wetted, which means that there is no boundary slippage. Part AB of surface 2 is fully non-wetted or partially wetted and has a critical shear stress tc for slippage occurrence. Considering the force equilibrium of a lubricant element yields dtx dz \u00bc dp dx (1) Assuming that pressure p is a constant across the film, tx can be written as tx \u00bc dp dx z \u00fe C0 (2) In region AB where the slippage occurs, the shear stress of the lubricant at z \u00bc h0 is tx \u00bc tc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003251_j.comcom.2006.02.012-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003251_j.comcom.2006.02.012-Figure5-1.png",
        "caption": "Fig. 5. View movement.",
        "texts": [
            " Any entity, Dx, can only execute a directive if the NC value piggybacked is the same as the current view number. That is, if an entity is in viewi, it is allowed to execute the directive with NC value equal to i. By enforcing this scheme, NC can ensure the atomic execution of every directive on all the entities. Once an entity executes a directive, it notifies the completion of the directive to other entities in the dependency region. The progress of views within a dependency region, which consists of two sensors and one actor is illustrated in Fig. 5. In the figure, at a certain time all the entities have moved into viewi, as illustrated in the left ellipse area. So all of them are allowed to execute the directive with NC = i. After the execution, each entity notifies the other entities about the execution of the directive. Whenever an entity receives notifications from all other entities, it will move to the next view, viewi+1, as illustrated in the right ellipse area. We will now show that by enforcing neighborhood clock synchronization, in the dependency regions, all four hazards identified in Section 3 can be avoided reliably"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000918_s1474-6670(17)44296-0-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000918_s1474-6670(17)44296-0-Figure2-1.png",
        "caption": "Figure 2. The configuration of the parallel robot is given by its leg lengths vector:",
        "texts": [],
        "surrounding_texts": [
            "A self calibration method using extra sensors on some passive joints of the U-joints is proposed in Zhuang and Liu (1996). Redundant sensors on the U-joints are generally used to reduce the number of solution of the DKM and to simplify its resolution (Han, et al., 1995; Merlet, 1993; Etemadi and Angeles, 1995). The idea is to minimize a residual between the measured and the computed values of some passive joints. The values of the set of passive joints em are computed as a function of the measured leg lengths qr and of the nominal kinematic parameters ~m : For a set of s configurations : Y m = g(Q .. ~m> = [e~ ... e:n]T with: Qr = [q~ .. . q~]T (5) (6) Thanks to the extra sensors, the real measured values of the passive joints are given by : (7) The calibrated kinematic parameters ~r have to be identified such as : (8) This problem will be solved using a non linear optimization function. If there is a number of c sensors, the product cxs must be greater than the number of parameters to identify. 3. 1. Algorithm This method only needs 3 redundant sensors to identify the set of 30 parameters. So 3 sensors are installed on 3 V-joints. The calibration procedure of Zhuang and Liu's method uses the following steps : 1) For s configurations of the robot, obtain the measurements of the passive joints 9r and of the leg lengths qr' 2) Compute the values of the passive joints of Y m using a method called \"general DKM method\". This method will be shortly described below. 3) Vse the non linear Least Square Levenberg Marquardt algorithm in order to minimize Y r - Y m while modifying ~m. The algorithm will compute the parameters error such as : dY = '\u00a5(Qr, ~~ d~ (9) where '\u00a5 is the jacobian matrix of the geometric parameters which is computed numerically and dY =Yr-Ym. 4) Vpdate the nominal parameters with ~k + d~. 5) Repeat steps 2 to 4 until dY or d1; become small enough. 3. 2. The general DKM method In their paper, Zhuang and Liu used the method presented in (Wang and Chen, 1993) which is based on the Cyclic Descent Method (CCD) of (Wang and Chen, 1991). It allows to compute the DKM and the passive joints of parallel robots. A brief summary of their work is given here. A parallel robot consists of 5 independent loops. By cutting 5 spherical joints (s-joints), these loops are breaked. The prismatic joints are fixed to their real values and the passive joints to random values . The values of the passive joints are then adjusted in order to close all opened chains under the constraints of the cut joints. As S-joints have been cut, the close constraints consist only on minimizing positioning errors. If the values are close enough to the solution, the convergence rate of the CCD method is less than quadratic. This is the reason why the method switch to a Newton-Raphson (NR) method to obtain a fast convergence rate. The passive joints obtained with this method are the 6 V-joints and the spherical joint that has not been cut: this represents a total of 15 passive joints. 3. 3. Conclusion This self calibration method can be applied with only 3 redundant sensors. But the use of the CCD-NR method made it computationally expensive : in order to define the search direction, 9m is evaluated 30 times for each iteration (i.e. one evaluation per identifiable parameter). This CCD-NR method was programmed with Matlab on a Pentium 90 Mhz PC and the average computation time for an evaluation is 20 seconds. This is the reason why a different way to compute 9m is proposed in the following section. 4. MODIFIED SELF CALIBRATION METIlOD WITII EXTRA SENSORS Actually the main reason to modify the precedent calibration method is the fact that the computation of the whole set of 15 passive joints of the CCD-NR method is not needed: only the values of the passive joints on which the sensors are installed is important. The following 3 steps procedure has been chosen: 1) The classical DKM of the parallel robot is computed as usual for all the configurations with the method presented in equations (3) and (4) to get the situation o.rm of the platform. 2) The coordinates of points Bi corresponding to the legs on which extra sensors exists can be expressed in coordinate system Fo as follows : (10) 3) The IKM of the position of a leg is then used to compute the passive joints with sensors. This corresponds to the I.K.M. of a 3 d .o.f. serial robot consisting of the 2 d.o.f. V-joint and a prismatic joint. The position of the center of the S-joint of leg i can be obtained as : OpBu = Op Ail< + qi Sin(91i) COS(92i) OpBiy = Op Aiy - qi Sin(92i) OpBiz = Op Aiz + qi Cos(9\\i) COS(92i) (11) (12) (13) Two solutions of (91i, 92i) are computed from above: The value of 92i is limited to ]-7tl2, 7tl2[ in order to have a single solution for (e\\i, e 2i). 4. 1. Implementation of the modified method The modified method is programmed using Matlab software. The values of the passive joints are obtained with an average computing time of 0.2s, which is 100 time faster than the CCD-NR method. The identification of the parameters is based on the Levenberg-Marquardt algorithm using leastsq Matlab function: the passive joints are evaluated 30 times before obtaining the convergence direction. As only small modifications affect the kinematic parameters for each iteration, the initial \u00ab7m used in the DKM will correspond to that obtained in the precedent iteration. This will increase the calculation speed. The algorithm used is represented in Figure 3 where k represents the Levenberg-Marquardt iterations. This corresponds to \"major iterations\" for the leastsq Matlab function: the leastsq function iterations are updated for each em evaluation , that means 30 times before a major iteration. This procedure has been applied to the following parallel robot, all lengths are expressed in meters OpAl=[ 0 0 0 ]T OpA2=[ 1.1 0 0 ]T OpA3=[ 3.8 -3.1 0.05 ]T \u00b0PA4=[ 2.7 -3.65 -0.04 ]T OpAS=[ -1.4 -4.4 0.1 ]T OpA6=[ -2.7 -2.7 0 ]T \"'PB1=[ 0 0 0 ]T \"'PB2=[ 2.1 0 0 ]T \"'PB3=[ 2.3 -0.45 -0.02 ]T \"'PB4=[ 1.26 -2.02 0.03 ]T \"'PBS=[ 0.68 -1.9 -0.05 ]T \"'PB6=[ -0.49 -0.54 0 ]T qmin = [3.2 2.85 2.9 3.17 2.96 2.95 ]T qmax = [5.2 4.85 4.9 5.17 4.96 5.95 ]T The nominal kinematic parameters are supposed to be: OpAl=[ 0 0 Op~[ 1 0 OpA3=[ 3.5 -3 OpA4=[ 2.5 -4 .~--Yr Figure 3 : Algorithm of the modified self-calibration 0.3 0.25 0.2 0.15 0.1 0.05 oL--~--~--~--~~~--~--~ 100 200 300 400 500 600 700 nb 01 iterations Figure 4 : Maximum error on the parameters OpAS=[ -1.5 -4 OpA6=[ -2.5 -3 \"'PB1=[ 0 0 \"'PB2=[ 2 0 \"'PB3=[ 2.5 -0.5 \"'PB4=[ 1.25 -2 \"'PBS=[ 0.75 -2 \"'P86=[ -0.5 -0.5 qmiD = [3 3 3 3 3 3]T qmax = [5 5 5 5 5 5]T o ]T o ]T o ]T o ]T o ]T o ]T o ]T o ]T Supposed errors on the parameters are up to 10% and there are 20 cm as error on some parameters. 20 simulated configurations are used. Using 3 sensors, we obtain 60 equations to identify 30 parameters. Figure 4 represents the infinity norm of the difference between the real kinematic parameters and the identifiable parameters. Figure 5 represents the infinity norm of the error matrix dY. These results are obtained with a computation time of about 18 minutes on a Pentium 90Mhz and the parameter error converged to less than 10-8 meter. Th~re are 650 iterations, the number of the \"major iterations\" is about 19. 11 dY 11 .. degrees 18 16 IL 14 12 10 8 6 4 ~ 2 0 100 200 300 400 500 600 700 nb of iterations Figure 5 : Maximum error on the passive joints 4. 2. Conclusion The new contribution resides in calculating the values of the passive joints: the self calibration became lOO times faster. This method need extra sensors and still have problems if the redundant sensors offsets values contain errors. In the next section, a calibration method is proposed which needs only the values of the prismatic joints. 5. FULLY AUTONOMOUS CALffiRA nON METHOD In this method, the direction of a leg is fixed by means of a mechanical lock, this means to fix the U joint of this leg. In this case, the robot has 4 degrees of freedom : the platform can rotate about the center of the spherical joint which can translate along the leg direction. It is to be noted that the method presented by Nahvi et al. (1994) cannot be used to solve this system. In fact, the shoulder-joint robot system used in Nahvi et al. (1994) has only 3 d.o.f. and it must verify a particular geometry with double joints on each platform point. Let us denote by i the fixed leg. The corresponding passive joints of the U-joints can be calculated using the general DKM as presented in section 4 : y = g(qr'~...) (14) where y = [eli e2i ]. Since the leg direction is fixed, the U-joints must have the same values. k . 11 y -y 11 =0 (bj) (15) The kinematic parameters ~r are identified such as : [ 2 I] [ . 1 y -y : . k k-I \u2022 C = : _ = y -.y = mm yS _ y' I : (k = 2 .. s) (16) This is also a non linear optimization problem that will be solved by the leastsq function of Matlab. In order to obtain more exciting configurations and better results, several links are fixed successively (one leg is fixed at a time). For s configurations we get 2x(s-l) equations. 5. 1. Algorithm When the first two legs are fixed successively, the algorithm of this calibration method uses the following steps: 1) Get s different configurations of the robot for each leg. 2) Compute the values of the two V-joint angles of the fixed leg as a function of nominal parameters. This computation is identical to that proposed in the modified self calibration of section 4.1 . 3) Vse leastsq function to find a parameter error d~ that minimize the error matrix : ek ~ek-ll 2i 2i k=2, .. ,s 4) Update the kinematic parameters with d~. 5) Repeat steps 2 to 4 until C or d~ is small enough. 5. 2. Results The procedure is simulated on the robot of section 4 .2 with the same kinematic parameter errors. All 30 parameters are identified with this method by fixing successively two legs. These parameters have been identified with a precision of 10.8 meters in about 29 minutes and 960 iterations giving about 28 \"major iterations\". Only 10 configurations per fixed leg are simulated. That means that there are 2x2x(lO-1) = 36 equations for 30 unknowns parameters. Figure 6 represents the infinity norm between the real kinematic parameters and the identifiable parameters. Figure 7 represents the infinity norm of the error matrix dC. It is to be noted that this method is relatively slower than the first one but its main advantage is that no extra sensor is needed. As the optimization criteria is the difference between the two computed values of the U-joint angles, there is no offset angles problem with this method. 6. CONCLUSION In this article the computational speed of an existing self calibration method is enhanced. This method is based on minimizing the difference between calculated and measured values of passive joints. The solution procedure used to obtain the computed values of these joints has been modified. This method is now 1 ()() times faster. Then a fully autonomous method is proposed where only the position sensors of the motorized prismatic joints are needed. The idea is to fix a leg direction in order to maintain the values of the U-joint angles to a constant. For several configurations these values must be the same. The optimization program minimizes the difference between two consecutive values of the fixed joints. Simulation showed that both methods can identify big errors in the geometric parameters."
        ]
    },
    {
        "image_filename": "designv11_24_0000991_bf02473422-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000991_bf02473422-Figure1-1.png",
        "caption": "Fig. 1 Concentrated line load.",
        "texts": [
            " In this paper it is shown that such displacement depends on the contact area, and some limits are given to improve experimental measurements and numer ica l modelling of quasi-concentrated loads. The adopted approach is that of plane linear elasticity. 0025-5432/94 ~-': RILEM 2. DISPLACEMENTS DUE TO A QUASICONCENTRATED LINE LOAD ON THE SURFACE OF A SEMI-INFINITE BODY The purpose of this section is to derive an expression for the relative displacement between a point on the contact zone and another point of the body, far away from the application of the load. This result will be needed for the analysis of some experimental measurements as well as for numerical comp(atations. Fig. 1 shows a compressive line load of magnitude P per unit length, applied at right angles to the surface of a linear elastic body which is assumed to extend to infinity in all directions below the free surface in the crosssectional plane shown. In the absence of body forces and temperature changes, the vertical displacement u at point (r, 0) is [2] 2 P l n d P ( l + v ) u = sin 2 0 (1) roE r ~E where E and v are the generalized modulus of elasticity and Poisson coefficient to take into account for plane stress or plane strain conditions and d is a reference distance such that u = 0 for r = d and 0 = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003996_tase.2005.846289-Figure11-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003996_tase.2005.846289-Figure11-1.png",
        "caption": "Fig. 11. Flat volume and interfaces.",
        "texts": [
            " Volume Decomposition and Interface Between Volume Units From the preceding section, an array of continuous flat surface patches is extracted from which the envelope box for each patch can be calculated. The volumetric units can thus be obtained by slicing the STL model with six surface planes of the envelope box. Since it is associated with the flat surface, the resultant volumetric unit is termed as a flat volume. To ensure the manufacturability of these flat volumes, one problem that should be considered is to determine the interface between the neighboring volumetric units and the slicing direction of this volume (as shown in Fig. 11). According to the formation of the flat volume, there are at least one and at most six planes that are the natural planes to be utilized as the interface. The interface is determined according to the following rules. 1) If vertical interfaces exist, select the interface with the largest area and the direction perpendicular to it as the slicing direction. 2) If no vertical interface exists, select one horizontal interface as the direction between the or axis along which the cube has a smaller range as the slicing direction of this flat volume"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002649_tec.1987.4765838-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002649_tec.1987.4765838-Figure3-1.png",
        "caption": "Fig. 3. Example of electric connection of stator wind- Fig. 4. Examples of arrangements of rotor windings of ing for self-cascaded induction motor self-cascaded machines",
        "texts": [
            " When the concept 4 =(f4Ip2)= 52\"3 = 5152W1-Pl/P2 = \u00b03 - ar ---(7) of the self-cascaded machine is applied to the system of where f4[Hz] is the power frequency in the IM2 stator. Fig. 2, two kinds of rotating magnetic flux with 2p and Fig. 5 shows these relations. Fro-m equations (l)-(7), 2q, which are numbers of poles, are provided by making ar = (1 - s1s2)* 21Tfl/(pl + P2)]-(8 two kinds of currents flow in the stator winding. An example of the electric connection relating to the stator The motor rotates in the same or opposite direction winding of such a self-cascaded machine is shown in to the rotating direction of the flux b lWb] when the Fig. 3[12]. The stator winding connection of Fig. 3 can value of W, is positive or negative, respectively. also be applied to a synchronous generator[13]. The num- We caii obtain the following equation from equation ber of phases Q2 of the rotor winding is taken to be (7), by neglecting voltage drops on various parts. equal to p+q in a wound or squirrel cage rotor in Fig. Ei = s-s2E02 - 4. It can be understood that such a single rotor can act in a manner similar to the two cascaded rotors of Fig. where, Ei is the phase voltage on o'ltput terminals of 2. the inverter in V, and E02 is the voltage of Ei at Thus, the construction of the arrangement in Fig. 2 standstill(sls2=l) in V. In the DC circuit of the concan be simplified by combining Fig. 3 with Fig. 4. verter, El1cosa = Eicosy ------- ----------------------- v10 ) PRINCIPLE OF OPERATION where E1 is the phase voltage of the AC bus in volts, The angular velocity 1 [rad/s] of the rotating mag- and a and y are respectively control angles of the con- netic flux 0i [Wbl produced in the stator of the first verter and the inverter in rad. From equations (9) and induction motor IM1 having the pole pair number p1 by an (10), AC exciting current of a frequency fl [Hz] from a bus is w f l2 = E-cos--/(E-2cosy)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001967_910017-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001967_910017-Figure8-1.png",
        "caption": "Fig. 8 Establishment of Vehicle's \"Screw Axis\" with use of \"Three-Axis Theorem\"",
        "texts": [
            " The instant screw axis of F is the screw axis of the suspension with respect to the chassis, the instant screw axis of E is the screw axis of the tire with respect to the ground, and the instant screw axis of G is the screw axis of the chassis with respect to the ground, The Three-Axis Theorem states that the line GEF in three dimensional space intersects all of the three instant screw axes with perpendicularity. Since a vehicle, assumed as a rigid body in three dimensional space, should have one instant screw axis with respect to the ground at any instant, we use this Three-Axis Theorem four times; once for each of the four independent suspensions, to establish the vehicle's screw axis for the instantaneous motion with respect to the ground. As shown in Fig. 8, each of the four suspension-tire sets establish a common normal line in space and all the four common normal lines, of course? intersect the vehicle's instant screw U because this instant screw U is common to each of the four suspension-tire sets. CONCLUSION When each of the different suspensions are modeled as a spatial mechanism for guidance with one degree of freedom, the velocity matrix of instant pitch provides the instant screw axis of the tire (spindle assembly). The instant screw axis of the tire with respect to the ground is, of course, much more difficult and quite a different problem"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002427_20.104551-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002427_20.104551-Figure6-1.png",
        "caption": "Fig. 6. Concentration contour plot for vo = lo-' m s - ' ~ 0*075 and initial condition c(r,,O) -- 0.",
        "texts": [],
        "surrounding_texts": [
            "1868\nRESULTS\nA number of simulations have been performed to model the capture of manganese pyrophosphate (Mn,P,0,.3H20) particles (b = 1.2 x in aqueous suspension on a thin stainless steel wire (a = 5 x m, M = 8.61 x lo5 A m-l). In all cases a magnetic field of H, = lo7 A m-1 and a fluid velocity of V, = m s-l have been used where appropriate with a concentration of particles entering the area of c, = 10-3. Results of particle retention for two different initial conditions are presented here.\nParticle retention for the initial condition c(r,, 0) = co\nr -- 0 in an area of homogeneous concentration c(r,,O) = c, will now be discussed.\nFirst, to compare with previous single space calculations and experiments [l-31, Figs. 2 and 3 show the results of calculations with the magnetic field H, = lo7 A m-l only, i.e. for V, = 0. These results exhibit similar characteristics as those presented in [ I -31, although it is noted that different data are used in each case.\nm, x = 2.03 x\nThe effects of switching the magnetic field on instantly at time\nThe derivation is carried out in metric coordinates and real time. The resulting particle concentration time rates, (sa) and (5b), are given in the normalized dimensionless variables ra, 8 and r.\nThe terms ac/ar, and ac/% have to be determined by using the mesh next to the surface and the neighbouring mesh. Expressions (5a) and (5b) are only terms which appear in equation (2) for %/a7 at the wire surface. Expression (sa), for example, is used for a mesh at the wire surface to provide the contribution in the ra direction. The appropriate terms in equation (2) are used for the 0 direction and therefore equation (2) is replaced by\nIn addition to using expression (5a) at the wire surface, a saturated region is modelled by assuming that it is impervious. Therefore, expressions (sa) and (5b) are used to provide terms for meshes next to saturated areas in both the radial and azimuthal directions.\nEarlier studies [ 1,2] used a different boundary condition, namely &/ar, = G,c, by setting the particle flow to zero at the wire surface. It is noted this is an approximation to expression (5a) since it may be also obtained by setting the left hand side of (5a) equal to zero. Hence, boundary conditions (5a, b) used here are dynamic conditions, whereas a l a r , = G,c used in [1,2] is a quasi-steady-state condition.\nOuter boundary conditions The numerical model of HGMS capture necessarily covers a finite area and therefore, for the same reasons as at the wire surface, it is necessary to provide boundary conditions at the outside edge of the area, where the calculation takes place.\nFor meshes where the flow is into the area of computation the concentration is determined by the conditions upstream. It is assumed that the concentration there is constant and therefore at the upstream boundary the concentration is fixed, that is c = c,,.\nAt the downstream boundary, where the flow is outward, it is reasonable to assume that the concentration parallel to the direction of flow is constant. This is, however, not congruent with the symmetry of the (ra,O) coordinate system. Therefore, a simplified boundary condition is assumed, namely that, whilst the azimuthal terms in equation (2) apply, the radial concentration gradient is zero, that is w a r , = 0.\nFig. 3.\nConcentration contour plot for V, = 0, r = 0.20 and initial condition c(r,,O) = c, =\n' -a :;yo/*7oo -9\n-10\nRadial concentration profiles for V, = 0, r = 0.20 and initial condition c(r,, 0) = c, =\nThe effect of flow velocity is -shown in Figs. 4 and 5, where concentration contours are plotted for H, = lo7 A m-l, V, = m s-1, r = 0.075 and 0.25, respec.:vely.",
            "1869\nParticle retention for the initial condition c(rar 0) = 0 m\ns-1 in an area of concentration c(r,,O) = 0 at T = 0 is shown in Figs. 6 and 7. These figures show contours for r = 0.075 and r = 0.25, respectively. It may be seen that the results are similar to those given in Figs. 4 and 6. However, the effect of transporting particles into a previously empty region is to introduce a delay in the buildup of particles, especially behind the wire. It is noted that for T = 0.075 there is no saturated buildup on the downstream side of the wire.\nThe effect of instantly switching H, = lo7 A m-1 and V, =\nDISCUSSION AND CONCLUSIONS\nA two dimensional theoretical model for the capture of ultra-fine particles on an HGMS collector has been developed. A full set of boundary conditions has been derived and in particular dynamic boundary conditions at the wire surface have been formulated. The results show areas of depletion, accumulation and saturation at intuitively expected locations of space after appropriate periods of time. The model gives pointers for future experimental work which is needed for its full validation.\nThe comparison between results shown in Figs. 4, 5 and Figs. 6,7 indicates that, for the cases investigated herr-, the particles retained at the downstream side of the wire are supplied by forces of diffusion and not by fluid flow. This is a valuable result since the origin of the rear capture is still a subject of discussion.\nREFERENCES\nR. Gerber, M. Takayasu and F. J. Friedlander, IEEE Trans.Magn. MAG-19 (1983) 21 15. M. Takayasu, R. Gerber and FIJ. Friedlander, IEEE Trans.Magn. MAG-19 (1983) 21 12. M. Takayasu, J.Y. Hwang, F.J. Friedlander, L. Petrakis and R. Gerber, IEEE Trans. Magn. MAG-20 (1984) 155. R. Gerber, IEEE Trans.Magn. MAG-20 (1984) 1159. J.P. Glew and M.R. Parker, IEEE Trans.Magn. MAG-20 i1984) 1165. D. Fletcher and M.R. Parker, J.Phys.D: Appl.Phys. 17 (1984) L119. R. Gerber and R.R. Birss, High Gradient Magnetic Separation, Chichester: RSP-John Wiley & Sons, 1983."
        ]
    },
    {
        "image_filename": "designv11_24_0003858_j.measurement.2005.11.012-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003858_j.measurement.2005.11.012-Figure1-1.png",
        "caption": "Fig. 1. Diagrams explaining errors occurring in wheel operated systems.",
        "texts": [
            " The reason is that, the properties of braking system of this equipment stay same. In other words, this error is multiplicative. Results of wheel operated systems are related with wire tense before jumping. If the wire is more stretched than required, the value shown on the display is greater than the normal value or vice versa. Even if the athlete bends his legs during the stretching of wire, equipment makes faulty measurements. The errors occurring on the wheel operated equipments consist of the structure of system and these are subjective errors. Fig. 1 explains the errors on the wheel operated vertical jumping equipment. There 1\u2014shows the wheel. Before the athlete breaking of the floor he is gaining a distance as (H3\u2013 H2) + (H2\u2013H1). The bigger the foot of athlete is, the greater the error is. Tabulated list method is the simplest and most widely used method. Usage of this method and measurement errors are shown in Table 1. Tabulated list is mounted on the wall or on a portative postament. The athlete defines the initial height using his hand, head, the paint on his or her hand and etc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000868_s0022112093001417-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000868_s0022112093001417-Figure4-1.png",
        "caption": "FIGURE 4. (a) A plot of the equilibrium orientation of a family of three-dimensional flows that contains a given two -dimensional flow in which the orientation dynamics are structurally unstable (Example 11). The equilibria are plotted over the parameter range e = - 1.6 (open circles) to e = 1.6 (closed circles). Perturbations ( E + 0) do not change the number of equilibria, but do change their stability type and therefore also the phase portrait. (b) The real eigenvalue (A , of IC) associated with the equilibrium orientation shown in (a) versus the parameter e. Note that for E + 0, the equilibrium is a stable focus, thus breaking the closed orbital trajectories that exist in the degenerate case e = 0, in which the equilibrium orientation is a centre (metastable).",
        "texts": [
            " Of course, the small three-dimensional perturbation is not arbitrary, and so this analysis does not constitute a proof of robustness but merely a demonstration. We begin with a two-dimensional example flow taken from SWL, $2.2; we set Ei, = 0 except for Ell = -Ezz = 3, and O,, = 0 except for a,, = -O,, = 2. When G = 1, there is a single attracting equilibrium orientation and a repelling equilibrium orientation in the (x,y)-plane, and a saddle on the z-axis. The phase portrait for the particle orientation dynamics is shown in figure 4 of SWL. The (generic) particle orientation dynamics in this unperturbed flow are therefore an example of case 1 in table 1. Next, we add a small rotational component to the flow about the y-axis, with associated vorticity E : 0 0 -& a,= 0 0 [, 0 8 1. Thus, the full flow K = GE+Q+Q, is slightly three-dimensional for small E . When E + 0, we compute the eigenvalues and eigenvectors of K. For - 1.6 < E 6 1.6, we find a stable node, an unstable node and a saddle, together with their symmetric opposites, at every value of E ",
            " When G = 1, there is no attracting equilibrium orientation. There is only a centre on the z-axis. The phase portrait of the particle orientation dynamics in the unperturbed flow is shown in figure 2 of SWL. Clearly, the (non-generic) unperturbed flow is neither an example of case 1 nor of case 2a or b. As in Example I, we add Q,, a small rotational component to the flow about the y-axis, with associated vorticity E . As we vary the perturbation vorticity E , the location of the equilibrium in this family of flows shifts, as shown in figure 4(u) for the range - 1.6 < E < 1.6. It would seem, at first glance, that the unperturbed flow K = G \u20ac + Q is robust to the perturbation Q,, as the number of equilibria do not change. However, the stability type of the equilibrium does change when e + 0. In figure 4(b), we plot the (real) eigenvalue that characterizes the stability of the equilibrium orientation (A, of K). Note that when 6 = 0, A, = 0 corresponding to the centre in the unperturbed flow. When E is different from zero, no matter how slightly, the corresponding equilibrium orientation becomes an attractor, and all the closed trajectories of the unperturbed flow are broken except, of course, for the invariant great circle. Under the perturbation, the non-generic unperturbed flow is transformed into a generic example of case 2a of table 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003956_tia.2005.863899-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003956_tia.2005.863899-Figure1-1.png",
        "caption": "Fig. 1. Rotor lamination of synchRel.",
        "texts": [
            " Eventually, to validate the synchRel model, the computed dynamic and steady-state performance were compared with the experimental results. They revealed a good match. In the present work, a four-pole 1.5-hp 60-Hz 460-V 1800-r/min synchRel was initially chosen for the purpose of study. Its stator has a single-layer concentric three-phase distributed winding with 36 slots. The stator winding resistance is 3.4 \u2126/phase. The machine has a rotor with 24 damper bars. The damper bars facilitate the self-starting of the machine and also damp out the machine oscillations. The rotor lamination of the machine is shown in Fig. 1. The salient-pole synchronous motor under consideration is a three-phase 208-V 1800-r/min 60-Hz 2-kW four-pole machine having 36 stator slots. The stator has a three-phase double-layer lap winding with a resistance of 0.6 \u2126/phase. The machine has 20 damper bars. The rotor lamination of the machine is shown in Fig. 2. In order to model the machine, various stator inductances are to be computed using the WFA. Its stator has a three-phase single-layer concentric winding with 47 turns per coil. The turns function of the stator phase A winding of the synchRel is shown in Fig",
            " The inverse air-gap function of the synchRel is shown in Fig. 4. The inverse air-gap function of the machine, g\u22121(\u03c6, \u03b8), can also be expressed using the Fourier series as given in (4) g\u22121(\u03c6, \u03b8) = aog + \u221e\u2211 k=2,4,6,... akg cos {pk(\u03c6\u2212 \u03b8)} (4) with aog = 2 \u03c0 (D\u03b8d +Q\u03b8q) and akg = 4(Q\u2212D) \u03c0k (\u22121) (k+4) 2 sin(k\u03b8q) where D = 1/(effective air gap along the d-axis) and Q = 1/ (effective air gap along the q-axis). \u201c\u03c6\u201d is the space angle (mechanical radian) with respect to the stator frame of reference and \u201c\u03b8\u201d gives the rotor position. \u03b8d and \u03b8q are shown in Fig. 1. By using WFA, the inductance between any two phases, phase \u201cu\u201d and phase \u201cv\u201d of stator winding, can be given as Luv = \u00b5orl 2\u03c0\u222b 0 [ nu(\u03c6)Nv(\u03c6)g\u22121(\u03c6, \u03b8) ] d\u03c6 (5) with Nv(\u03c6) = nv(\u03c6) \u2212 \u3008nv(\u03c6)\u3009 = nv(\u03c6) \u2212 aos where \u201c\u00b5o\u201d is the permeability of the free space, \u201cr\u201d is the radius of the rotor, and \u201cl\u201d is the stack length. By substituting for nu(\u03c6), Nv(\u03c6), and g\u22121(\u03c6, \u03b8) in (5), the general expression for the inductance between any two phases with any number of winding harmonics (m) and air-gap harmonics (k) can be obtained as given in (6) Luv=  Z0+ \u221e\u2211 k=2,4,6,"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002619_095440605x31481-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002619_095440605x31481-Figure2-1.png",
        "caption": "Fig. 2 Cutting geometry of a CV1-gear in two singleindexing cycles, R/m \u00bc f/m \u00bc 10",
        "texts": [
            " The geometrical features and attributes of the different forms of Cgears are detailed. The limitations and demerits of these gears and their machining methods are also brought forward. This information should be valuable to design engineers who would envisage using C-gears in particular applications; where their earlier mentioned advantages are deemed to outweigh all other issues of concern. This is a form of CV-gear that is generated by two sets each of identical cutters, on two cutter heads, in two consecutive single-indexing cycles. As depicted in Fig. 2, one set has outside-cutting straight edges that are inclined to the axis at the midplane-pressure angle fm and generate the concave flanks with a circular-arc tooth trace of radius R. The other set has inside-cutting straight edges that are oppositely inclined and generate the convex flanks with an identical tooth trace. Thus, a CV1-gear has equal circularthickness teeth, and a pair of such gears will mesh in line contact. Still, there is a possibility of crowning the teeth by making the radius to the outside cutters larger than it is to the inside cutters",
            " A generated-gear tooth profile is a true involute only in the midplane, and it distorts as the transverse plane moves away. The transverse pressure angle also increases towards the side planes. From the geometry in Fig. 5, it can be shown that the side-plane pressure angle (slope of tangent to the hyperbola at the pitch plane) is given by fs \u00bc tan 1 tanfm cosb (2) Proc. IMechE Vol. 219 Part C: J. Mechanical Engineering Science C01505 # IMechE 2005 at UNIV OF VIRGINIA on July 12, 2015pic.sagepub.comDownloaded from where the tooth trace inclination at the side planes is given from Fig. 2 by b \u00bc sin 1 f 2R (3) Owing to the pressure angle variation across the face, which is the same for both flanks, a CV1-gear has a barrel-shaped base surface \u2013 the pitch surface still being cylindrical. The surface of action between two meshing gears becomes an oppositely warped, symmetrical, ruled surface that inflects about the pitch (surface) element. The deviations of the rack transverse profile from its tangent \u2013 at the pitch line \u2013 at the working depth limits, in a direction parallel to the pitch line are derived from Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003809_detc2005-84681-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003809_detc2005-84681-Figure1-1.png",
        "caption": "Figure 1: The HSM spindle bearing system",
        "texts": [
            "org/ on 02/03/2016 T \u03c1 Material volume mass \u00b5 Section mass per length \u00b5 section inertial operator qe Generalized nodal displacements ziyixizyixi uuu \u03b8\u03b8\u03b81 Nodal coordinate of node i )(xN Shape function matrix eT Kinetic energy element Ke Stiffness matrix element Me Mass matrix element Ce Gyroscopic matrix element ( )tef Nodal force element M Total mass matrix K Total stiffness matrix D Viscous damping matrix C Total gyroscopic matrix Nq Nodal displacement ( )tF Force vectors. A technological analysis makes it possible to identify the structural elements that contribute to the total dynamic behavior of the spindle. The structural entity (spindle body, rotating shaft entity, rear guide) and its connections are presented in figure 1. Each element will be the subject of experimental dynamic characterization. DYNAMIC MODELLING Here the emphasis is on modeling the rotating shaft (rotor). Dynamic effects due to high rotational speed and elastic deformations, such as gyroscopic coupling and spin softening, can have a significant influence on spindle behavior. Rotor motion is considered as the superposition of rigid and elastic body displacements. In order to introduce elastic displacements, 2 Copyright \u00a9 2005 by ASME erms of Use: http://www",
            " To implement the finite element model into the computer program, every term in Eq.(14) has to be calculated. D Nq ( )tF Validation of the numeric model is carried out by comparing dynamic characteristics (natural frequencies, damping ratios and modal shape) obtained by experimental identification with those given by the finite elements model. The unknown parameters (such as the material properties of the rotor or tool holder mount), are readjusted until experimental data correlation with the numeric model is satisfactory. Each spindle entity (see figure 1) is characterized separately. Then intermediate assemblies and finally the complete spindle are characterized. Experimental modeling is articulated in two stages, first by studying the system at rest and second by studying the rotating spindle in operation. Modal parameter identification is based on a parametric model which assumes proportional damping and modal decoupling. The method employed (see figure 3) begins with an initial graphic estimation of the natural frequencies and damping ratios, associated with a MDOF curve approximation to determine the modal shape"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001904_70.988971-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001904_70.988971-Figure2-1.png",
        "caption": "Fig. 2. Morphism as a new frame definition.",
        "texts": [
            " Firstly, if the function is considered, a morphism has to be found that leads to the proposed goal where The interpretation is that a new space is proposed so that frame coincides with . Hence, the new Configuration Space is constituted by a unique configuration . Now, we define a function as if if (13) where is the subset of points that represent the link at configuration with respect to . For the second and third links, a morphism where In this case, a new space with a frame that coincides with and with is stated, as can be seen in Fig. 2. Then, the Configuration Space is constituted by the set ( ). Next, we propose the functions and given by if if (14) if if (15) where is the subset of points that represents the link at the configuration with respect to , and represents the third link, at the configuration . Then it is verified that , and . With this result and the relationships between functions we can obtain (16) As a result, the functions that define the robot links stand invariable if a translation is done with respect to the coordinates and "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002920_0301-679x(81)90098-0-Figure11-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002920_0301-679x(81)90098-0-Figure11-1.png",
        "caption": "Fig 11 Nomenclature used in Appendix 1",
        "texts": [
            " For an infinite roller on a flat plate, the contact width co ~3 is: a r e a = \" / r o b Iffg 1 Hertzian contact model used in developing elast& conformity parameter co = 2.15 (1) where P is the normal force, D the cylinder diameter, E the elastic modulus and l the length of cylinder. Assuming the total load, W, is shared equally by each of the cylindrical asperities, then from Fig 1 ,P = Wr/a. Also, if each cylindrical asperity flattened to a width r is assumed equivalent to total conformity, then ~o = r and i fR = D/2, Eq (1) gives a condition for elastic conformity as: Lab r Lab r W - 2.152R 4.6R (2) If the ridges have circular cross-sections, then from Fig 11, R ~ r 2/86 (Appendix 1) and from Eq (2) 8Eab6 r - - - (3) 4.6W For an elliptical contact, the nominal contact stress is f = W/rrab and Eq (3) becomes 6 4.6 ~ f - ( 4 ) 8E The mean absolute slope for a circular asperity of height 6 and width r is (Appendix 1): = 2~/r and the rms slope for a Gaussian distribution, (m2) '/2 = (rr/2) 1/1 ~- thus 1 4 . 6 n f . 4 .5 f (m2)1/2 = 2(~/2)1/2 ( ~ ) - E o r m 2 ~- (4f/E) 2 where m2 is the variance of the profile slope distribution, or the second moment of the profile power spectrum"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002175_1.1515333-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002175_1.1515333-Figure7-1.png",
        "caption": "Fig. 7 Tine junction constraints",
        "texts": [
            " l 2 sin u i2~lyi1ly~ i11 !! l 2 cos u i50 (8) where Ti5k~u i2u i21! (9) The free end of the tine, element n, experiences no reaction at the tine end, Fig. 6, and therefore the following set of equations may be derived. mRnv22lxn50 (10) Ft2lyn50 (11) And; Tn5k~un2un21!5Ftl cos un1mRnv2 l 2 sin un (12) At the constrained end of the tine, n51, the connecting spring cannot do any work. To overcome this a \u2018\u2018pseudo-link\u2019\u2019 is introduced such that this link deflects a negative amount from the steady state position, Fig. 7a. In order for the constraint to undertake zero work the negative work undertaken by the constraint must be equal to the positive amount of work done. Hence: f2u05u12f (13) And by comparing the situations in Fig. 7 ~a and b! and taking note of Eq. ~5!, it may be shown that for the condition in Fig. 7b to be true when: k15 2EIn L (14) The final condition ensures that the elements connect. Thus, if the radius at the center of mass of each element is Ri , then for a given element Rs : rom: http://dynamicsystems.asmedigitalcollection.asme.org/ on 08/16/201 Rs5Rr1 l 2 sin us1( s21 1 l sin u i (15) And for the initial element: R15Rr1 l 2 sin u1 (16) The limits at the free end of the tine have now been fully established. Equations ~3!\u2013~16! therefore constitute a set of nonlinear equations through which the free end, i5n , is readily analyzed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000305_s0003-2670(97)00435-2-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000305_s0003-2670(97)00435-2-Figure1-1.png",
        "caption": "Fig. 1. Cyclic voltammograms for the (a) composite rod (CR), (b) pyrolitic paste (PP) and (c) composite paste (CP) electrodes.",
        "texts": [
            "1 M, at which the system became stable, indicating that the concentration of supporting electrolyte is critical and not necessarily always very much higher than that of the analyte. According to the CV results TEAP is more suitable for our purpose because of the linearity and height of the signals. Besides, TEAP is quite soluble, 26 g per 100 ml, has a relatively low speci\u00aec resistance, i.e., 26 cm and a zero association constant in MeCN. The use of TEABF in organic solvents for graphite electrode was avoided as it produces an oxidation peak at around 0.8 V vs. SCE [23]. Fig. 1 demonstrates by CV that in the potential range used the CP electrode is the best choice amongst those tested as its peak current, Ip, is directly proportional to the scan rate, 1/2, and Ipa/Ipc is almost unity. It was suspected that the binder clay could have initiated the polymerization in a manner a traditional initiator does. Inspection on the pencil 2B lead using electron diffraction spectroscopy carried out on the SEM indicates that the lead contains (% w/w) Al (2.5), Fe (0.6), Mg (0.05), K (0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003762_j.jappmathmech.2006.03.010-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003762_j.jappmathmech.2006.03.010-Figure3-1.png",
        "caption": "Fig. 3.",
        "texts": [
            "15), the solution of Eq. (1.9), y(t) \u2192 0 as t \u2192 \u221e. If y(t) \u2192 0, then the function (t), which is defined by expression (1.15), also tends to zero, (t) \u2192 0. Then, as t \u2192 \u221e, the solution of Eq. (1.10) z(t) \u2192 0 for any initial value z(0). Note that the problem of stabilizing the magnetic suspension in a gradiometer has been solved11 by \u201csuppressing\u201d instability with respect to a single canonical variable. We will now consider a pendulum, the suspension point of which is situated at the centre O of a wheel (Fig. 3). The wheel, which is symmetrical about its axis O, can roll without sliding over a flat horizontal surface in a straight line. We will denote the mass of the wheel by M, its radius by R and the radius of inertia about the centre O by . We will denote the angle of counterclockwise rotation of some fixed radius (marked on the wheel), which, at the start of the motion, is directed along the horizontal axis X, by and we will denote by x the displacement of the centre of mass O along a horizontal straight line such that x\u0307 = \u2212\u0307R"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000091_002077299291796-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000091_002077299291796-Figure3-1.png",
        "caption": "Figure 3. Illustration of the AUV, showing its degrees of freedom and control surfaces.",
        "texts": [],
        "surrounding_texts": [
            "In this section, the results of modelling a six-degree of freedom Autonomous Underwater Vehicle (AUV) are presented. AUVs have become indispensable tools in exploring inhospitable, non-benign waters. The vehicle studied here is the Ocean Voyager, a torpedo-shaped vehicle with a maximum diameter of 13inches and a length of 22 feet3. The forward motion is produced by a propeller at the rear of the vehicle, and its direction and orientation are controlled by two control surfaces, the stern plane and rudder. A simulation of the dynamics of this vehicle, based on standard nonlinear equations of motion (Feldman 1979), has kindly been supplied by The Department of Ocean Engineering, Florida Atlantic University, and was used to generate the data. During modelling it is assumed that these equations are unknown. The AUV has three controls: the stern plane de\u00af ection; the RPM of the propeller; and the rudder de\u00af ection. The orientation of the submarine is described by the normal rotational axes; pitch, yaw, roll which are relative to horizontal and vertical references. In addition, the direction in which the submarine is travelling with respect to its orientation is given by the attack and drift angles. These angles specify the orientation of the AUV at any one moment in time and are illustrated in \u00ae gure 3. The depth and speed are also required to fully describe the state of the submarine, all these submarine outputs are made available via the AUV simulation. The control vector u(t) which can be used to change the current state of the AUV consists of three independent inputs: d R: rudder de\u00af ection ( \u00eb ), which must lie in the interval [ 5\u00eb , 5\u00eb ] d S : stern plane de\u00af ection ( \u00eb ), which is also restricted and must lie in the interval [ 10\u00eb , 10\u00eb ], and r : revolutions per minute for the propeller, restricted to the range [0, 600]. The current state of the AUV is summarized by the output vector, y(t), consisting of seven measurements: d: the depth of the submarine. For the purposes of this study, the sea bed is \u00ae xed at 100 feet; u: the translational speed of the submarine (ft/s); a : angle of attack ( \u00eb ); b : drift angle ( \u00eb ); \u00b5: pitch ( \u00eb ); w : yaw( \u00eb ); and u : roll ( \u00eb ) . The length and speed measurements are in feet and feet per second, respectively, and the angles are measured in degrees. The purpose of this study is to construct a model of the complete nonlinear dynamics of the AUV. Given this is a dynamical system identi\u00ae cation problem, a regressor containing time histories of past system inputs and outputs is required. A NARX model structure, equation (4), is assumed, and hence no model outputs are present in the regressor. To keep the dimension of the input space relatively small, the maximum tap delay permitted on each input and output is 4, producing a 40D input space. Using the notation for the input and output vectors introduced above, the complete regressor on which a model is identi\u00ae ed is given by: 2 It is assumed here that the model and noise assumption can accurately represent the data, if this is not the case there will be a third component due to model mismatch. 3 Due to the origin of the simulation, all length and speed measurements are in feet and feet per second, respectively. For reference, a foot is 0.304m and an inch is 0.0254m D ow nl oa de d by [ IN A SP - P ak is ta n (P E R I) ] at 0 0: 38 1 9 N ov em be r 20 14 x T(t) = [uT(t  1), . . . , u T(t  4), y T(t  1), . . . , y T(t  4)]. (15) Di erent single output models are used to model each of the AUV\u2019s outputs, the concatenation of which produces a dynamical model of the complete AUV. This study is used to demonstrate the capabilities of the data-driven model construction techniques described in section (2), hence no a priori knowledge is assumed. To identify the models, a data set which su ciently excites the dynamics is required. This was obtained by applying random steps with a period of 10s to all the control surfaces. The amplitudes of these signals were drawn from a uniform distribution de\u00ae ned on the allowed range of the controls. This random excitation was used to produce a data set consisting of approximately 5000 data pairs. To ensure this contained a good range of data, the AUV is set swimming from initial depths of 10, 30, 50, 70 and 90 feet, each for 500s. The resulting data set is prohibitively large and is likely to contain redundant data, hence a random sample consisting of 2000 data pairs (considered a reasonable size) was taken as a training set. The remainder of the data set is used to test the resulting model. An example of typical motion of the submarine is shown in \u00ae gure 4. 3.1. Linear Models In many modelling scenarios, it is often advantageous to investigate the e ectiveness of simple linear models. Such a study can suggest which dynamics are likely to be heavily nonlinear and can produce models which serve as a baseline benchmark. In this section very simple linear models, based on the basic understanding of the motion of the AUV, are tested. It should be emphasized that this brief study is not intended as a rigorous approach to producing a complete linear model of the AUV, but more an initial investigation. Each of the AUV\u2019s outputs modelled by a linear difference model based on the last two previous outputs and one input. The chosen input is the one which is intuitively considered the most relevant to the particular output. The regressors for these models and their performance across the di erent data sets, expressed as root mean squared errors (RMSEs), are presented in table 1. Considering the complexity and nonlinearity of the equations of motion for this AUV, these linear models perform surprisingly well. The main reason for this is that the pre-de\u00ae ned sampling rate is relatively fast with comparison to the dynamics of the AUV. This exercise has demonstrated that many of the AUV\u2019s outputs can be modelled reasonably well by linear models. In particular, the speed and yaw dynamics seem linear, while the depth seems the most nonlinear. These results also suggest that there is no (or very little) noise on the data. 3.2. Neurofuzzy Models Using the data-driven model identi\u00ae cation strategy described in section 2.1, a separate neurofuzzy model was constructed for each of the AUV\u2019s outputs. Assuming no a priori model structure the models summarized in table 3 were identi\u00ae ed. This table gives an indication of the model\u2019s complexity and structure, and it is clear that models based on a limited number of the regressors have been identi\u00ae ed. Detailed descriptions of the individual models will not be given. Despite the success of the linear models described in the previous section, the iterative structure identi\u00ae cation algorithm has identi\u00ae ed complex, nonlinear dynamics, which might suggest that the identi\u00ae cation algorithms have over\u00ae tted the data. This is not con\u00ae rmed by the performance of these models across the training and test sets shown in table 2; all the models appear to generalize well. The construction algorithm has successfully reduced this problem to a tractable size. The conventional D ow nl oa de d by [ IN A SP - P ak is ta n (P E R I) ] at 0 0: 38 1 9 N ov em be r 20 14 100 150 200 250 300 5 2.5 0 2.5 5 time (secs) dR ( de gs ) 100 150 200 250 300 10 5 0 5 10 time (secs) dS ( de gs ) 100 150 200 250 300 0 200 400 600 time (secs) R P M 100 150 200 250 300 40 45 50 55 time (secs) de pt h (f t) 100 150 200 250 300 3 4 5 time (secs) sp ee d (f t/s ) 100 150 200 250 300 2 0 2 4 time (secs) at ta ck ( de gs ) 100 150 200 250 300 2 0 2 time (secs) dr ift ( de gs ) 100 150 200 250 300 10 0 10 20 time (secs) pi tc h (d eg s) 100 150 200 250 300 5 0 5 time (secs) ya w ( de gs ) 100 150 200 250 300 0 5 10 time (secs) ro ll (d eg s) Figure 4. An example of the typical response of the AUV to step inputs of random amplitude. D ow nl oa de d by [ IN A SP - P ak is ta n (P E R I) ] at 0 0: 38 1 9 N ov em be r 20 14 approach to neurofuzzy modelling is infeasible due to the potentially 40D input space. However, conventional neurofuzzy models could, e.g. be identi\u00ae ed on the regressors used to de\u00ae ne the linear models described in section 3.1. Using a standard set of \u00ae ve fuzzy membership functions de\u00ae ned on each of the inputs, each output could be modelled by a neurofuzzy system containing 243 rules (or weights). Considering the sparse data set and size of the constructed models, (table 3), the resulting conventionally identi\u00ae ed models would inevitably generalize poorly. Unsurprisingly, the constructed neurofuzzy models perform better than the linear ones presented in the previous section, but the low one-step-ahead RMSEs do suggest that the models may have over\u00ae tted idiosyncrasies which appear in both the training and test data sets. One should remember that these data sets are randomly drawn from the same data set and are hence not truly independent. Bayesian estimation has been introduced to reduce the e ects of over\u00ae tting, and its application to the identi\u00ae ed models is described in the following section. 3.3. Bayesian Estimation Proposed as a method for controlling redundant degrees of freedom, Bayesian estimation (also referred to as regularization) is applied to the identi\u00ae ed neurofuzzy models described in the previous section. This produces the results shown in table 4. When regularization is applied, a proportion of the model\u2019s parameters are identi\u00ae ed by the data and the remainder by the regularizers. The number of parameters identi\u00ae ed by the data is referred to as the model\u2019s degrees of freedom (or the e ective complexity of the model) and is typically a non-cardinal value. Along with the models\u2019 performance, table 4 also shows the models\u2019 degrees of freedom. It can be observed that the degrees of freedomhave been reduced, which equates to a reduction in the model\u2019s variance, without adversely a ecting the RMSEs across the data sets. This result suggests that regularization has successfully controlled redundant degrees of freedom. Table 2. The results of neurofuzzy model identi\u00ae cation, the structure of these models is shown in table 3. df is the number of degrees of freedom in the models. RMSEs Model df Train Test Units depth (d(t)) 69 1.16e-4 1.19e-4 ft speed (u(t)) 69 4.46e-4 4.64e-4 ft/s attack ( a (t)) 30 1.48e-3 1.53e-3 degs drift ( b (t)) 49 1.61e-3 1.96e-3 degs pitch (\u00b5(t)) 15 1.07e-3 1.10e-3 degs yaw ( w (t)) 89 1.20e-3 1.38e-3 degs roll ( u (t)) 43 3.97e-3 2.80e-3 degs Table 3. Description of the neurofuzzy models identi\u00ae ed by the ASMOD algorithm, the subfunctions denoted by f l (\u00b7), are linear (bilinear etc). No. Model Structural decomposition weights depth (d(t)) f (d(t  1),\u00b5(t  4)) + f (u(t  1), a (t  4)) + f (u(t  1),\u00b5(t  2)) + f ( b (t  2), u (t  4)) + fl(\u00b5(t  3)) 85 + fl(\u00b5(t  1)) + f (r(t  3)) + fl( u (t  1)) + f ( d R(t  3)) + f ( d R(t  4)) speed (u(t)) f (u(t  2), u (t  3)) + f (r(t  1), u(t  1), u (t  1)) + fl(d(t  1)) + f ( d R(t  1), r(t  2)) + f (r(t  1), r(t  3)) 74 attack ( a (t)) fl( a (t  1)) + fl( a (t  2)) + fl( a (t  3)) + f ( d S(t  1), d S(t  2)) + fl(\u00b5(t  4)) + fl( d S(t  3)) 35 drift ( b (t)) fl( b (t  2)) + fl( b (t  3), u (t  1)) + f ( d R(t  3)) + f ( d R(t  1), d S(t  1), d S(t  2)) + fl( w (t  4)) + fl( w (t  3)) + fl( u (t  2)) + fl(r(t  1), b (t  1)) + fl( d R(t  2)) 57 pitch (\u00b5(t)) f (\u00b5(t  1),\u00b5(t  2)) + fl( d R(t  4)) + fl( d R(t  1)) + fl( a (t  4)) + f ( u (t  4)) + fl(\u00b5(t  3), u (t  3)) 20 yaw ( w (t)) fl( w (t  2)) + f ( d R(t  3), w (t  1)) + f ( d R(t  4),\u00b5(t  1), u (t  1)) + f ( d R(t  1), a (t  2), b (t  1)) + fl( d S(t  4), u (t  1), u (t  2)) + fl( b (t  4)) + f (\u00b5(t  1), u (t  4)) + f (r(t  2)) + f ( u (t  3)) 100 roll ( u (t)) f (r(t  2), u (t  1), u (t  2)) + f (r(t  1), u (t  1), u (t  3)) + f (r(t  1), r(t  2), u(t  1)) + fl(u(t  4)) + fl(u(t  2)) + f (r(t  4)) 51 D ow nl oa de d by [ IN A SP - P ak is ta n (P E R I) ] at 0 0: 38 1 9 N ov em be r 20 14 0 25 50 75 100 0 400 800 depth (a) 2 3 4 5 0 150 300 speed (b) 4 2 0 2 4 0 200 400 attack (c) 3 1.5 0 1.5 3 0 150 300 drift (d) 20 10 0 10 20 0 200 400 600 pitch (e) 30 15 0 15 30 0 400 800 yaw (f) 10 5 0 5 10 0 200 400 600 roll (g) 40 45 50 55 60 0 100 200 300 depth (h) Figure 5. Histograms summarizing the distribution of the data sets across the AUV\u2019s outputs, (a)-(g) show the distributions for the original data set and (h) is the distribution across the depth for new independent test set. D ow nl oa de d by [ IN A SP - P ak is ta n (P E R I) ] at 0 0: 38 1 9 N ov em be r 20 14 The success of regularization is further tested by generating an independent test set. The submarine was set swimming from a depth of 50 feet, and a data set containing 100s of data was collected. The performance of the various models across this new data set is presented in table 5. From these results it appears that this new data set is a good test highlighting inadequacies in the original submarine model. The unregularized depth model performs especially poorly on this new data set. Regularization applied to this model is now investigated further. By inspecting the distribution of the original data set across the various outputs, the reason for the poor generalization experienced by the depth model is clearly shown. Histograms showing the distribution of the original data (both test and training set) across the AUV\u2019s outputs are shown in \u00ae gures 5(a\u00b1 g). Figure 5(h) shows the distribution of the depth for the new test set, when comparing this with \u00ae gure 5(a) it can be seen that a majority of the new test data is at a depth for which there are no training data. As described in section 2.2, regularization aids model interpolation which is demonstrated by its application to the depth model, giving good generalization across the new data set. The depth model\u2019s structure is illustrated in \u00ae gure 6, consisting of 10 submodels with varying degrees of nonlinearity. Due to the simple transparent additive structure, these nonlinearities can be visualized by plotting the output surfaces of the submodels. The submodel outputs for the unregularized depth model are shown in \u00ae gure 7. In these \u00ae gures, the inputs to the various submodels have been normalized to lie in the interval [ 1.0, 1.0]. By inspecting the submodel\u2019s outputs in this way, it is clear that the last four models have extremely small gains and hence their contribution to the performance of the overall model is limited. These submodels can be pruned from the model without adversely a ecting the model. Manual model re\u00ae nement should be performed at the discretion of the modeller, and is only made possible by the additive model\u2019s structures. The e ects of regularization are clearly illustrated by inspecting the surfaces of the submodels, (\u00ae gure 8). Many of the model nonlinearities have been smoothed to produce near linear submodels, suggesting that these nonlinearities were used to \u00ae t noise and abnormalities found in the sparse training data. This is con\u00ae rmed by the improved performance across the new test set. Here, one of the advantages of neurofuzzy system identi\u00ae cation is demonstrated; from the initial complex nonlinear models, e ectively linear models (bar a few small nonlinearities) which accurately model the nonlinear dynamics of the submarine have been identi\u00ae ed. From this result, it is no surprise that conventional PID control has successfully been used to control this submarine. The reason the nonlinear dynamics of the submarine can be represented by these simple models is largely due to the fast sample rate predetermined by the simulation. The improved modelling capabilities can be further demonstrated by considering multi-step prediction, (\u00ae gure 9). Such multi-step ahead predictions rely on a model of the complete dynamics of the submarine in order to construct a complete 40D regressor each iteration. Therefore, this serves as a good test of the complete AUV model. Table 5. Results of the three model types, across the new test set. RMSEs across new data set Model linear Constructed Regularized Units depth (d(t)) 4.58e-2 3.35e-2 1.98e-4 ft speed (u(t)) 7.62e-4 8.04e-4 5.58e-4 ft/s attack ( a (t)) 4.00e-3 1.62e-3 1.62e-3 degs drift ( b (t)) 2.75e-3 1.77e-3 1.75e-3 degs pitch (\u00b5(t)) 6.47e-3 1.29e-3 1.28e-3 degs yaw ( w (t)) 3.44e-3 2.57e-3 2.28e-3 degs roll ( u (t)) 2.00e-2 1.42e-3 1.42e-3 degs D ow nl oa de d by [ IN A SP - P ak is ta n (P E R I) ] at 0 0: 38 1 9 N ov em be r 20 14 1 0 1 1 0 1 50 0 50 (t-4)q d(t-1) (a) 1 0 1 1 0 1 4 7 a u(t-1) (t-4) (b) 1 0 1 1 0 1 0 4 8 (t-2)q u(t-1) (c) 1 0 1 1 0 1 6.88 6.89 (t-2)b f (t-2) (d) 1.0 0 1.0 4 4.5 5 5.5 q (t-3) (e) 1.0 0 1.0 4 4.5 5 5.5 (t-1)q (f) 1.0 0 1.0 3 r(t-3) x10 2 + 4.268-4 1 (g) 1.0 0 1.0 (t-1)f 16 x10 + 5.155-4 6 (h) 1.0 0 1.0 R(t-3)d 12 x10-5 + 4.1948 3 (h) 1.0 0 1.0 R(t-4)d 2 x10 + 4.1198 0 -4 (j) Figure 7. The surfaces produced from the outputs of the individual submodels of the identi\u00ae ed depth model. D ow nl oa de d by [ IN A SP - P ak is ta n (P E R I) ] at 0 0: 38 1 9 N ov em be r 20 14"
        ]
    },
    {
        "image_filename": "designv11_24_0001484_s1474-6670(17)36653-3-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001484_s1474-6670(17)36653-3-Figure3-1.png",
        "caption": "Fig. 3. Planar view of the four phases of flight for cable tracking problem of an AUV.",
        "texts": [
            " LQG controller showing LQR gain and state estimator where the weighting matrices Q and R are chosen according to Maciejowski (1985) as Once the Kalman gain is evaluated for the desired specifications for all models, the LQR state feedback gains are calculated. An objective function is minimised given by The objective of any guidance law is to steer the AUV so that it intercepts the target in minimum time and maximum accuracy. The guidance law used in this paper utilises AUV speed as a means to formulate the problem. The complete mission is classified into four different phases utilising different guidance laws. These are i) launch phase, ii) midcourse phase, iii) terminal phase, and iv) tracking phase as shown in Figure 3. In the first phase called the launch phase or the boost phase, the vehicle is launched from a vessel and guided in the direction of the line of sight (LOS) with maximum speed, using the LOS guidance only. Once the vehicle approaches the LOS, midcourse guidance could be invoked. In midcourse phase, the vehicle follows the LOS angle with maximum speed using the way point guidance, (Healey and Lienard, 1993). During this part of the flight, changes may be required to bring the vehicle onto the desired course and to make certain that it stays on that course",
            " It should be noted that there is no need for the vehicle to submerge at this stage, as the objective is to approach the target area with maximum accuracy regardless of the orientation of (6) y (7) Vehicle I----1-----,P..,..ition Q = C T C, R '\" 0 I N[T T ]J = - I. x (k)Qx(k) + u (k)Ru(k) 2 k=O 3.3 LQR Design the vehicle with respect to the cable. When the vehicle reaches within the circle of acceptance, the third phase called the terminal phase is invoked. During this phase the vehicle must be slowed down and submerged in order to line up with the cable/pipeline as shown in Figure 3. The circle of acceptance in this case as opposed to Healey and Lienard (1993), should be taken at least the minimum turning radius of the vehicle in order to avoid overshoot. Finally, when the vehicle enters the waypoint, the fourth phase called the tracking phase is called up utilising any existing guidance law with the vehicle speed reduced to its minimum value. For example, the vehicle could use vision based guidance system to follow the cable. If the cable to be followed is an electrical/ communication cable, then magnetometers could be used to detect the radiation from the cable and guide the vehicle in the appropriate direction (Naeem et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000352_20.490252-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000352_20.490252-Figure7-1.png",
        "caption": "Fig. 7. Spindle-mounted \"Jump stop\"",
        "texts": [
            "d VJ U 0 500 1000 1500 2000 0 5 10 15 20 25 30 Tilt angle (degree) Fig. 5. Disk stress vs slider tilt angle 0.001 0.01 0.1 1 Fig. 6. Hertz's critical stress Collision velocity (m/s) based on steel-ball falling tests V. SHOCK RESISTANCE STRUCTURE The condition for no disk damage is that the stress given by equation (2) be less than the critical stress which depends on the material of the substrate. To decrease stress, we tried a \"Jump stop\" that limits the relative velocity and the slider tilt. Figure 7 shows this structure. The stopper spins with the disk, and is placed just above the slider park zone with a clearance of less than 100 pm. This is to avoid mechanical tolerance and vibration-induced disk bending caused by shock acceleration. Slider tilting is restricted by limiting the clearance space. Figure 8 shows the calculation results for various slider / disk collision velocities both with the \"Jump stop\" and without it. When the stopper is used, collision velocity is much lower than without it"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000094_10402009408983279-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000094_10402009408983279-Figure4-1.png",
        "caption": "Fig. 4--Test rig for power loss measurement.",
        "texts": [
            " The power loss is determined as the difference between two large figures of the input and the output power. 2. Calorimetric method measuring the steady state temperature of the transmission. The indirect measurement has to be calibrated to power loss by, for example, electric heating of the oil sump in the gear box to the same temperature. The method is very sensitive to changes in the heat dissipation, and the ambient coriditions must be held constant within very narrow limits. 3. Direct measurement of the power loss in a mechanical power circulating type test rig, shown in Fig. 4, with the highest possible accuracy. The primary disadvantage is the different power loss in the speed increaser compared to the speed reducer. Test Rig and Test Conditions The investigations were made in a back-to-back gear test rig with mechanical power circulation. The system was driven by a variable speed DC motor. The drive motor which had to feed the power loss to the test and the slave gear system was pivoted, and the reaction moment was measured as the force in a load cell at a certain moment arm, as shown in Fig. 4. Recent measurements applied a fixed motor and a torquemeter between the motor drive shaft and the slave gears. The influence of the lubricant on the load-dependent losses is thus defined by the coefficient of friction km, The main influence factors on the coefficient of friction in the D ow nl oa de d by [ N ew Y or k U ni ve rs ity ] at 0 5: 25 0 9 Ja nu ar y 20 15 Influence of Lubricants on Power Loss of Cylindrical Gears 163 gear lype C Fig. >Load and speed distributlon tor test gears C. For most of the investigations, gears type C, case carburized and ground, with balanced sliding at the tooth tip of the pinion and gear were used, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002162_s0022-460x(02)01256-7-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002162_s0022-460x(02)01256-7-Figure1-1.png",
        "caption": "Fig. 1. Universal joint system.",
        "texts": [
            " The mathematical model consists of a set of coupled, linear partial differential equations with time-dependent coefficients. Use of Galerkin\u2019s technique leads to a set of coupled linear differential equations with time-dependent coefficients. Using these differential equations some effects of internal viscous damping on parametric and flutter instability zones are investigated using the monodromy matrix technique. The flutter zones are also obtained on discarding the time-dependent coefficients in the differential equations which leads to an eigenvalue analysis. Shown in Fig. 1 is a shaft BC (length l) driven through a universal joint by a shaft AB which is rotating at a constant angular velocity O about its z-axis. (xyz is an inertial set of axes.) (Note that in this model the dimensions of the joint are neglected.) External viscous damping (taken as being due to the end mount) and internal viscous damping are included. For the case of initial angles between the driving and driven shafts equal to zero,1 the equations of motion for the driven shaft are (in non-dimensional form) X2 @4U @Z4 \u00fe v2 @2U @t2 \u00fe d1v @U @t z\u00bc1 L\u00f0Z 1\u00de \u00fe d3v @U @t \u00fe V \u00fe G1p4\u00f0t\u00de d\u00f0L\u00f0Z\u00de\u00de dZ \u00fe G1 @3V @Z3 \u00bc X3v 2 @4U @Z2 @t2 \u00fe X4v 2 @3V @Z2 @t ; X2 @4V @Z4 \u00fe v2 @2V @t2 \u00fe d2v @V @t z\u00bc1 L\u00f0Z 1\u00de \u00fe d3v @V @t U G1p3\u00f0t\u00de d\u00f0L\u00f0Z\u00de\u00de dZ G1 @3U @Z3 \u00bc X3v 2 @4V @Z2 @t2 X4v 2 @3U @Z2 @t : \u00f01\u00de The equations of motion were developed with respect to the inertial frame xyz; with the z-axis directed along the driven shaft axis and origin at the center of the universal joint (details are given in Ref",
            " G1 \u00bc T0 rAO2 0l 3 ; X2 \u00bc EI rAO2 0l 4 ; X3 \u00bc R2 0 4l2 ; X4 \u00bc 2X3: d1 \u00bc Cx rAO0l ; d2 \u00bc Cy rAO0l ; d3 \u00bc Civ rAO0 : p3\u00f0t\u00de \u00bc 1 2 @U @Z Z\u00bc0 \u00f01\u00fe cos 2t\u00de \u00fe @V @Z Z\u00bc0 sin 2t : p4\u00f0t\u00de \u00bc 1 2 @V @Z Z\u00bc0 \u00f01 cos 2t\u00de \u00fe @U @Z Z\u00bc0 sin 2t : U \u00bc u=l; V \u00bc v=l are dimensionless elastic transverse deformations of the shaft neutral axis measured with respect to xyz and Z \u00bc z=l: L\u00f0Z\u00de \u00bc lD\u00f0z\u00de; where D stands for the Dirac delta function. E denotes Young\u2019s modulus, I the area moment of inertia, r the mass density and A the cross-sectional area. t denotes non-dimensional time \u00f0t \u00bc Ot\u00de: Cx and Cy are damping coefficients associated with the dashpots shown in Fig. 1 (Kx and Ky are springs rates). T0 is the torque applied to the driving shaft AB: Civ is the internal damping coefficient per unit length. Eq. (1) constitute a set of coupled homogeneous partial differential equations with timedependent coefficients. The spatial dependence in the equations is satisfied by using Galerkin\u2019s 1Non-zero initial angles lead to forced motion problems, items that are not of interest in the current work. method. The solutions are assumed to have the form U \u00bc XN i\u00bc1 Fi\u00f0Z\u00deFi\u00f0t\u00de; V \u00bc XN i\u00bc1 Ci\u00f0Z\u00deGi\u00f0t\u00de; \u00f02\u00de where Fi\u00f0Z\u00de and Ci\u00f0Z\u00de are Galerkin comparison functions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000589_bf02467567-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000589_bf02467567-Figure1-1.png",
        "caption": "Figure 1 Detector cell: 1, reference electrode; 2, glass holder; 3, adapter; 4, perspex holders; 5, screws; 6, O-rings; 7, PTFE-tubings; 8, electric cable; 9, conducting epoxy cylinder; 10, channel; 11, PVC-matrix membrane; 12, perspex cylinder body.",
        "texts": [
            " The THF-sensing membrane mix consisted of 4 weight % tetradodecylammonium bromide (TDDA-Br), 66 weight % dibutylphtalate (DBP), 28 weight % polyvinylchloride (PVC), 2 weight % potassium-tetrakischlorophenylborate (KTCIPB) and tetrahydrofuran (THF). The epoxy resin mixture used to bind the graphite in preparing the internal conducting support of the electrode was made from Araldite 2005 (Ciba-Geigy). The powdered graphite was mixed with the epoxy resin in a ratio 1:1. The detector cell consisted of a flowthrough tubular PVC matrix membrane electrode and a reference electrode as is shown in Figure 1. When not in use the tubular electrode was kept dry after washing with deionized water. It was reconditioned with primary ion solution before use. The calibration curve of the detector was obtained by a constant volume dilution method as previously described [23]. All standard solutions of anions and eluent were prepared from their analytical reagent grade sodium or potassium salts in deionized water, then diluted to the desired concentrations. The identification of species was performed by comparing retention times of peaks with those of standards"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002009_28.855960-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002009_28.855960-Figure3-1.png",
        "caption": "Fig. 3. Structure of the rotor.",
        "texts": [
            " 2(b) with the rotor in the same position, the magnetic flux of the stator winding and rotor are at right angles to each other; this is the -axis position. The fourth step is to perform the dc decay test in the -axis position and obtain the -axis impedance relating to each frequency using (1) in the same way as for the -axis position. The - and -axes operational impedances (per phase) at motor startup are calculated from (2) and (3) where is the slip , and is the angular frequency of the power source (rad/s), respectively. B. Equivalent Circuit Constants Fig. 3 shows the rotor structure of the tested PM motor. Because the damper winding has a double-squirrel-cage structure, the - and -axes equivalent circuits of the tested PM motor at standstill are expressed as Figs. 4 and 5, respectively. Here, and are the leakage inductances caused by leakage fluxes interlinked with only the upper winding, and those by leakage fluxes interlinked with only the lower winding, and and are by leakage fluxes interlinked with both upper and lower windings. The - and -axes operational impedances and , calculated by (2) and (3), correspond to values obtained by dividing the impedances between the a\u201d and b\u201d terminals of Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003560_physreve.74.032801-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003560_physreve.74.032801-Figure3-1.png",
        "caption": "FIG. 3. Series of helical ribbons with the parameter =13\u00b0, 40\u00b0, and 50\u00b0.",
        "texts": [
            " This time the pitch angle is = arctan 1/ 2 + 1 + 2 \u2212 4 C/A 1/2 , 15 where the parameter = 0 / . In Fig. 2 we present plots of the pitch angle as a function of the ratio C /A for fixed values of . We see that the pitch angle decreases as the ratio C /A increases when is greater than 1. The actual torsion is larger than the spontaneous torsion in this case. On the contrary, the pitch angle increases as the ratio C /A increases for less than 1. In that case, the actual torsion is smaller than the spontaneous torsion. Figure 3 gives the change of helical ribbons from low pitch to high pitch. Each structure is characterized by the pitch angle . For three values of the pitch angle =13\u00b0, 40\u00b0, and 50\u00b0, we find, respectively, C /A=1.85, 0.23, and 0.5 in this analysis we have: =3 for =13, and =0.3 for =40\u00b0 and 50\u00b0 . These results show that the conformation of the helical ribbons varies with the elastic properties of the ribbons. In particular, in elastic models of DNA, the torsional rigidity C is commonly assumed to exceed the bending rigidity A 26 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000803_s0924-0136(00)00614-2-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000803_s0924-0136(00)00614-2-Figure2-1.png",
        "caption": "Fig. 2. An example of FE simulation of buckling of the billet.",
        "texts": [
            " Veri\u00aeed FE models were used to simulate the development of \u00afow-dependent defects; this was conducted with consideration of the variation of several prevailing process parameters \u00d0 friction at the billet/anvil interface, the unsupported length of the billet, the homogeneity of work-material property, the constraint to the billet. Several work-materials (aluminium and steel) were simulated, the simulation being enabled using several simulation procedures developed in the research, such as the simulation of the * Corresponding author. 0924-0136/00/$ \u00b1 see front matter # 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 0 ) 0 0 6 1 4 - 2 buckling of billet and the folding of the free surface of the material. An example of the simulation of buckling of billet is shown in Fig. 2. Simulation of tool loading and unloading was also conducted in which work-material and tool elasticity was considered. Several types of \u00afow-dependent defects occurred during injection forging of solid billets, these being classi\u00aeed using the approach depicted in Fig. 3, each type of the defects referring to a mechanism of initiation of the defects. The development of fracture in the work-material issuing from the injection chamber is one of major defects occurring during the injection forging of \u00afanged or branched components"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000476_s0045-7949(99)00201-1-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000476_s0045-7949(99)00201-1-Figure5-1.png",
        "caption": "Fig. 5. Curved cantilever sti ened plate subjected to a vertical point load at one corner: (a) geometry and material properties; and (b) \u00aenite element discretization.",
        "texts": [
            " These sti ness terms are de\u00aened such that the equilibrium is not disturbed in the global coordinates, as numerically veri\u00aeed by Zienkiewicz [34]. The performance of the shell element was veri\u00aeed with numerous examples concerning small and large de\u00afection analyses of composite plates and shells in earlier papers by Tessler and Hughes [31], Tessler [30], and Barut et al. [3]. The capability of the sti ened shell element is demonstrated by considering a curved cantilever sti ened plate with \u00aeve equally spaced stiffeners that is subjected to a vertical point load as shown in Fig. 5(a). The inner and outer radii of the curved (circular) plate are 4.5 and 5.5 m, respectively. The plate and the sti eners are both isotropic, with Young's modulus 2.07 1011 kN/m2 and Poisson's ratio 0.3. While one end of the plate is clamped, the other end is subjected to a vertical point load at the inner corner (see Fig. 5(a)). As depicted in Fig. 5(b), four di erent \u00aenite element discretizations, of orders (1 30), (2 20), (4 30), and (5 30), are considered in the analysis. This pro- blem was also considered by Jiang and Chernuka [9]. In their study, they presented a degenerated isoparametric sti ened shell element with eight nodes. The results obtained from the present analysis and those reported by Jiang and Chernuka [9] are shown in Fig. 6. The results converge monotonically as the grid size is increased. The comparison of the results between the present \u00aenite element model and those reported by Jiang and Chernuka [9] using a \u00aenite element mesh with a grid order of (2 16) is in close proximity for all grid sizes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001202_1.550462-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001202_1.550462-Figure1-1.png",
        "caption": "FIG. 1. Schematic diagram of the falling-ball experimental arrangement in the NMR imaging probe. Also shown are the approximate locations of the imaging volumes. 1: Falling ball. 2: rf coil (height=23 mm), 3: rf shield. 4: Gradient coils. 5: 15-mm glass tube for rf coil support. 6: Glass sample tube (o.d.= 10 rnm, Ld.=9 mm). 7: XY image slice. 8: Z profile volume. The X and Z laboratory coordinate axes are shown. In this view, the Yaxis points into the figure, away from the viewer. The bottom view shows the orientation of the Y axis and the location in the XY plane of the Z profile volume. This entire apparatus is placed inside a solenoidal NMR magnet during imaging, Note that dimensions in this figure are approximate and the various features are not on a common scale.",
        "texts": [],
        "surrounding_texts": [
            "Figure I is a depiction of the experiment showing the arrangement of the suspension-containing tube in the NMRI probe. The approximate locations of the imaging volumes are shown as shaded regions in Fig. I. Two types of images were collected: transverse (XY) 2D images defined by a thin layer (slice) perpendicular to the tube axis and located at the center of the radio-frequency (rf) coil along Z, and 1 D profiles of a rectangular volume parallel to the tube axis (Z) and approximately centered on the ball. The rate of data acquisition in both cases was fast compared to the ball motion so that each data set gives a \"snapshot\" view of the suspension. With the imaging parameters used, protons in the solid beads do not give a mea surable image signal. Therefore, pixel intensity is directly related to the volume of liquid within the corresponding volume element of the image slice (or profile) and is reduced from that of pure fluid only by the occluding volume of the particles. The XY images give information on the evolution of the local particle concentration as the ball falls through the image slice. The Z density profiles give information on the micro structure evolution in the direction of the ball's descent and can be used to determine the ball's Z position (and hence Z velocity) during its transit through the rf coil. In both cases the pixel resolution in the direction of the image is finer than the dimensions of the suspended particles so that individual particles are resolved. All lH MNRI measurements were performed at 4.7 T (200 MHz) on a Bruker MSL spectrometer equipped with a super wide-bore superconducting magnet and an imaging accessory. For transverse images (XY), slice selection was achieved with a 250 us, Gaussian-shaped rf pulse and a Z gradient of sufficient magnitude to excite magnetization in a 0.5 mm thick slice perpendicular to the tube axis. The XY images were collected via a gradient echo method (Haase et al., 1986) which was optimized to allow rapid acquisition. The time period between the middle of the Gaussian pulse and the top of the gradient echo (NMR signal) was 3.6 ms. Each scan for a 128X 128 Redistribution subject to SOR license or copyright; see http://scitation.aip.org/content/sor/journal/jor2/info/about. Downloaded to IP: 68.199.200.70 On: Mon, 28 Apr 2014 05:01:48 4 CHOW, SINTON, AND IWAMIYA image with X, Y resolution of 98 /Lm required - 2 s, and 8 scans were averaged together for signal-to-noise improvement. Thus, each averaged image took a total of 16 s to acquire. During this acquisition time, the ball fell less than 70 /Lm in all cases and even less in most runs, based on the NMR-derived velocities (see below). The obser vation point (Z slice position) was 25 to 35 mm above the bottom of the sample tube, and at the start of the imaging experiments the ball was 30 to 50 mm above the observation point. The Z profiles were formed by selecting a volume in the sample tube defined by the intersection of three orthogonal slices and collecting a spectrum (a one-dimensional profile) of this volume in the presence of a Z gradient. The Z distance scale was determined by calibration of the Z magnetic field gradient with images of objects of known size. The Z resolution of all profiles is 220 /Lmper point. The amplitude of each point is proportional to the total hydrogen density (i.e., the amount of fluid) in the XY Redistribution subject to SOR license or copyright; see http://scitation.aip.org/content/sor/journal/jor2/info/about. Downloaded to IP: 68.199.200.70 On: Mon, 28 Apr 2014 05:01:48 SUSPENSION MICROSTRUCTURE 5 plane of the intersecting volume at the corresponding Z position. Each Z profile is an average of 24 acquisitions which required 24 s to accumulate. Volume selection for the Z profiles was accomplished with three consecutive rf pulses and corresponding gradient pulses in the three directions. The Z slice was 17.6 mm thick and was prepared using a I ms \"sine\"-shaped rf pulse with 12cycles and the appropriate Z gradient pulse. The sine-shaped rf pulse was defined by the function pulse amplitude= B1 sin(2mrtltp)/(2mrtltp ) , where tp is the pulse duration, t ranges in the interval -(tpl2)<,t<,(tpl2), n=12, and B1 is the maximum rffield amplitude. X and Y slices were prepared similarly except that the pulse shape contained 3 cycles (n = 3). The thickness of these slices was either 2 or 4 mm, the choice being dictated by a tradeoff between signal-to-noise ratio and the desire to maximize the dip in the profile formed by the ball. The best profiles for locating the Z position of the ball were obtained when the long axis of this volume coincided with the center of the ball. This match was made by moving the centroid of the volume in the XY plane via adjustments in the X and Y slice positions. The two bigger balls (l/8 and 3/16 in.) each fell close to the center of the tube and adequate Z profiles were obtained with the selected volume centered on the tube axis. The 1116 in. ball fell off center and was only captured in the Z profiles after its position in the XY plane was determined from the transverse images. In this case, even with a narrow slice, the dip in the profile from the ball was more difficult to discern and only a few velocity data points could be determined. The Z position of the ball was extracted from the Z profiles by determining the displacement of the ball from a reference location in the Z profile. We found that this was most easily done by comparing each Z profile to a reference profile and shifting them to match the dips in amplitude caused by the ball. We estimate that this method determines the relative position of the intensity dip reliably to within one point (i.e., \u00b1220 !Lm). It might be possible to reduce the Z position error by interpolating points into the Z profiles as a way of artificially increasing the Z resolution. We did not do this because, as we show below, the stated Z resolution is adequate for our purposes. The sensitivity of the Z profiles to proton density is not constant along Z because of inhomogeneities in the rf fields, inhomogeneities in the coil receptivity, and imper fections in the slice selection method. These effects can be corrected for by weighting the profile point by point with data from a profile of the pure fluid taken under identical conditions (Assink et al., 1988). This correction has been applied to all profiles shown in this paper."
        ]
    },
    {
        "image_filename": "designv11_24_0003162_iros.2005.1545603-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003162_iros.2005.1545603-Figure5-1.png",
        "caption": "Fig. 5. The four possible sections. (a) For a straight line compliant section, we need to find a push plan in which the pusher is at one of the illustrated positions. (b) For a circular compliant section the push range rotates as O advances on its section. (c) For a noncompliant section of O, there is only 1 push position. (d) If the pusher is outside the push range at the start of a section, a contact transit is necessary.",
        "texts": [
            " In the rest of this paper we shall denote this union boundary of the Minkowski sum by the union boundary. Since the Minkowski sums of each pair of line segments are pseudodisks and the obstacles together form a collection of pseudodisks, the complexity of the union boundary is O(n) (see [6]). In order solve the problem stated in Section II-B, we need to create a push plan for P such that P avoids the obstacles. Without loss of generality, we divide the problem into four subproblems all representing one type of section. All 4 cases are illustrated in Fig. 5. \u2022 creating a push plan for straight-line compliant sections \u2022 creating a push plan for circular compliant sections \u2022 creating a push plan for noncompliant sections \u2022 finding a contact transit to reach VPR(\u03c4(is)) at the start of section i \u2208 I . A. Straight line compliant sections For a straight line compliant path segment i \u2208 I on the domain s \u2208 [is, ie], the corresponding push plan may consist of multiple push plan sections because P may need to avoid obstacles. We call a push plan monotonically descending when \u03c3(s) only moves in the direction of PRb(\u03c4(s)) while pushing O along the section"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002150_tia.1985.349572-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002150_tia.1985.349572-Figure2-1.png",
        "caption": "Fig. 2. (a) Conduction mode. (b) Commutation modes.",
        "texts": [
            " As a consequence, a complete steady-state solution can be obtained by analysis of any interval that is 600 in length. The 600 interval chosen for this analysis begins when thyristor T5 turns off, and ends when thyristor T6 turns off. 0093-9994/85/0700-1016$01.00 \u00a9 1985 IEEE COLBY et al.: LCI FED SYNCHRONOUS MOTOR DRIVES IN STEADY STATE This interval comprises two modes of operation, which will be denoted the conduction and commutation modes. During the conduction mode, thyristors TI and T6 are on, and the dc link current flows from phase a to phase b, as seen in Fig. 2. The commutation mode begins when thyristor T2 is gated on. A short circuit is established between phases b and c, and a circulating current ik flows from phase c to b, eventually turning off phase b. At the start of the commutation interval the rotor angle is defined to be 0= -'Yo, (1) and the duration of the commutation interval is given by the commutation overlap angle it, in electrical degrees. The firing angle yo is equivalent to the internal power factor angle neglecting overlap, i.e., it is the angle between the fundamental component of current, neglecting overlap, and the internal voltage of the synchronous machine"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003956_tia.2005.863899-Figure17-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003956_tia.2005.863899-Figure17-1.png",
        "caption": "Fig. 17. Flux distribution of synchRel under the no-load condition (without flux barriers).",
        "texts": [
            " The readings near the no-load condition have been considered in order to minimize the effect of flux barriers, as the effect of flux barriers was not modeled initially. This can be explained using stator voltages and currents under no-load (VtnL and IanL, respectively) and full-load (VtfL and IafL, respectively) conditions are shown in Fig. 6. For a synchronous machine under the no-load condition, \u03b4nL is low. With the polarized section of the rotor lying almost right below the poles of the rotating magnetic field, the influence of flux barriers is minimal (compare Fig. 17 with Fig. 18). In the case of the synchRel, the sample calculations of case 1) k = 2 and m = 1 are given as follows: L0 and L2 can be obtained by considering fundamental space harmonic. Using (15) and (16) Ld =Ll + 1.5[L0 + L2] Lq =Ll + 1.5[L0 \u2212 L2] (17) where L0 = 2\u03c0\u00b5orlaog(a2 1s/2) and L2 = 2\u03c0\u00b5orla2g(a2 1s/4). Substituting the values of various quantities in (17), we have[ 0.2158 0.0188 0.0779 0.1566 ] [ D Q ] = [ 342.4 172.5 ] . (18) Solving (18), we have d = 1 D = 0.6418 mm q = 1 Q = 3.0724 mm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001539_rob.10079-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001539_rob.10079-Figure2-1.png",
        "caption": "Figure 2. A 4-DOF Stanford-type manipulator.",
        "texts": [
            " (7) assumes the form x y z vx vy s23 0 0 0 s4 c23 0 0 0 c4 0 1 1 1 0 d2c23 a2s3 0 0 0 d2s23 a2c3 0 a3 0 q\u03071 q\u03072 q\u03073 q\u03074 q\u03075 . (38) The determinant of the Jacobian matrix is det J1 a2a3s3 s23c4 c23s4 . (39) Letting det(J1) 0 results in two singular conditions: a sin 3 0, b sin( 2 3 4) 0. Condition (a) corresponds to the boundary singularity where the joint screw system loses its full rank and condition (b) corresponds to the case when s234 0 for which vz cannot be chosen as a dependent variable. Figure 2 shows a Stanford-type 4-DOF manipulator composed of three revolute joints and one prismatic pair. The coordinate frames assigned to each link of the manipulator are shown in Figure 2, and the corresponding D-H parameters are listed in Table II. The analysis procedure is similar to that presented in the preceding section. The base frame o0 x0 y0 z0 is selected as the reference frame. The Jacobian matrix J for this 4-DOF manipulator is a 6 4 matrix, 0J 0 s1 0 c1s2 0 c1 0 s1s2 1 0 0 c2 0 d1c1 c1s2 d2c1c2 d1s1s2 0 d1s1 s1s2 d2s1c2 d1c1s2 0 0 c2 d2s2 . (40) There are two reciprocal screws for a four-system. Applying Eq. (25), we obtain two reciprocal screws: $r1 s2c2 c1 , 0, s2 2, d2c1 , d2s1c1 d1s2c2 c1 , 0 T , (41) $r2 s1 c1 0 d1c1 d1s1 0 T",
            " (47). Then, the joint angles and displacements are calculated by multiplying the joint velocities by a small time increment, and the coordinates of the end-effector tracking point are obtained by computing the direct kinematics of the manipulator. The simulation process is illustrated using the follow chart shown in Figure 3. Figure 4 shows the simulated manipulator configurations corresponding to the given trajectory. In Figure 4, z1 , z2 , z3 , and z4 correspond to the joint axes as shown in Figure 2. Figures 5(a) and 5(b) illustrate the joint angular velocities and joint linear velocity versus the tracking time. Figures 6(a) and 6(b) give the joint angles and joint linear displacement versus time. Figure 7 compares the velocity of the tracking point given by Eq. (49) and the velocity computed by using Eq. (47). It can be seen that the velocity generated by the path tracking algorithm matches exactly with that of the desired velocity profile, unlike the generalizedinverse method which will generally produce some errors between the two"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001455_50006-1-Figure5.34-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001455_50006-1-Figure5.34-1.png",
        "caption": "FIGURE 5.34 Linear actuator with shorted turn.",
        "texts": [
            "239) are solved subject to initial conditions i(0)= i0, x(0)= x 0, and u(0) = dx( t ) /d t ] t= o - u o. The coupled equations (5.239) can be rewritten as a first-order system and solved numerically using techniques such as the Euler or the Runge-Kutta method (Appendix C). Rapid parametric simulations are possible once drive voltage Vs(t ) and resistance R are specified. The response time of a linear actuator is limited by the time constant of the coil rcoil = L/Rcoi l . However, the response time can be reduced by putting a conductive sleeve around a segment of the stator as shown in Fig. 5.34. The sleeve is referred to as a shorted turn [18]. Consider an equivalent magnetic circuit for the coil-stator-sleeve system (Fig. 5.35). This is basically a transformer with the drive coil as the primary, and the shorted turn as the secondary. The electrical equations for this system 5.12 LINEAR ACTUATORS 419 are V(t) =/coilRcoil -1- L c o i l - - dicou dis, + M dt dt dist 0 = istRs, + L~, ~ + M - d/coil dt ' (5.241) where Rcoil and Lcoil are the resistance and self-inductance of the coil, R~, and Ls, are the resistance and self-inductance of the shorted turn, and M is the mutua l inductance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001359_s0020-7683(99)00190-0-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001359_s0020-7683(99)00190-0-Figure4-1.png",
        "caption": "Fig. 4. Material con\u00aeguration ` B of layer `): lateral surface ` S:",
        "texts": [
            " Ebciog\u00c6lu / International Journal of Solids and Structures 37 (2000) 6705\u00b16737 6709 s` HM h\u00ff s s` Z\u00ff s` h\u00ff , \u00ff s s` Z s` h i R, 7 and HM [ `2N ` H the domain in the thickness direction of the whole multilayer shell. Since the projection of all material centroidal surfaces ` A, 8` 2N, onto the plane fx1, x2g is denoted by A R2, the material domain of layer (`), denoted by ` B, and the material con\u00aeguration B can be expressed by ` B A ` H, B A H [ `2N ` B: 8 Further, we de\u00aene ` SM@A ` H 9 to be the material lateral surface of layer `), where @A is the boundary of A; see Fig. 4. Then S [ `2N ` S 10 is the (material) lateral surface of B: It follows from Eqs. (8) and (9) that the outward normal ` n ` naEa to the material lateral boundary surface ` S, which is de\u00aened in Eq. (9), is such that ` n 0 n, 8` 2Nnf0g: 11 That is, the outward normals to the material lateral boundary surfaces ` S are the same for all layers. In other words, the surfaces ` S are all parallel to each other, and orthogonal to the material centroidal surface A 0 A (see Figs. 3 and 4). Let the initial con\u00aeguration of the multilayer shell be denoted by B0 R3, and the current (spatial) con\u00aeguration denoted by Bt R3 (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000041_1.1392031-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000041_1.1392031-Figure6-1.png",
        "caption": "Figure 6. Scale drawing of a graphite slice. (a) general view and (b) hole arrangement.",
        "texts": [
            " (iv) The multisectioned porous electrode itself (D), consisting of the ten porous graphite slices. Each current feeder is connected to an independent current generator, and the current applied to each section can be set automatically. The potential differences between each working\u2013electrode slice and the counter electrode, as well as the potential differences between the reference electrodes and the counter electrode, are recorded continuously with a computerized data-acquisition system (Testpoint\u00ae on a Pentium\u00ae 75 processor). Porous graphite slices.\u2014Figure 6 illustrates one of the ten graphite slices which constitute the porous sectioned electrode. Graphite slices of 5 mm thickness are cut from a cylindrical bar of graphite (Ref. 34/95) supplied by Le Carbone Lorraine (Pont\u2013\u00e0\u2013Mousson, France). The central position of each graphite slice is subsequently perforated by a numerically controlled drilling system with 1014 holes of 0.8 mm diam according to the arrangement shown in Fig. 6b. The obtained apparent porosity is then 0.3, and the cross\u2013sectional surface area for electrolyte solution flow is 5.1 3 1024 m2. Two Journal of The Electrochemical Society, 146 (8) 2933-2939 (1999) 2935 S0013-4651(98)08-021-5 CCC: $7.00 \u00a9 The Electrochemical Society, Inc. 3 mm diam holes are positioned near the perimeter of each slice for alignment when mounting the cell. Insulation of the graphite slices from each other is achieved by intercalating thin porous Teflon mesh between consecutive slices"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003458_robot.2006.1641982-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003458_robot.2006.1641982-Figure2-1.png",
        "caption": "Fig. 2. Plu\u0308cker motion basis (a), and example (b)",
        "texts": [
            " To establish the relationship between v\u0302 and its coordinates, we define the following basis on M6: DO = {dOx, dOy, dOz , dx, dy, dz} \u2282 M6 , (5) 1Coordinate vectors are underlined to distinguish them from the vectors they represent. 2Spatial vectors other than basis vectors are marked with a hat. Basis vectors are left unmarked. in which dOx, dOy and dOz are unit rotations about the directed lines Ox, Oy and Oz (which pass through O in the x, y and z directions, respectively), and dx, dy and dz are unit translations in the x, y and z directions (see Figure 2(a)). Thus, if the body were rotating about Ox with an angular velocity of magnitude \u03b1, then its spatial velocity would be \u03b1 dOx. Likewise, if the body were translating with a linear velocity of vO, then its spatial velocity would be vOx dx + vOy dy + vOz dz . Note the difference between this expression and the one in (4): the former is a spatial vector (i.e., an element of M6), and the latter a Euclidean vector (an element of E3). A third example is shown in Figure 2(b). This example shows a rotation of magnitude \u03b1 about an axis that is parallel to the z axis and passes through the point (0, r, 0). This motion is represented by the spatial vector \u03b1dOz +r\u03b1dx. Observe that the translational component equals the velocity of a particle at the origin that is rotating about (0, r, 0) with an angular velocity of \u03b1. It can be seen, by inspection, that the spatial vector v\u0302 = \u03c9x dOx + \u03c9y dOy + \u03c9z dOz + vOx dx + vOy dy + vOz dz (6) represents the same rigid-body velocity as that described by the two vectors \u03c9 and vO above"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002583_cdc.2003.1273083-FigureI-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002583_cdc.2003.1273083-FigureI-1.png",
        "caption": "Fig. I . Swileh position based A-modulator",
        "texts": [],
        "surrounding_texts": [
            "by means of a A-C-modulator. as previously discussed, 1 2 U = - ( l + s i g n ( z ) ) ; t = e = u a y - u\n= a + (; - b) (Y), + (1 - M y -B)\n+ko l(d0) -\n(d. = - p - f (I&) - 4 d g (4.14)\nUnder ideal sliding conditions on the sliding surface, z = 0, the corresponding dynamics is precisely represented by the condition U = uou. The stability analysis canied out for the closed loop behavior of the average system under a GPI controller thus becomes valid. The sliding mode controller results in the origin of the tracking error, y - B, to be an exponentially asymptotically stable equilibrium point for all motions that do not saturate the control input u..(t) beyond the interval [0,1].\nFigure 6 shows computer simulations depicting the closed loop response of the system to the actions of the GPI controller implemented through a A-C-modulator. The controller design parameters and the system parameters were chosen to be exactly the same as those used in the previous simulation of the average GPI feedback controlled responses.\nIn order to test the robustness of the A-C-modulator implementation of the proposed average GPI controller, we tested the system with an unmatched sudden constant perturbation, denoted by q l ( t - r), appearing at time r = 0.004 [SI of value 7 = 0.6667 [A]. i.e. we used the model:\n1 0\nV. CONCLUSIONS\nAverage feedhack controller designs usually represent the desirable equivalenr conrrol in sliding mode control implementations. The exact synthesis of the equivalent control is not physically possible in systems commanded by switches, and sign non-linearities, such as in traditional, and double bridge, LZ-to-DC power converters. Knowledge of the feedhack law defining the equivalent control leads to consider a linear partial differential equation, for the sliding surface, stating that the closed loop vector field should be orthogonal to the sliding surface gradient. However, it is still not obvious how to synthesize a sliding surface, that corresponds to a given equivalent control, due to the indeterminacy, and\narbitrariness, of the boundary conditions in the defining linear partial differential equation that needs to be solved.\nIn this article, we have demonstrated that the use of classical A-modulators, and the closely associated A-% modulators, can solve the sliding mode implementation problem of average feedback controllers in a rather efficient manner. The proposed approach retains, in an average sense, the desirable features of the designed average feedback controller. When the proposed controllers are synthesized using only inputs and outputs, as in GPI control, the explicit asymptotic estimation of the state becomes unnecessary and, moreover, the inarchirig conditions, intimately related to the state space representation of the system, are no longer needed.\nWe have used a A - C-modulator implementation of a sliding mode controller for a given average GPI continuous controller in a \u201cbuck\u201d DC-to-DC power converter. Other nonlinear switched controlled systems may immediately benefit form the sliding mode feedhack controller design framework based on A - C-modulators and nonlinear feedback controllers arising from current nonlinear systems theory (for instance, geometric, differential algebraic, flatness, passivity, energy methods, H,, etc.). For DC-to-DC power converters, in particular, average passivity based controllers, such as those developed in 141 may he readily implemented via sliding mode controllers in a direct fashion.\nACKNOWLEDGMENT Research supported by Conacyt-MCxico Grant 4223 I-Y.\nVI. REFERENCES\n[ I ] C. Edwards and S. K. Spurgeon, Sliding Mode Conrml, Talylor and Francis, London, 1998. [2] M. Fliess, R. Marquez, and E. Delaleau, \u201c State Feedbacks without Asymptotic Observers and Generalized PID regulators\u2019\u2019 Nonliriear Conrml in rhe Year 2000, A. Isidori, F. Lamnabhi-Lagarrigue. W. Respondek, Lecture Notes in Control and Information Sciences, Springer, London 2000. [3] W. Permqueni and J. P. Barbot, Sliding mode conrml in Engineering Marcel Dekker Inc., New York, 2002. 141 H. Sira-Ramirez, R. Ortega, R. PCrez-Moreno and M. Garcia-Esteban, \u201cPassivity-Based Controllers for the Stabilization of DC-twDC Power Converters:\u2019 Auromatica, Vol. 33, No. 4, pp. 499-513, 1597. IS] H. Sira-Ramfrez, \u201cSliding modes, A-modulators, and Generalized Proportional Integral Control of linear systems\u201d Asian Jourrial of Cfinrrol, Special Issue on Variable Structure Systems (to appear). [61 R. Steele, Delra Modulurion Sysfems, Pentech Press, London, 1975. 171 V.I. Utkin, Sliding modes and rheir applicurions in Variable Srructure Systems, MU Publishers, Moscow, 1978.",
            "L 1\n...............\n. . . . . . . . . . .... .. Fig. 7. a GPI swhilizing conuoller acting on a 'buck\" convener undergoing an unmatched stcp penurbaion input Rohustness of a Sliding mode-A modulator implcmenlation of - uep = E"
        ]
    },
    {
        "image_filename": "designv11_24_0001020_analsci.8.553-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001020_analsci.8.553-Figure8-1.png",
        "caption": "Fig. 8 K+ measurements of sera in the pathological concentration range (2.5 - 7.6 mM K+) (see also Fig. 4).",
        "texts": [
            "6 mM K+,115 -161 mM Nat, respectively) the K+ measurements are in very good agreement with the theoretical value (3.15 mM found plasticizer and PVC as the matrix. The diffusion barrier as presented in Fig. 2 was employed. The y-axis shows the activities a1(s) of the potassium reference solution values (of the following concentrations: 2.75, 3.25, 4.25, 5 and 5.75 mM K+, respectively), the x-axis indicates the expression 10EMFx/s. 10EMFx/ s. 558 ANALYTICAL SCIENCES AUGUST 1992, VOL. 8 compared to 3.13 mM expected, see Fig. 8). The Na+ values are still 3% too high, compared to the theoretical value (108 mM measured compared to 104.5 mM expected, see 4 mM. Deviations of the measured a;(r), ANALYTICAL SCIENCES AUGUST 1992, VOL. 8 theoretical values, are only found when measuring serum samples, not aqueous solutions. They may therefore be explained by uncertainties in the calibration of FAES, by uncertainties in the protein/ lipid volume effect of 7%, by unusual liquid junction potentials of the reference electrodes in contact with serum samples or by uncertainties due to the Debye-HUckel formalism, which perfectly describes aqueous systems, but not necessarily serum samples"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000159_0165-0114(94)90214-3-Figure11-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000159_0165-0114(94)90214-3-Figure11-1.png",
        "caption": "Fig. 11. (e, ~ ) - ( d , sp)-Transformation in the two dimensional phase space.",
        "texts": [
            " (R2) lUNI should increase as the distance grows between the actual state and the switching line. (R3) ]UNI should increase as the distance grows between the actual state and the line perpendicular to the switching line, for the following reasons: -discontinuities at the boundaries of the phase plane can be avoided, - the central domain of the phase plane can be arrived at very quickly. (R4) Normalized states es, eN that fall out of the phase plane should be covered by the maximum values [UNJmax with the respective signs of UN. From these design rules an important transformation (see Figure 11) follows. Now, both the distance Sp of eN from the sliding surface and the distance d from the direction of the normal vector of the sliding surface are evaluated by fuzzy rules. Then, for the fuzzy part of the controller the ith rule of a set of rules can be stated as if Sp = Sp, and d = di then u = ui (2) with linguistic terms like Positive Small, Negative Big, etc. for the Sp,, eli and ui. This method can be extended with respect to FCs of higher order: According to rule (R3) for the 2-dimensional case let (1, (n 1 I)2N, (n ~ 1)22, \u2022 \u2022 \u2022, 2~4-1) T nN = I(1, (~ ~- ')N, (~ ~ 1)22 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003118_3-540-31761-9_37-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003118_3-540-31761-9_37-Figure1-1.png",
        "caption": "Fig. 1. (a) Non-dimensional normal load vs. non-dimensional normal approach diagram. The thick line represents the range of correction solutions. (b) Nondimensional tangential load vs. displacement diagram. The thick line represents the general load cycle, the dot line curve is the largest load cycle for a given normal load.",
        "texts": [
            " When rough surfaces are considered, difficulties arise because the stick region is not easily quantifiable, contrarily to problems involving profiles described by closed-form expressions. In this case, it can be useful to introduce the following non-dimensional formulation, in order to generalize the original Mindlin and Deresiewicz procedure. First the normal load P is applied, and, if the elastic solids are similar, no slips occur on the onset of contact. The load-displacement curve is, as well-known, non linear. Figure 1 shows this general relationship where the load is normalized with respect to the maximum achieved load P0, whereas the normal approach \u03b4z is normalized analogously, with respect to the maximum \u03b4z0. For our purpose, this curve can be either calculated by applying the code ICARUS, or obtained experimentally. Subsequently, the tangential load Q is increased monotonously. We assume that the load is increased up to the value Q lower than or equal to the maximum admissible load (i.e. Q0 = fP0 ). Thanks to the Cattaneo analogy [9, 11], it is straightforward to obtain the following nondimensional parametric expression:    \u03b4ILx \u03b4x0 = 1\u2212 \u03b4\u2217 z \u03b4z0 , 0 \u2264 \u03b4ILx \u2264 \u03b4x, QIL Q0 = 1\u2212 P\u2217 P0 , 0 \u2264 QIL \u2264 Q, (1) where the superscript (IL) refers to an incomplete loading (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003996_tase.2005.846289-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003996_tase.2005.846289-Figure1-1.png",
        "caption": "Fig. 1. Cusp height and cusp triangle.",
        "texts": [
            " Although the multidirection slicing has been mentioned in [21]\u2013[23], our method is to use the proposed multidirection deposition [24] to reduce staircase errors and supports needed. In this paper, a volumetric error is employed to quantify the slicing error, and a method based on two slicing directions is used to reduce the slicing error. 1) Cusp Height: The layered process error is typically represented by the cusp height , which is defined as the maximum distance between the sliced layers and the desired surface measured along the direction of the surface normal. As shown in Fig. 1, is the angle between the surface normal and the build direction, and the layer thickness is approximately given by (1) It can be seen from (1) that, when is nearly to 90 , can be quite large, and is also limited by the maximum allowable thickness of the LM system. 2) Sectional Error: Sectional error caused by the slicing can be approximated by the area of (as shown in Fig. 1), which is called cusp triangle , i.e., (2) 3) Volumetric Error: Since the model in consideration is the faceted model, the cusp triangle formed by slicing in one facet is constant along the cross-sectional contour. Thus, the volumetric error is proportional to the sectional error and (2) is thus used to represent the relationship between the volumetric error and the cusp height. From this equation, it is obvious that, if a uniform cusp height criterion is applied to a part, the resultant volumetric error could be different in the regions of different value"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000835_9.256382-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000835_9.256382-Figure2-1.png",
        "caption": "Fig. 2",
        "texts": [
            " Although the H region considered above is a half plane only, the results obtained could be used to analyze the robust eigenvalue assignment in a stable region R , which is the common region of some half-plane H regions. This is illustrated in the following example. It is noted that the nominal system matrix A should be a stable matrix for getting a robust stable eigenvalue assignment. 111. ILLUSTRATIVE EXAMPLE In this section, an example is provided to illustrate the pro- Example: Consider the complex plane as shown in Fig. 2 with posed method of robust eigenvalue assignment analysis. some data given below line cy 0 tan 0 L1 - 1.5 0\" 0 L2 0 45\" 1 L3 0 315\" - 1 and the nominal system matrix A is given by A = [ 1 - 5 1 1 . -6 1/2 1/3 0 1/2 -4 The eigenvalues of A are found to be h ( A ) { -3.458, -5.0837, -6.3705). Trivial calculation yields q 1 ( A ) = -2.667, q * ( A ) = -3.9410, q , ( A ) = -3; ql( -jA) = 1.333, U,( -jA) = 0.3910, q,( -jA) = 2; ql( - A ) = 7.000, q,( - A ) 6.4211, q,( - A ) = 7; q,(yl) = 1.333, q,(jA) = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000857_s0045-7825(99)00448-x-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000857_s0045-7825(99)00448-x-Figure2-1.png",
        "caption": "Fig. 2. Deformation under end tensile force.",
        "texts": [
            " The dimension ratio of the three sides is 20:1:1 and the applied tensile force is 2 Pa. On each end face, 81 collocation points are uniformly distributed and the constant k is taken to be 7 in the trial functions (7). The resultant relative displacements in the x-direction at points 1; . . . ; 25 (see Fig. 1(b)) of section x 20 are given in Table 1. In this table, NOP denotes the number of points, FEM represents the solution arrived at by the \u00aenite element method and WRM represents the solution achieved by our method. The initial and deformed \u00aegures are shown in Fig. 2(a), (b) and (c), respectively, where Fig. 2(b) was produced using the FEA method and Fig. 2(c) was produced by the proposed method. Case 2. The same block is now under an end tensile displacement, rather than force. The dimension ratio of the three sides is chosen to be 5:1:1 and the applied relative displacement (i.e. the ratio of the speci\u00aeed end displacement to the unit length) is 0.5. The same boundary conditions and collocation points as those in the \u00aerst case were applied. Constant k was set to 5 in the trial functions (7). The resultant relative displacements of points 1; . . . ; 25 at section x 4:375 in the x-direction are given in Table 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002332_1.1510593-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002332_1.1510593-Figure8-1.png",
        "caption": "FIG. 8. Experimental setup.",
        "texts": [
            " Hence, we know the condition for the maximum braking torque at vm51/g is ]Tb ]v U v5vm 5tnormBz 2e2agvm~agvm21 ! 5tnormBz 2e2a~a21 !50. ~34! Equation ~34! always is satisfied if a is unity. Finally, Tb is obtained as Tb52tnormBz 2ve2gvk\u0302, ~35! where g and tnorm are obtained numerically. We can find out the braking torque for the various velocity and applied flux density. The computed results of the braking torque are compared with the experimental ones in Sec. III. To validate the accuracy of the proposed model, the braking torque is measured experimentally. The experimental setup in Fig. 8 is composed of a rotating disk, an electric motor, an electromagnet, and a load cell. The electric motor is used to rotate the disk with constant angular velocity. The electromagnet supplies the magnetic flux which penetrates the pole projection area in the disk. The braking torque is generated in the rotating disk and the reaction torque is exerted on the electromagnet. The reaction torque is translated to the load cell. As a result, the braking torque can be measured by reading the output voltage of the load cell"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002369_095440602760400977-Figure9-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002369_095440602760400977-Figure9-1.png",
        "caption": "Fig. 9 Gear test rig",
        "texts": [],
        "surrounding_texts": [
            "Since the exact location of the strain gauges in the llets of the driving gear is not known, the object of the calibration measurements was to determine the relation between the strain gauge signals and applied contact force for each of the two teeth on the driving gear. Here the assumption is made that a gauge signal only depends upon the magnitude and position of the contact force on the tooth of which the strain gauge is fastened. Thereby the two strain gauges were located in the llet of two succeeding teeth. The disturbance in the measurement of one tooth load due to load on the other tooth was minimized by locating the two gauges as far away from each other as possible, on opposite gear anks on different teeth. The two studied teeth of the driving gear were loaded throughout an entire mesh period, one at a time. Signals obtained from the preceding tooth, of the driving gear, with the strain gauge positioned on the tension side of the tooth is illustrated in F ig. 10a for different torque levels applied to the driven gear. By tting an approximate formula, based upon spline curves, to the signal from the 125N m load levels, a continuous function is obtained which describes the gauge signal throughout the mesh cycle for that speci c load level. The formula is expanded by introducing an appropriate scale factor depending upon load, able to be valid for all levels of torque applied to the driven gear, as shown in F ig. 10b. Finally, by rerunning the same procedure for the second tooth on the driving gear, the torque contribution from each of the two driving gear teeth upon the driven gear is known for an arbitrary set of strain gauge signals and angles of the gears. The friction coef cient is assumed to be constant throughout the experiment. Since the torque contributions from the two pairs of C04602 # IMechE 2002 Proc Instn Mech Engrs Vol 216 Part C: J Mechanical Engineering Science at RICE UNIV on November 23, 2014pic.sagepub.comDownloaded from mating teeth is known, the magnitude of the two contact forces must be calculated. This calculation requires knowledge of: (a) the working pressure angle, (b) the position of the pitch point in the mesh period, (c) the friction coef cient. The working pressure angle and point of contact is assumed to be close to the theoretical. By studying F ig. 10a it is quite obvious that the pitch point, where the friction force changes direction, is located at 0.8 within the mesh period; hence the position of the pitch point is known. While assuming a proportionality between the normal force and the strain gauge signal in a speci c mesh position, fundamental spur gear geometry gives the friction coef cient according to m 1 tan a 1 \u00a1 E\u00a1 E E \u00a1 E 1 \u00b3 \u00b4 , E \u00a1 E 4 1 20 where a is the working pressure angle and E \u00a1 and E are the gauge signals of the preceding tooth just prior to and past the pitch point respectively. Theory gives a working pressure angle of 21.18 and the relation between the two signals was measured to 0.877, resulting in a friction coef cient of 0.170."
        ]
    },
    {
        "image_filename": "designv11_24_0003270_1.2360598-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003270_1.2360598-Figure5-1.png",
        "caption": "Fig. 5 The natural frequencies and mode shapes for the central disk /stinger assembly",
        "texts": [
            " Additionally, the material had to be stiff enough that, t high frequencies and high amplitude of motion, the deformaions of the inner ring/disk assembly would remain small. A FEA was conducted to identify the natural frequencies of the nner ring/disk and stinger assembly. In this FEA model, the oundary condition included elements that contain both stiffness nd damping to be representative of the bump foil damper during ynamic testing. The central disk/stinger natural frequencies and ode shapes resulting from the FEA are presented in Fig. 5. Since he operation frequency was chosen in the range of 0\u2013400 Hz, ote that mode shapes one and two 214.4 and 310.8 Hz are ig. 4 Central disk with plate stiffener and top dead center ole for stinger connection ithin the range of operation. It was decided that if the resonant om: http://gasturbinespower.asmedigitalcollection.asme.org/ on 01/29/201 frequencies were causing large error in data reduction, an additional stiffener would be fabricated and initial impact tests would be conducted to identify the resonant frequencies"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002102_gt2002-30579-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002102_gt2002-30579-Figure1-1.png",
        "caption": "Figure 1 - Layout",
        "texts": [
            " The capabilities of advanced designs now meet the requirements for advanced applications, with unit loadings in excess of 689 kPa [3], and adequate damping to allow successful operation above the first system bending critical speed [6]. The bearing designs used in this machine have also been designed to have a low start-up torque. This feature is important for machines such as this one, where the motor drive system cannot supply large amounts of start-up torque. The low start-up torque and a low lift-off speed also combine to provide long bearing life. Figure 1 shows the layout of the basic high-speed, direct drive, two stage compressor. Not shown are coolers, motor drive, etc. The machine is configured around a two stage compressor, with one compressor wheel at each end of the rotor. The high-speed, permanent magnetic drive is located at the center of the rotor. A liquid cooled stator is used. The double acting foil thrust bearing is located at one end of the rotor adjacent to the journal bearing. Foil journal bearings are located just inboard of the compressor wheels"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001301_1.1406537-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001301_1.1406537-Figure8-1.png",
        "caption": "FIG. 8. ~a! Fit of the filament ~dense set of points! with an auxiliary circle ~short dashed line! of radius r(t). The left circle ~thick black line! is a cut through the physical sphere with radius R590 and center at O by a plane containing the filament. ~b! Detail showing the intersection of the filament with the sphere surface, point P .",
        "texts": [
            " These observations suggest that meandering has little effect on the results for shrinking and drifting in these parameter values. Starting with an initially straight filament passing through the poles of the sphere, for b50.75, after some transient time, the filament adopts the shape of an arc of a circle and maintains this shape as it shrinks. Since the filament tangent vector t at the surface of the sphere is normal to the sphere surface, one can readily calculate the radius of curvature of the filament at any time. We have done this for two different sphere radii, R590 and 45. Figure 8~a! shows a cross section of the physical sphere taken in the plane in which the filament lies, as well as an auxiliary circle that fits the filament and from which we may extract the radius of curvature. The filament is taken to lie in the xszs plane. Since initially the filament lies on the sphere z axis and remains parallel to this axis at all times, the plane of the filament is always perpendicular to the xy plane and the zs and z axes always coincide. We may use Eqs. ~7! to derive equations for the time evolution of the filament. The calculation is easier for the Downloaded 14 Sep 2012 to 152.3.102.242. Redistribution subject to AIP lic intersection point P in Fig. 8 of the filament with the surface where various simple trigonometric relations apply. Figure 8~b! shows the geometry at some particular time t in the plane of the filament. The thick black line represents the physical sphere of radius R and the dotted line is a sketch of the filament at that particular time. Let r denote the distance of the tip of the filament to the z axis. It is easy to see that r5 R r AR22r25 Rz r . ~8! Applying Eqs. ~7!, point P moves in the direction of the normal n ~tangent to the surface! with speed vn5ck5 c r . ~9! The horizontal component of this velocity is vn ,r5vn sin f5 vnz R , ~10! ense or copyright; see http://chaos.aip.org/about/rights_and_permissions where the angle f is defined in Fig. 8. Substitution of Eqs. ~9! and ~8! yields a differential equation for r , vn ,r5 dr dt 5 c R2 r , ~11! which can be readily solved to give r~ t !5r~0 !ect/R2 . ~12! This equation can be expressed in terms of the lifetime t f by noticing that r(t f)5R . Thus, r~ t !5Rec(t2t f )/R2 . ~13! Finally, substituting into Eq. ~8! we obtain r~ t !5R~e2c(t f 2t)/R2 21 !1/2. ~14! From this equation, other features, such as the length of the filament, L , can be calculated. We have L~ t !52R~e2c(t f 2t)/R2 21 ",
            " Redistribution subject to AIP lic Lateral drifting of scroll rings has been observed when the diffusion coefficients are unequal25,26 as is the case in this work. However, the presence of a spherical surface introduces an important qualitative difference. Because of the curvature of the surface at which both tips of the filament are attached, the binormal component of the filament results in a slow rotation of the filament plane around the axis of symmetry of the sphere. The situation is illustrated in Fig. 11 where the projection of the filament on the xy plane is shown for three different times. The plane of this figure is perpendicular to that of Fig. 8. The rotation of the filament plane can be described by an angle u with respect to an arbitrary axis. As shown in Fig. 8~b!, the intersection of the filament with the sphere is located at point P at a distance r from the z axis. The analysis is similar to that for the shrinkage of the filament, but in this case both proportionality constants, b and c in Eq. ~7!, enter the equation of motion. From Figs. 8 and 11 the component of the velocity vector in the direction of the x axis is dx dt 5vx5vn cos u sin f2vb sin u 5 cAR22r2 rr cos u2 b r sin u . ~16! Using dx/dt5(dr/dt)cos u2r sin u(du/dt) and Eq. ~8!, we obtain a differential equation for u, du dt 5 b RAR22r2 5 b R2A12e2c(t2t f )/R2 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003622_acc.1995.531369-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003622_acc.1995.531369-Figure1-1.png",
        "caption": "Figure 1: Inverted pendulum on a cart.",
        "texts": [
            " Thus, under suitable conditions on the coefficients y,, PI, and the norms of the perturbations we achieve convergence of ( z , e ) to a neighborhood of the origin. This convergence implies approximate tracking with bounded and well-behaved internal dynamics. I t may be verified that the non-vanishin part of the nonlinear perturbation in (22) is due to y&\"? Thus, only for g&n) = 0 can our scheme achieve asymptotically exact tracking. 3 An Example The classical control experiment of the inverted pendulum on a cart (see Figure 1) will be used to illustrate both the problem in which we are interested as well as application of the control technique we have described. The position of the cart is parameterized by z1 E R, the linear velocity of the pendulum pivot by 22 E R, the angle of the pendulum away from upright by 01 E (-7r/2, 7r/2) c SI, and the and the angular velocity of the pendulum by a2 E R. We will assume that sufficient force is available so that we may consider the welocity of the cart to be the input U to our system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002985_icnsc.2005.1461311-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002985_icnsc.2005.1461311-Figure2-1.png",
        "caption": "Fig. 2. When the robot switches to boundary following behavior, a cubic spline is generated to connect its current position C and an LTG node 01.",
        "texts": [
            " We should note an extreme case here, i.e., the line segment CO1 lies so close to another obstacle\u2019s boundary that to avoid that obstacle, the generated spline approximates the line segment Col. It means that in the worst case, where a smooth path is not possible, the path generated by our algorithm is the same as that by TangentBug. When the robot finds that it will be trapped in the basin of attraction of a local minimum, it will switch from moving-towards-target behavior to boundary following behavior (see Figure 2). Here another shortcut takes place. In the same way as above, we use a cubic spline to connect C and 01 and the robot will move along it. In buundary following behavior the robot makes use of the LTG to plan shortcuts relative to the boundary and for testing the leaving condition. Because we have assumed that all the obstacles\u2019 boundaries are smooth, there is no shortcut relative to the boundary. Therefore, the only shortcut in this behavior happens when the leaving condition (see Section III-A) is satisfied, the robot can leave the obstacle\u2019s boundary and switch to moving-towards-target behavior (see Figure 3)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002490_978-94-017-0657-5_37-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002490_978-94-017-0657-5_37-Figure8-1.png",
        "caption": "Figure 8. Momentary reconfiguration by moving the actuation and by extension of the mechanism",
        "texts": [
            " This last fact is discussed in the following chapter. Two principally different approaches are possible to enable a mechanism to pass a singularity. Firstly, the singularity can be momentarily removed by changing the mechanism itself. Secondly a force can be applied to the parallel mechanism manipulator in the singularity pose to apply a preferred direction out of the singularity. Since the regarded singularities are no configuration space singularities their positions can be moved by changing the mechanisms actuated joints. In Fig. 8 (left) this principle is explained. An additional actuator is attached to the joint B. This actuator can be very small and does not need to guarantee any accuracy. It has only to be activated when the singularity has been approached. In the same moment the actuator in Bo is deactivated and the actuated joint B can move the manipulator across the no longer existing singularity. Mter the singularity has been passed the actuator in B is deactivated and the one in Bo is reactivated. Subsequent to that procedure the manipulator can be moved in the new workspace. A second change of the mechanism is to extend it with an additional elastic two-bar that can be braked. In Fig. 8 (right), a circulatory toothed belt is added as a two-bar. If in Eo or Fo a brake is applied to the synchronous pulleys and one of the actuators is disabled the mechanism can be moved through the removed singularity. If the belt provides sufficient elasticity this procedure could even be executed without disabling any of the actuators. By not modifying the mechanism to remove the singularity the effort to realize a singularity passing can be significantly reduced. In Fig. 9 the mechanism is extended by a compression spring at the joint B"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002427_20.104551-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002427_20.104551-Figure7-1.png",
        "caption": "Fig. 7. Concentration contour plot for vo = lo-' m S-l, 0.25 and initial condition c(r,, 0) = 0.",
        "texts": [],
        "surrounding_texts": [
            "1868\nRESULTS\nA number of simulations have been performed to model the capture of manganese pyrophosphate (Mn,P,0,.3H20) particles (b = 1.2 x in aqueous suspension on a thin stainless steel wire (a = 5 x m, M = 8.61 x lo5 A m-l). In all cases a magnetic field of H, = lo7 A m-1 and a fluid velocity of V, = m s-l have been used where appropriate with a concentration of particles entering the area of c, = 10-3. Results of particle retention for two different initial conditions are presented here.\nParticle retention for the initial condition c(r,, 0) = co\nr -- 0 in an area of homogeneous concentration c(r,,O) = c, will now be discussed.\nFirst, to compare with previous single space calculations and experiments [l-31, Figs. 2 and 3 show the results of calculations with the magnetic field H, = lo7 A m-l only, i.e. for V, = 0. These results exhibit similar characteristics as those presented in [ I -31, although it is noted that different data are used in each case.\nm, x = 2.03 x\nThe effects of switching the magnetic field on instantly at time\nThe derivation is carried out in metric coordinates and real time. The resulting particle concentration time rates, (sa) and (5b), are given in the normalized dimensionless variables ra, 8 and r.\nThe terms ac/ar, and ac/% have to be determined by using the mesh next to the surface and the neighbouring mesh. Expressions (5a) and (5b) are only terms which appear in equation (2) for %/a7 at the wire surface. Expression (sa), for example, is used for a mesh at the wire surface to provide the contribution in the ra direction. The appropriate terms in equation (2) are used for the 0 direction and therefore equation (2) is replaced by\nIn addition to using expression (5a) at the wire surface, a saturated region is modelled by assuming that it is impervious. Therefore, expressions (sa) and (5b) are used to provide terms for meshes next to saturated areas in both the radial and azimuthal directions.\nEarlier studies [ 1,2] used a different boundary condition, namely &/ar, = G,c, by setting the particle flow to zero at the wire surface. It is noted this is an approximation to expression (5a) since it may be also obtained by setting the left hand side of (5a) equal to zero. Hence, boundary conditions (5a, b) used here are dynamic conditions, whereas a l a r , = G,c used in [1,2] is a quasi-steady-state condition.\nOuter boundary conditions The numerical model of HGMS capture necessarily covers a finite area and therefore, for the same reasons as at the wire surface, it is necessary to provide boundary conditions at the outside edge of the area, where the calculation takes place.\nFor meshes where the flow is into the area of computation the concentration is determined by the conditions upstream. It is assumed that the concentration there is constant and therefore at the upstream boundary the concentration is fixed, that is c = c,,.\nAt the downstream boundary, where the flow is outward, it is reasonable to assume that the concentration parallel to the direction of flow is constant. This is, however, not congruent with the symmetry of the (ra,O) coordinate system. Therefore, a simplified boundary condition is assumed, namely that, whilst the azimuthal terms in equation (2) apply, the radial concentration gradient is zero, that is w a r , = 0.\nFig. 3.\nConcentration contour plot for V, = 0, r = 0.20 and initial condition c(r,,O) = c, =\n' -a :;yo/*7oo -9\n-10\nRadial concentration profiles for V, = 0, r = 0.20 and initial condition c(r,, 0) = c, =\nThe effect of flow velocity is -shown in Figs. 4 and 5, where concentration contours are plotted for H, = lo7 A m-l, V, = m s-1, r = 0.075 and 0.25, respec.:vely.",
            "1869\nParticle retention for the initial condition c(rar 0) = 0 m\ns-1 in an area of concentration c(r,,O) = 0 at T = 0 is shown in Figs. 6 and 7. These figures show contours for r = 0.075 and r = 0.25, respectively. It may be seen that the results are similar to those given in Figs. 4 and 6. However, the effect of transporting particles into a previously empty region is to introduce a delay in the buildup of particles, especially behind the wire. It is noted that for T = 0.075 there is no saturated buildup on the downstream side of the wire.\nThe effect of instantly switching H, = lo7 A m-1 and V, =\nDISCUSSION AND CONCLUSIONS\nA two dimensional theoretical model for the capture of ultra-fine particles on an HGMS collector has been developed. A full set of boundary conditions has been derived and in particular dynamic boundary conditions at the wire surface have been formulated. The results show areas of depletion, accumulation and saturation at intuitively expected locations of space after appropriate periods of time. The model gives pointers for future experimental work which is needed for its full validation.\nThe comparison between results shown in Figs. 4, 5 and Figs. 6,7 indicates that, for the cases investigated herr-, the particles retained at the downstream side of the wire are supplied by forces of diffusion and not by fluid flow. This is a valuable result since the origin of the rear capture is still a subject of discussion.\nREFERENCES\nR. Gerber, M. Takayasu and F. J. Friedlander, IEEE Trans.Magn. MAG-19 (1983) 21 15. M. Takayasu, R. Gerber and FIJ. Friedlander, IEEE Trans.Magn. MAG-19 (1983) 21 12. M. Takayasu, J.Y. Hwang, F.J. Friedlander, L. Petrakis and R. Gerber, IEEE Trans. Magn. MAG-20 (1984) 155. R. Gerber, IEEE Trans.Magn. MAG-20 (1984) 1159. J.P. Glew and M.R. Parker, IEEE Trans.Magn. MAG-20 i1984) 1165. D. Fletcher and M.R. Parker, J.Phys.D: Appl.Phys. 17 (1984) L119. R. Gerber and R.R. Birss, High Gradient Magnetic Separation, Chichester: RSP-John Wiley & Sons, 1983."
        ]
    },
    {
        "image_filename": "designv11_24_0001474_s0167-8922(08)70580-7-Figure6.1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001474_s0167-8922(08)70580-7-Figure6.1-1.png",
        "caption": "FIGURE 6.1 Flat circular pad bearing with a central recess.",
        "texts": [
            " In this chapter, the mechanism of film generation in hydrostatic bearings together with methods of calculating basic bearing operational and design parameters are discussed. Commonly used methods of controlling the bearing stiffness are also outlined. The analysis of hydrostatic bearings is much simpler than the analysis of hydrodynamic bearings. It is greatly simplified by the condition that the surfaces of these bearings are parallel. Flat Circular Hydrostatic Pad Bearings Consider, as an example, a flat circular hydrostatic pad bearing with a central recess as shown in Figure 6.1 [2]. Chapter 6 HYDROSTATIC LUBRICATION 309 Pressure distribution The pressure distribution can be calculated by considering the lubricant flow in a bearing. For a bearing supplied with lubricant under pressure, the flow rate given by equation (4.18) becomes: h3 i3~ q =-- I 12q ax Since the bearing is circular, the flow through the elemental ring at radius 'r' is: rearranging and integrating yields (surfaces are parallel, i.e. h f f(r)): Boundary conditions from Figure 6.1 are: p = O at r = R Substituting into equation (6.2), yields the constant TI: (6.1) (6.3) Hence the pressure distribution for this type of bearing in terms of lubricant flow, bearing geometry and lubricant viscosity is given by: (6.4) Lubricant Flow By rearranging equation (6.4), the lubricant flow, i.e. the minimum amount of lubricant required from the pump to maintain film thickness ' h in a bearing, is obtained: Q=-- a 3 p 1 611 In(R/r) Since at r = R,, , p = p, then: (6.5) 310 ENGINEERING TRIBOLOGY where: p, h q R R, Q is the recess pressure [Pal; is the lubricant film thickness [ml; is the lubricant dynamic viscosity [Pas]; is the outer radius of the bearing [ml; is the radius of the recess [ml; is the lubricant flow [m3/sl. It can be seen that by merely substituting for flow (eq. 6.5), the pressure distribution (eq. 6.4) is expressed only in terms of the recess pressure and bearing geometry, i.e.: P = P , - (6.6) Load Capacity The total load supported by the bearing can be obtained by integrating the pressure distribution over the specific bearing area: W = pdA= pdxdy s ss .. A A It can be seen from the pressure distribution shown in Figure 6.1 that for the bearing considered, the expression for total load is composed of two terms; one related to the recess area and the other to the bearing load area. The general integral for load shown above can therefore be conveniently divided into two integrals: W = 121;rrd\u20ac)dr +l'x!rd\u20ac)dr Since the recess pressure is constant the P r t-----l-h expression is reduced to: W = ppR: + 2 n l F r d r Substituting for pressure (eq. 6.6): dx = dr dy=rd\u20ac) d X W = ppR; + 2np, - l l n ( F ) d r In(R /Re) (6.7) Chapter 6 HYLIROSTATIC LUBRICATION 311 Integrating by parts and substituting yields: After simplifying, the expression for the total load that the bearing can support is: where: W is the bearing load capacity \u201c1",
            "4 The parameters of a hydrostatic bearing, such as bearing area, recess area, lubricant flow rate, etc., can be varied to achieve either maximum stiffness, OPTIMIZATION OF HYDROSTATIC BEARING DESIGN 320 ENGINEERING TRIBOLOGY maximum load capacity for a given oil flow or minimum pumping power. Since the bearing is almost entirely under external control, it is possible to regulate the characteristics of these bearings to a far greater extent than, for example, those of hydrodynamic bearings. Minimization of Power As can be seen from Figure 6.1, if the recess in the bearing is made almost as large as the bearing diameter, then supply pressure is maintained over virtually the entire area of the bearing. This would ensure a higher load capacity than with a smaller recess but with the disadvantage of requiring a very high rate of lubricant supply pumping power. The total power required is the sum of friction power and the pumping power, i.e.: H, = H,+ H, Pumping power 'Hi is defined as the product of the lubricant flow 'Q' and the recess pressure 'pi, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003828_ejc.12.57-70-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003828_ejc.12.57-70-Figure3-1.png",
        "caption": "Fig. 3. Bending modes of the ARIANE launcher.",
        "texts": [
            " to the previous model to compose the complete linearized dynamics of the rigid launcher. Owing to lack of tests and system complexity, internal uncertainties and dispersions have to be faced. They mainly concern the propulsion system, aerodynamic coefficients, mass model and inertia, flexible modes (elastic and sloshing), actuators and sensors modelling. The wind (shear and gusts) is considered as an external disturbance. The first five bending modes are taken into account into the complete model (Fig. 3) and their characteristics are considered to be not exactly known (four uncertain parameters per mode) leading to the definition of a discrete-time uncertain LFT simulation model of order 17 and 2 R 22 22. During the atmospheric flight phase, the physical constraints and objectives defining the requirements that the autopilot must fulfill are the following. (1) Guidance demand tracking. (2) Robustly stabilize the launcher, i.e. the controller must be stabilizing for all parameters in a prespecified set "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002829_physreve.71.031702-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002829_physreve.71.031702-Figure6-1.png",
        "caption": "FIG. 6. Schematic diagram of the elliptical geometry: sad cylindrical coordinate system for elliptical geometry, sbd surface molecule alignment with respect to the elliptical surface and the applied magnetic field.",
        "texts": [
            " An improved interfacial surface-layer model has been proposed and implemented in many systems f10g. The profile of the surface-induced nematic order is modified as Ssxd = HS0, 0 \u00f8 x \u00f8 l0, S0e\u2212sx\u2212l0d/j, x . l0, J s10d where l0 is the interfacial thickness of the surface layer scharacterized by a constant degree of nematic orderd and is approximately of the order of molecular dimensions. A. Ellipsoidal droplet The shape of stretched PDLC droplets can be represented as ellipsoidal, as suggested by the SEM image fFig. 1sbdg. Figure 6 introduces the coordinate system: the z axis is taken along the long axis of the droplet swhich coincides with the 031702-5 bipolar axis of the nematic alignmentd and r is the distance from the z axis. Here we discuss the case in which the NMR magnetic field is directed along z. The droplet center is chosen at z=0. Splitting the ellipsoid into slices along z and following the approach used for cylindrical cavities presented in Ref. f10g, one can adapt the result given in Eq. s10d and approximately write Ssr,zd = HS0, Rszd \u00f9 r \u00f9 Rszd \u2212 lszd , S0e\u2212hfRszd\u2212lszdg\u2212rj/jszd, Rszd \u2212 lszd \u00f9 r \u00f9 0. J s11d Here Rszd=R0 \u00ce1\u2212z2 /Z0 2 is the radius of the slice centered at z, with R0 and Z0 denoting the length of the ellipsoid axes ssee Fig. 6d. Denoting with uszd the angle between the surface bipolar vector and the z axis, lszd= l0 /cos uszd and jszd =j / cos uszd define the thickness of the ordered interfacial layer, with cos uszd =\u00ce Z0 2 \u2212 z2 Z0 2 \u2212 z2s1 \u2212 r\u22122d . s12d sHere r=Z0 /R0 is the aspect ratio of the ellipse.d Figure 7 shows Ssr ,zd /S0 as a function of r /R0 at different z: the ellipse composed of cylindrical slices with diameters Rszd. The Ssr ,zd order parameter profile can now be used to predict the quadrupole splitting in 2H-NMR spectra. For tangential anchoring in an ellipsoid with the major axis parallel to the spectrometer magnetic field, the director will change its relative direction to the magnetic field parametrized by the angle uBszd, as shown in Fig. 6. In the case of strong anchoring it is uBszd=uszd. Assuming complete diffusional averaging, the quadrupole splitting can be obtained as a spatial average of Eq. s2d\u2014i.e., kdnsrdl = dnB SB E 0 Z0 E 0 Rszd rdrdzSsr,zdF3 2 cos2 uBszd \u2212 1 2 G E 0 Z0 E 0 Rszd rdrdz = 3S0Esrd 4R0 dnB SB sl0 + jd , s13d where Esrd = 2r2 + 1 rsr2 \u2212 1d + rs2r2 \u2212 5d sr2 \u2212 1d3/2 arctans\u00cer2 \u2212 1d . s14d Above, Rszd@j , l0 has been assumed, which fails in the very vicinity of droplet poles at z= \u00b1Z0; however, the corresponding contribution to kdnsrdl is negligible"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001392_cdc.1998.757988-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001392_cdc.1998.757988-Figure2-1.png",
        "caption": "Figure 2: Frenet frames associated with the nonholonomic points Pi.",
        "texts": [
            " A point P in the plane is isomorphically described by a Frenet frame moving on a given path y when the path itself is a sufficiently smooth continuous curve with a lower bound rymin in the radius of curvature and with the point P located at an absolute distance z < rrmin from its orthogonal projection on the path (the origin of the Frenet frame). With \u201csufficiently smooth\u201d path 31 24 we mean that the path must be a simple curve E C1. The continuity of the curvature function is not required and so also simple paths, composed of straight lines and arcs of circle, can be considered. In our case we consider n + 1 Frenet frames moving on the curve to follow, corresponding to the projections on y of the n + 1 nonholonomic points Pi of the vehicle. In our frames, we assume to have chosen a base with the conventions of Fig. 2 where 7\u2018 and Y\u2019 are the unitary vectors respectively tangent and normal to y. Each of the curvilinear frames is represented by two coordinates (syi, Ori) where syi is the line integral along the path to follow, up to the actual projection of the point Pi on the path itself (that is the time evolution of the projection of Pi on y): and e, is the orientation of the frame with respect to the inertial frame. In the Frenet frame, the point Pi is represented by the signed distance zi between the point itself and its projection and by the relative orientation angle 6Ji - 0,\u2018"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003090_iembs.2006.259233-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003090_iembs.2006.259233-Figure3-1.png",
        "caption": "Figure 3. The degrees of freedom for one arm of the slave manipulator",
        "texts": [
            " This system allows complicated treatment to be performed with the added benefit of easy and intuitive control for the endoscopist. III. THE SLAVE MANIPULATOR The 3D model of the intended slave manipulator can be seen in Fig 2. In order for the surgeon to perform the necessary dexterous actions, the slave manipulators should possess a high number of Degrees of Freedom (DOF). The emphasis of the 1-4244-0033-3/06/$20.00 \u00a92006 IEEE. 3850 project is to make the slave manipulator to be as intuitive to control as possible. As such, the DOF and joints of the slave manipulator are modeled after a simplified human arm as shown in Fig 3. Altogether there are 5 DOF for positioning of the slave and an extra DOF for manipulating the end effector and the axis or rotation. Two slave manipulators are used instead of one since it can perform actions such as pulling and cutting of polyps or suturing bleeding sites. Furthermore two slave manipulators are more intuitive to use since they resemble the two human arms. In order for the slave manipulator to be able to go through human GI tract, the slave manipulator has to be small yet flexible"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001383_iros.1998.724803-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001383_iros.1998.724803-Figure2-1.png",
        "caption": "Figure 2: Collision detection in the explicit workspace by computing the minimum distance d between robot m d obstacles",
        "texts": [],
        "surrounding_texts": [
            "ported earlier for industrial robot arms with 6 degrees of freedom in an on-line given 3 0 environment. It has online capubilities by searching in an implicit und descrete conjguration space and detecting collisions in the Cartesian workspace by distance computation bused on the given CAD model. Here, we present different methods for specifying the C-space discretization. Besides the usual uniform und heuristic discretization, we investigate two versions of an optimal discretization for an user-predtlfned Cartesian resolution. The difSerent methods are experimentally evaluated. Additionally, we provide a set of 3- dimensional benchmark problems for a fair comparison of path planner. For each benchmark, the run-times of our planner are between only 3 and 100 seconds on a Pentium PC with 133 MHz.\nKeywords: industrial robots, path planning, on-line algorithms, search algorithms, discretization\n1 Introduction\nThe issue of robot path planning has been studied for a couple of decades and many important contributions to the problem have been made [Hwang92]. Path planning algorithms are of great theoretical interest, but are rarely used in practice because of their computational complexity [Kama196]. Here, we make a step in the direction of practical path planning.\nMany of the future robotic tasks (e.g. recycling, robot guidance, tele-operation, assembly and disassembly, medical surgery) can often only be completed in dynamic environments. Therefore, powerful on-line path planners for industrial robots with six degrees of freedom (DOF) are needed. The on-line capability' means that the planner does not require any time-consuming off-line computations in order to directly react to dynamic changes in the environment.\nAn introduction to motion planning in dynamic environments is given in [Fujimura91]. In several examples,\ndifferent approaches especially for mobile robots are presented. In [Fiorini96], a motion planner for industrial robots based on velocity adaptation is discussed. It plans only for a 2 DOF workspace for two robots and their offline known movements. In [Ralli96], a potential-field approach based on the explicit calculation of the workspace and the C-space is proposed. When a new object is detected, the new path is sought within a few seconds, but the planner works only with 5 DOF in a very small search space, which is unfavorable for industrial applications.\nIn summary, to date, no planners for 6 DOF robots exist, which can deal with dynamic environments and have low on-line computation times. Our aim is to develop a path planner satisfying these requirements for robots with up to 6 DOF. We focus on industrial robots, which constitute a considerable fraction of all robots used currently and in future.\nThe remainder of the paper is organized as follows: In Section 2 the basic approach of our on-line path planner is introduced. Section 3 describes and compares different methods for C-space discretization. Section 4 introduces a set of benchmark problems for robots with 6 DOF based on 2 DOF examples. Experimental results are given in Section 5 . The paper closes with the conclusion and an outlook to the future research in Section 6.\n2 Basic approach Most of the off-line path planners are based on some explicit representation of the free C-space. This representation can either be retrieved by transforming the obstacle into the C-space and approximating the free-space or by randomly sampling the C-space and interconnecting the samples by collision-free links. Both approaches are very time consuming and not suited for on-line calculations, especially, if a full geometric CAD model for the robot and the obstacles is used. In order to avoid these time consuming calculations, one can search in an implicitly represented C-space and detect collisions in the workspace. This strategy enables the planner to cope with on-line provided environments. See Figure 1 and 2.\n' Here, \"on-line\" does not include to meet given time constrains as required for \"real-time\".\n0-7803-4465-0/98 $10.00 0 1998 IEEE 1479",
            "For searching in the implicit C-space, any best-first search mechanism can be applied. We choose a variation of the well known A*-search algorithm [Hart68]. Robot configurations (nodes) still to be processed are stored in OPEN, while already processed nodes are stored in CLOSED. Contrasting to the original A*, here, no reopening of nodes in CLOSED is performed. As evaluation function f (n) = (1-w) g(n) + wh(n) is used, where g(n) is the number of nodes of the path from the start node to node n , and h(n) is the Airplane distance in C-space between node n to the goal node. Increasing the weight w E [0, 11 beyond 0.5 generally decreases the number of investigated nodes while increasing the cost of the solutions generated. To improve the on-line capabilities of the path planner, our search is strongly directed to the goal by setting w = 0.99 [Sandmann97].\nCollisions are detected by a fast, hierarchical distance computation in the 3D workspace, based on the polyhedral model of the environment and the robot provided by common CAD systems [Henrich92, Henrich97el. With the help of the \"MaxMove Tables\", introduced in [Katz96], the Cartesian distances are then transformed into joint angles in order to determine whether the current configuration collides or not.\n3 C-space discretization As mentioned previously, the path planning takes place in a discretized configuration space of the robot manipulator. The resolution settlement of discretization is also an important issue. There is a trade-off in the granularity of discretization or resolution: too fine will increase the search space and too coarse may result in failing to find a path even if there exists one.\nFormally, for the i-th coordinate 4, of the C-space, let N I be the number of intervals along 4,. Then we can & termine NI by2\nN , = j\"yA;p\"\" 1, where 4,\"\" and 4,\"\"\" are the limits of joint motions and A4, is the resolution of joint i. The question is now how to determine the Aq,'s.\n3.1 Discretization methods We now investigat different methods to determine the discretization resolution Aq = (A4,, ..., 4D) of a Ddimensional C-space. In the most simple method, the user specifies a uniform discretization for all joints of the robot manipulator, thus, A q , = c for some constant c. With a reasonable joint resolution of one degree, the uniform discretization result in huge C-spaces. For example, a discretization of the Puma260's joints with Aq = (lo, I\", I\", lo, lo, 1\") results in a C-space with 2.13*10\" states.\nTo avoid the huge search space of uniform discretization, usually a heuristic discretization is applied. Here, reasonable Aq, are estimated by the user to balance the resulting Cartesian movement Ax, when the different joints i are moved for A4,. The underlying problem is illustrated in Figure 3a. For the Puma260, one may choose A4 = (lo, 2\", 3\", 4\", 5\", 6\") . In this way, generally, the nearer a joint is to the base the finer the discretization resolution is for the corresponding joint angle.\nInstead of having a uniform or a heuristic resolution along each configuration coordinate, an optimal discretization can be calculated. Therefore, the resolution along each coordinate is set according to the maximum movement of the robot endeffect at each step the robot moves along this coordinate. The result of this discretization is illustrated in Figure 3b. Analytically, this can be achieved by setting\n* Here, denotes the next smaller integer of x.",
            "where 1, is the distance between the center of joint i to the farthest point the endeffect can reach, and MaxMove is a pre-set distance the robot may move at one step along the coordinate [Qir196b].~ Altogether, the optimal discretization results in Cartesian movements Ax, of joint i which meets the condition Ax,,,, I MaxMove, where Ax,,, = max(hr, , V i }, For MaxMove = 10 mm of a Puma260, the optimal discretization equals to Aq = (0.96', 0.98', 1.40', 2.83', 2.84', 10.33\"). The size of the corresponding C-space is 1.88*1013 states. This is two magnitudes less than for the uniform discretization (Aq, = 0.9640) applying the same maximum movement.\nAdditionally to the optimal discretization with the strict condition Ax,,,, 5 MaxMove, this condition can be released to Ax,,,,, (MeanMove, where Ax,,,,, = mean{ Ax,, V i ] .s This is interesting in applications where it is not necessary to meet a given upper bound for the Cartesian movement of the robot. Instead, it may be sufficient that the robot's Cartesian movement equals to the pre-defined value MeanMove in average.\nThe ideal discretization would result in Ax, = MaxMove, for all i. Unfortunately, the Ax, depend on the current configuration. Thus, a variable resolution along\nThis kind of geometric reasoning was used by [Lozano87] to build up the approximation of the configuration space by calculating the maximum movement of links. Similarly, [Beer921 used this idea to provide analytical formulae for a specific robot model to reason on the occupancy of C-obstacles. 4 ' Please note, that the Ax, depent on the current configuration of the robot. We have omitted this in the formalism for a better clarity. Anyhow, in the most formulae, the worst case is assumed, which restricts the robot to some straight configuration.\neach coordinate is necessary. This cannot be achieved for an implicit representation of the C-space as needed here for on-line path planning. In the case where an explicit representation of the C-space is applicable, a configuration dependent resolution of C-space can be calculated. For example, a neural network representation of the C-space can be adapted in a training phase to achieve a good Cspace discretization [Ralli96].\n3.2 Experimental comparisons To give a better insight to the effects of the different discretization methods, experimental comparisons are presented in this subsection.\nThe most important property of C-space discretization for path planning is a small number of configuration states while meeting a given (Cartesian) accuracy of robot's motion. This can be achieved by balancing the resolution of the joint discretization such that the resulting Cartesian movements Ax, are similar for the different joints i. As indicator for this balance, we use the ratio Ax,JAx,,,,, where Ax,,,,,, = min(Ax,, Vi 1 and Ax,,,,, is defined as above. The ratios for the different discretization methods are shown in Figure 4. The ratios differ about a factor of ten between uniform and optimal discretization.\nThe resulting number of states in the discrete C-space for different resolutions are given in Figure 5. There is only a small difference between the MaxMove and MeanMove discretization. Huge differences in C-space size occure between the optimal and the other discretization methods. One can clearly improve the resolution when changing from uniform to heuristic to optimal discretisation without changing the C-space size."
        ]
    },
    {
        "image_filename": "designv11_24_0001902_eurbot.1996.551894-Figure9-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001902_eurbot.1996.551894-Figure9-1.png",
        "caption": "Figure 9: Definition of p, a and @ for the position controller.",
        "texts": [
            " The position controller employed for the MOPS project is an improvement of the controller described in [l]. Due to the construction of the manipulator mechanism and the guide rails in the pigeon holes the position controller must have a very high accuracy, i.e. the position controller must be able to reach a given goal point within an accuracy of 3 mm (x, y) and 1 degree (e). In [5] it was shown that position feedback controller with the control law of equation 4 (4) v = k,\u201d) = (k ,a+k+b)g ( t ) with f(p) as in equation 5, g(t) is as in equation 6, f t\\4 (5) and p, a and 4, corresponding to figure 9 is globally stable. This controller ensures that the MOPS follows the planned trajectories, and avoidance manoeuvres, and its accuracy is high enough to enable reliable docking by the pigeon holes. The current version of the position controller has an accuracy of less than one millimetre in x and y and 0.1 degree in orientation [8]. A typical trajectory for this controller when executing a sideways translation of 1 m is visualised in figure 10. 6. Conclusions This paper has described: the robot system, the navigation and control architecture, the localisation method, and the position controller that are in use on the MOPS for its task of distributing the mail at the Swiss Federal Institute of Technology"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000951_978-94-009-1718-7_10-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000951_978-94-009-1718-7_10-Figure1-1.png",
        "caption": "Figure 1. Manipulability ellipsoids for the 5R linkage.",
        "texts": [],
        "surrounding_texts": [
            "In this section we examine the manipulability of two planar closed chains. The first mechanism is a nonredundant 5-bar linkage, while the second mechanism is a redundant 6-bar linkage. In both cases we ignore orientation and consider only Cartesian position of the tip."
        ]
    },
    {
        "image_filename": "designv11_24_0001978_robot.1992.220277-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001978_robot.1992.220277-Figure7-1.png",
        "caption": "Fig. 7 Variation of three angles.",
        "texts": [],
        "surrounding_texts": [
            "where 4 is given by bwl sin 8 + v1 cos 8 + d,w2 -bwl cos 8 + VI sin 8 - dyw2 * 4 = tan-\u2019 The equations of motion for a D. C. motor is given by where T is output torque of a motor. Geometry o a wheel gives us the following equation for torque balance. The following relations hold between wheels\u2019 4~ and 4~ and robot\u2019s velocities v1 and w1. (7 T + 134 + cd = ku T = ( D + p3N3)r rr$L = v1 - a1w1 T ~ R = V I + alwl ( 8 ) (9) Substituting eqs. (7)\u2019 (8)\u2019 and (9) into ( 5 ) and (6)\u2019 we have 1. translation ( M i + M2 + +)+I + 3~1 = ~ ( U L + U R ) - ~ ~ ( N J L + N ~ R ) + M2bw: + M2{(dyrj2 + d,w; - g p 3 cos+) sin 8 2. rotation + (-d,w: + dywz - g p 3 sin +) cos 8) (10) 2 2 I(I1 ++)dl + 9 = F b ( U R - U L ) - P 3 f ( N 3 L +N3R)+ M 2 b ( v l ~ l - b d l ) - M 2 { ( d , r j 2 + d , ~ ~ - ~ 3 g ~ 0 ~ + ) COS 8- (-d,rj2 + d,w$ - p3g sin +)sin 8) Equations (10) and (11) represent total dynamics of our system including a robot, a box and two driving motors. g, goal direction WZl a mobile robot Fig.3 Symbols in the feedback control. 4 The control strategy Based on the ordinary feedback control theory we derive the control law for our mobile robot's pushing operation. By the condition 8 of the section 2, a set of points (gi; i = 1, ... n) is given to a mobile robot. Assume a robot just passed through the (i-1)th point, and is going toward the ith point. The situation is shown in Fig. 3. The line from 02 to g; is called the goal line, and to G2 the centroid line. The angle of the goal line from the centroid line is the goal angle, and written as 8,. All angles are measured counter clockwise. Now, assume that a robot has no pushing object. In this case, as mentioned earlier, the robot goes on a circular trajectory. The center of rotation is written as 0, and its radius as R. The contact point 02 makes a circular motion whose r-adius is 002. The direction perpendicular to 0 0 2 is ozF, the force line. The angle of the force line from the the centroid line is the force angle, 8 ~ . By the Mason's theorem, in order to direct the object toward the goal the robot has to push the opposite direction of the goal line from the centroid line; that is, the centroid line must be in between the goal line and the force line. The larger the force angle is , the more quickly the object turns toward the goal. There- for, we define OF = -Ice, (12) where K is a feedback gain. The lower limit of 8~ is needed because the contact plate has to stick to the object. The objective state is that the centroid line coincides with the goal line. That is, 8, = 0. The goal angle 6, represents the error of the control system. Equation 12) is the control law with the proportional feedback. L y the geometrical relation we have in AOoloZ. Substituting eq.(12) into eq.(13) we have The relation between the input voltages and the r& dius of rotation is given by Deleting R from eqs.(l4) and (15) we have uL UR b tan(6' + tan-' 2 - KO,) + a b tan(6' + tan-' 2 - KO,) - a This is the basic feedback control equation for the push-a-box operation by a mobile robot. This determines the ratio of the control inputs. Their absolute values decide the time to reach the goal, which is not discussed in this paper. In the process of deriving Eq. p 6 ) , we assume the force free motion of the robot. lso we neglect the transient response of the D. C . motors. But these do not play the essential role. The fumdamental low we used in the derivation is the rotational property of a pushed object. All ambiguities of the control system are concentrated in the feedback gain I - . In more general cases we may not locate the centroid G2, if for example the frictional force distribution on the floor is not even, or the load distribution of a pushed object is unknown, etc. Human workers could find the position of the centroid by the learning process. To provide a robot with this learning capability is a very interesting research, but is left for future works. (16) - = 5 Simulations and experiments The Runge-Kutta numerical method is applied to the equations of motion (10) and (11). Solutions are computed in a workstation (Sun Microsystems SPARC station 2.) The time interval of numerical solution is 0.01 second. We call this program the simulation model. On the other hand we have actually built an experimental vehicle, whose photograph is shown in Fig. 4. We adopt the functional parallel processing architecture as a control system. We have one master and cessor controls two driving wheels, and the other handles the sensing devices (in this research only an input 1 - two slave processors in this system. One slave p r e 0 from the potentiometer, that is the pushing angle 8, -1 (y -@ -, I I I I 1 are able to adjust the various parameters in the simulatiqn mydel. An exptrimeFtal data never exactly sample for comparison is shown in Fig. 5. The solid line represents an actual trajectory of the robot which has small wave-like variation. A broken line is a simulation result, which is smooth. The diferences in large might come from the assumptions made in Section 2. For example, while we assumed the frictional coefficient from the floor is uniform and constant, it will not match the real situations. Although many actual mobile robots exhibit small vibrations during its movement, it is hard to simulate these small vibration in the simulation model. By this and other evidences we concluded that the parameters in the simulation model are sufficiently identified. Next, let us consider feedback control experiments. We computed Eq. (16), setting coincides its corresponding sn\u201dation result, but a, d, = 0 eF = -mg = -100, and sustituting actual values into a, b, and d,. Based on this equation we made a decision table. This is a look-up table which will be used in the real-time control experiments. Since real-time control requires quick decisions, we have to rely more on memory (or table) than computing ability of the master processor. Before a control experiment, we measure d, from the box and decide the value of IC. By the assumption, the robot is able to know the exact potitions of itself, the object, and the goal. Using these data it computes the goal angle Bg, and then the force angle 8 ~ . This force angle together with the present pushing angle decides the control pair from the decision table. The sampling time for control is 0.1 second. By this algorithm we have done many experiments, a sample of which is shown in Fig. 6. tions of three direction; (1 the direction of the robot, of the goal. Two direction of the object and the goal show good coincidece. The direction of the robot has a tendency to direct toward the goal with some time delay. By observing this and other results we could conclude that the equations of motion derived here are valid, and the proposed control algorithm satisfies the expected effects. (2) the direction of the o L ject and (3) the direction classical feedback control theory. The problem is how to decide the value of K , which is determined by the trial and error manner in this research. To increase the response time of the control system, all the variables are divided into some nonuniform intervals, and the control equation is converted into the decision table. The table is stored in the main memory of the master processor. This table reduces the computing time for the control nearly to zero. The results seems to prove the feasibility of our control system, at least in the motor control of the push-a-box opera, tion by a mobile robot. The situation we considered here is very simple, but as the first step we think it is enough. To proceed toward the real problem we need to attack more complex problems. The possible future works are Many experiments have been done. 0 avoid various obstacles 0 variable frictional coefficient 0 consider jobs in the goal position 0 possible discontinuity of motion, and 0 ability to plan trajectories. There are many more interesting problems in this research area to make a mobile robot do some meaningful jobs. 6 Conclusion Driven by the hope to make a robot do some meaningful jobs other than the path planning and the obstacle avoidance problem, We proposed a method to make a mobile robot push a box from one place to another. The distance between them is rather short, and the lowest motor control level is formulated and tested in the experiments. First, we defined the situation and derived the equations of motion for a robot and a pushed object, which also include the dynamics of electrical motors. These equations are solved in a workstation to be cross-checked by the real experiments. Next, we have built an experimental robot. The functional parallel processing system is installed. The various parameters are adjusted during the experiments. The experiments and simulations show good coincidence. We adopt the goal seeking control. The objective of the control is to direct a pushed object toward the goal. By the theorem already known, in order to direct the object to the goal we have to push the opposite side of the object. Taking the principle of the proportional control, we concentrate all the uncertainty included in the system into the gain I<. If the gain is small, the restoration force toward a goal is weak. If I< is large, it quickly turns. These phenomena are popular in the 7 Refernces [l] M. T. Mason, Mechanics and Planning of Manipulator Pushing Operations, Int. J. of Robotics Research, Vol. 5, No. 3, p. 53, 1986. [2] M. A. Peshkin and A. C. Sanderson, Planning Sensorless Robot Manipulation of Sliding Objects, Proc. [3] M. A. Peshkin and A. C. Sanderson, The Motion of a Pushed, Sliding Workpiece, IEEE J. of Robotics and Automation, Vol. 4, No. 6, p. 569, 1988. [4] J. C. Trinkle and R. P. Paul, Planning for Dextrous Manipulation with Sliding Contacts, Int. J. of Robotics Research, Vol. 9, No.3, p. 24, 1990. [5] B. R. Donald, Planning Multi-Step Error Detection and Recovery Strategies, Int. J. of Robotic Research, Vol. 9, No. 1, p. 3, 1990. [6] D. T. Pham, K. C. Cheung, and S. H. Yeo, Initial Motion of a Rectangular Object Being Pushed or Pulled, Proc. of IEEE Int. conf. on Robotics and Automation, Vol. 3, p. 1046, 1990. [7] R. A. Brooks, A Robust Layered Control System for a Mobile Robot, IEEE J. of Robotics and Automb tion, Vol. RA-2, No. 1, p.14, 1986. 81 J. C. Alexander, On the kinematics of Wheeled 6 obile Robots, Int. J. Robotics Research, Vol. 8, No. 5 , p. 15, 1989. [9] J. Barraquand and J-C Latombe, Nonholomic Multibody Mobile Robot: Controllability and Motion Planning in the Presence of Obstacles, Proc. of the IEEE Int. Conf. on Robotics and Automation, p.2328, 1991. of AAAI-86, p. 1107, 1986."
        ]
    },
    {
        "image_filename": "designv11_24_0001498_cdc.1998.762074-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001498_cdc.1998.762074-Figure2-1.png",
        "caption": "Figure 2: Missile airframe",
        "texts": [
            " It is worthwhile to mention that this model has been used as a benchmark by several authors (see for instance [Zl, 15,201). The desired motion pattern is expressed, as commonly, in terms of given performances, namely, the peak time t, 5 0.35 s , the overshoot D I 10% - 20% and the accuracy no worse than 5%. The actuator is saturated in position and speed (this last being normalized by the input, i.e. 0.44radl s l g ) . The model is valid as long as -0.4 rad <a < 0.4 rad . Consider the tail controlled pitch axis missile airframe depicted in Figure 2 and which dynamics are nonlinear and described by the following equations: (1) a( t ) = K,MC,Ca(t),6(t)lcos(a(t)) +dt) { 4(t) = K q M 2 C \" , r a ( ~ ) > w ) l [ where a denotes the angle of attack, q is the pitch rotational rate, 6 is the tail fin deflection, C,, and Cn, are the aerodynamic coefficients, the expressions of which depend on a,6 and the Mach number M : C,(a,&) = [ana3 +b,,(ala +c,a]+d,F C,(a,S)= [a,a'+b,,lala +c,a]+d,6 The output of the system is the normal acceleration The remaining parameters are constant: K, = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001539_rob.10079-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001539_rob.10079-Figure1-1.png",
        "caption": "Figure 1. A 5-DOF elbow-type manipulator.",
        "texts": [
            " Any reciprocal screw in the (6 n)-system can be expressed as a linear combination of these basis vectors. Since the Jacobian matrix is configuration dependent, the system of reciprocal screws is configuration dependent. Their characteristics may vary, for example, from a finite-pitch wrench into a zero-pitch or infinite-pitch wrench during motion. The change in constraint characteristics of the reciprocal screw system results in different singularities for low-DOF serial manipulators, as will be explained further in the following section. Figure 1 shows a 5-DOF elbow-type manipulator in which the second, third, and fourth joint axes are parallel to one another, the first joint axis is perpendicular to the second joint axis, and the fifth joint axis is perpendicular to the fourth joint axis. Using Denavit-Hartenberg convention,10 the coordinate systems are defined in Figure 1 and the DenavitHartenberg (D-H) parameters are given in Table I. To simplify the Jacobian analysis, the third link frame is chosen as the reference frame. Let xi , yi , and zi be three mutually perpendicular unit vectors along the x , y , and z axes of the ith coordinate frame, respectively, and pi be the position vector of the origin of ith coordinate frame with respect to the reference frame. Then, the transformation matrix between the ith coordinate frame and the reference frame is given by 3Ti xi yi zi pi i 1,2,4, and 5 , (26) and the ith unit joint screw, $\u0302 i , can be written as $\u0302 i zi pi zi "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001509_a:1016329527130-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001509_a:1016329527130-Figure8-1.png",
        "caption": "Figure 8. (a) shift phase ab \u00b7 cab, (b) reduce phase ab \u00b7 cab.",
        "texts": [
            " \u2013 Reduce by X\u2192 a from state 0 of layer 0 to state 9 of layer 1. \u2013 Reduce by X\u2192 a from state 0 of layer 8 to state 19 of layer 1. \u2013 Reduce by R\u2192 RX from state 0 of layer 0 to state 8 of layer 1. Shift phase. The current configuration is shown in Figure 7(d). \u2013 Local error in states 1, 16 and 19 of layer 1. \u2013 Transition by b from state 10 of layer 1 to state 17 of layer 2. \u2013 Transition by b from state 9 of layer 1 to state 2 of layer 2. \u2013 Transition by b from state 8 of layer 1 to state 17 of layer 2. Reduce phase. The current configuration is shown in Figure 8(a). \u2013 Reduce by R\u2192 \u03b5 from state 2 of layer 2 to state 11 of layer 2. \u2013 Reduce by X\u2192 b from state 10 of layer 1 to state 19 of layer 2. \u2013 Reduce by X\u2192 b from state 9 of layer 1 to state 9 of layer 2. \u2013 Reduce by X\u2192 b from state 8 of layer 1 to state 19 of layer 2. \u2013 Reduce by R\u2192 RX from state 0 of layer 0 to state 8 of layer 2. \u2013 Reduce by R\u2192 RX from state 1 of layer 1 to state 10 of layer 2. Shift phase. The current configuration is shown in Figure 8(b). \u2013 Local error in states 2, 17 and 19 of layer 2. \u2013 Transition by c from state 11 of layer 2 to state 24 of layer 3. \u2013 Transition by c from state 9 of layer 2 to state 3 of layer 3. \u2013 Transition by c from state 8 of layer 2 to state 18 of layer 3. \u2013 Transition by c from state 10 of layer 2 to state 23 of layer 3. Reduce phase. The current configuration is shown in Figure 9. \u2013 Reduce by C \u2192 c from state 9 of layer 2 to state 20 of layer 3. \u2013 Reduce by K \u2192 Rc from state 0 of layer 0 to state 5 of layer 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002175_1.1515333-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002175_1.1515333-Figure2-1.png",
        "caption": "Fig. 2 Geometric definitions of brush parameters",
        "texts": [
            " Manuscript received by the ASME Dynamic Systems and Control Division, November 2000; final revision, May 2002. Associate Editor: Y. Hurmuzlu. Copyright \u00a9 2 rom: http://dynamicsystems.asmedigitalcollection.asme.org/ on 08/16/201 teristics of the brush as the tines deflect. It should be noted, however, that the model developed in this paper is for the case of the brush running horizontally on the road, i.e., w50 in Fig. 1. Adopting the notation of Stango @4#, a typical large diameter cup brush, as shown in Fig. 2, is manufactured by forcing groups of brush bristles, or tines, into a mounting board at an angle f. The tines have a common length L and constant flexural rigidity EI throughout their length. If there are nt tines mounted in a given brush, then they may be described such that ng tines are each housed in nm mounting points. The mounting holes in turn are split with nri groups of tines mounted about set radii Ri r , the free end of the tines being at radii Ri t . It should be noted that there may be more than one row of tines",
            "org/about-asme/terms-of-use Downloaded F Practical Investigations To validate the theory a test rig has been developed to analyze and record the performance of large diameter cup brushes in a controlled environment. The test rig ~Fig. 8! has been developed to investigate all the main process variables. An automated test procedure using the graphical programming language in \u2018\u2018Labview\u2019\u2019 has been developed to ensure repeatability of test results. Tests were undertaken at a set rotational speed from zero brush penetration, referenced to the static geometry of the brush ~Fig. 2!. The test procedure can be best summarized using a flow chart ~Fig. 9!. It should be noted that the test data points were recorded both when the brush axial load was being increased and also decreased to allow an analysis of the hysteresis. Each test was repeated a minimum of three times and an average was taken to show the mean brush characteristics. In terms of brush analysis, the following constants were measured directly from the sample brush: Tine Length, L 5 280 mm Tine Width, b 5 3.5 mm Tine Breadth, d 5 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000868_s0022112093001417-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000868_s0022112093001417-Figure3-1.png",
        "caption": "FIGURE 3. Equilibrium orientations of a family of three-dimensional flows that contains a given twodimensional flow in which the orientation dynamics are structurally stable (Example I). The equilibria are plotted over the parameter range E = - 1.6 (open circles) to e = 1.6 (closed circles). Perturbations ( E + 0) do not change the qualitative nature of the dynamics, which remains an example of case 1 even under a strong perturbation.",
        "texts": [
            " Next, we add a small rotational component to the flow about the y-axis, with associated vorticity E : 0 0 -& a,= 0 0 [, 0 8 1. Thus, the full flow K = GE+Q+Q, is slightly three-dimensional for small E . When E + 0, we compute the eigenvalues and eigenvectors of K. For - 1.6 < E 6 1.6, we find a stable node, an unstable node and a saddle, together with their symmetric opposites, at every value of E . Thus, all the flows with - 1.6 < E < 1.6 belong to case 1 of our general analysis. The locations of the equilibria shift as we vary 6, as shown in figure 3. However, even after a substantial perturbation of this structurally stable flow the dynamics retains the same character as in the unperturbed flow, i.e. the flow remains an example of case 1. 3.4. Example 11: two-dimensionalj2ows without an attracting equilibrium orientation are structurally unstable In the second example, we illustrate the fact that strictly two-dimensional flows without an attractor are structurally unstable. We add a small three-dimensional perturbation to a two-dimensional flow that rotates every initial orientation along a unique periodic trajectory, analogous to the \u2018Jeffery\u2019 orbits of particles in simple shear flow (cf"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002829_physreve.71.031702-Figure12-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002829_physreve.71.031702-Figure12-1.png",
        "caption": "FIG. 12. Bipolar droplet with 20% strain at T=1.20: simulated director field sad and nematic order parameter map sbd shalf and whole XY cross section through the droplet center, respectivelyd, calculated by diagonalizing the MC-time-averaged local ordering matrix Qsid= 1 2 s3kui ^ uil\u2212 Id f40g.",
        "texts": [],
        "surrounding_texts": [
            "In this section we briefly describe Monte Carlo simulations of paranematic ordering in nematic droplets for a strained PDLC sample, where the deformation of the polymer matrix is assumed to result in an ellipsoidal droplet shape. There are several reasons for performing MC simulations in this case: sid they avoid the simplifying assumptions used in the phenomenological part of the study, siid they provide direct insight into molecular ordering mechanisms, and siiid they can be used to predict dynamic NMR spectra. Our simulations are based on the Lebwohl-Lasher sLLd lattice model f39g in which uniaxial nematic molecules or close-packed molecular clusters are represented by unit vectors s\u201cparticles\u201dd ui. The particles are fixed onto sites of a cubic lattice whose lattice spacing p is estimated as 1 nm & p&5 nm assuming that the molecular clusters contain up to 102 nematic molecules f23g. The standard N-particle LL Hamiltonian reads f23,39g UN = \u2212 J o ki,jl P2sui \u00b7 u jd , s18d where P2sxd; 1 2 s3x2\u22121d, J.0 is a constant, and the sum runs over nearest-neighbor particles only. The Hamiltonian s18d promotes parallel alignment, which facilitates the formation of the nematic phase. The boundary conditions are determined by a layer of \u201cghost\u201d particles whose orientations are fixed during the simulation. In our case we choose perfect bipolar boundary conditions\u2014appropriately rescaled for strained droplets\u2014in agreement with experimental observations reported in Sec. IV. Moreover, the bipolar and tensile axes are chosen to coincide. The interaction strength J is taken equal for nematic-nematic and nematic-ghost interactions, which implies strong anchoring, as already assumed in Sec. V A. Because of strong confinement translational diffusion cannot be ignored in the simulation of the NMR experiment ssee the estimate in Sec. IIId. The calculation of 2H-NMR spectra from the MC simulation output hence follows the procedure described in Ref. f24g, which is applicable also in presence of significant molecular motion. First, the FID signal is generated in a reference frame rotating with Larmor frequency, i.e., Gstd =KexpFiE 0 t VQ j st8ddt8GL j , s19d and is then Fourier transformed to yield the spectrum Isdnd =eexpsi2pdntdGstddt. In Eq. s19d one has VQ j std = \u00b1pdnBSB \u22121f3su j \u00b7bd2\u22121g, where u j =u jstd stands for the \u201cinstantaneous\u201d orientation of the jth particle, b represents a unit vector along the magnetic field of the NMR spectrometer, and k\u00afl j denotes an ensemble average over all particles 031702-8 in the sample. The orientations u j are obtained on the fly from the MC simulation, reproducing the effect of fluctuating molecular long axes. In addition, translational diffusion is simulated by an isotropic and homogeneous random walk process on the lattice f24g. The simulation box size was set to 70370370 particles, allowing us to study droplets of size 68p in diameter. This already approaches 92 nm, the average droplet size in our experiment ssee the above estimate for pd. In case of strain the simulation box dimensions were adjusted according to Eq. s1d to roughly maintain the volume of the droplet sapproximately 172 000 particlesd: 68368374, 64364384, 503503138, and 323323342 for 5%, 20%, 100%, and 400% strain, respectively. For each droplet geometry a separate temperature scan was performed, starting from a random configuration at T=kBT /J=1.2 and then simulating a gradual cooling down to T=1.12 with a step of DT=0.01 srecall that the NI transition in the bulk LL model occurs at TNI <1.1232 f23gd. At each temperature, 853103 MC cycles were performed for equilibration, followed by 2653103 production cycles. During the acquisition of the FID signal, 1024 diffusion steps per NMR cycle were performed. This gives a root-mean-square molecular displacement of 32p per NMR cycle in the nematic phase f40g sand correspondingly more in the isotropicd, which is already comparable to the unstrained droplet radius s34pd and thus approaches the fast diffusion limit. Like in the experiment, the spectrometer magnetic field was applied along the bipolar stensiled axis\u2014 i.e., b parallel to X. Figure 12sad shows the director field for the droplet with 20% strain at T=1.20. Bipolar paranematic ordering is well pronounced only in the vicinity of the substrate, with molecules on average aligned along the droplet symmetry axis, while in the bulk isotropic phase is restored. This surfaceinduced ordering is characterized by a nonzero nematic order parameter fsee Fig. 12sbdg decaying to zero approximately exponentially, as assumed in Sec. V, with a characteristic length j,4p on moving away from the substrate. This is also obvious from Fig. 13 showing nematic order parameter profiles for different temperatures, plotted along one of the short principal axes of the droplet. One can clearly see the temperature dependence of the characteristic length j, while the subsurface value of the order parameter sS0d exhibits a rather weak temperature dependence. The latter observation supports the use of the temperature-independent model for S0 given by Eq. s17d. There is, however, no major strain dependence for S0 values since in the simulation the stretching process is only taken to affect the droplet shape, while only perfect si.e., smoothd boundary conditions are considered. Note also that for strongly strained droplets se.g., 400%d the length of the short droplet axis is substantially reduced, which leads to a capillary-condensation-like effect: due to the proximity of the opposing walls, nematic order is restored throughout the droplet even at temperatures several degrees above the bulk TNI sFig. 13d. Examples of the simulated 2H-NMR spectra are shown in Fig. 14. Note that all spectra are double peaked, with no additional structure, which indicates that they are indeed highly diffusion averaged. The temperature dependences of the quadrupolar splitting for all droplets sestimated from the peak-to-peak distance for each spectrumd are summarized in Fig. 15. One can readily observe that the splitting decreases with increasing temperature and that it increases with strain, which are both seen also experimentally. The former effect is mainly because of the decrease of j\u2014i.e., the thickness of the paranematically ordered subsurface layer\u2014while the latter is due to a more pronounced orientation of nematic molecules along the tensile axis sand the spectrometer magnetic fieldd, as well as due to an increase of the droplet surface area upon stretching the polymer matrix. Note, however, that all simulated values of the quadrupole splitting are noticeably higher than the experimental ones. This is a consequence of the rather strong coupling between nematic and ghost particles chosen in the simulation, resulting in an overestimate of the degree of paranematic order, including S0. On the other hand, examining the increase of the quadrupole splitting upon stretching at a given temperature, one observes that at all temperatures the relative increase obtained experimentally is significantly larger than the corresponding MCsimulated value. Recall again that the simulations presented so far were performed with perfectly smooth bipolar boundary conditions at the droplet surface, while the actual appearance of the polymer substrate is far from smooth. Imperfections of the polymer surface lead to a decrease of the subsurface degree of ordering S0 f40g, which in a real system seems to be the case especially for weakly strained droplets trapped within a fairly disordered polymer. Then, with increasing strain, polymer chains disentangle, which is accompanied by an increase of S0 sFig. 11d. In the simulated model systems we have shown, the increase of the quadrupolar splitting with stretching can be attributed solely to the change of droplet shape. In a real system this effect seems to be enhanced by the disentanglement process in the polymer matrix. For this reason, a set of simulations for partially disordered droplet surfaces has also been performed. A perturbation of bipolar boundary conditions was generated following a P2-type orientational distribution with a controllable degree of surface order Ss f40g. This modification indeed reduces the quadrupole splitting, as can be easily concluded from Fig. 16. Extrapolating Ss\u21920 towards experimentally relevant values and using the experimental splitting data on stretching from 5% to 400% at T=1.16 s<312 Kd, the simulation predicts an increase of Ss by a factor of ,9. The experimental S0 data from the fit, on the other hand, merely give a factor of ,3.4. Note that in the low-Ss range the accuracy of curves plotted in Fig. 16 is limited as the magnitude of the resulting splitting already approaches the resolution of our spectra. VII. CONCLUSION In this paper, we have studied the alignment of 5CB-ad2 in stretched PDLC\u2019s using 2H-NMR. We have directly observed liquid-crystal alignment along the tensile axis in the nematic phase. Moreover, we have investigated paranematic surface-induced ordering and analyzed it using Landau\u2013de Gennes theory. The elliptical model we propose is shown to well describe the surface ordering of liquid-crystal molecules confined to elliptical cavities. The measured surface value of the order parameter turns out to be largely temperature independent and is seen to increase with increasing strain. The latter observation is in agreement with the results obtained from optomechanical measurements f29g: on stretching, polymer chains of the PDLC matrix disentagle and thereby modify surface anchoring conditions for liquid-crystal molecules. Our experimental results are well correlated with qualitative trends obtained from Monte Carlo simulations of paranematic ordering in elliptical droplets. ACKNOWLEDGMENTS Financial support was provided by Fuji Photo Film Co. Ltd., the National Science Foundation sGrant Nos. DMR0079964, DMR-9875427, and 0306851d, and the Slovenian Office of Science sProgramme No. P1-0099 and SloveneU.S. Project No. SLO-US/04-05/32d. 031702-10 f1g P. Sheng, Phys. Rev. Lett. 37, 1059 s1976d; Phys. Rev. A 26, 1610 s1982d. f2g T. J. Sluckin and A. Poniewierski, in Fluid Interfacial Phenomena, edited by C. A. Croxton sWiley, New York, 1986d, Chap. 5. f3g G. P. Crawford, R. J. Ondris-Crawford, S. \u017dumer, and J. W. Doane, Phys. Rev. Lett. 70, 1838 s1993d. f4g G. P. Crawford, R. J. Ondris-Crawford, J. W. Doane, and S. \u017dumer, Phys. Rev. E 53, 3647 s1996d. f5g K. Miyano, Phys. Rev. Lett. 43, 51 s1979d; J. Chem. Phys. 71, 4108 s1979d. f6g P. Guyot-Sionnest, H. Hsiung, and Y. R. Shen, Phys. Rev. Lett. 57, 2963 s1986d. f7g R. Barberi and G. Durand, Phys. Rev. A 41, 2207 s1990d. f8g W. Chen, L. J. Martinez-Miranda, H. Hsiung, and Y. R. Shen, Phys. Rev. Lett. 62, 1860 s1989d; T. Moses and Y. R. Shen, ibid. 67, 2033 s1991d. f9g G. P. Crawford, D. K. Yang, S. \u017dumer, D. Finotello, and J. W. Doane, Phys. Rev. Lett. 66, 723 s1991d. f10g G. P. Crawford, R. Stannarius, and J. W. Doane, Phys. Rev. A 44, 2558 s1991d. f11g P. Ziherl, M. Vilfan, N. Vrban\u010di\u010d-Kopa\u010d, S. \u017dumer, R. J. Ondris-Crawford, and G. P. Crawford, Phys. Rev. E 61, 2792 s2000d. f12g T. Jin, G. P. Crawford, R. J. Ondris-Crawford, S. \u017dumer, and D. Finotello, Phys. Rev. Lett. 90, 015504 s2003d f13g G. S. Iannacchione, G. P. Crawford, S. \u017dumer, J. W. Doane, and D. Finotello, Phys. Rev. Lett. 71, 2595 s1993d. f14g G. S. Iannacchione, G. P. Crawford, S. Qian, J. W. Doane, D. Finotello, and S. \u017dumer, Phys. Rev. E 53, 2402 s1996d. f15g G. S. Iannacchione, S. H. Qian, G. P. Crawford, S. S. Keast, M. E. Neubert, J. W. Doane, D. Finotello, L. M. Steele, P. E. Sokol, and S. \u017dumer, Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 262, 13 s1995d. f16g S. Kralj, G. Lahajnar, A. Zidan\u0161ek, N. Vrban\u010di\u010d-Kopa\u010d, M. Vilfan, R. Blinc, and M. Kosec, Phys. Rev. E 48, 340 s1993d. f17g D. Finotello, H. Zeng, B. Zalar, and G. S. Iannacchione, Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 358, 237 s2001d. f18g B. Zalar, R. Blinc, S. \u017dumer, T. Jin, and D. Finotello, Phys. Rev. E 65, 041703 s2002d. f19g G. P. Crawford and S. \u017dumer, Liquid Crystals in Complex Geometries sTaylor & Francis, London, 1996d. f20g A. Golemme, S. \u017dumer, D. W. Allender, and J. W. Doane, Phys. Rev. Lett. 61, 2937 s1988d. f21g I. Vilfan, M. Vilfan, and S. \u017dumer, Phys. Rev. A 40, 4724 s1989d. f22g M. Vilfan, N. Vrban\u010di\u010d-Kopa\u010d, B. Zalar, S. \u017dumer, and G. P. Crawford, Phys. Rev. E 59, R4754 s1999d. f23g edited by P. Pasini and C. Zannoni, Advances in the Computer Simulations of Liquid Crystals, sKluwer, Dordrecht, 2000d. f24g C. Chiccoli, P. Pasini, G. Ska\u010dej, C. Zannoni, and S. \u017dumer, Phys. Rev. E 60, 4219 s1999d; 62, 3766 s2000d. f25g R. K. Bharadwaj, T. J. Bunning, and B. L. Farmer, Liq. Cryst. 27, 591 s2000d. f26g I. Amimori, J. N. Eakin, G. P. Crawford, N. V. Priezjev, and R. A. Pelcovits sunpublishedd. f27g P. S. Drzaic, Liquid Crystal Dispersions sWorld Scientific, Singapore, 1995d. f28g O. A. Aphonin, Yu. V. Panina, A. B. Pravdin, and D. A. Yakovlev, Liq. Cryst. 15, 395 s1993d. f29g I. Amimori, N. V. Priezjev, R. A. Pelcovits, and G. P. Crawford, J. Appl. Phys. 93, 3248 s2003d. f30g P. S. Drzaic, J. Appl. Phys. 60, 2142 s1986d. f31g B. G. Wu, J. H. Erdmann, and J. W. Doane, Liq. Cryst. 5, 1453 s1989d. f32g L. H. Sperling, Introduction to Physical Polymer Science, 2nd ed. sWiley, New York, 1992d. f33g M. Vilfan, V. Rutar, S. \u017dumer, G. Lahajnar, R. Blinc, J. W. Doane, and A. Golemme, J. Chem. Phys. 89, 597 s1988d. f34g G. P. Crawford, M. Vilfan, J. W. Doane, and I. Vilfan, Phys. Rev. A 43, 835 s1991d. f35g A. Golemme, S. \u017dumer, J. W. Doane, and M. E. Neubert, Phys. Rev. A 37, 559 s1988d. f36g P. G. de Gennes, The Physics of Liquid Crystals sOxford Uni- versity Press, London, 1974d. f37g P. G. de Gennes, Mol. Cryst. Liq. Cryst. 12, 193 s1971d. f38g H. J. Coles, Mol. Cryst. Liq. Cryst. 49, 67 s1978d. f39g P. A. Lebwohl and G. Lasher, Phys. Rev. A 6, 426 s1972d. f40g C. Chiccoli, P. Pasini, G. Ska\u010dej, C. Zannoni, and S. \u017dumer, Phys. Rev. E 65, 051703 s2002d. 031702-11"
        ]
    },
    {
        "image_filename": "designv11_24_0003962_jmr.2005.0208-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003962_jmr.2005.0208-Figure1-1.png",
        "caption": "FIG. 1. (a) Ternary diagram and projection of liquid phase for the Al\u2013Sn\u2013Si system. The figure shows all the three binary eutectic reactions. (b) Schematic illustration of the experimental set up used in the present study.",
        "texts": [
            "4 The present study aims to understand the microstructure evolution of soft dispersoids of tin in an aluminum-silicon-tin lasercladded alloy. Tin was chosen since it possesses excellent anti-friction properties. Aluminum-silicon alloys on the other hand possess excellent wear resistance. Therefore, suitable experiments were designed to disperse soft tin phase by laser surface alloying technique onto an aluminum substrate containing a small amount of silicon to obtain the best combination of tribological properties of both aluminum-tin and aluminum-silicon alloys. Figure 1(a) shows a schematic illustration of the phase diagram of the three binary systems. We have carried out detailed microstructural analyses of these alloy samples processed under different remelting speed and tried to rationalize our microstructural observations in terms of theoretical understanding using various solidification models. A schematic illustration of the laser cladding and remelting process is shown in Fig. 1(b). It consists of a CO2 laser; a substrate holder mounted on a computer controlled X-Y stage and a powder feeding system. The details of the experimental conditions are listed in Table I. The laser beam was directed onto the surface of the aluminum substrate containing a small amount of silicon, and a melt pool was created. Simultaneously, a jet of metal powder consisting of commercial purity Al and Sn blended in 9:1 weight ratio was propelled onto the melt pool with the aid of the carrier gas"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002200_s0924-0136(02)00293-5-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002200_s0924-0136(02)00293-5-Figure2-1.png",
        "caption": "Fig. 2. The stress state of an element of the rotating circular disk.",
        "texts": [
            " Once the flow stress and frictional coefficient (or friction factor) are given, the compression force, the stress distribution and the power needed can be calculated by this study. The authors have established an analytical model for the compression forming of a rotating circular disk considering Coulomb friction. The formulae of the compression pressure and the compression force on the circular disk are derived by the slab method. The schematic diagram of the rotating circular disk is shown in Fig. 1. Fig. 2 shows schematic diagram of a small element of the circular disk. For deriving the analytical model of the rotating circular disk, the following assumptions are employed: (1) The circular disk compressed is a rigid-plastic material. (2) Axis-symmetrical compression is assumed, so the radial stress (sr) equals the circumferential stress (sy). (3) The stresses distributed within the elements are uni- form. The radial stress (sr), the circumferential stress (sy), and the vertical stress (sz) are regarded as principal stresses"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002655_s0022-0728(83)80545-2-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002655_s0022-0728(83)80545-2-Figure8-1.png",
        "caption": "Fig. 8. Charge-potent ia l curves for the adsorpt ion of Q R showing the effect of various t ime delays between the potential step and the beginning of current integration. E 1 = - 1 .80 V ( 0 - 4 . 0 0 0 s): Q = f t ' + ' \u00b0 4 \u00b0 i d t ; t : ( . . . . . . ) 4 . 0 0 0 s ( c u r v e A ) ; ( ) 4 . 0 0 1 s; ( . . . . . ) 4 . 0 0 2 s ; ( . . . . . ) 4 . 0 0 4 s ; ( - - - - - - ) 4 . 0 0 8 s . Inset: C h a r g e - t i m e transients for the adsorpt ion of QR: ( . . . . . . ) 1 .35 V ; ( ) - 1.30 V.",
        "texts": [
            " Since neither QN nor QR are tensioactive in this potential range, the concentrat ion-distance profiles are not affected by adsorption, and can be regarded as complementary, if it is assumed that the two diffusion coefficients are similar and that spherical diffusion effects are negligible during the short time interval required by the measurements. The successive drops are submitted, after 4 s, to a slow positive-going potential ramp, such that the potential applied to each individual drop can be considered as practically constant (reverse pulse polarography). If the resulting current is integrated during the 40 ms immediately following the potential step, the charge-potential curve (Fig. 8, curve A) has a sigmoidal part with an amplitude of approximately 8.3 ~C cm -2 (at - 1 . 40 V), compared with 10.2 /~C cm 2 for the desorption of QN at this potential. Since this value does not depend (after correcting for drop growth during the latter) on the length of the prepolarization and integration periods, it can be assumed that there is no diffusion control and that the process is essentially capacitive in nature. The charges at potentials more negative than 1.45 In addition, the local concentration of QN is so depressed that its readsorption may only occur at much less negative potentials (cf. Fig. 1). The differential capacity of the interface when QR is adsorbed was found from the slope of the charge-potential plot (Fig. 8 curve A) in the potential range - 0 . 5 to - 1.3 V to be about 8 .5 / ,F cm -2 which is distinctly greater than that of QN in the same potential range (6/*F cm-2) . If a delay A~- is programmed between the potential step and the beginning of the current integration, the charge-potential curves (for an integration time kept at 40 ms) exhibit peaks which decrease in width as well as in amplitude as the delay is lengthened (Fig. 8). This behaviour, which is already well documented with other systems [18], means that adsorption is not an instantaneous process, and that its rate is enhanced as the potential becomes less negative. Typically, at - 1.35 V, it takes about 8 ms to reach half-coverage, while this time reduces to < 1 ms at - 1.0 V. The corresponding charge-time curves present a falling morphology which indicates that the film is established in a random manner, which is not controlled by a nucleation and growth mechanism"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000120_0003-6870(94)90075-2-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000120_0003-6870(94)90075-2-Figure1-1.png",
        "caption": "Figure 1 Schematic of manually driven flywheel motor",
        "texts": [
            " Keywords\" Experimental modelling, manually energized flywheel motor, optimization With a manually driven brick-making machine developed by Modak (1982) the muscular power of the rider is used to drive the production process. The machine consists of three units: a pedal-driven flywheel with a step-up transmission (the flywheel motor); a mechanical transmission consisting of a spiral jaw clutch and torque amplification unit between the flywheel shaft and process unit input shaft; and the process unit, consisting of an auger, cone and die. A schematic of the flywheel motor is given in Figure 1. M consists of the rider's thigh (O1A), the rider's leg (AB), the pedal length (BO2), and the fixed link distance from hip joint to pedal axis (O102). The rider pedals via mechanism M, converting oscillatory motion of the thighs into rotational motion of the counter shaft CS. This is made possible by using various mechanisms such as a quick return ratio drive, a double lever inversion, and an elliptical sprocket drive, which improve human energy utilization by 17%, 34% and 18% respectively (Modak, 1984)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001568_2.2731-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001568_2.2731-Figure1-1.png",
        "caption": "Fig. 1 Nonslender delta wing model.1",
        "texts": [
            " Although vortex-induced loads dominate on slender delta wings, causing the observed wing rock,2 they play no signi cant role in generatingthe nonslenderwing rock phenomenon of the present 45-deg delta wing. However, an importent consideration for these wings is that they have large leading-edge radii, rather than being sharp-edged, as in the case of the con gurations exhibiting slender wing rock. As a representativecon guration for investigationof the low-speed aerodynamics of an aerospace plane during the landing approach, the authors of Ref. 1 selected a thick 45-deg delta wing with cylindrical leading edges (Fig. 1). Low-speedtestsat Re D 0:22\u00a3106 ofa 45-degdeltawing1 (Fig. 1) gave a maximum lift close to that for a NACA-0012 airfoil3 (Fig. 2). At \u00ae < 10 deg the lift slope of the delta wing is roughly 60% of that for the airfoil. Correcting for the effect of aspect ratio (AR) and assuming elliptic lift distribution, one obtains CL\u00ae D cl\u00ae=.1 C cl\u00ae=\u00bc AR), giving CL\u00ae=cl\u00ae D 2 3 for cl\u00ae D 2\u00bc and ARD 4. Thus, at \u00c1 D \u00af D 0 the CL.\u00ae/ characteristics of the 45-deg delta wing are similar to those for a straight wing. Applying the stall angle \u00aes for the NACA-0012 airfoil to the cross ow separationangle \u00aeLE on the delta wing gives the angle of attack \u00aev for starting vortex shedding as follows4: \u00aev D tan\u00a11.tan \u00aeLE sin \u00b5LE/ (1) With \u00aeLE D \u00aes D 11 deg for NACA-0012 (Fig. 2) and \u00b5LE D 45 deg (Fig. 1), Eq. (1) gives\u00aev D 8 deg. The experimentalresults in Fig. 2 indicate that the leading-edge stall occurred at \u00aev \u00bc 10 deg, compared to \u00ae \u00bc 12 deg for the NACA-0012 airfoil, resulting in leading-edge vortex shedding at \u00ae \u00a1 \u00aev > 0. Based upon the straight-wing type of CL .\u00ae/ behavior up to maximum lift at \u00ae D 25 deg (Fig. 2), one expects the delta wing to exhibit symmetric rolling moment characteristics,Cl.\u00a1\u00c1/ \u00bc Cl .\u00c1/ at inclinations \u00be < 25 deg of the roll axis below wing stall, in basic agreement with the measured Cl ",
            "19 Thus, the roll-rate-induced camber should generate roll damping for a sharp-edged 45-deg delta wing, and the measured wing rock around \u00c1 \u00bc 50 deg at \u00be D 25 and 30 deg (Fig. 9) must have been caused by the rounded leading edge. For \u00be D 30 deg and \u00c1 D 50 deg Eq. (2) gives 3 D 21 deg for the windward wing half. That produces the situation illustrated in Fig. 12. Thus, oneneeds to analyze the ow over a moderatelyswept wing leadingedge.The effectiveangleof attack for the leading-edge cross section in Fig. 12 is determined as follows9: \u00aeeff D tan\u00a11.tan \u00be cos \u00c1/ (3) For \u00be D 30 deg and \u00c1 D 50 deg Eq. (3) gives \u00aeeff \u00bc 24 deg. As the AR for the right wing half is 4.00 in Fig. 1 and 4.85 in Fig. 12, \u00aeeff is close to the angle for maximum lift \u00ae D 25 deg in Fig. 2. Thus, during wing rock the right wing half in Fig. 12 would be describing roll oscillations that produce a plunging motion of the rounded leading edge at an angle of attack close to that for maximum lift. When this motion is taking place in the near-stall region, as in the presentcase, undamping-in-plunge has been measured for airfoils20 (Fig. 13). The negative damping-in-plunge has been shown to be generated by the moving wall effect on the initial boundary-layer formation near the forward ow stagnation line,21 as illustrated in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001382_robot.2000.844729-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001382_robot.2000.844729-Figure3-1.png",
        "caption": "Figure 3: A Counter-clockwise Tip-over",
        "texts": [
            " Path curvature may not be zero, even if the vehicle moves in a straight line, due to terrain topography. Moving uphill on a strictly straight line is, therefore, not affected by this constraint since sliding in this case is not a function of vehicle speed. Sliding on a straight uphill slope is a static constraint, and can be easily determined from simple calculations of the friction force. 4.2 Tip-Over Constraint The tip-over constraint is obtained by expressing the limiting condition before the vehicle is about to tip-over in-terms of i, s. Referring to Figure 3, the vehicle is about to tip-over counter clockwise if the total reaction force R is applied on the left wheels, and the lateral friction force, f,, points downward, as shown (the vehicle will not tip-over CCW if the friction force is applied in the opposite direction). The moment created by the reaction force and the friction force around the vehicle's center of mass causes the tip-over. The vehicle will not tip-over CCW if the resultant moment around its center of mass is positive: f q h + R b 2 0 (21) where h and b are defined in Figure 3, and R is the total reaction force between ground and the vehicle. The condition for not tipping-over CCW is therefore: b h f q 2 -R- Similarly, the condition for not tipping-over clockwise is: b f, I R x These conditions can be combined to one constraint equation: (24 ) b f; I (RxI2 Substituting (8) and ( 9 ) into (24 ) transforms the tipover constraint to a quartic inequality in s: where a1 = sin2e (26 ) a2 = nn,sin@cose (27) a3 = g sin B(kt sin 0 + k, cos e) (28) a4 = n2(n; cos2 e - p\":) (29 ) a6 = g2[(kt sine + IC, - p2k3 (31) a5 = ng(n, cos 8(kt sin 6 + k, cos 8) - p2n,k,1[30) and p = b / h "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003122_acc.2003.1239789-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003122_acc.2003.1239789-Figure4-1.png",
        "caption": "Figure 4: A sectional view of the E-7 dual circuit valve",
        "texts": [
            " Compressed air acts on the brake chamber diaphragm providing a mechanical force that is transmitted to the brake pads through the push rod and the S-cam. 3 The Experimental Setup The experimental test bench at Texas A&M University is essentially the front axle of a tractor. Compressed air is supplied by a compressor and a pressure regulator is used to modulate the pressure ofthe air being supplied to the treadle valve. Figure 3 shows a schematic of the experimental setup. The treadle valve used is the E-7 dual circuit valve mannfactured by Allied SignalslBendix (see Figure 4). The primary circuit is actuated by the pedal force and the secondary circuit acts essentially as a relay valve. A detailed description of the operation of the treadle valve can be found in [lo]: The compressed air from the treadle valve is supplied to the brake chamber through brake hoses. A pneumatic actuator is used to apply the treadle valve. The input pedal force and displacement are measured with a Proceedings ol the Ameli@\" Camrol Conteience Denver, Colorado June 4-6, 2003 1417 load cell and a linear potentiometer respectively",
            " Data is collected through a PCI-1203 Data Acquisition (DAQ) board (Manufacturer - National Instruments). An application program written in MATLAB records all the collected data and plots it. 4 Modeling the air brake system We adopted a lumped parameter approach in modeling the pneumatic subsystem of the air brake system. A model for the pneumatic subsystem of the air brake system must take into consideration the dynamics of the treadle valve and the flow of air in the system. A sectional view of the the E-7 dual circuit valve is shown in Figure 4. We will now derive the equations of motion of the components of the treadle valve. Let F, denote the force input to the valve plunger. Let x,, x, and xpv denote the displacements of the valve plunger, primary piston and primary valve assembly gasket from their initial positions respectively. Let xpr denote the distance traveled by the primary piston before it closes the primary exhaust. Let K,,, K p p and Kpv denote the spring constants of the stem spring, primary piston return spring and the primary valve assembly return spring respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003204_j.conengprac.2004.11.013-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003204_j.conengprac.2004.11.013-Figure2-1.png",
        "caption": "Fig. 2. CD drive mechanism.",
        "texts": [
            " Herein information, or data, is stored via lands and pits; see Fig. 1. For CD, a pit roughly varies in length between 0.9 and 3:3mm whereas the pit width is about 0:6 mm: Sequences of lands and pits, which for a single disc revolution represent the subsequent disc tracks, fill the disc surface. For optical data read-out, a lens unit is positioned about a disc track both in radial direction, i.e. perpendicular to the track but in the disc plane, and in focus direction, i.e. perpendicular to the disc plane; see Fig. 2. The lens unit contains an objective lens that guides the light emitted by laser diodes and reflected by the disc. Supported by wires, the lens unit can move almost freely in either focus or radial direction but is hampered in any other direction. The lens unit contains the coils of two voice coil actuators, one for focus and one for radial servo control. The corresponding magnets are mounted on the so-called sledge: a carrier supported by a linear guidance that is controlled in radial direction only"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001075_0022-0728(93)80285-p-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001075_0022-0728(93)80285-p-Figure7-1.png",
        "caption": "Fig. 7. Cyclic voltammograms for the electrocatalytic reduction of CIO~-: a, CIO~- at a PAn fi lm modified GC electrode; b, CIO~--free solution at a PAn + MMo s fi lm modified GC electrode; c, ClOy at a PAn + HMo 8 fi lm modified GC electrode. C10~ concentration, 2.8 x 10 -2 M; electrolyte, 0.5 M H2SO4; scan rate, 20 mV/s . Electrode prepared by two-step method.",
        "texts": [
            " The cathodic current of the third redox wave of HMo s increases up to a plateau and the corresponding anodic current almost completely disappears when ClOy is added to 0.5 M H2SO 4 which has been degassed with argon. These results show that the H M o 8 + PAn modified electrode has a strong electrocatalytic effect on ClOy reduction. The film electrode can be cycled many times, removed, rinsed and transferred to pure 0.5 M H 2 S O 4 , but it continues to show the original pat tern with the same current intensity (Fig. 5, curve b). The catalytic current I k is linearly proportional to the C10 3 concentration in the range 1.0 \u00d7 10-3-1 .2 x 10 -2 M (Fig. 6). Figure 7 shows the cyclic vol tammograms of an HMo 8 + PAn modified electrode prepared using the two-step method. Curve c (broken curve) shows the vol tammogram obtained in the presence of 5.0 x 10 -3 M CIO 3 . The occurrence of catalysis on the second and third peaks of HMo 8 can clearly be seen, and the catalytic wave current is even larger than that obtained on electrodes prepared using the one-step method. The reason for this difference is not clear. The anodic current disappears completely and the negative and positive branches overlap, while the catalytic wave exhibits a peaked form. This may result f rom a limitation due to the narrow conductivity range of PAn film. In the presence of 5.0 x 10 -3 M C10~-, the H M o 8 + PAn assembly (Fig. 7, curve c) shows a transient catalysis on the second and third waves of HMo 8. However, on subsequent potential runs, a massive leakage of HMo 8 is observed, leaving the polymer apparently undamaged. Curve a of Fig. 7 was obtained just before complete leakage of the HMo s. The 53 electrode was rinsed and then cycled in pure 0.5 M H2804; the PAn film appeared to be stable. The important implication of this observation is that the HMo 8 + PAn films prepared by the two-step method are not stable when CIO~- is present in the solution. It is known that HMo 8 can be adsorbed on the GC electrode surface. In the case of the two-step method, it may also be adsorbed on the external surface of the conductive PAn film. Simultaneously, HMo 8 as a dopant may exchange with the sulfate at binding sites in the polymer and become immobilized in the PAn film"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003681_j.jcis.2005.12.002-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003681_j.jcis.2005.12.002-Figure1-1.png",
        "caption": "Fig. 1. A cross section through the line of centres AB of the spherical oil drop and the spherical solid particle.",
        "texts": [
            " An explicit expression for the attachment free energy involving the radius of the three-phase line of contact and including the effect of line tension was derived by Aveyard et al. [6]. However, it would appear that a criterion for the maximum stability of a particle attached to an emulsion drop has not hitherto been reported. In the present paper we show that a remarkably simple relationship exists between the Young\u2019s angle for maximum stability and the size of the particle relative to the detached drop. Fig. 1 depicts a spherical particle attached to the surface of an oil drop in water with the Young\u2019s contact angle \u03b8 . In order to evaluate the stability of the equilibrium position we consider both 1 and 2, defined by 1 = Esep \u2212Emin and 2 = Eeng \u2212 Emin, where Esep, Emin, and Eeng refer to total interfacial free energies, when the particle is respectively (i) totally in the water phase, (ii) attached to the drop with the Young\u2019s contact angle, and (iii) totally engulfed by the drop. The particle is considered to be most strongly attached to the drop when the lesser of 1 and 2 is at maximum. For values of \u03b8 ranging continuously from 0\u25e6 to 180\u25e6, the radius a of the drop increases monotonically from a0 at separation to a1 at engulfment. If x = b/a0, the ratio of solid particle radius to the radius a0 of the separated drop, then (4)a1 = a0(1 + x3)1/3. The angles and radii in Fig. 1 are related by (5)\u03c6 + \u03c8 = \u03b8, (6)a sin\u03c6 = b sin\u03c8. In Fig. 1, the plane through P , perpendicular to the line AB , divides the oil drop into two sphere segments. The volumes of the larger and smaller segments are 1 3\u03c0a3(2 + 3 cos\u03c6 \u2212 cos3 \u03c6) and 1 3\u03c0a3(2 \u2212 3 cos\u03c6 + cos3 \u03c6), respectively. Also, the areas of the corresponding curved surfaces are 2\u03c0a2(1 + cos\u03c6) and 2\u03c0a2(1 \u2212 cos\u03c6). For the particle, replace a and \u03c6 by b and \u03c8 in the previous expressions. These properties are used in the derivation of Eqs. (7) and (8), which follow. At separation the drop volume is 4\u03c0a3 0/3. Equating this to the drop volume when the contact angle is \u03b8 gives (7) 4a3 0 = a3(2 + 3 cos\u03c6 \u2212 cos3 \u03c6) \u2212 b3(2 \u2212 3 cos\u03c8 + cos3 \u03c8). The total interfacial energy for the equilibrium configuration shown in Fig. 1 is Emin = 2\u03c0 ( \u03b3OWa2(1 + cos\u03c6) + (\u03b3SO \u2212 \u03b3SW)b2(1 \u2212 cos\u03c8) (8)+ 2\u03b3SWb2) and the energies at separation and engulfment are easily calculated as (9)Esep = 4\u03c0 ( a2 0\u03b3OW + b2\u03b3SW ) , (10)Eeng = 4\u03c0 ( a2 1\u03b3OW + b2\u03b3SO ) . The last two expressions are consistent with setting \u03b8 = \u03c6 = \u03c8 = 0, a = a0 in Eq. (8) to give Esep and with setting \u03b8 = \u03c8 = \u03c0,\u03c6 = 0, a = a1 to give Eeng. Equations for 1 and 2 may now be obtained from Eqs. (8)\u2013(10) (11) 1 = 2\u03c0\u03b3OW ( 2a2 0 \u2212 a2(1 + cos\u03c6) \u2212 b2 cos \u03b8(1 \u2212 cos\u03c8) ) , (12) 2 = 2\u03c0\u03b3OW ( 2a2 1 \u2212 a2(1 + cos\u03c6) + b2 cos \u03b8(1 + cos\u03c8) ) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001455_50006-1-Figure5.50-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001455_50006-1-Figure5.50-1.png",
        "caption": "FIGURE 5.50 Magnetic circuit of stator element.",
        "texts": [
            " Each coil is mounted on a soft-magnetic stator element that consists of two opposing toothed components and a flux return ring. The number of teeth on a stator equals the number of poles on the rotor. The drive coils are assembled by first sliding the coil and flux return ring on one of the toothed components and then inserting the remaining toothed element into the assembly in such a way that the stator teeth are equally spaced. A cross section of the interior of an assembled four-pole stator is shown in Fig. 5.49a. An \"unrol led\" perspective of an assembled stator element (without the coil) is shown in Fig. 5.50. 440 CHAPTER 5 Electromechanical Devices In the can-stack motor each rotation step is initiated by activating a single phase. Specifically, when one phase is activated (with the other phase off) the rotor experiences a torque that rotates it into magnetic alignment with that phase. The stator teeth of the two phases are offset from one another by half-a-tooth (or pole) pitch in an angular sense. Therefore, by sequentially activating the two phases the rotor can be repetitively stepped an angular measure equal to half a pole pitch",
            " As the gap between neighboring teeth is small (q5~ << qbt), we assume that the potential is linear between the teeth and this implies a profile for qo~(R~, qS) as shown in Fig. 5.51b. To solve the BVP we need a Fourier series representation for qo~(Rs, q5). First, we derive an expression for qOma x in terms of the motor's physical parameters. Let g denote the gap between adjacent stator teeth, and let H~ denote the field in the gap region (Figs. 5.49b and 5.50). We assume that the potential is linear between adjacent teeth. Therefore, 1 Acpm (5.285) H~ = R~ Aq5 qOmax (5.286) where Aq5 = q5~ and 9 = Rsq5~. We apply Eq. (3.138) from Section 3.5 to the dotted path in Fig. 5.50 and obtain ni H~ = - - . (5.287) g Therefore, ni (#max = -- - - \" (5.288) 2 Now that we know qOma x, we can represent the potential along the stator qom(Rs, qb) in terms of the Fourier series where qom(Rs, oh) = ~ A k cos(~k~b), (5.289) k = 1 , 3 , 5 . . . . 8 maX cos( l cos( k t A k - - _ ~k2Npole r 4 n i = rck2Npol~ 4---g [cos(krc) - 1 ] c o s ~k , ( 5 . 2 9 0 ) and c~ k = kNpole/2. We evaluate Eq. (5.284) at r = R~, compare this with Eq. (5.289), and obtain 444 CHAPTER 5 Electromechanical Devices Thus, the potential in the interior of the stator is oo q)m(r, qb) = ~ Ak ( r ']~ k= 1,3,5 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003207_019-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003207_019-Figure3-1.png",
        "caption": "Figure 3. Schematic of the petal micromotor operation. A\u2014initial state (t = 0), B\u2014slider position and petal shape after the end of the first voltage pulse (t = tp) and C\u2014slider position and petal shape after the first series of voltage pulses (t = T ).",
        "texts": [
            " A Ar value larger than that observed during the rolling on the ferroelectric film can be achieved by using a higher voltage, since the greater thickness of ferroelectric ceramics allows one to apply a voltage that is higher by a factor of 2\u20135 than that used for rolling on the ferroelectric film. The prototype of the \u2018ceramic\u2019 electrostatic motor has the same construction as the micromotor based on ferroelectric films [6], see figure 2(a). This allows one to reliably compare experimental data obtained for both types of micromotors. Figure 3 shows the schematic of the \u2018ceramic\u2019 electrostatic micromotor. The stator consists of a ferroelectric ceramic plate with an electrode applied to its bottom surface fixed on the substrate. A moving plate (slider) with thin metallic films (petals) of length l, that are created on its surface by methods of microelectronic technology (see figure 2(b)), moves with respect to the stator along the guides. The motion consists of several stages of petal shape change. When the voltage pulse is applied between the petal in its initial state A (part of the petal is mechanically pressed to the stator surface, ferroelectric ceramics, see F) and the electrode, the petal begins from its end to be attracted to the ceramic surface by the electrostatic forces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003480_iros.1992.601506-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003480_iros.1992.601506-Figure2-1.png",
        "caption": "Fig. 2 shows the overall view and the interior structure of the finger-shaped tactile sensor using an optical waveguide previously developed and employed for the experimental hand. The optical waveguide is a hemispherical shell made of glass, and infrared LEDs are allocated at the edge of the waveguide. The light of LEDs injected into the waveguide is total internally reflected at the boundary surface of the waveguide and travels inside it. The waveguide is covered with an elastic cover with appropriate clearance between them. When an object contacts the surface of the cover, it will be depressed and a part of it will make contact with the surface of the waveguide. In this case, the light in the waveguide is scattered at the contact location because the total internal reflection conditions will not be satisfied any more at that location.",
        "texts": [],
        "surrounding_texts": [
            "Considering the small deviation of the position and the orientation in (1) using (5)-(6) , it is transformed as follows:\nAx\", + R-l(tas) AX,, -[R-l(<\"s) xs , ]@A[\", = (7)\nAx\"', + R-l({\"o) AxoC -[R-1(5ao) X ~ , ] @ A { \" ~ .\nAlso from (3), we obtain:\n17-1({as) AX', = AxoC. (8)\nFurhermore, from the kinematic constraint of the finger represented by (4), the relation between the small translation and the rotation of the fingertip can be linearized using matrix H E R3x3 as:\nA[\", = H AX\",. (9)\nRepresenting the position of three joints of the finger by ~ E , R ~ , matrix H is defined except at the singular point of the finger as:\nwh.ere:\n111. MAWULATION CONTROL ALGORITILVI USING nIE TACTILE FEEDBACK\nU:;ing the linearized equations for the kinematics of manipulation, the control algorithm is derived so as to de.termine the motion of the fingertip necessary to achieve the dcsired manipulation of the object. For this purpose in (l), it is possible to eliminate the location of the contact in the object coordinate system xoc using other parameters. After that from (7)-( lo), the small translation of the fingertip Axus is combined with the translational and rotational motion of the object Ara, , A l a o using matrices M,, M ~ E R ~ ~ ~ as:\nAxus = M , AX\"', + M < At\"', (1 1)\nwhere:\nIn the components of the matrices M , and M t , the position xus and orientation tus of the fingertip, and the matrix H can be determined by solving the forward kin'ematics of the finger using the known parameters of the structure and the joint position measured by the intrinsic sensors. Also the location of the contact at the fingertip xsc is detected by the tactile sensor. Additionally, the position of the object Xa, is estimated as an accumulation of the small translation of the object during the manipulation as:\nxuo = CAX\"',. (14)\nFrom the above considerations, it is found that the matrices M x and M c can be determined from available sensory information and it is remarkable that the geometrical model of the object shape is not necessary for the proposed manipulation control algorithm. Once the matrices M x and M < are determined, they allow to determine the motion of the fingertip Axas according to the desired translation Axa', and rotation A t a o of the object. After that, the motion of the fingertip is transformed into the rotation of the finger joint by solving the inverse kinematics. Each joint will be adequately controlled to trace the desired position resulting in successful manipulation of the object with rolling contact at the fingertip, even though the shape of the object is unknown.\nThe above mentioned manipulation control algorithm for each finger is summarized as follows:\n1.\n2.\n3 .\n4.\n5 .\n6.\n7. 8. 9.\nPlanning of the desired trajectory of the object Xao(t),\nDividing the desired trajectory of the object into small translation Axno and rotation Atu,. Sensing of the joint position and the location of the contact xSc. Estimation of the fingertip position xuS, fingertip orientation tax, matrix H , and the position of the object xuo. Determination of the matrices M,, M < using (12)-\nDetermination of the fingertip motion AxU, using\nSolve the inverse kinematics of the finger. Position control of the joint. Go back to 2nd step and repeat the procedure.\nP O ( 0 .\n(13).\n(11).",
            "The scattered light arising at the contact location is transmitted onto the surface of a position sensitive detector (PSD) through a fiber optics plate (FOP) which is a bundle of optical fibers transmitting an image from one end to the other without image deformation or loss of information. And the electric signals corresponding to the location of the centroid of the optical input is obtained as the PSD outputs. Since the geometrical relation between the surface\nof the waveguide and the PSD is known, it is possible to detect the contact location of the object on the sensor by processing the PSD output with the computer.\nThe performance of the tactile sensor in detecting the contact location of an object is shown in Fig.3, where the contact locations of the object are expressed by square plots, and the corresponding sensory output by circle plots in a polar coordinate system allocated on hemispherical surface of the sensor. It was found that the deviations between the specified contact locations and the measured locations were about 5\" at most, and the suitable area for detection was within about 60\" from the pole of the sensor.\n$6=90\u00b0\n0 specified Conuct location 0 Measured contact lmadon\n$6=270\"\nFig.3 Output of the tactile sensor for contact.\nV. EXPERIMENTS\nTo evaluate the proposed manipulation control algorithm in two-dimensional plane, it is implemented on twofingered hand. Each finger is provided with the fingershaped tactile sensor at the fingertip. In this twodimensional case, since each finger has only two joints, one virtual joint is assumed at each finger for the determination of the matrix H defined at (lo), and it is considered to be fixed.\nFor the experimental manipulation in o\"-X\"y\" plane of the absolute coordinate system, a translational manipulation of the object in P axis direction without rotadon as shown in Fig.4 is specified.\nAt first, for the comparison, the manipulation control without considering the rolling contact is carried out.\nAssuming that the fingertip and the object make point contact without rolling as shown in Fig.5, the trajectory of each fingertip for desired manipulation can be easily determined as a straight line which is parallel to the desired trajectory of the object. This is mathematically represented",
            "by (15) which can be derived from (1 1)-(13) introducing the condition xsc = 0 as:\nAxas = A P o - [xus - xuo ]@ Atao. (15)\nDesired psitionionentadon \\\nFig.4 Desired manipulation for experiment.\nWhen such a straight trajectory as shown in Fig.6 is employed at each fingertip of the hand, the object will rotate from the desired orientation during the manipulation as shown in the sequential photograph of Fig.7. Since the fingertip and the object make rolling contact actually, the location of the contact will change on the both surface of the fingertip and the object during the manipulation resulting in such an unsuccessful manipulation.\nw \\ C .\nDesired fingertip trajectory\nFig.5 Planning of the trajectory of fingertip assuming point without rolling.\nInterval of circle plot: 5 s ra\nFig.6 Trajectory of fingertip without tactile feedback. .. .,\nI L , *. , >' >,', ' \" ) ,.: . .\nFig.7 Manipulation without tactile feedback.\ncontact\nOn the other hand. when the proposed manipulation control using tactile feedback is employed, the trajectory of the fingertip of each finger is controlled as shown in Fig.8. The change of the location of the contact caused by the rolling contact is detected by the tactile sensor, and based on the proposed algorithm, the motion of each fingertip is\ndetermined so ils to compensate the rolling and to maintain the desired orientation of the object without using any information of the object shape. The effect of tactile feedback arises as a motion of the fingertips in y a direction. From the result of an experimental manipulation shown in Fig.9, it is found that the object is successfully"
        ]
    },
    {
        "image_filename": "designv11_24_0002383_robot.1996.506891-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002383_robot.1996.506891-Figure3-1.png",
        "caption": "Figure 3: \u201cRim\u201d contacts: Only the five joint kinematic chain of riml is shown; that of rim2 is completely similar.",
        "texts": [],
        "surrounding_texts": [
            "the number of contacts or in the type of a contact. This detection is also based on the total energy error EA (4). As mentioned above, on-line identification keeps E A continuously small (theoretically zero) as long as the geometrical uncertainties remain small. However, topological changes in the contact situation give rise to sudden jumps in the modelled geometry, or even to a contact situation that cannot be modelled by the current J and G . When a transition takes place, EA rises suddenly and drastically. Hence detecting transitions in the contact topology means finding sudden jumps in one signal only: E A .\n2.3 Practical implementation issues\nIn practice, force and velocity measurements are influenced by noise and friction, which disturbs the identification and monitoring drastically. However, the relative accuracy of the force measurements with respect to the velocity measurments can be taken into account by giving more or less importance to the potential energy term in (4) than to the kinetic energy term. Friction can also be taken into account in G , the model of the constrained vector space. Due to computational complexity, real-time implementation of the presented identification and monitoring algorithm is not yet viable in the near future. However, identification need not always be done on-line. For example, in the insertion experiment as described in section 3, the alignment operation starts with a large alignment error. Although perfect alignment can not be achieved until the uncertainties are solved, the alignment operation can be carried out for a sufficient length of time within safe angle limits. Having obtained sufficient data, the alignment operation is then halted for a short period of time to allow an off-line identification of the contact uncertainties. Unlike identification, monitoring does not require complex calculations, and can be done on-line.\n3 Peg into Hole Insertion Strategy\nThe task described and experimentally verified in this paper is a complete insertion of a cylindrical peg in a hole in a poorly structured environment, including finding the hole and aligning the axes of the peg and the hole. The insertion strategy consists of the following subtasks:\n1. The peg is attached to, or gripped by, the robot in an accurately known way. In its free space start position the peg is not perpendicular to the hole\u2019s plane but the start angle between the peg\u2019s axis and the normal to the hole\u2019s plane is about 60 degrees (this angle is identified afterwards). In this\norientation the peg moves downwards until it contacts the plane of the hole. The contact is such that the tip of the peg now points towards the expected location of the hole.\n2. While keeping contact the peg now moves forward over the plane in the direction in which the hole is expected until the peg \u201cfalls\u201d into the hole. This is guaranteed because the peg has previously been tilted. If the direction of search is too uncertain, other high level search strategies must be used.\n3. A three-point contact configuration is then established by slightly pushing the peg into the hole.\n4. Now the alignment is executed while keeping the three-point contact configuration. The alignment motion stops when the alignment error is zero. The alignment motion is described in [6].\n5. After the alignment motion, the peg is inserted.\nThis insertion strategy consists of a sequence of different contact situations. The task starts in free space. Then, a curve-face contact is established. Subsequently a three point contact configuration and finally a cylindrical contact are reached. The continuation of this section describes the models of these different contact situations. The possible transient contacts between the curve-face contact and the three point contact are not modelled. The next section discusses the identification of the unknown geometrical contact parameters and the detection of transitions between different contact situations for a real experiment.\n3.1 Free space This situation is modelled by the twist and wrench Jacobians J f s and Gf, [5]:\nJ f s =: I , G f , = 0. (7)\n(8) Hence: 1 E 2 = -wTCw. 2\nThis contact situation has no geometrical uncertainties.\n3.2 Curve-face contact The bottom rim of the peg contacts the plane of the hole. This is modelled by means of a five degrees-offreedom virtual manipulator (Fig. l), with twist and wrench Jacobians J,f and G,f [5]:\n0 0 0 0 -c, \u201c 1 - T O 0 1\n0 1 0 0 o o o o s , 0 I , G c f =\nO 1 o c , o O S a 0 0 O I",
            "J c , =\n- - - 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0\n0 0 0 0 0 1 0 0 1 Gc, = 0 0 1 0 \u2018 (10) 0 1 - - 0 0 0 0 -\nr is the peg radius. s, and c, are, respectively, the sine and cosine of a, the angle between the axis of the peg and the contact normal (Fig. 1). This contact situation has two identifiable geometrical uncertainty parameters: the rotation angle 19 of the peg about its own axis, and the angle a between the peg axis and the contact normal.\n3.3 Three point contact\nThere are three distinct contacts:\n1. surf: the contact between the outer surface of the peg and the rim of the hole.\n2. riml and rim2 the two contacts between the bottom rim of the peg and the rim of the hole. These two contacts are positioned symmetrically with respect to the plane through the peg\u2019s axis and through surf.\nEach of the three point contacts is modelled by means of a five degrees-of-freedom virtual manipulator [5]\n(Figs. 2 and 3). These manipulators form three parallel connections between the hole and the peg, and constrain the peg\u2019s motion freedom in the same way as the contacts. This means that the total number of degrees of freedom of the peg with respect to the hole is reduced to three:\n1. Slip: rotation of the peg about its own axis.\n2. Slide: rotation of the peg about the hole\u2019s axis.\n3. Align: rotation of the peg about the tangent to the hole\u2019s rim, at the contact point.\nFor a detailed description of the alignment motion and the twist and wrench Jacobians see Bruyninckx et al. [6]. The three point contact has two identifiable geometrical uncertainty parameters: the alignment error (i.e. the angle between the axes of peg and hole), and the rotation angle about the peg axis.\nThis contact situation has no identifiable geometrical uncertainty parameters.",
            "4 Experimental Results\n4.1 Test Setup\nThe test setup consists of an industrial KUKA IR 361/8 robot equipped with a six component flexible force/torque sensor of which the deformations are measured. Its end effector holds a peg with radius r = 100mm. The experiment is executed without contact model but with a task frame based compliant motion robot controller [7]. The insertion strategy is as explained in Section 3. The measured twists and wrenches are stored during execution and are used afterwards for off-line identification and monitoring of the different contact situations. The measurements are filtered by a low pass filter with a cut-off frequency of 3 Hz.\n4.2 Identification\nThis section shows the results of the off-line identification of uncertainties in the different contact situations. As mentioned in Section 3, only the curve-face and the three point contact have identifiable uncertainty parameters. Fig. 5 shows the result of the identification of geometrical uncertainty parameters in the curve-face contact. The angle between the peg's axis and the contact normal remains constant, about 0.85 rad; whereas the rotation angle of the peg about its own axis is small. This means that the contact point belongs to the Y-2 plane (Fig. 1). Fig. 6 shows the identified uncertainty parameters of the three point contact. Due to friction disturbancies on the forces measurements, only the kinetic energy error term of (4) is minimized. In the top figure the identified alignment error (full line) is compared with the specification (dashed line). When the alignment error is small, the insertion can start. The rotation angle about the peg axis (bottom figure) is small. This means that the surfcontact belongs to the Y-2 plane (Fig. 2).\n4.3 Monitoring The detection of the transitions between the different contact situations is based on the total energy error function of the expected model. Jumps in Ea are detected with the Page-Hinckley test. Fig. 7 shows the total energy error for the successive contact situations. The insertion starts in free space. After 16 seconds a jump in the energy error is detected which means that the transition to the curve-face contact takes place. From now on, the model of the curve-face contact is valid. The energy error is low until t = 30 sec. Then a jump in the total energy error occurs, which means that the curve-face contact is no more valid. The peg has fallen into the hole and the controller is asked to"
        ]
    },
    {
        "image_filename": "designv11_24_0002441_iros.2000.893186-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002441_iros.2000.893186-Figure3-1.png",
        "caption": "Figure 3: Proof of Theorem 2 (a) and feasible solution ignored by Algorithm 1 (b)",
        "texts": [
            " Proof: If the distance between P and 0 decreases step by step, the convex hull will approach the origin gradually. Since P is the centroid of the convex hull, all primitive contact wrenches contribute evenly to the change of P. Therefore, if the motion of one primitive contact wrench makes the distance llPOll decrease, the convergence can be guaranteed. Suppose wi(i = 1, ..., 1 - 1,l + 1, ..., N) remains unchanged and only w1 has been moved along the direction t . W;+l = wl\" +at (14) Note that the direction t should satisfy constraints eq. (10) of the QP problem(See Figure 3(a)). Fkom eq. (14)-(16), we get (17) 1 N From eq. (16) the motion of w1 along direction t will result in the movement of centroid P along the same direction but with smaller step size a/N. As the direction t forms an acute angle with the ray PO, the intersection point 5' between OPk and its p k + l = p k + -at perpendicular line passing Pk+l falls between P k and 0, i.e. OS 5 OPk(See Figure 3(a)). Compared with the length O P k , the step size a/N is small enough. Therefore, OS = OPk+'cos9 M OP\"' 5 OPk (18) The above equation implies that the distance llPOll will never increase. For one case, if llPOll decreases step by step until llPOll < IIPQll, the form-closure grasp can be found. Another case is that llPOll remains the same after decreasing several times, which means all the primitive contact wrenches can only be moved along the direction w$h 90 degrees to the ray PO, i.e. (wf+l(r) - w,\") 0 P O = 0, therefore, in order to make sure the minimal distance between wf+' and w,\" defined in eq",
            " If so, the program ends with proper solution found. Step 3: Using eq. (13) to calculate the desired primitive contact wrenches w!. Step 4: By the quadratic programming, obtain the new position vectors and then calculate the new primitive contact points w;+'. Step 5: Check the distance OPk++'. If it remains the same with OPk , the program ends with no solutions found and if it descends, turn to Step 2. It should be noted that constraints eq. (10) for the QP problem impose stricter constraints than necessary, e.g. in Figure 3(b), to satisfy constraints eq. (lo), the primitive contact wrench w$ cannot move along the direction in the shaded portion such as direction t , as it forms an angle more than 90 de- - 1226 - grees with the ray PO. However, it can be observed easily that moving w: along direction t enables the convex hull to approach the origin to some extent, i.e. in Figure 3(b) the new facet E' is closer to the origin than the old one E. Therefore, in each iteration some feasible grip points will be ignored by A)gorithm 1. As a result, in some cases the algorithm is unable to find a proper set of position vectors even if there does exist a solution. To compensate the deficiency, we consider to define another desired direction, i.e. the normal vector e' = (e1,ez, ..., e6) (eq. (8)) of the facet E intersected by the ray PO (See Figure 3(b)) so that more feasible grip points are considered during the iterations. In this case, the motion of each primitive contact wrench should form an acute angle with direction Z, which ensures the distance difference llPOll - IIPQll decrease step by step. However, we note that using the new desired direction also causes the loss of some feasible grip points which can be considered by Algorithm 1. So in practice, we adopt a two-step measure, i.e. when Algorithm 1 reports a failure, we use the revised one"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003296_1.1767099-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003296_1.1767099-Figure2-1.png",
        "caption": "Fig. 2. The definition of the vectors rWD and RW con ~a! and force diagram ~b!. While the ball rotates, both rWD and RW con have constant lengths (rD and Rball); however, rWD rotates with the ball while RW con is always directed downward. If rD is nonzero, the difference between gravity and the vertical component of the contact force FW con provides the force allowing vertical acceleration of the center of mass.",
        "texts": [
            " Initially the ball slides along the lane and, before it reaches the pins, it may or may not begin rolling without slipping. Consider a coordinate system ~see Fig. 1! where the x axis extends from the foul line (x50) to the pins, the y axis extends from the right gutter (y50) toward the left, and the z axis extends upward from the center of the ball (z50). Let rW be the position of the ball\u2019s center of mass, and let rWD and RW con be vectors extending respectively from the center of mass to the center of the ball, and from the center of the ball to the point of contact on the lane ~Fig. 2!. If the ball has mass M, moment of inertia tensor I, and rotates with angular velocity vW , the force and torque equations about the center of mass are MrW\u03085FW con1FW g , ~1! d dt ~IvW !5~rWD1RW con!3FW con , ~2! where FW g and FW con are the gravitational and the contact force applied by the lane to the ball, respectively. In the simplest case where I is diagonal and rWD is zero, Eq. ~2! becomes IaW 5t , ~3! where aW is the angular acceleration and t is the frictional torque RW con3FW con . 1170\u00a9 2004 American Association of Physics Teachers license or copyright; see http://ajp"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000903_942087-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000903_942087-Figure5-1.png",
        "caption": "Figure 5: An illustration of the spatial variation of the heat transfer coefficient as calculated by CRD methods",
        "texts": [],
        "surrounding_texts": [
            "equation applies for those interface elements that are in contact. For all other interface elements q = 0.\nFrictional heat can be input as a flux at the contact surface and/or as volumetric heating within the interface element, and no artificial partitioning of the generated heat between pad and disc is required. The heat, once generated, may be conducted across the friction surface automatically according to the overall thermal conductive matrix.\nINTERFACE CONTACT CONDUCTANCE AND AUTOMATIC ENERGY PARTITION - The partitioning of the energy dissipated at the brake's friction interface cannot be determined accurately without a complete thermo-mechanical analysis. For example in multi-stop cases such as a mountain descent, convective heat transfer from the rotor also significantly influences the heat partitioning.\nThe formation of surface layers and interfacial wear products have a significant effect upon heat transfer from the interface. The rotor and friction material surface temperature are significantly different due to interface contact resistance. Rotor bulk temperatures, measured by a rubbing thermocouple on a specially prepared track round the outer edge of the rotor, were consistently lower than the corresponding measured surface temperatures of the friction material.\nThe thermal conductance of a contact interface element forms one part of the heat flow path. As the true pad surface temperature is higher than the disc surface temperature, higher thermal conductance will reduce the pad surface temperature and increase the disc surface temperature. An infinite thermal contact conductance will ideally lead to identical pad and disc surface temperature. The effect of contact conductance on surface temperature is more significant to the pad surface than the disc surface.\nThe conductance used in the present study is determined empirically based on measured disc temperatures, and is a function of the thermal conductivities of both pad and disc materials. Since contact between the pad and disc surfaces only occurs over a small part of each revolution, the conductance used in the axisymmetric model is an equivalent one, based upon the pad angle and contact pressure.\nThe model was also used to investigate the effect of the interface conductance upon the heat partition and the difference in surface temperature of the pad and disc. The results are shown in Fig. 4. It can be seen that in each case the pad temperature is above that of the disc, which is in agreement with experimental results.\nCONVECTIVE AND RADIATIVE BOUNDARY CONDITIONS - \"At the end of the eighth brake stop, 2065 Btu's have been absorbed by the rotor and lining. Of this amount, 33% is thermally stored in the rim, 5.6% stored in\nThe boundary conditions that define the rate at which thermal energy is transferred from the rotor to ambient consists of convective heat transfer coefficients and radiation emissivity. At the early stage of braking, a significant amount of frictional heat is stored in the disc and also a large part of the energy is dissipated by convective cooling. At the later stage of braking, such as at the later stage of a mountain descent, the disc wall surface becomes very hot and convection becomes more dominant. Since the convection accounts for more than 90% of all heat dissipation to ambient for almost all braking conditions, the definition of the appropriate convection coefficient for each exterior surface of the model is critical.\nEmpirical relationships for convection coefficients available in the open literature were generally determined for geometries and flow conditions that only approximate those found in and around a brake system. On a vented rotor there are two different types of convective cooling: air cross-flow over the rotor surface and air pumped through the vents. The rotor environment does not approach the pure state created in the laboratory. The calliper, pads, and suspension members seriously affect the air flow pattern.\nThe T&N Technology approach is a combination of empirical determination together with theoretical",
            "As part of the above it was found reasonable to assume that the heat transfer coefficient varies as the 0.8 power of the velocity. It also varies with the thermal conductivity and kinematic viscosity of air, hence it varies with the actual film temperature (average of ambient and surface temperature). By simulating the measured disc surface temperature, it was found that during a multi-stop braking operation, the heat transfer coefficient was gradually reduced due to the increased film temperature.\nRadiation from the rim outer faces was accounted for by adding an equivalent radiation heat transfer coefficient to the normal convective heat transfer coefficient:\nwhere a is the Stefan constant, E the emissivity, T, is the absolute temperature of the radiating surface, T, is the absolute ambient temperature.\nThe convective and radiative heat transfer on the rotating disc surface includes the hub area, vented area and contact area where the surface is periodically in contact with pad and in exposure to the surrounding air in turn. Therefore the heat transfer coefficients used in the braking model are the resultant ones, analogous to the steady state heat transfer coefficient on the engine combustion wall surface which is periodically exposed to the transient gases [441.\nTREATMENT OF VENTED AREA - The area of the ductlweb was represented using elements with a reduced thermal conductivity coefficient, i.e. these elements were factored by a relative area ratio, and with a reduced density, hence reduced thermal capacity. On the other hand, the vented ribs increase the convective surface area, and hence the heat transfer coefficient in the axisymmetric model is the equivalent coefficient 4, derived from the local heat transfer h by the equation\nwhere A is the real vented surface area and %, is the surface area used in the axisymmetric model.\nComputational fluid dynamic analyses indicated that the local heat transfer coefficient on the vented surface is in the order of 50 WlmZK. The effect of increasing the vented surface area through the use of a multi-vented design is simulated by an increase of the equivalent heat transfer coefficient.\nRESULTS AND VALIDATION\nPREDICTION OF HOT SPOTS IN A CALLIPER DISC BRAKE - The analytical procedures outlined in the previous section have been applied to a thermomechanical investigation of a calliper type disc brake. Such a disc has been also studied experimentally at T&N Technology Ltd.\nThe friction materials used are variants of those found in conventional vehicle brakes with the rotating disc being cast iron. The pad backplate is of steel.\nConsidering an ideal situation, if it is assumed that the friction pad and rotating disc are both initially relatively smooth and that, upon initial application of the brake, the contact pressure varies only because of the loading conditions and the backplate rigidity. In such a situation it can be expected that the pressure distribution will vary from a relatively low value at the edges to a maximum near to the centre. The sliding velocity, however, increases with the radius. In consequence there is a tendency for the highest rate of heat generation to occur between the centre and the outer radius of the disc. This will very quickly lead to a",
            "curves: one pair at the piston loading side and the other on the finger side. For each pair, one temperature is at the hot zone, and the other at the cool zone. It can be seen that the temperature increases rapidly at the contact area, but increases more gently at noncontact area.\nDisc temperature (\"C)\nfinger side (hot spot) /\npiston side (hot spot)\nC - C - _ . . - . - .\nC\npiston side (cool region)\n'4 1 e\nI I I I I 3 4 5 6 7\nTime (s) c3 Figure 9: The different rates of temperature rise seen in\nand away from the hot bands\nThe forming of the hot bands and the higher hot spot temperature at the finger side predicted by the model are confirmed by the experimental results. Fig. 10 shows the history of disc temperature distribution by using the thermal imaging method [7].\nBecause of the large temperature gradient at the surface of the disc in the region of a hot spot, both in the radial and axial direction, and because of the rapid change"
        ]
    },
    {
        "image_filename": "designv11_24_0000761_s0890-6955(97)00059-x-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000761_s0890-6955(97)00059-x-Figure6-1.png",
        "caption": "Fig. 6. Drive and the counterweights using result 12.",
        "texts": [],
        "surrounding_texts": [
            "The optimum balance of the drag-link drive with adding disk counterweights for minimizing the shaking force and shaking moment is studied in this paper. For the multi-objective optimization, the two-phase optimization technique is proposed. Excepting the balancing effects, their effects on the flywheel and brake of using the balancing designs are also evaluated. Based on the results, the following points are concluded. 1. The two-phase optimization technique starts with an initial estimate, but generates a few feasible designs, and it is quite easy to use. It is also shown that the results obtained with the technique are all better than those using the design criterion (CV) as the objective function in phase one, which is the way that the traditional technique is used. 2. When adding disk counterweights on links 2 and 4, the total balancing effect of result 12 shows that CV is reduced from 4 to 2.0231 and there is a 49.4% reduction; however the maximum difference of the kinetic energy is increased 14.4%, the maximum kinetic energy is increased 18.9%. 3. Comparing the results of with and without the tangent constraints, the balancing effects have only small differences, but the counterweights of those with the constraints are smaller, thereby they are better. 4. Comparing the results of adding counterweights on: (1) link 2, (2) links 2 and 4, and (3) links 2, 4 and 5, the CV values are reduced 25.2%, 49.4% and 51.2% respectively. If the amounts of added mass are considered, then result 12 obtained in case (2) has the greatest effect/mass ratio and it is the most cost-effective design. Acknowledgement\u2014The authors are thankful to the National Science Council of the Republic of China for supporting this research under grant NSC 82-0401-E006-450."
        ]
    },
    {
        "image_filename": "designv11_24_0002860_s0109-5641(86)80043-4-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002860_s0109-5641(86)80043-4-Figure1-1.png",
        "caption": "Fig. 1. Drawings of the soldering equipment. A: View from outside B: Section through the center of the equipment. 1 Vacuum chamber 2 Specimens to be soldered 3 View port 4 Halogen lamp 5 Ellipsoidal reflector.",
        "texts": [
            " The conventional soldering technique is very difficult to perform without resulting in defects in the soldered joints. The aim of the present investigation is to develop a new soldering technique avoiding gas flame as the heat source, the ambient oxygen-hydrogen atmosphere, and the flux. The technique was explored by performing a series of solderings with 3 different alloy systems. The technique is characterized by the ability to control the atmosphere around the specimens to be soldered and by using infrared radiation from halogen lamps as a heat source (Fig. 1). The equipment consists of 2 parts, which can be moved independently of each other. The upper part comprises 2 eUipsoidal reflectors*, goldplated for maximum reflectance in the IR region and mounted at an angle of 45 ~ . Halogen lamps? of 800 W are situated at the upper 2 foci, and the lower focus, which is common to both reflectors, is the point at which the soldering is performed. Between the reflectors is a view port through which the soldering process can be observed. The lower part of the equipment is a vacuum chamber covered by a glass lid"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002071_robot.1986.1087709-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002071_robot.1986.1087709-Figure7-1.png",
        "caption": "Figure 7. We have E = 7r + cy - \u20197",
        "texts": [
            " Therefore t \"le locus' boundaries of the COR locus too can be found by considering only dipods, This is a stronger statelnellt than h,fasoll:s tllcorenl 5, which It is but that the locus {qr 1 we requires tripods, A4dditiona11y, we have found the taro points consider different locations of the center of rotation i . In Figure G constituting L1le dipods. H ~ ~ ~ ~ ~ ~ , i t sl1ould be noted t,Ilat the we have plotted several { G r } loci for different values of i . Note sufficiency of tripods holds for any objecc, whereas dipods are that varying the m a g n i t u d e of j: continuously changes the shape or sufficient only or a disk. size of the {$,} loci. But changing the direc t ion of i only causes a corresponding rotation of the {rj, } locus. 5. The variables of Equation 12 are shown geometrically in Figure 7. Shown is a candidate value of i aud the locus {7 j r } for tha t i-'. We then calculate and plot the value of ?j, required to satisfy Equation 12. If the value of a, required does not fall in {a, } , theu the value of 7 shown is not in the COR locus. If the value of a, required does fall in {GV } , then the value of i shown is in the COR locus. COR In Figure 7 the value of \u2019 j r required to satisfy equation 12 happens to be on the boundary of the {a, } locus. The boundary of the COR locus is generated by such cases. Interior points of the COR locus me generated when the a, required is interior to the (a, } locus. Since we are interested only in the boundary of the COR locus, we will consider only values of \u2019jr which are on the boundary of Lhe {a, } locus, as shown. If r < a, the boundary of { $ 7 } is a circle. The condition that a, lie on the circle can be expressed in terms of the angle \u20187 as ( l a v l - ( r - 6 )cos q ) \u2019 + ( ( r - 6 )sin q)\u2019= b 2 (13) where 6 is the radius of the circle, from Equation 10"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000425_970682-Figure10-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000425_970682-Figure10-1.png",
        "caption": "Figure 10) from the remaining loads. Applying the law of sine's to the force triangle, then substituting EQ ( 38 ) and re arranging, we obtain the rollerway speed at which eccentricity rollerfloat will occur for a specified spring force",
        "texts": [
            " = 270\u00b0 [11]- Hence, with little loss of accuracy, the angular acceleration of the roller p can be approximated by The tangential component of the roller inertia force is then given as Equation ( 38 ) yields the eccentricity roller float force, Pt(r). We may say that Pt(r) is the force which we must supply to the roller for it to remain in contact with the inner race roller-way. This force is supplied via the energizing spring. Another component of the roller inertia force is due to the angular velocity of the roller about the center of curvature of the cam. This force is given as In the event of roller float, Pn(\u00a1) is equal to zero. As with the previous analysis, we can build a force triangle (see As you may note from Figure 9 and Figure 10, we are neglecting the frictional forces which act between the roller and the spring, outer race, and inner race. It can be shown that by ignoring the frictional forces we compute a more conservative roller float speed. As an alternative analysis, we can re-write EQ ( 40 ) to give us the spring force required to prevent eccentricity roller float for a given clutch and inner race overrunning speed. This is given as wherein we have substituted co = 9(\u00a1).With the spring force obtained via EQ (41), the OWC engineer can compute the stress level in the selected energizing spring"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003809_detc2005-84681-Figure10-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003809_detc2005-84681-Figure10-1.png",
        "caption": "Figure 10: Spindle graphic interface and 2nd mode shape",
        "texts": [
            "org/about-asme/terms-of-use Dow At this stage of the study and in the light of experimental results obtained, simulations are performed only on the experimentally adjusted rotating entity linked to rigidity matrix models for each rolling bearing [8]. Preload values used in the roller bearing rigidity matrices are calculated from the initial preload and the force-induced preload. By solving the system equations generated by the proposed finite element model, the natural frequencies and mode shapes of the spindle-bearing system can be obtained. Mode shapes are validated by comparison with experimental results. Modal analyses can be performed with or without the presence of the rolling bearing. Figure 10 represents the graphic user interface to represent the spindle geometry and to perform modal analysis. nloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/03/2016 Simulations are performed using a modal reduction method. The frequency band of interest is 6500 Hz. This technique substantially reduces calculation time by reducing the number of degrees of freedom from several hundred to about ten. Furthermore this approach enables the introduction of the Quality factor Q [7], whose value was obtained experimentally from the frequency response of the non-rotating spindle in the diagonal term of matrix D as referred to in the following equations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001861_tia.2003.818995-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001861_tia.2003.818995-Figure3-1.png",
        "caption": "Fig. 3. Cross section of the analyzed structure (flux lines of the first slice).",
        "texts": [
            " is the end-winding inductance (9) Matrices and consider the permeability and conductivity. and are the connection matrices of the stator currents and rotor bar voltages. and are the flux linkage matrices of the stator winding and rotor conductors. The inter-bar currents are obtained directly from vector defined as the vector that contains the entire inferior ring segments currents, the inter-bar currents and the last superior ring segment current. The presented methodology was used to simulate one three phase induction motor, shown in Fig. 3, rated 1000 kW, eight poles, 60 Hz, 6000 V, 890 r/min, and with two rotors, one skewed and one nonskewed. The number of slices adopted in this paper to apply the multislice technique is four . The skewing angle of the rotor slots is 1.25 (1/4 stator slot pitch). The end-ring segment resistance and reactance of the motor are 1.23 and 8.49 , respectively. The periodic condition was used over the borders of the domain for the finite-elements resolution. The number of slots in the stator and rotor are 72 and 88, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003768_j.mechmachtheory.2005.10.010-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003768_j.mechmachtheory.2005.10.010-Figure2-1.png",
        "caption": "Fig. 2. Meshing coordinate systems for toroidal drive.",
        "texts": [
            " It consists of three components including the sun-worm, planet worm-gears and the stationary internal toroidal gear. The meshing rollers are media in the meshing contact of these components. A planet carrier is the output of the drive. Focusing on the meshing characteristics between a planet worm-gear and the sun-worm, the meshing properties between the planet worm-gear and the stationary internal gear can be revealed by setting up relevant coordinate systems between a planet worm-gear and the sun-worm and between a planet worm-gear and the stationary internal gear as in Fig. 2. In the figure, the global coordinate system S1(i1, j1,k1) is attached to the centre of the sun-worm. The rotatable coordinate system S10 \u00f0i10 ; j10 ; k10 \u00de is attached to the sun-worm and rotates about the axis k10 of the centre of the sun-worm by angular speed x1. The global coordinate system S1 represents the original location of S10 . The angle u1 represents the rotational angle of the sun-worm. The transformation from S1 to S10 can be described as 10 1 M. The coordinate systems of the planet worm-gear are presented with a fixed-orientation coordinate system S2(i2, j2,k2) fixed at the centre of the planet worm-gear and a rotatable coordinate system S20 \u00f0i20 ; j20 ; k20 \u00de attached to the planet worm-gear and rotating with the worm-gear about the axis k20 of the centre of the worm-gear by angular speed x2. The initial orientation of location of S20 is the same as the orientation of the orientation-fixed coordinate system S2. Angle u2 is the rotating angle of the worm-gear. The transformation matrix of these two coordinate systems is given by 2 20M. Similarly, the coordinate systems of the stationary internal gear are also illustrated in Fig. 2. The fixed-orientation coordinate system S3(i3, j3,k3) is attached to the centre of the stationary internal gear. A rotatable coordinate system S30 \u00f0i30 ; j30 ; k30 \u00de is attached to the internal gear and rotates about the axis k30 of the centre of the internal gear by x3 in the inverted motion in which the internal gear is presumed to move. The initial orientation of location of S30 is the same as the orientation of the orientation-fixed coordinate system S3. Angle u3 is the rotating angle of the stationary internal gear in inverted mechanism",
            " The induced normal curvature is the relative normal curvature between the two meshing surfaces and can be used in stress analysis, tooth profile machining and tooth contact analysis. The induced normal curvature of meshing between a planet worm-gear and the sun-worm is given as 1 2Kr \u00bc 1 \u00f0kr20uk2kr20hk2 \u00f0r20u r20h\u00de2\u00deW \u00f0kr20uk2\u00f0Uu\u00de2 2\u00f0r20u r20h\u00de \u00f0Uu\u00de \u00f0Uh\u00de \u00fe kr20hk2\u00f0Uh\u00de2\u00de. \u00f011\u00de Different rollers have different effects on the meshing properties of a toroidal drive. To develop the mathematical model reflecting these effects, a body-attached coordinate system S(i, j,k) is fixed at the centre of the meshing roller in Fig. 2. The relationship between this roller coordinate system and the rotatable planet wormgear coordinate system S20 is given as M \u00bc 1 0 0 r2 0 1 0 0 0 0 1 0 0 0 0 1 2 6664 3 7775; \u00f012\u00de where r2 represents radius of reference circle of planet worm-gear. To develop the mathematical model of the conical roller meshing of the toroidal drive, a conical roller in body-attached coordinate system S is illustrated in Fig. 3, where u and h represent the meshing parameters and radius q and angle b are the geometric parameters of the conical roller"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000206_a900490d-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000206_a900490d-Figure1-1.png",
        "caption": "Fig. 1 Experimental set-up for calibration of the oxygen sensor. (1) Ar carrier gas; (2) exponential dilution flask; (3) magnetic stirrer; (4) injection syringe; (5) flow cell situated in spectrofluorimeter; (6) gas vent; (7) excitation light beam; (8) emission light beam. The dotted line shows the flow path of the Ar carrier gas.",
        "texts": [
            " The dry [Ru(dpp)3][(4-Clph)4B]2 adsorbed on silica gel was then kept in a desiccator for further use. [Ru(dpp)3][(4-Clph)4B]2 adsorbed on silica gel was packed in a laboratory-made flow cell19 and placed securely in a spectrofluorimeter containing a lamp power supply (Model LPS-220), a xenon lamp (Model A1010) and a photomultiplier detection system (Model 710), from Photon Technology International (London, Ontario, Canada). Different concentrations of O2 standards from an exponential dilution flask (Fig. 1) were injected into the flow cell. All fluorescence measurements were made at room temperature (23 \u00b0C) and atmospheric pressure. Fig. 1 illustrates the flow injection of an air sample into the flow cell. A stream of argon (Ar) carrier gas at a flow rate of 110 cm3 min21 was continuously supplied to the flow injection system. An open air (20.95% v/v) sample (0.2\u20130.5 cm3) was injected into the exponential dilution flask (135 cm3) with a Hamilton gas-tight syringe (Supelco, Bellefonte, PA, USA) through a rubber stopper. The injected air sample was then drawn into the flow cell by the Ar carrier gas. Employing this experimental arrangement, an initial concentration, C0, in the flask is exponentially diluted according to the expression20,21 C = C0 exp (2Ft/V) (2) where C is the concentration at time t, F is the volumetric flow rate of the Ar carrier gas, V is the effective volume of the exponential dilution flask and t is the time after introducing the air sample"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003282_j.jmatprotec.2004.04.404-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003282_j.jmatprotec.2004.04.404-Figure2-1.png",
        "caption": "Fig. 2. Direct metal laser sinter (DMLS) process.",
        "texts": [
            " This can be considerably improved with a treatment of, e.g. epoxy infiltration. For many purposes the strength needs to be improved which can also be done by post-processing with epoxy infiltration. Two-manufactured rapid tool SLS-P inserts are shown in Fig. 1(c). Direct metal laser sintering (DMLS) is a layer manufacturing process for various classes of materials, whereby fine layers of powder material are applied to a building platform and sequentially fused together by a scanning laser beam, Fig. 2. Laser sintering is a two-step process [12]. Here the powder feeding and energy output occur successively. In the first step a well-defined plain powder layer is formed using a levelling device. In a second step the laser beam is subsequently steered across this powder layer according to the component contour to be manufactured. The metallic powder is sintered with a liquid phase. Through subsequent lowering and addition of a new powder layer, the layered structure of the component results. The tools made by DMLS powder metallurgy process are die inserts to compact flask-less sand moulds with DISAmatic\u00a9 foundry technology, Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001388_icsmc.1997.633290-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001388_icsmc.1997.633290-Figure3-1.png",
        "caption": "Fig. 3. Kinematic configuration.",
        "texts": [],
        "surrounding_texts": [
            "\\Ye searcli [.lie joint. traject,ories which minimize a.n energet,ic crit.erion X subject. to a constraint. C(y ) > 0. Forces and t,orques a.re calculat,ed using t,lie dynamic model of t.he robot. A. Dynaniic model on the model of our biped robot see [3]. The model used is given in Eq.(l). For more details r , , ( q ) = A ( q ) i i + H ( q , i ) + r F + r G + J T F , x i (1) \\v 11 ere r,(y) : Motfor torque, A ( q ) i : Torque due t.o inertia, H ( q , q ) : Torque due to centrifugal and Coriolis r F : Torque due to dry and viscous friction, r(;(q) : Torque due to gravity, J ( q ) : Jacobian matrix computed at the Fezt : Force on mobile foot due to the . forces, a.pplica.tion point of the force FeZt . contact with the floor. B. Oplimzzatzon criterion Rather than optimizing the energy consuniption during a step which is highly dependent on the shape of the floor, we have chosen to minimize the sum of mechanical losses, r$j, and motor Joule losses, Consequently, we use the following cost function A. m;f, FM. When Fext exists, its contribution is taken into account via r M . C. Constraint During a step the mobile foot must be above the floor. This yields to the calculation of the kinematic"
        ]
    },
    {
        "image_filename": "designv11_24_0003913_s0076-6879(05)96007-2-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003913_s0076-6879(05)96007-2-Figure1-1.png",
        "caption": "FIG. 1. Blood drop experiments were conducted by suspending approximately 20 l of rabbit arterial blood within the helical reference electrode. The blood drop was held in place by capillarity and kept fluid by a continuous flow of warm humid gas.",
        "texts": [
            " For example, we suspended a 20- l drop of rabbit aortic blood restrained by surface tension within a helix of silver wire 1.85 mm in internal diameter. The helix was coated with silver chloride so it could function as the electrically stable reference electrode of a two-electrode electrochemical cell. Centered within the drop and coaxial with the reference electrode was an NO\u2013specific electrode, approximately 100 M in diameter and 3 mm long. The drop and the associated electrodes were housed within a water-jacketed 4-ml airspace, which was maintained at 30 (Fig. 1). Humidified gas mixtures were allowed to flow past the drop and were alternated between an air\u2013CO2 mixture (20% O2, 5% CO2, 75% N2) and a CO2\u2013nitrogen mixture (5% CO2, 95% N2). Gas flow was maintained at constant rate. NO-specific electrodes were fabricated according to a procedure described in detail by Wang et al. (submitted for publication). Briefly, platinum wires, approximately 100 in diameter, were coated with aligned, multiwalled carbon nanotubes using the fluoropolymer Nafion as adhesive",
            " Electrochemical activation and measurements of NO oxidation and electrical resistance can be performed on any suitable potentiostat. For example, we used a BAS 100 B/W potentiostat equipped with a low-current module. The amperometric responses (nA/ M ) of the electrode for ascorbate, L-cysteine, DPG, sodium nitrite, and sodium nitrate were normalized to the response for NO and are shown in Table I. Signals consistent with NO oxidation were seen in blood-drop experiments involving gentle deoxygenation. In the system of Fig. 1, these apparent NO oxidation signals were first detected from 200 to 400 s after the flowing gas was changed from the oxygen-containing mixture to the oxygen-free mixture. An initial oxidation spike was followed by a continuous signal of 1\u20132 nA, which would correspond to nitric oxide in the tens of nM (Fig. 3A). Such signals were not seen when blood was exposed for the same length of time to only the oxygen-containing mixture (Fig. 3B). The blood-drop preparation described here may represent a useful approach for further investigation of the response of NO levels in various biological fluids to alterations in concentration of other dissolved gases, such as oxygen"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003988_1.2401213-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003988_1.2401213-Figure1-1.png",
        "caption": "Fig. 1 Configuration of a fluid-film journal bearing",
        "texts": [
            " It is shown that the designed bearing cannot estabilize the Jeffcott rotor with any shaft stiffness at any rotating peed for all the eccentricity ratios. Moreover, if the length-toiameter ratio is smaller, the designed bearings have nearly the ame magnitude of load capacity and frictional torque as those of full circular bearing. It is also shown that the optimal value of he whirl-frequency ratio is so deteriorated by truncating higher erms of the series that the whirl instability occurs for ome eccentricity ratio. Formulation of Optimization Problem A pressure distribution is developed in a fluid-film journal bearng Fig. 1 and described by the Reynolds equation for a onstant-viscosity incompressible fluid. Furthermore, pressure ,z vanishes at the bearing boundary, p , \u00b1L /2 =0, where L s the bearing length, and is axially symmetric about the bearing idplane, p / z ,0 =0, and circumferentially a continuous unction, p ,z = p +2 ,z . It is also assumed that only the ositive values of the pressure are integrated to yield the reaction orce of the bearing, that is, the pressure should satisfy the G\u00fcmel boundary condition",
            " Therefore, a performance index is chosen to improve the stability characteristics of fluid-film bearings as follows J = k=1 M Max s 2 \u0304k ,0 0 \u03041 \u03042 \u00af \u0304M 9 where \u0304M 1\u2212 0 1 if A B, Max A ,B =A, otherwise, Max A ,B =B, and M is the number of eccentricity ratios. The performance index is minimized subject to many constraints as follows: The first M constraints are k k,X tan k + S p\u0303 \u0304k, k sin \u2212 k dS Sp\u0303 \u0304k, k cos \u2212 k dS = 0 k = 1,2, \u00af ,M 10 where p= p\u0303 3 D2 /Cr 2 with being viscosity. It is now assumed that the reaction force of the bearing is directed along the negative Y axis Fig. 1 , and Eq. 10 then defines k as an attitude angle in a steady state. The pressure is a function of k, and Eq. 10 is JANUARY 2007, Vol. 129 / 107 of Use: http://www.asme.org/about-asme/terms-of-use u b c s n M w T m w a m t t t c t \u0304 t s b M = w l m c M w fi I a p r T F s r T i f t 1 Downloaded Fr sed to solve the dimensionless Reynolds equation for p\u0303 with k eing unknown. When the clearance configuration is not a full ircle, an iterative procedure is generally used to find the pressure olution satisfying Eq",
            " For the five length-todiameter ratios, the optimal values of the Fourier coefficients are shown in Table 2, and Fig. 2 compares the optimal clearance configurations with a full circle. These optimal configurations resemble an offset two-lobe one 1 for smaller length-to-diameter ratios, and, however, they are oriented in a different direction to the applied load from that of the general offset two lobe. Here, we define an orientation angle as the circumferential coordinate at which the clearance takes the maximum value, originating from the positive Y axis Fig. 1 . When the major axis corresponds to the X axis, an elliptical bearing takes an orientation angle of 90 deg in terms of this definition. The designed bearings have an orientation angle of about 30 deg as shown in Table 3. Many offset two-lobe bearings have an orientation angle of 90 deg, whereas Wang et al. 9 design an elliptical bearing with an orientation angle of 30 deg, maximizing the film pressure in the two lobes. It is also shown in Fig. 2 that the designed bearings have the same value of the minimum clearance, Cr, owing to Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000944_s0094-114x(96)00075-4-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000944_s0094-114x(96)00075-4-Figure1-1.png",
        "caption": "Fig. 1.",
        "texts": [
            " Meanwhile, a point A, which does not belong to the line L, traces a curve FA in fixed frame 0 - (/k, but each position of A at FA always corresponds to a position of L on Z, or the point A is adjoint to the line L, hence, the curve FA is adjoint to the ruled surface Z. We define Z as an original ruled surface and FA as an adjoint curve of Z. Thus, the vector equation of FA can be written as FA: RA = rp + x~E~ + x2E2 + x3E3, (4) where (x~, x_,, x3) are the coordinates of the point A in Frenet frame {re, El, E~,, E3}, shown in Fig. 1. Based on equation (3), the first derivative of RA with respect to a is given by dRA da = AIE~ + A2E2 + A3E3 (5) where dxl dx2 _ [3x3, A3 = [3x2 + dx3 A, =-d--d-x2 + ~, A2=x~+-d-- d -d--d+~, By differentiating the above equation with respect to a further, any order of derivative of RA will be obtained and the invariants of the curve FA can be represented by the invariants of the ruled surface Z, which will be discussed later. In particular, if the point A is a fixed point in the fixed frame 0 - 0'k, we have dRA/da = 0, which implies dx~ A~ = -d-~-a - x2 + ~ = 0 dx2 fix3 = 0 A2 = x~ + ~ - dx3 A3 = fix2 + ~ + ~ = 0 (6) In that case, the point A is called a fixed point and equation (6) is defined as a fixed point condition of a curve adjoint to a ruled surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001575_jsvi.2000.3351-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001575_jsvi.2000.3351-Figure1-1.png",
        "caption": "Figure 1. Engine mounting system.",
        "texts": [
            " The analysis indicates that the mounting forces and moments can be fully re-constructed as long as the velocity spectra and 0022-460X/01/170321#11 $35.00/0 ( 2001 Academic Press the phase di!erence between three orthogonal directions (X, >, Z) at each point are provided. The equations are derived and the combined genetic and gradient-based optimization methods are applied to solve these non-linear and overdetermined equations. The engine is modelled as a rigid body that is supported by four vibration isolators \"xed to a rigid #oor as showed in Figure 1. A rigid-body model is suitable for a structure whose geometry points remain \"xed relative to one another [5]. The right-hand global co-ordinate system Gxyz has its origin at the center of mass of the engine when in static equilibrium. The three orthogonal co-ordinate axes, which are shown in Figure 1, are set with> and Z-axis parallel to the #oor and X normal to the #oor. The crankshaft of engine is in the direction of Z-axis. Under the assumption of &&small'' motion, the engine-mount system equation can be written as [M] MxK N#[K] MxN\"MFNe*ut, (1) where [M] is the 6]6 engine's rigid mass matrix, MxTN\"[xg yg zg h x h y h z ] the displacement vector at c.g. of the engine, [K] the 6]6 sti!ness matrix, MFN the 6]1 vector of excitation forces and moments and u the forcing angular frequency. The majority of mounts used in the engine mounting are of a rubber bonded to metal, or elastomeric construction",
            " However, a quadratic, rather than a linear approximation of objective function is used. The optimization problem is thus approximated by a quadratic programming (QP) problem at each iteration. This QP sub-program is solved using a standard QP solver. The problem terminates if the minimum is reached and all constraints are satis\"ed. If not, the solution of QP guarantees that the further descend is possible and approximation process repeats. An overview of SQP is found in Fletcher [13]. Consider a typical engine that is installed as illustrated in Figure 1. The engine is supported at four corners by four identical isolators. The location of each mount is listed in Table 1. TABLE 1 Mounting locations of isolators X(m) >(m) Z(m) C.g. 0 0 0 Mount 1 !1 0)8 2)2 Mount 2 !1 !1)2 2)2 Mount 3 !1 !1)2 !1)8 Mount 4 !1 0)8 !1)8 The engine mass in 9600 kg. The mass moment of inertia I\"[I xx I yy I zz I xy I xz I yz ]\"[15 100 15 999 6399 2000 900 1200] kgm2. The damping loss factor g is 0)1. The isolator sti!ness are K x \"K y \"1)9]106 N/m, K z \"4)6]107N/m. The running speed of engine is 1500 r",
            " The orientation of each isolator is set such that, in each direction, the absolute value of angle of each mount is the same but it may be arranged in the negative direction to satisfy the balance requirement of engine installation. The arrangement of four mount orientations meet the following requirement: !a 1 \"a 2 \"a 3 \"!a 4 , (20) b 1 \"b 2 \"!b 3 \"!b 4 , (21) c 1 \"c 2 \"c 3 \"c 4 , (22) where a, b, c, are the Euler angles with the \"rst rotation around positive Z-axis, then >-axis followed by X-axis as shown in Figure 1. The selected absolute values of a, b, c are 0, 743, 793, respectively. In the direct problem, the excitation force and moment are the input parameters. The output parameter is the velocity at mounting points in three directions. For the force excitation as listed in Table 2, the velocities at mounting points are calculated based on the direct equations and listed in Tables 3 and 4. If the real and imaginary parts in Tables 3 and 4 can be accurately measured, the excitation force and moment can be exactly re-constructed from equation (9) to obtain the force and moment in Table 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003854_tmech.2005.852450-Figure15-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003854_tmech.2005.852450-Figure15-1.png",
        "caption": "Fig. 15. Experimental reachable area obtained by rotating the active link clockwise (\u03c350 < \u03c3 < \u221e).",
        "texts": [],
        "surrounding_texts": [
            "We experimentally confirm the theoretically obtained reachable and stabilizable area of the tip of the free link (Fig. 13). The active (first)link is actuated by an AC servomotor with a rotary encoder (Mitsubishi Corp., HC-MFS73 [maximum torque: 7.2 N\u00b7m, rated output: 750 W)]. The free (second) link does not have an actuator or a sensor. A CCD camera (Sony Corp., XC-77) is used for collecting the data of the stable equilibrium points of the tip of the free link; this data is not used for any motion control. The experimentally obtained reachable and stabilizable areas of the tip of the free joint are shown in Figs. 14 and 15, which are in the cases when we rotate the active link counterclockwise and clockwise, respectively. They are in good agreement with the theoretically obtained reachable and stabilizable areas in Figs. 11 and 12. Furthermore, we show the change of the configuration of the manipulators in the motion control of the free joint from the initial state to the position (d)U +. The configurations of the manipulator where the tip of the free link reaches the points in Figs. 14 and 15, (b)U\u2212, (a)U 0, (b)U +, (c)U +, and (d)U +, are shown in Fig. 16(b)\u2013(f), respectively; Fig. 16(a) shows the initial setting of the manipulator. Here, the excitation frequency of the active link is constant at 45 Hz in the motion control from Fig. 16(b) to (f). Each configuration is stable and can be kept without state feedback control of the free joint. If we stop changing \u03b81off , at each configuration, the configuration is kept stable without state feedback of the free joint."
        ]
    },
    {
        "image_filename": "designv11_24_0003010_1.2149394-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003010_1.2149394-Figure2-1.png",
        "caption": "Fig. 2 Cross section of journal and one pad of bearing in local coordinates",
        "texts": [
            " The equations of the motion of journal center Oj can be written as mX = FX X,Y,X ,Y + me 2 cos t mY = FY X,Y,X ,Y + me 2 sin t \u2212 mg 1 Equation 1 has the following dimensionless form: mC 2x\u0308 = 6 Rb 4 C2 fx x,y, x\u0307, y\u0307 + me 2 cos mC 2y\u0308 = 6 Rb 4 C2 fy x,y, x\u0307, y\u0307 + me 2 sin \u2212 mg 2 Introducing the dimensionless rotating speed = e /g, eccentricity to clearance ratio =e /C and combined parameter =6 Rb 4 /mC3 \u00b7 e /g, Eq. 2 can be rewritten as x\u0308 = fx x,y, x\u0307, y\u0307 + cos y\u0308 = fy x,y, x\u0307, y\u0307 + sin \u2212 1 2 3 A new model of calculating the fluid-film forces fx, fy is shown in the next section. Figure 2 represents the cross section of the journal bearing in local coordinates and the pad in circular cylindrical coordinates. The pad domain is separated into two sets = + 0. The fluid-film forces can be obtained by integrating the pressure p over the area of the journal sleeve. The pressure distribution p of one pad can be calculated as follows. Based on the variational inequality theory 24 , the problem of solving the pressure under Reynolds boundary condition can be rom: http://vibrationacoustics"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001455_50006-1-Figure5.51-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001455_50006-1-Figure5.51-1.png",
        "caption": "FIGURE 5.51 Stepper motor stator: (a) reference frame; and (b) profile of scalar potential along the stator surface.",
        "texts": [
            " 442 CHAPTER 5 Electromechanical Devices Thus, we can represent H in terms of a scalar potential, H = -Vq), , (Section 3.4). The field problem reduces to a boundary value problem (BVP) in cylindrical coordinates (Section 3.6.2). Specifically, we solve V2q)m = 0. (5.282) The general solution to Eq. (5.282) that is well behaved at r = 0 is of the form o o q0m(r, q~) = ~ apr p sin(p~b) + bpr r cos(p~b). (5.283) p = l We choose a coordinate system in which q5 = 0 coincides with the center of a stator tooth (Fig. 5.51a). In this coordinate system q)m(r, d~) must be an even function of q5. Thus, we discard the sin(nq5) terms in Eq. (5.283) and obtain o o q)m(r, ~b) = ~ brrP cos(p~b). (5.284) p = l We determine the coefficients b r by matching the boundary conditions at the interior surface of the stator. We assume that the potential qom (R~, q5) along this surface is constant across each tooth and alternates from qOma x to --qOmax on successive teeth. As the gap between neighboring teeth is small (q5~ << qbt), we assume that the potential is linear between the teeth and this implies a profile for qo~(R~, qS) as shown in Fig. 5.51b. To solve the BVP we need a Fourier series representation for qo~(Rs, q5). First, we derive an expression for qOma x in terms of the motor's physical parameters. Let g denote the gap between adjacent stator teeth, and let H~ denote the field in the gap region (Figs. 5.49b and 5.50). We assume that the potential is linear between adjacent teeth. Therefore, 1 Acpm (5.285) H~ = R~ Aq5 qOmax (5.286) where Aq5 = q5~ and 9 = Rsq5~. We apply Eq. (3.138) from Section 3.5 to the dotted path in Fig. 5.50 and obtain ni H~ = - - "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003816_bio.811-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003816_bio.811-Figure1-1.png",
        "caption": "Figure 1. Schematic diagram of FIA setup. A, carrier solution (5 \u00d7 10\u22122 mol/L NaOH); B, oxidant solution (NBS or NCS); P, peristaltic pump; S, sample solution; H, sealed housing; M, mirror; F, glass spiral flow cell; D, detector; I, computing integrator; C, computer; W, waste.",
        "texts": [
            "225 g NBS (Merck) and 1.703 g NCS (Merck) in water, and diluting to 250 mL with water. Luminol solution (1 \u00d7 10\u22122 mol/L) was prepared by dissolving 0.177 g luminol (Merck) in a minimal amount of NaOH, and diluting to 100 mL with water. The minimum number of dilution steps possible was used for preparation of more dilute solutions. All other common laboratory chemicals were of the best grade available and were used without further purification. A schematic diagram of the flow injection CL analyser is shown in Fig. 1. The 12-channel peristaltic pump (Desaga PLG) was equipped with silicon rubber tubes (1 mm i.d.). The sample solution was injected with a Rheodyne sample injector, Model 7125. The carrier stream merged with the oxidant solution stream (NBS or NCS) in a spiral flow cell in front of a photomultiplier tube (PMT). The flow cell was a glass spiral (2 mm i.d., 600 \u00b5l internal volume) positioned in front of a mirror in a sealed housing. The signals from the PMT (RCA 931 VA) were sent to a computing integrator (Philips PU 4815) and then to an IBM-compatible computer (Model 486 DX4), using an RS232 port. A filter fluorometer (LS-2 B, Perkin-Elmer) was used for recording the CL spectra. The FIA manifold used is outlined in Fig. 1. In order to achieve good mechanical and thermal stability, the instruments were allowed to run for 10 min before the first measurement was made. A solution of 5 \u00d7 10\u22122 mol/L oxidizing agent (NBS or NCS) and 5 \u00d7 10\u22122 mol/L NaOH (carrier stream) were each pumped at 3.5 mL/min. The blank solution, which only contained 5 \u00d7 10\u22127 mol/L luminol, was injected into the carrier stream with the aid of an injection valve with a 600 \u00b5L loop and a stable blank signal was recorded. Then the sample or the standard riboflavin solution, which contained not only 5 \u00d7 10\u22127 mol/L luminol but also an appropriate concentration of riboflavin, was injected into the carrier stream and the CL signal was recorded"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003325_j.mechmachtheory.2006.09.008-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003325_j.mechmachtheory.2006.09.008-Figure1-1.png",
        "caption": "Fig. 1. Changing of gear blank after modification.",
        "texts": [
            " Thus pitch parameters are modified, and the bearing capacity and strength of the hypoid gear designed by the modified pitch cone method are improved, similar to Liang\u2019 non-zero modification design method. A hypoid gear pair has been designed by the Gleason method. On the condition of the invariant mean working depth and invariant outer diameter of gear, we set the gear addendum coefficient fa 6 0, new pitch cone is coincident to face cone or out of the gear solid. The changing of gear blank after modification is shown in Fig. 1. In Fig. 1, P1Q1 = X2/2, X2 is the outer diameter of gear, Points O2, Oa2, Of2, H2 are intersect point of gear shaft with pinion shaft, intersect point of gear face cone with gear shaft, intersect point of gear root cone with gear shaft, and intersect point of gear pitch cone with gear shaft before modification, respectively. Points H 02, P 02 are the intersect point of gear shaft with gear pitch cone, and the intersect point of gear shaft with the mean point of gear width on the pitch cone after modification, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001694_0301-679x(89)90008-x-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001694_0301-679x(89)90008-x-Figure1-1.png",
        "caption": "Fig 1 Elliptical bearing geometry",
        "texts": [],
        "surrounding_texts": [
            "Flow-field\nThe laminar flow, neglecting the local and convective inertia of an incompressible lubricant in the clearance space of each lobe of an elliptical journal bearing, is described by the following non-dimensional momentum and continuity equations:\nR O , ( 2 0 ~ f i )\nR = # ~ V2~ ~ 2 d 0 f2\n@ = ~, (v2~,) 0~., (1)\nwhere\nV2 = / 02 1 0 1 02 1 02 \"~\nloft [0~ ~'~ 1 09v r dO-b k0Z-r + ~) + ~ -~--z = 0 (2)\nThe following boundary conditions are used for the lubricant flow-field in terms of pressure, pressure gradient and velocity components:\n~ = 0 at 0=0~\n~ = 0 a t e = +1\n@ 0 at 0 0~ dO (3)\nfi, ~, ~ = 0 at ~ = R + h\n~ = 0 a t ~ = R\nf i = l - ~ - ~ c o s 0 + sin0 a t ~ = R\n~ = - ~ - ~ s i n 0 - cos0 a t ~ = R\nThe solution of Eqs (1) and (2) using the boundary conditions (3) give the velocities u, v, and # and the pressure distribution ~. Using the finite element formulation based on Galerkin's technique and applying the boundary conditions (3) at the element equation stage, the following non-dimensional global system equations 1 ~ are obtained after assembling the contributions of all the elements in the discretized flow-field:\n[~_,] {~} = R a + &\u00a2{R,} + @ {R,,} (4)\nThree-dimensional isoparametric elements with 20 nodes for velocity and 8 corner nodes for pressure are used for discretization of the positive pressure fluid film region in the clearance space.\nDisplacement field\nThe bearing liner is discretized by 8 noded isoparametric elements in which displacement is assumed to be linear. Using the minimum potential energy principle, a set of algebraic equations is obtained in terms of a nodal displacement vector {a} = [~=, ~,, ~,_]r 6, for the displacement field\n[g] {a} = q'{F} (5)\nwhere the force vector {F} is due to surface traction caused by the hydrodynamic pressure acting on the interface between the fluid and the bearing liner.\nTemperature field\nEnergy equation The temperature variation in the fluid film is described by the following non-dimensional energy equation which is derived from the three-dimensional energy equation, using the simplifications and approximations as suggested by Lund and Hansen13:\n+ ~ ~d (6) where\nfTC ' ) \" % = ~ - 1/(L/O) a o ,/z, ,7 = #\n1 fL ~i 3\nThe temperature profile (7) across the film thickness is expressed as\nT= At/4 + Bt/3 + 0/2 + Dq + 7\" B (7)\nThe constants A, B, C and D are evaluated from the following boundary conditions13: (i) fi = 0 at q = 0, that is, at the inner surface of the bearing (ii) dT/a0 = aT J00 = 0 at q = 1, that is, at the journal surface, (iii) 7 = T, at r/= 1 (8) and defining a mean film temperature 13,\n7m -- 1 -- ~I'f (~ -- 3~I'f~ + 3~' f~2)~1~\nUsing Galerkin's technique, the element equation corresponding to Eq (6) can be derived in the following form:\n[H] ' {7.} ' = {F~}' + {F2}\" {Tn}' (9)\n{F,} ' = J\" N,([ , + [27 d0, {Ira2}\" = f R , ~ d0\n{n}=j'(R,-~aRJ ___\\_ + NtNjido) dO\nwhere, i, j = number of nodes per element.\n10 T\u00b0 = ~(1 - (17/14)~f);\nkl = ~ 5 - 28\n~ b d 10/3 + 5~, 2Pc* ~2 = h(1 - ~f); k3 - (1 - (17/14)~fX1 - ~e) h2\n.F:'\u00b0r,\"n '1 ~ li it 37i 1/(L/D) T~' T~i' - 2 Pe* h + ~- L\\~-/\n[0p'\\2-1 aP +k-~z)]dz-T-2~l/(L/D)~;m(-~)dz}\nTRI BOLOGY international 45",
            "By the usual assembly procedure/6, the global system equations for temperature variation in the lubricant flow-field are obtained as\nI :n ] { rm} = {F , } + (10)\nFourier heat conduct ion equation The two-dimensional heat conduction equation is written in the following non-dimensional form to establish the temperature field, assuming that the axial variation of temperature is negligible:\nO2'F 1 D~ r 1 t32~r c~2 + ~ ~ - I - ~2 002 - 0 (11)\nUsing the finite element method and Galerkin's technique, the following global system equations are obtained:\n[6 ' ] {TB} = {Fa} (12)\nBoundary conditions for temperature field in the lubricant fi lm and the bearing body\nThe following boundary conditions are used for the temperature field in the lubricant film and the bearing body:\n(i) T= T t at 0 = 0\n(ii) T=T~ a t ~ = R\nt3/T (13) OT kbush 1 koi I (iii) h C ~ r/=0 th ~=R~\n(iv) kbu'ht~T h T~ t h ~rr r--R2---- c( I =R2- -Ts )\nThe heat balance due to the mixing of make-up oil and the recirculated oil at the inlet is expressed by the following equation 14 from which the inlet oil film temperature is calculated:\nVET L = VT[Tt -- F,(TT - Ts)- F2(TT - 7',)]\n+ (i/L -- VT)T, (14)\nwhere F'~ and F 2 are empirical coefficients whose sum cannot exceed unity and whose values are each taken as 0.05 ~4. Subscript L denotes the leading edge of the fluid film and T the trailing edge.\nSolution procedure\nThe solutions for pressure distribution in the lubricant flow-field, deformation in the bearing liner and the temperature in the lubricant film and the bearing body are obtained using a successive iteration scheme 4' s. The trailing edge of the fluid film satisfying the Reynolds boundary condition in each lobe of the elliptical bearing, and the equilibrium locus for the journal centre position for vertical load support, are found by iteration. The solution scheme also corrects the inlet oil film temperature of the lubricant by considering the mixing of make-up oil and the recirculating oil flow at the inlet.\nResults and discussions\nTo establish the validity of the present analysis, its solution algorithm and the computer program, sample\nresults of load carrying capacity of a circular journal bearing are calculated and compared with published results 6 for # = 0.5 and 0.7 by taking the deformation coefficient \u2022 = 0.0, 0.03 and 0.07 and piezoviscous coefficient ~ = 0.0 and 0.1 (see Table 1). The comparison is quite good and the mean film temperature of the oil film obtained from the present analysis also compared well with the results of Lund et a114 Fig 2.\nThe computed displacements of the nodes of the bearing liner at its interface with the fluid film and the corresponding pressure distribution for deformation coefficient, \u2022 = 0.0, 0.1 and eccentricity ratio, Z, c = 0.35, are presented in Fig 3 for (i) isoviscous, (ii) piezoviscous and (iii) thermopiezoviscous lubricants. These curves indicate that the maximum pressure developed in the fluid film decreased with an increase in the deformation coefficient in all those cases.\nThe effect of bearing deformation on the load carrying capacity, attitude angle, and the power loss are presented in Figs 4 and 5 for isoviscous, piezoviscous and thermopiezoviscous lubricants. It is seen that for any deformation coefficient, the values of the load carrying capacity, the attitude angle and the power loss obtained for\n46 February 89 Vol 22 No 1",
            "C\u00a3 = 0.0 C\u00a3 = 0.03 ~ = 0.1\nao ~ = 0 . 0 ~ = 0 . 1 ~ = 0 . 0 ~ = 0 . 1 ~ = 0 . 0 ~ = 0 . 1\n1 2 1 2 1 2 1 2 1 2 1 2\n0.7 8.02 7.65 9.53 9.39 6.57 6.49 8.00 7.61 5.82 5.49 6.51 6.28 0.5 3.50 3.36 3.71 3.59 3.39 3.28 3.50 3.46 3.26 3.1 4 3.38 3.21\n1 Present work,\" 2 Published result 7. L/D = 1.0, th/R i = 0.1, ~ = 0.3\npiezoviscous lubricants are more than those obtained for the isoviscous lubricants. For the thermopiezoviscous lubricants, these values are less than those for piezoviscous lubricants, but more than those for isoviscous lubricants. Table 2 shows the percentage changes in the values of load capacity, attitude angle, end leakage and power loss obtained for flexible bearings (~ = 0.1) with (i) piezoviscous and (ii) thermopiezoviscous lubricants, when compared with the corresponding values of those characteristics for rigid bearings with isoviscous lubricants.\nFig 6 shows the effects of deformation coefficient on the threshold speed and damped frequency of whirl. The\n8 I- q 9 0\nL/Z? = I.O, #p = 0 . 5 , fh/Rj =OI,ts/fh=lO.O,~=0.3 I ~c = O.35, ~.= 0 2 #c = 0 . 3 5 , 6. =0.1 3 #c = 0 . 3 5 , 6 .=O. I , Pe*=O.2 4 ec = 0 . 2 5 , Ct= O\n5 ~c = 0 . 2 5 , 6 .=O. I 6 #c = O . 2 5 , O . = O . l , P e * = O.2\n80\n7 0\n8 5- 60 c,. I o \u00b0 2 2 . .~ 4. 3 ~ - 5 0 _~\nb\n~ 3 - - \" - - - - - - 4 0 ~\n5 ~ ' / ~ 30 6-- /\n~t-- H2o\n:: ol I , t I I,o O O.I 0 .2 0.3 0.4 0.5\nDeformotion coefficient d 2 : 1\nFig 4 Effect of deformation coefficient, on. load capacity ( ) and attitude angle (-,~-) '\nthreshold speed increases and the whirl frequency decreases with the increase in deformation coefficient, in all the cases. When piezoviscous coefficient changes from 0.0 to 1.0, the calculated value of threshold speed is more than that for isoviscous lubricants. For thermopiezoviscous lubricants, the values of the threshold speed and damped frequency of whirl lie in between their values obtained for the isoviscous and piezoviscous lubricants.\nTable 3 shows the percentage changes of the threshold speed and damped frequency of whirl for the deformation coefficient \u2022 = 0.3 and eccentricity ratio #o = 0.25, when compared with the corresponding values obtained for the rigid bearing with isoviscous lubricants.\nC o n c l u s i o n s\nOn the basis of the results presented, the following conclusions are drawn.\nTRI BOLOGY international 47"
        ]
    },
    {
        "image_filename": "designv11_24_0002006_978-3-662-09769-4-Figure4.19-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002006_978-3-662-09769-4-Figure4.19-1.png",
        "caption": "Figure 4.19: Diagrams associated with the computations of this section",
        "texts": [
            "f;]\u00b7 [Y~o + ( ( 1'x;O~ ~x 1 ) - bx \u00b7 cos '!j;) \u00b7 ~] . (4.249c) 4.6.3 Physical interpretation of some expressions of the model equations The Lagrange multiplier A: The Lagrange multiplier is identical with the negative constraint reaction force cpx which acts on the body (see (4.231a)). The expression of the La grange multiplier ( 4.248) L \"2 \u2022 L .. A=m\u00b7cos'!j;\u00b7Xcp1 \u00b7'!f; +m\u00b7sm'!f;\u00b7xcp1 '!f;-Fe\u00b7cos('!f;+'!f;e) (4.248) includes the projection of the external force Fe onto the exR-axis, the pro jection of the centrifugal force (Figure 4.19a) F R ni,2 ARL L ,i,2 ARL L 0 =-m2\u00b7<r \u00b7 \u00b7Tp1 c=m2\u00b7<r \u00b7 \u00b7rcp1 = m . ~2 . ( c?s '!j; , - sin '!j; ) . ( x~ p1 ) Sill '!j;, cos'lj; 0 or F R _ ( m \u00b7 ~2 \u2022 X~ p1 \u2022 COS '!j; ) G- \"2 L \u00b7 m \u00b7 '!j; \u00b7 XC p1 \u2022 Sill '!j; (4.250a) onto the exwaxis ( 4.250b) and the projection of the transversal force R .. RL ( L ) l_ \u2022\u2022 RL ( L ) l_ F T = m \u00b7 '!j; \u00b7 A \u00b7 r p1 c = -m \u00b7 '!j; \u00b7 A \u00b7 r c p1 = -m . ;(; . ( c~s '!j; , - sin '!j; ) . ( 2 ) slll '!j;, cos'!j; Xcp1 4.6 Vertical vehicle model (one tr. DOF, one rot. DOF) 197 with ( TL )_!_=(0,-l)\u00b7(X~p1 ) CPl 1' 0 0 ' or F~ = ( m \u00b7 ~ \u00b7 sin 7/J \u00b7 xf p 1 ) -m \u00b7 7/J \u00b7 cos7/J \u00b7 x 0 p 1 (4.251a) onto the exR-axis (Figure 4.19a) R ( R) .. L \u00b7 Frx = Pr(x) F T = m \u00b7 7/J \u00b7 x0 p 1 \u2022 sm 7/J. (4.251b) Coupling terms of the mass matrix: The first equation of (4.247) includes on the left-hand side the coupling term -m \u00b7 Ctx \u00b7 cos7/J \u00b7 7/J (4.252a) which appears because the reference point P is chosen different from the center of mass C of the body. This implies also the associated coupling term of the second equation of ( 4.24 7) o/, \u00b7\u00b7R -m \u00b7 Ctx \u00b7 cos '+' \u2022 YPo\u00b7 Moment of inertia: (4.252b) The moment of inertia which is included in the second equation of ( 4.24 7) consists of four terms. The first two terms (4.253a) describe the standard moment of inertia J foz of the body for rotations around the point P 1 (Figure 4.19b). The remainder terms of the moment of inertia can be written in the form m \u00b7 (( X~pJ 2 - a;) \u00b7 sin2 7/J = m \u00b7 ( X~p1 + Ctx) \u00b7 ( X~p1 - Ctx) \u00b7 sin2 7/J .._\"_, =: bx S: L \u2022 2 \"/' S: \u2022 2 0 j, = m \u00b7 ux \u00b7 Xe p 1 \u2022 Sill '+' - m \u00b7 ux \u00b7 Ctx \u00b7 Sill '+' \u2022 (4.253b) The third equation of the DAE ( 4.223), which corresponds to the second equation of (4.247), includes the term \u2022 o/, \u00b7\u00b7R m \u00b7 Ctx \u00b7 sm '+' \u2022 x PO (4.253c) 198 4. Planar models of a rigid body under absolute constraints which is contributed by the constraint acceleration equations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000641_1.364548-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000641_1.364548-Figure1-1.png",
        "caption": "FIG. 1. Schematic diagram of modified slider and mounting bracket.",
        "texts": [
            " The measured capacitance is inversely proportional to the slider-disk separation and is used to calculate the film thickness within 5 nm. The disk is clamped to a spindle which is belt driven by an electric motor. The motor can provide either a constant velocity or a velocity ramp at constant acceleration. It was found that with the standard suspension supplied with the commercial suspension-head slider assembly the slider would pitch when the friction force exceeded ;900 mN. To prevent this, the slider suspension and mounting bracket were modified, as shown in Fig. 1. The flexure was removed from the suspension and a 38 mm thick brass shim was glued between the slider rails with epoxy. The head slider was then reattached to the load beam by soldering the shim to the load beam. An additional beam attached to the mounting bracket was pressed against the load beam to increase normal load on the slider. The modified slider is stable up to a friction force of 1.9 N. The disks used were 95 mm diam polished disks with an amorphous carbon overcoat. The rms surface roughness and P\u2013V distance were 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001921_20.43960-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001921_20.43960-Figure4-1.png",
        "caption": "Fig. 4: Boundary element-finite element mesh for two angular positions of the rotor.",
        "texts": [
            "X=F (18) The unknowns (X) of the problem are the potential at internal nodes of saturable region s. the potential and its normal deri vative along interfaces. the potential or its normal de\ufffdivative along outer boundaries. Due to saturation effects the system (18) is non linear. A New ton-Raphson method is used to solve it . Application The described method is applied to the SRM as shown in figure 1. With such a method the stator and the rotor only have to be meshed. An example of mesh is g iven in figure 4 where the current is supplied to one stator winding pair . In 4 (a) the position of the rotor corresponds to the maximum inductance value, while in 4 (b) thi s value is minimum. No mesh distorsion occurs when the rotor position is modified and in that case the angular value only has to be changed into the dataset. In the representation of figure 4 the solid shaft has been taken into account with boundary elem ents, neglecting saturation effect in that part . Numerical simulations have been done for several combinations of angular positions of the rotor and current intensities. In the same time a prototype was realized, the main d imensions being : rotor pole radius=O.079m, s ta tor pole inner radius=0. 08m , mach ine length=0. 3m. Stand stil l experimental results were obtained for comparison. In figure 5 the evolution of the inductance versus rotor positions is shown",
            " The finite elements are well ad apted in s aturat ion effect simulation while boundary elements completely disconnect stator and rotor meshes, avoi d any air gap mo de1isation difficulties and allow an easy torque evaluation. (a) maximum induc tance (b) minimum ind uctance 478 2. 22 +', I.B '\" 1.& S IA \ufffd ;' 1.2 \ufffd \" \ufffd \"e:: \" , ' -'-': \" '-': 0,8 , ' ''-:: -- '-': o. 0,4 \" -_ ', (0) \" '- _ _ \"1bj 0,2 (aj'<>---- -- - , o - 12 .& 20 24 28 ROTOR POSlTIQN (D.I!!G J Fig: .\ufffd: Inductance evolution against rotor pos lt lon for the configuration of figure 4. o degrees position corresponds to 4a, while 30 degrees to 4b. The computed evolution (c) js compared with the simplified model in which the inductance linearly varies from Lmax to Lmin. These extremum values being estimated using Ampere law in (a) and measured in (b). 2.4 2.2 1.0 \" 1.B .5 L. tl z 12 \u00a7 5 0,8 OB 0.4 0.2 ------\ufffd COMP\\.M't\ufffdO EXPER1MENT relation 19. fig. 8: Example of flux distribution lines through the iron parts. References [1) P.J. Lawrenson, J.M. B l enkinsop , J. Corda, N.N. Fulton, \"Variable speed switched reluctance motors\" in lEE proc , Vol 127B, 4,1980,p"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001913_tia.2002.1003419-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001913_tia.2002.1003419-Figure2-1.png",
        "caption": "Fig. 2. Directions of traverse for the flux vector.",
        "texts": [
            " The synchronous frame flux/charge modulator uses a simple set of switching rules for its operation, which can be identified by examining the movement of the inverter flux/charge output on the two-dimensional space-vector diagram for a two-level VSI and a two-level CSI, as illustrated in Fig. 1(a) and (b), respectively. Now, if only the two nearest space vectors are used in each sextant to minimize harmonic distortion, the flux/charge vector can only move in two discrete directions. For example, when the reference voltage vector is in sextant S1 of a VSI, the two nearest switching states are SV1 and SV2 and flux vector can move only in the two directions shown in Fig. 2. The only other inverter output is a null vector, which freezes the flux/charge vector and hence makes it move backward relative to the reference in the synchronous frame. From this understanding, the simple switching rules shown in Table I can be formulated to maintain the flux/charge error within the rotating rectangular bounding box shown in Fig. 2, where the dimensions of the bounding box are in the radial and in the transverse directions, respectively. Fig. 3 shows the general sequence of state transitions that could be expected to occur under these switching rules, for the example in Fig. 2. Note that while in a null state, the flux/charge vector moves tangentially backward from LR2 to LR1 at an approximately TABLE I BOUNDARY BOX SWITCHING RULES FOR FLUX/CHARGE MODULATOR constant speed of ( length of actual flux/charge vector) irrespective of the reference vector angular position. This means that for a bounding box with fixed dimensions, the time interval for all null states will be the same. In contrast, the duration and number of active states during depend directly on the instantaneous angular position of the flux/charge vector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003088_robot.2003.1241570-FigureI-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003088_robot.2003.1241570-FigureI-1.png",
        "caption": "Fig. I . Parametrization of SLIP with pitching dynamics.",
        "texts": [],
        "surrounding_texts": [
            "Assume a hybrid mechanical system whose time evolution is described by holonomically constrained autonomous conservative vector fields f,, a E I with configuration space variables qa: 1, = f,(x,) with xa = (4, qa)T E V,. The open flow domains V, are called charts [15]. Transitions between vector fields are governed by threshold functions h! which can depend on the initial condition x, = x,(f = 0) E V,, time t , and the current state fk(xa,).\u2019 We require that for each chart there is only one threshold function h t . Transitions to the vector field f are uniquely defined by to (x ) = min,,o{t : hp (f\u2018 (x ) x t ) = 0). In addition, all transition map- map r! for the a t h vectorfield is implicitly defined via t P a, by re : xa, H f$(xa,). where xa, is assumed to he the result of a preceding chart transition. We will define a partial return map for evolutions on individual charts V,. Under the assumption that a periodic orbit of the whole dynamical system is composed of pseudo-symmetric orbits (to be defined below) on individual charts, volume preservation of the full return map 9 can be determined in some cases without explicitly computing re. This will he the case if the vector field f a has additional structure, namely a time reversal symmetry. Assume that the vector field f a admits a time reversing symmetry (For a survey see [17].) 9, : V, - V,, i.e. P a,% pings , , 7, 7 \u2019 \u201d \u201d \u2019 are assumed to he volume preserving. Theflow i p d dt - ( Y ~ o x , ) = f a ( Y , a x , ) o i , = f a ( x , ) (1) that is also an involution: Ya o Ya = id. This implies 9, o fi o Y, = f;\u2018. We now investigate a composition of two partial return maps, x,, = SC, o$(xa,), followed by xa, = 9, o rg(x,,). If the functional identity tn =to a, a, holds, then i.e. 9, o rp is also an involution. A sufficient condition for tP = t p is given by =I a, - = 0) (4) which can be considered an invariance of the threshold function under the partial return map Ya ore : xa, - S, o \u2018Note that this definition generalizes 1151, where h i only depends on f&). rc(xa,). This essentially checks that the threshold function h i \u201cpreserves\u201d the time reversal symmetry of f a . Given that 9, o re 09, o r! = id we obtain D ( Y a o r t o Y a or: ) = l,,, ( 5 ) = DY,(.8, o 9, o 4) .D&(y6, o DY,($) .Ore Next, we call a trajectory on a chart V, pseudosymmetric if its initial condition, X, is a fixed point of the partial return map 9, o r t , i.e. 9, o $(fa) = fa . Evaluation of expression ( 5 ) at such a fixed point then allows us to determine the square of the determinant of the Jacobian of r; (the monodromy matrix): 2 ( ~ ~ , ( ( ~ B , ( & Z ) ) . D ~ B , ( Z , ) ) = I,,, detZ(DY,((rS,(la)).D4(f,)) = 1 If 9, is linear, as is the case in all of the examples in this paper, then det?(DYa) = I and therefore detZ(Drc(X,)) = 1 Hence if a periodic orbit described by a fixed point of the full return map 9 is composed of pseudosymmetric orbits on V, and conditions (3) hold on each chart, the full return map 9 is volume-preserving at this fixed point. If conditions (3) do not hold or if periodic orbits of the full return map are not composed of pseudosymmetric orbits, no conclusions can he drawn from this argument. Note that here \u201cvolume\u201d is defined with respect to the state variables chosen, and in general is not a phase space volume, and that the computation (at the fixed point) is local. 111. APPLICATION TO HYBRID MODELS OF LEGGED LOCOMOTION A. SUP with pitching The SLIP model consists of a rigid body of mass m and moment of inertia I with a massless springy leg attached to an unactuated hip joint which is a distance d away from the center of mass (for details see [SI). A full stride consists of a stance phase with the foothold fixed and the leg under compression, and a flight phase in which the body describes a ballistic trajectory. Hence there are two vector fields f , (for stance) and f for flight) and the return map can he written as 9 = 2\u2019 o r i o 4\u2019 o 3. We assume that a periodic orbit of period one is composed of pseudosymmetric stance and flight phases? *This was proven in 181 for SLLP without pitching dynamics and without gravity in stance. 1) Stance phase of SUP with pitching: The equations of motion that describe the stance phase of SLIP with mass m and moment of inertia I read in the conventions of Fig. 1 (see also [SI): d V e = c+gcosy-- \u2018 (5 +dcos ( y + e ) ) mn with spring potential V ( q ) where the compressed spring length q = d d 2 + c 2 + 2 d 5 c o s ( y l + 8 ) 5qo, the relaxed spring length being denoted by \u2018lo. The distance between the \u2018hip\u2019 pivot and the mass center is d and all joints, including the toe-ground pivot, are assumed frictionless and moment-free. The involutive time reversing symmetry Yl of (6) acting on xI = (5 y 0 4 is given by the linear map Yl = d i a g ( l , - l , - l , - l , l , l ) . (7) Under Yl, the spring length q remains invariant: Yl ( q ) = q. Transitions to flight occur when the spring length has reached its rest length qo which is also the initial spring length at the beginning of stance. Hence the threshold function can be written as h:(xl(t),xlo,t) = q2( t ) - qi . ?hen the partial return map .ip1 o + is volume-preserving at a fixed point, because (4) holds: 2 - 2 2 h?(x,(t?J,xlB1~io) - q (f1~1-d * h?(y l .x lo ,y1 . ~ l ( t ? o I , ~ ? o ) = qo\u2019 - q2(t?J = 0 = 0 This result is independent of the specific form of the spring potential V ( q ) . For d = 0, the two-dimensional SLIP system describing a point mass on a massless spring is recovered. 2) Flight phase of SLIP with pitching: The equation of motion of the center of mass that describe the flight phase of SLIP read y = o , Q=-*, e = O (8) where the z-axis points vertically upwards, the y-axis points in a horizontal direction, and 8 denotes the SLIP body\u2019s pitching angle with respect to the horizontal. The linear involutive time reversing symmetry Y2 of (8) acting on x2 = ( y z 8 y i 6)\u2019 is given by Y2 = d i a g ( & l , l , - l , ~ l , - l , l ) . (9) Here, the sign ambiguity in 8 was resolved by matching 8\u2019s transformation to that of the stance phase (7). The transfonnation law of y under .Y2 is not needed in subsequent calculations3 and is left unresolved. Hence from now on, we work with a reduced state vector x2 - The simplicity of the equations of motion (8) allows us to explicitly compute the determinant of the monodromy matrix of Y2 o i-4 for a given leg recirculation scheme. Therefore the application of the formalism of Sec. 2, which only provides a sufficient condition for volumepreservation, but not for non-preservation, is relegated to the appendix. The equations of motion for the z and 6 coordinates can be explicitly solved and read in dimensionless variables: iz i(i) = iO+ZLi 0 -? t(7) = ?o-i ~ ( i ) = G0+$i e(?) = eo (10) (2 8 i 0)T. . - w i t h i = t f i , i = k , i= &, o - 8 , , a n d 6 = 6 E . We now want to explore different strategies to position the leg during flight. Since the leg is assumed massless, any leg angle trajectory #(i,Pz0) where @ is defined in Fig. 1 can be commanded. The threshold function h$ for a recirculating leg reads in dimensionless variables h$~,~(i) ,iz0, i) =i(i) + dcos(8(i)) - cos($( i , i2 , ) ) (1 1) where d= d Setting (11) to zero determines the time \u2018lo \u2018 from leg liftoff (iLo = 0) to leg touchdown iTD := iio, for which in general a closed form solution does not exist. Then the flow map ri takes the dimensionless state vector f - (i 5 ii from its value at leg liftoff to that at 3 j is determined by conservation of energy and y is not a periodic 20 - variable. touchdown: ri(i2 ) = fz(iro). A fixed point of a pseudosymmetric Higlt trajectory satisfies fzo = 9, or: (.Q. The determinant of the monodromy matrix of r: can easily be computed from the Right trajectory expressions (IO), bearing in mind that the Hight time iTD also depends on the initial conditions: det(Dri) = 1 - J; La irD+&J,oi,D+$J~oiTo (12) In this expression, the leading term 1 is a consequence of Liouville's theorem, because i and t and 6 and 6 are canonically conjugate up to a trivial rescaling, whereas the remaining terms make the non-applicability of Liouville's theorem to this hybrid system with a state-dependent threshold function (1 1 j explicit. Hence using implicit differentiation of (1 I ) the determinant can be written in terms of partial derivatives of @(i f ): ' 20 with Ai\"\"\"' = sin(@(i,f2J). ( J4 @(i,f2J - ?,,Jj0 4 (i,.s,o) - 6,, J g @ (i,f,,)) 0 , +i- t,, +dsin( Q 6 , Aiden = sin($(i,~za))Ji@(i,fz~) -i+?,, - dsin(eO)6, Albeit irD cannot he computed explicitly in general, irD = 2i0 at a symmetric (period-I) fixed point of 9; o ri, sin(@(&,,Zz0)) = -41 - (io+dcos(6,,))2 and O ( i r D ) = -eo. The eigenvalues of the partial return map 9; o r$ at such a fixed point are I , = 1 (vertical energy), = 1 (rotational energy), = -1, and I4 = -det(Dri(22,0)). It must be emphasized, however, that the eigenvalues of this partial return map are not equal to the eigenvalues of the total return map 9 at the fixed point. In particular, the eigenvalues of I can be complex, as in Fig. 2 , below. Setting (13) to 1 yields a partial differential equation for leg recirculation schemes @(if ) that are volume preserving. In the following, for simplicity, we apply formula (13) to different leg recirculation schemes for SLIP without pitching dynamics, i.e. d = 0 and no 6, 6 dependence. The investigation of Leg recirculation strategies of SLIP with pitching dynamics will he detailed in [IO]. For SLIP without pitching, the determinant at the fixed point simplifies to 3 20 -~ det(Dr:(P2J) = 1 + (14) sin(@(i,P2J) ( Ji, @(i,a,J - 4 JT0@(i,f2J) + i -e, sin( @(i,X,J) Ji$(i,Xz0) - i + t,, I- - f=lrD 31 Analysis of Recirculation Sfrategies: Consider now @(f,izo) =karccos(i,,)+a(i-l?,,): k , 1 > 0 (15) For k # 0 leg recirculation starts at an angle proportional to the leg liftoff angle; if l = 1, a certain angular trajectory is specified starting at apex (see the leg retraction scheme in [91). 20 The application of the partial return map 9, or: on ,t in the threshold function h i (4) in order to determine for which parameters of the leg recirculation schemes (15) volume is preserved is relegated to the appendix. Instead we proceed by explicitly computing det(Dri(fzo)). With the angular trajectory (15). the determinant becomes det(Dr$(iz,)) = I + (16) the following family of leg recirculation schemes I :=irD Hence for different leg angle protocols we obtain 1 ) Constant leg touchdown angle protocol: k = 1 = 0, a = 2n - p =+ det(Dr:(i;,)) = 0. The twodimensional monodromy matrix has rank one for all iTD. and the return map becomes one-dimensional. In [7] this return map was parametrized by apex height, whereas in [SI the angle of the touchdown velocity was chosen. No information about the behavior of this lower-dimensional return map can be obtained from this argument. 2) Leg retraction (91: k = 0, I = 1, and a( i - $) = a, +6(i-$ where a, is a constant angle and I3 = mJ$ is a constant dimensionless angular velocity. Then again det(Dr;(P2,)) = 0 and the behavior of the remaining one-dimensional return map cannot be determined from this argument. 3) Leg recirculation (starting at leg liftom: I = 0, k > 0, and a(i) = a, + ai. This exemplifies the fast rotation phase of the open loop policy used by RHex [l], although a full analysis is beyond the scope of the present paper. Then the determinant of the monodromy matrix a t the symmetric $xed point becomes: (17) &,(l- k ) + det(Dr;(f2J) = 1 - < I : O < k < l I : k = l > 1 : k > l In order to illustrate the predictive power of (17), we numerically approximate the determinant de t (Dg( i ) ) of the full return map for fixed SLIP parameters E = & = 2.1, y = 3 = 13, and fixed recirculation parameters U,, = 6, 6~ = 14 for different k E {1/6,0.5,1,2,3.3}. Here, E is the total energy of the system and the spring potential is V ( q ) = (K/2)(q - qO)', We then compare these values to the values of the determinant obtained by inserting the numerically determined fixed points ,? - 20 - (4 6)' into (17). The determinants obtained in those two different ways are plotted in Fig. 2a and agree to a high precision (ldet(D%?(i)) -det(Dr;(,?? ))I < lo-'). Barring an improbable numerical cancellation between stance and flight phase dynamics, this also demonstrates that the SLIP'S stance phase is volume preserving? In Figs. 2b-d iterations of the return map in (To $)-space are shown for k E {l /6 ,1 ,3 .3} and initial conditions off the fixed point. The eigenvalues are complex conjugate pairs in all three cases. For k = 1/6 the trajectory spirals towards the fixed point, as expected from a stable fixed point (Fig. 2c), fork = 1 the trajectory is a deformed circle around the fixed point? indicating neutral stability (Fig. 2d), and for k = 3.3 the trajectory spirals away from the fixed point, indicating instability (Fig. 2b). E. Lateral leg-spring model The lateral leg-spring (LLS) was introduced in [6]. We focus here on the three-degree-of-freedom version with pairs of 'virtual' elastic legs in intermittent contact with the ground. A full stride consists of two stance phases: a phase where the first elastic leg pivots around a \"foothold\" on one side of the rigid body, followed by a phase where the second elastic leg pivots around a \"foothold\" on the opposite side. See [6] for details. The equations of motion of both stance phases can be cast into the form (6) (with g = 0). Hence the stance phases from leg touchdown to liftoff are volume preserving. They are related by a transition mapping q2 which maps the state at liftoff of the 1. leg to the state at touchdown of the 2. leg, and an analogous map &I. Thus the return map reads 1 = 92 o ri o q2 o4. The dynamics of the LLS model can he described by four state variables ( v > ~ , @ , w ) , here v is the center of mass speed, 6 is the angle between the body axis and the mass center velocity vector, 0 is the angle between the body axis and an inertial frame and o = 6. In [61 these four variables are augmented by two fixed parameters: p, mg -q 'This is not m e for approximalions to the stance phase dynamics which violate the time reversing syrnmeuy Sq SNumerical evidence shows that closed EUWCS persist in any neighbor^ hood around the fined point. Since the deleminant away from the fired point is no1 1. the standard KAM theorem for 2-dimensional maps (see e.g. 1181) is not applicable here. However, the reverse time symmetry of the leg reticulation strategy in this example can be shown lo entail the existence of Kolmogorov tori around the fixed poinl. This is, a consequence of a result on reversible syslcms [I9, TI!eorem:2.91, for more details see 1101. , the leg touchdown angle with respect to the body axis, and I,, the relaxed leg length and from the values of these six quantities at liftoff one can find the initial data for the next stance phase. In these variables, the transition mapping .7,* (omitting 1,) reads where n stands for the nth stance phase, LO for liftoff, and P is held constant for all stance phases. If, as implicitly assumed for the SLIP treated above, P (and/or I , ) are regarded as state variables rather than parameters, then since they are 'reset' to fixed values at touchdown, independent of their values at liftoff, the transition mapping q2 has rank four, volume is not preserved, and no deductions can be made regarding the reduced four-dimensional map. Restoring a nontrivial dynamical role to the variable P , for example, via a leg swing feedback strategy similar to (15), could lead to a non-degenerate mapping. IV. CONCLUSIONS In this paper we used the example of the SLIP locomotion model to show how factored analysis of the return map may be a useful new tool in the stability analysis of hybrid Lagrangian systems. Specifically, we obtained a necessary condition for the asymptotic stability of SLIP in the presence of a leg recirculation strategy relevant to the operation of the robot RHex [I]. This condition is formulated in Sec. III.A.3 for a particular family of leg recirculation strategies as an exact algebraic expression despite the non-integrability of the SLIP system. Hence leg recirculation strategies that violate the above condition can he discarded without recourse to cumbersome numerical simulations. Application of this formalism to the robot RHex requires a more elaborate parametrization of leg recirculation schemes modeled after RHex's open loop controller. This analysis can provide for the first time a partial explanation for the surprising self-stable behavior observed empirically in RHex. It also paves the way for a more principled investigation of detailed, biologically motivated leg placement strategies in the LLS model [6] which captures many aspects of cockroach locomotion [20]. v. ACKNOWLEDGEMENTS This work is supported in part by DARPNOM Grant N00014-98-1-0747. Helpful discussions with R. Ghigliazza are gratefully acknowledged. VI. APPENDIX: INVARIANCE OF THE THRESHOLD EQUATION FOR SLIP WITHOUT PITCHING In this appendix we show that the invariance- of the threshold equation (1 1) under S, o ri : Pz0 H S , o fp (i, ) be taken into account when inverting the cosine: arc cos(^) = -(karccos(i,, +ioirD - T ) i 2 D +a(frD+l(f0-FrDj)) +2a @ cos(karcc0s ('(fro))) -cos (arCCOS(i,) +a (irD +I($ - f r D ) ) ) = o k=l.l=LI - # Z ( f T D j -cos (arccos(in) + = 0 For k = 1 and I = 0 this does reduce to the original threshold function (18) and we conclude that Idet(Dri)l = 1 , as was explicitly derived in (17). For other values of k and 1 this does not in general reduce to (18), although we have not ruled out that for specific values of k and I and a specific form of a the original threshold function (18) is recovered. +a (iTD + r ( f 0 - irD))) = o VII. REFERENCES [11 U. Saranli, M. Buehler, and D.E. Koditschek. Rhex: A simple and highly mobile hexapod robot. The InFor a solution of this equation with the leg recirculating only once during flight $(io,&,iTD) E (51; ,2~) . This must ternarional Journal of Robotics Research, 20(7):616 631, 2001. [2] R. Altendorfer, N. Moore, H. Komsuoglu, M. Buehler, H.B. Brown Jr., D. McMordie, U. Saranli, R. Full, and D.E. Koditschek. Rhex: A biologically inspired hexapod runner. Autonomous Robots, 11:207-213, 2001. [3] R. Blickhan and R. Full. Similarity in multilegged locomotion: Bouncing like a monopode. J. Comp. Physiol., A(173):509-5 17, 1993. [4] M.H. Raibert. Legged Robots that Balance. MIT Press, Cambridge, MA, 1986. [5] T. Kubow and R. Full. The role of the mechanical system in control: a hypothesis of self-stabilization in hexapedal runners. Philosophical Transactions of the Royal Society of London Series B - Biological Sciences, 354(1385):849-861, 1999. [6] J. Schmitt and P. Holmes. Mechanical models for insect locomotion: dynamics and stability in the horizontal plane I. Theory. Biological Cybernetics, 83:501-515, 2000. [71 A. Seyfarth, H. Geyer, M. Gunther, and R. Blickhan. A movement criterion for running. Journal of Biomechanics, 35:649-655, 2002. [8] R. M. Ghigliazza, R. Altendorfer, P. Holmes, and D. E. Koditschek. A simply stabilized running model. to appear in SIAM Journal on Applied Dynamical Systems, 2003. [91 A. Seyfarth, H. Geyer, R. Blickhan, and H. Herr. Does leg retraction simplify control in running? In IV. World Congress of Biomechanics, Calgary, Canada, 2002. [IO] R. Altendorfer, R. M. Ghigliazza, P. Holmes, and D. E. Koditschek. Hopping on a springy leg: \u201clow attention\u201d feedback control. In preparation, 2003. [ 1 I] H.M. Herr and T.A. McMahon. A trotting horse model. International Journal of Robotics Research, 19 (6):566-581, 2000. [ 121 P. Holmes. Poincark, celestial mechanics, dynamical systems theory and \u201cchaos\u201d. Phys. Rep., 193(3):137- 163, 1990. [I31 E Scheck. Mechanics: from Newton\u2019s laws to deterministic chaos. Springer-Verlag, Berlin, 1999. Thud edition. [I41 A. Ruina. Nonholonomic stability aspects of piecewise holonomic systems. Reports on mathematical physics, 42 (1-2):91-100, 1998. [15] J. Guckenheimer and S . Johnson. Planar hybrid systems. In Hybrid systems II: Lecture notes in computer science, pages 202-225. Springer-Verlag, Berlin, 1995. 1161 M.J. Coleman and P. Holmes. Motions and stability of a piecewise holonomic system: the discrete Chaplygin sleigh. Regular and chaotic dynamics, 4(2):55-77, 1999. 1171 J.S.W. Lamb and J.A.G. Roberts. Time-reversal symmetry in dynamical systems: A survey. Physica D, 1121-39, 1998. [I81 J. Moser. Stable and random motions in dynamical systems. Princeton University Press, 1973. [I91 M.B. Sevryuk. Reversible Systems. Number 1211 in Lecture notes in mathematics. Springer-Verlag. 1986. [20] J. Schmitt, M. Garcia, R. Razo, P. Holmes, and R.J. Full. Dynamics and stability of legged locomotion in the horizontal plane: A test case using insects. Biological Cybernetics, 86 (5):343-353, 2002."
        ]
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        "image_filename": "designv11_24_0000835_9.256382-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000835_9.256382-Figure1-1.png",
        "caption": "Fig. 1",
        "texts": [
            ", Vp(a-4 + (1 - a ) B ) I a q p ( A ) + (1 - a ) q p ( B ) Vu E [0,1], V A , B E C\"'\" e) -&( -A) I Re A(A) I &(A) whenever A(A) is an eigenvalue of A. For a specific norm on C\", in general, it is not always easy to obtain the explicit expression of the induced norm as well as the matrix measure. However, corresponding to the norms II .Ill, [I. 112, and ( 1 . [Irn the induced norms and matrix measures have explicit expressions as shown in Table I [12]. Consider a line L-which separates the complex plane into two half planes H and H (Fig. 1). The line intersects the real axis at (a,O) and forms an angle 8 with respect to the imaginary axis where 0 < 0 I 2 r in counterclockwise sense. By applying some essential properties of the matrix measures, a simple sufficient condition for eigenvalue assignment is derived in the following theorem. Theorem 1: All the eigenvalues of a constant matrix A are located in the H region if q p ( e - J B A ) < a cos e (1) where j = R, p = 1 or 2 or 00. Proofi It is seen that all the eigenvalues of a constant matrix A are located in the H region if and only if all the eigenvalues of the corresponding state space system 2(t> = e-IB(A - a z ) X ( t ) lie in the open left-half complex plane"
        ],
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    },
    {
        "image_filename": "designv11_24_0001967_910017-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001967_910017-Figure1-1.png",
        "caption": "Fig. 1 A plane suspension mechanism",
        "texts": [
            " 1- In this case the numerical solution is obtained as (x, ,y, ,z,) = (0.0000, -1740.1610, -418.2749) \"SCREW AXIS\" TO REPLACE \"ROLL AXIS\" Currently a \"roll axis\" is used for all suspension analysis and vehicle dynamics (4). The roll axis is defined as the axis which passes through the front and rear suspension \"roll centers.\" These roll centers are all in front or rear suspension planes, and are located by plane suspension geometry with plane instantaneous kinematic theory which is called the \"Kennedy Theorem\" or KennedyAronhold Theorem\" (7) (as shown in Fig. 1). In previous sections we found that the velocity pole F (Fig. 1) no longer exists in three dimensional suspensions and instead we found a screw axis of instant pitch SIP for each of the three different suspensions. Hence, we are naturally ready to consider a screw axis to replace the roll axis since a roll axis is a purely two dimensional product made with purely two dimensional geometry of suspensions. Let us consider an expansion of the Kennedy Theorem in three dimensional space. Beggs (8) called the expanded theorem the \"Space Dual\" of the Kennedy-Aronhold Theorem in Plane Motion\", and Suh (9) called it simply the \"Kennedy Theorem in Space\" or \"Three-Axis Theorem"
        ],
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    },
    {
        "image_filename": "designv11_24_0002326_dac-34138-Figure11-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002326_dac-34138-Figure11-1.png",
        "caption": "Figure 11 Situations require interruption by machining",
        "texts": [
            " For uniform layers, it is prudent to do machining after a number of layers are built, therefore it is important to decide where to switch the processes. There are two different situations to consider when making a switch to machining process during building uniform layers \u2022 The current layer has a much bigger area than the next layer where geometry continuity is broken. As shown in Copyright 2002 by ASME Copyright \u00a9 2002 by ASME f Use: http://www.asme.org/about-asme/terms-of-use Down \u2022 If collision happens after one layer is built, the machining process will be conducted before the layer is deposited. As shown in Figure 11(b), after the small cylinder is built, the chuck collides with the bottom area of that cylinder; therefore the process has to switch to machining before the whole cylinder is finished. (b) Collision occurs while machining Layer i Layer i+1 Layer i Layer i+1 (a) Broken geometry continuity Collision happens 66 loaded From: http://proceedings.asmedigitalcollection.asme.org/ on 01/28/2016 Terms The machining process is also needed to form some internal structures or entrapped areas recognized and hidden from the deposition process [18]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001275_03093247v263147-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001275_03093247v263147-Figure4-1.png",
        "caption": "Fig. 4. Finite element mesh for stacked springs. (a) Springs in parallel (b) Springs in series",
        "texts": [
            " It can be seen that the parallel stacked spring deflection is equal to that of a single disc spring in the stacking and the load carrying capacity is JOURNAL OF STRAIN ANALYSIS VOL 26 NO 3 1991 (0 IMechE 1991 the sum of the load carrying capacities of individual springs in the stacking. There is a close comparison between the present analysis and that of Almen and Laszlo (1) for parallel stacking. 6.2 Series stacking When two springs are stacked in series, node 41 becomes the common node for both the individual springs (Fig. 4(b)). This results in an increase in the bandwidth of the system from 16 to 20. The coordinates of all nodes were calculated accordingly and the analysis was carried out. It is seen that for the series stacked springs, the deflection is the sum of the deflections of the individual disc springs in the stacking, and the load carrying capacity is that of a single disc spring in the stacking (Fig. 11). There is also a close similarity between the results of the present analysis with that of Almen and Laszlo (1)"
        ],
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    },
    {
        "image_filename": "designv11_24_0002619_095440605x31481-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002619_095440605x31481-Figure5-1.png",
        "caption": "Fig. 5 Geometry of the hyperbolic rack-tooth profile in the side plane, R/m \u00bc f/m \u00bc 10 and fm \u00bc 228",
        "texts": [
            "25, and any fm, the maximum number of teeth to be cut is deduced as 9N 4 4 R m 2 6:4 R m f m 2 \u00fe4:8 (1) Equation (1) is plotted in Fig. 4 and shows that both R and f should be large in proportion to the module if large numbers of teeth are required, while a reasonable value of b is maintained. Similar conditions pertain to almost all of the following C-gear forms. Each set of cutting edges envelops a conical frustum, which intersects any off-centre transverse plane of the generating rack in a hyperbola. As shown in Fig. 5, this gives a slightly concave transverse profile on the concave rack flank and a slightly convex profile on the convex one; the tooth section becoming asymmetric. A generated-gear tooth profile is a true involute only in the midplane, and it distorts as the transverse plane moves away. The transverse pressure angle also increases towards the side planes. From the geometry in Fig. 5, it can be shown that the side-plane pressure angle (slope of tangent to the hyperbola at the pitch plane) is given by fs \u00bc tan 1 tanfm cosb (2) Proc. IMechE Vol. 219 Part C: J. Mechanical Engineering Science C01505 # IMechE 2005 at UNIV OF VIRGINIA on July 12, 2015pic.sagepub.comDownloaded from where the tooth trace inclination at the side planes is given from Fig. 2 by b \u00bc sin 1 f 2R (3) Owing to the pressure angle variation across the face, which is the same for both flanks, a CV1-gear has a barrel-shaped base surface \u2013 the pitch surface still being cylindrical. The surface of action between two meshing gears becomes an oppositely warped, symmetrical, ruled surface that inflects about the pitch (surface) element. The deviations of the rack transverse profile from its tangent \u2013 at the pitch line \u2013 at the working depth limits, in a direction parallel to the pitch line are derived from Fig. 5 as d m \u00bc R m cosb+ tanfs ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R m + tanfm 2 f 2m 2 s (4) where the plus signs give the deviation at the tips of the concave tooth flanks (also at the working depth of the convex ones) and the minus signs for the opposite. For example, with R/m \u00bc f/m \u00bc 10 (hence b \u00bc 308), and fm \u00bc 228, it results that fs \u00bc 25.018 and, at the tooth tips, dcav/m \u00bc 2"
        ],
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    },
    {
        "image_filename": "designv11_24_0000273_0167-8442(94)00004-2-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000273_0167-8442(94)00004-2-Figure2-1.png",
        "caption": "Fig. 2. Combined and equivalent loading on gear tooth.",
        "texts": [
            " This is accomplished by application of a weight function derived from the crack opening * Corresponding author. displacement. The results are compared with those obtained experimentally. 2. Analytical treatment Consider a gear tooth loaded by an isolated force F at B in Fig. l(a). The location of B is at the engagement point that changes position as the gear engages and disengages with its mating part. Note that t h e line of action in Fig. l(b) rotates with the gear motion. An edge crack [2] of length a is assumed to prevail at the root of the gear tooth as shown in Fig. 2(a) where the tooth width is S. The isolated force F may be replaced by an equivalent force and moment system. This is illustrated in Fig. 2(b). The analysis will be limited to narrow gears [1] such that the stress state can be approximated as two-dimensional. Analyzed will be the effect of bending and forces on the cracked portion of the gear tooth. 0167-8442/94/$07.00 \u00a9 1994 Elsevier Science B.V. All rights reserved SSDI 0 1 6 7 - 8 4 4 2 ( 9 4 ) 0 0 0 0 4 - K 2.1. Weight function For two-dimensional crack problems, the stress intensity factor expression can be written as [3]: K= J;o'(x)m(a, x) dx (1) where m(a, x) is known as the weight function. It can be calculated from a reference solution to be taken as the compact test specimen in this work. The tractions on the crack are ~(x) such that the crack is along the x-axis, Fig. 2(a). A form of m(a, x) is E 3Vr(a , X) m(a, x) - gr 3a (2) for plane stress. For plane strain, the Young's modulus in Eq. (2) can be replaced by E/(1 - u 2) with u being the Poisson's ratio. The crack opening displacement is G(a, x). The subscript r refers to the reference problem. Since or(x) can be negated by another problem of the same geometry without a crack, this gives the solution for a free surface crack. Such a procedure is wellknown and needs no further elaboration. Referring Eq. (1) to the reference state and making use of Eq",
            " Yt(a) is referred to as the shape factor and G(a) is given by G(a) = - - [ I i ( a ) - 4~/-dlE(a)Yt(a)] (5) I3(a) The quantities Ij ( j = 1, 2, 3) stand for f[[vt( l l (a) = \"tr~/2-O'o a)12a da 12(a) = trr(x a - x dx, I3(a) = f;O'r(X)(a - x ) 3/2 dx (6) In Eq. (4) and the first of Eqs. (6), cr 0 refers to the nominal stress in the problem. Substituting Eq. (4) into Eq. (2) and performing the differentiation with reference to the normalized crack length variable a, the result is [ a-x m(a,x) ~/'rr(a---x) l+ml ( \" - -~ ) + m 2 ( - ~ ) 2] (7) such that mj (j = 1, 2) are given by 1 m, = yt(a ) [2aYt'(a) + 3G(a)] + 1 1 m 2 - - [2aG'(a) -G(a)] (8) 4Yt(a) The prime denotes differentiation with respect to 0~. 2.2. Crack surface tractions Returning to Fig. 2(a), the stresses induced by the forces and moment can be computed. Assume that Fy introduces a uniform stress Fy (9) %0 = b--S on the x-axis where the edge crack prevails. The gear thickness is b. The moment caused by F x and Fy is M r =FxL -FyC (10) This is balanced by a linearly distributed stress field with the neutral axis at x = S/2 such that 6M r / 2x O'm(X ) = -~-T [1 - --~- ) (11) The combined stress %(x) can thus be obtained: O'y(X) = &re(X) --O'y 0 (12) Equations (9) and (11) can be put into Eq",
            " (17) for extension can be written as Fy Vr~-~- yt ( a ) (25) K Fy = _ - ~ where use is made of Eq. (9). The shape factor Yt(a) for the gear tooth is assumed to be the same as that for the compact tension specimen, i.e., + m a - x 2 d x The specific form of Yt(a) is already given by Eq. (20). To summarize, Eq. (17) takes the form K = - ~ ~ cos 4) - ~ sin 4) Ym(~) s 1 - - - i n 4~Yt(a ) (27) 6L 3. Experimental approach The experimental setup is shown in Fig. 3. The gear test piece [1] has 18 teeth supported 190 mm apart. The distance L in Fig. 2(a) is 15 mm. This corresponds to a three-point bend test for determining the shape factor. The gear is made of AISI 4130 steel, the chemical composition of which is given in Table 1. The mechanical and fracture properties can be found in Table 2. A least square fit is made for the experimental data. Y(a) = 2.2486135 - 3.7173537a + 33.95a 2 - 137.5356a 3 + 210.91a 4 (28) more elaborate stress analysis would have to be made. For instance, Eq. (11) no longer applies because the neutral axis in bending would shift as the uncracked ligament reduces for increasing crack length"
        ],
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    {
        "image_filename": "designv11_24_0000843_20.582598-Figure12-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000843_20.582598-Figure12-1.png",
        "caption": "Fig. 12. Magnetic saturation at top of stator slot teeth(slip=0.06)",
        "texts": [
            " The analytical results is compared with experimental data. The experiment is carried out under the condition that the primary currents are constant, that is, 1.OA. The rise of the temperature in the motor is neglected and the conductivity of the bars and end-rings are regarded as 3.5~107 S/m (at 20T). The inter-bar currents [8] and effects of skew are also neglected. In the 3D analysis, only a bar pitch is considered with following periodical boundary condition [7]. A n =Ar2 exp (j7tlN) (14) I697 Fig. 12 shows the relative permeability at the top of the stator slot teeth. The results show obvious difference between the proposed and 2D method. The flux density and the magnetic saturation in induction machines are determined by both of the primary and the secondary currents. In this case, primary currents are given as 1.OA. Thus the difference must be caused by the misestimation of the secondary currents by the 2D analysis. V. CONCLUSIONS The 2D time-stepping induction machine analysis is modified by the coefficient calculated by the linear 3D analysis using edge-elements with the gauge of A9=O"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003529_gt2004-53611-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003529_gt2004-53611-Figure4-1.png",
        "caption": "Fig. 4 Load and bearing angular orientations grouped in pairs",
        "texts": [
            " Once the dynamometer touches the bearing, the loading process starts from 0 N to 224 N (0 lb to 50 lb). The bearing deflections are irregular for small loads (< 44 N), and therefore more collection of data pairs (static load, bearing deflection) are recorded in this load region. A reasonable time between individual loading processes is taken to ensure the repeatability of the displacement data. The loading process is performed along eight angular positions 45\u00b0 apart from each other; each angular position is labeled, as shown in Figure 4. The spot weld on the foil bearing is a reference for the origin of the circumferential coordinate (\u03b8), with angles measured from the free end towards the fixed end. The FB structural characteristics can be distinguished from the measurements. The static cross-coupled bearing deflection is negligible compared to the deflection along the load direction. Figures 5 display the recorded deflections versus loads for journals of diameter (D1) through (D3), i.e. for increasing preloads. Deflection-versus-load curves corresponding to applied loads at opposite sides (180\u00b0 apart) of the bearing sleeve are grouped as paired measurements, i",
            " The correlation coefficients of the polynomials exhibit values larger that 99.3% for all test data pairs. Appendix A shows the coefficients of the polynomial fit functions. For journal diameters D1 and D2, the static load versus deflection curve at position 1 (0\u00ba) is distinctly different than those results shown for other angular positions, as shown in Figures 5a and 5b, and labeled as spot weld effect. At position 1 (\u03b8 = 0\u00ba), the load pushes the bearing into the shaft at the spot weld, as depicted in Figure 4. Hence, the top foil and bumps around the spot weld are being compressed. The bumps located at the fixed end are more constrained than the bumps located at the free end. The foil bearing, when subjected to small loads applied at the location of the spot weld, tends to move toward the free end since the bumps near this angular position provide less resilience to the movement than the bumps located at the fixed end [7, 8]. Once the load increases, the bumps next to the fixed end become active and the bearing develops larger stiffnesses"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002092_an9871200697-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002092_an9871200697-Figure1-1.png",
        "caption": "Fig. 1. Arrangement for voltammetric FIA. A = Carrier stream; B = peristaltic pump; C = injection valve; D = electrochemical detector; R = recorder; M = sample; W = waste",
        "texts": [
            " Carbon electrodes have a wider potential range than mercury electrodes and can be used to determine compounds by either oxidation or reduction processes, the latter being applicable to compounds such as 1,4-benzodiazepines. In this paper an FIA method is described for the determination of nitrazepam and flunitrazepam using an electrochemical detector based on a glassy carbon working electrode. This system has been used to determine nitrazepam and flunitrazepam in tablets. The arrangement of the apparatus used for flow injection analysis is shown in Fig. 1. The carrier stream was pumped by the pump (B) (Watson Marlow 202 U/1 peristaltic pump) through the detector (D) and the stream was then discharged to waste. The sample was introduced into the carrier stream at M by a six-way injection valve (Rheodyne Type 50) and was transported as a plug by suitable lengths of 0.58 and 0.71 mm i.d. tubing to the detector (a Metrohm 656 detector with a Metrohm EA-1096 flow-through wall-jet cell). The working electrode was glassy carbon and the reference electrode was a silver - silver chloride electrode containing 3 M KCl"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003032_s1474-6670(17)55336-7-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003032_s1474-6670(17)55336-7-Figure2-1.png",
        "caption": "Fig . 2 . Free body diag r am of l i nk i -I.",
        "texts": [
            " 3 in Paul, 1981), besides existance of the geomet ri cal singularity (Huston , Passerello, 1980) . INVERSE DYNAMICAL SYSTll1 In a space, if a moving basis or frame is chosen, then any vector x can be written as x = s + u, where u is the relative part with resp;ct to the origin- of th is frame. Then the t i me differential vector of ~ is (Appendix C in Cannon, 1967) . . Du x = s + ~- + w x u -- Dt-(4) , where w is the angular ve l oci ty of this frame, and D/ Dt- denotes the relative time differential operator with respect to this f rame. In fig. 2, 0 i-1 is the ori gin of the (i -1 )th frame, ~-1 i s the distance from 0i-1 to the center of mass of link i-1. Let superscript <i > mean the representation of a vector with respect to coordinate frame i, the distance from 0i_1 to 0i is then <i-1 > h -1 (5) f ( 1) A d sv sa w cl are ram eq. \u2022 n -j,-1' -j,-1' -i-1' -i-1 absol ute veloc i ty, absolute acceleration at 0i_1' and angular velocity, angular accelerat ion of link <i-1> <i-1> Note, D/ Dt( '\u00a31_1 ) = D2/Dt2('\u00a3i_1 ) = 0. Let Ki = 0 for rotational axis i, Ki 1 for translational axis i, then Dh<i> =~ 0 , for Ki 0 , -1 (9a) Dt [Q \u00b0 <'lilT, for Ki 1\u00b7 , 2<i> =~ ~~ for Ki = 0 , D h\u00b7 -1 (9b) Dt2 \u00b0 ihlT, for Ki = 1; The angula r vel oc ity of link i is the vector sum of that of link i-1 and the angul a r velocity of dri ving ax is qi' i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002479_cca.1999.801153-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002479_cca.1999.801153-Figure1-1.png",
        "caption": "Figure 1 The FUN^ pendulum.",
        "texts": [
            " The reason for using the Furuta pendulum as an example application is that friction greatly deteriorates control performance. The friction nonlinearity result in large limit cycles when using linear state feedback stabilisation. With efficient friction compensation the limit cycles can be eliminated. 2. The Furuta Pendulum The Furuta pendulum [4] consists of two connected inertial bodies; An actuated rotating center pillar rigidly connected to a horisontal arm, and a pendulum arm connected to the horisontal arm by a 1-DOF joint, see Figure 1. The arm position is denoted by 9, the pendulum position by 0, and their corresponding time derivatives by 4 and e. The pendulum is driven by a torque input U on the horisontal arm. The @ joint exhibits significant friction. Let F denote the friction torque. The friction on the pendulum joint is assumed to be negligable. Let r a (@,4 ,8 ,b )T . he linearized dynamics of the pendulum at the unstable upright position are (1) dx db _ - Ax + B ( u - F ) 0-7803-5446-X/99 $10.00 8 1999 IEEE 1260 with 0 1 0 0 0 0 A = ( : a: :), B - ( a : "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000720_1.369978-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000720_1.369978-Figure2-1.png",
        "caption": "FIG. 2. Moment distribution and net remanent magnetization M following exposure to saturating field H for: ~a! random noninteracting ^100& easy axes, ~b! with internal demagnetizing fields, ~c! with easy axis dispersion by",
        "texts": [
            " Processing history generally includes sufficient recrystallizing heat treatments to randomize crystal orientations. Thus with K1.0, the magnetization in each crystal, following exposure to a saturating field, will lie along the ^100& axis nearest the field direction. In the absence of interactions between crystals, the local magnetizations will thus be uniformly distributed within a cone having a 55\u00b0 generatrix. The resulting remanent magnetization, M, is found3 to be 0.8312 of the saturation magnetization, M s . A plane section through the axis of this cone is illustrated in Fig. 2~a!. Under the demagnetizing influence of the fields arising at the boundaries between unaligned grains, some antiparallel domains will likely arise giving a spin distribution more like that shown in Fig. 2~b!. Figure 2~c! reflects the additional dispersive influence of the microstructural inhomogeneities. Clearly, M for these latter distributions will be less than 0.8312 M s ; in fact, remanence ratios of untextured steels are typically 0.5\u20130.7.4 Nevertheless, if the magnetizing direction is circumferential, any distribution dominated by a large enough cubic anisotropy is further stabilized by the absence of macroscopic demagnetizing fields and a scarcity of ~near! axially directed 180\u00b0 domain walls. The symmetry of these distributions about the magnetizing direction also precludes macroscopic components along the shaft axis",
            " Transducer operation is based on the reorienting effects of torsional stress on individual moments. In response to the magnetoelastic energy associated with the biaxial principal stresses by which torque is transmitted along the shaft, each moment will rotate towards the nearest positive principal stress ~1s! direction and away from the nearest 2s direction. Figure 3 shows, in planar projection, the directions of movement of moments initially lying in each spherical sector. The table in this figure graphically illustrates, for the distribution of Fig. 2~c!, the resulting changes in the axial component of each sector. Considering that a decrease in one axial direction is equivalent to an increase in the opposite direction and that the contributions from the most heavily populated A and B sectors are cooperative, the torsional stress indicated is seen to result in a right directed net axial magnetization component. The divergence of this component at the edges of the polarized band is the source of a magnetic field in the space around the shaft. Reversal of the torque will interchange the positions of 1s and 2s, thereby reversing the field polarity. The torque induced axial components of magnetization (M a) for several well characterized initial distributions in thin rings have been analytically determined.1,5 In addition to the basic uniaxial case,1,5 other distributions, including the noninteracting, randomly oriented ^100& easy axes shown in Fig. 2~a!, have also been studied.5 In all of these cases, M a , has been shown to be of the form M a5M sS als K1bNM s 2D , ~1! where constants a and b reflect the remanent moment distribution function, l is the magnetostriction ~assumed as isotropic!, K is the ~single! effective anisotropy, and N is the ~single! demagnetizing factor based on geometric features of the ring. The detected field, H, is then found from H5cNM a , ~2! where the constant c(1>c>0) reflects the position and orientation of the field sensor relative to the ring"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002809_j.comcom.2004.12.046-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002809_j.comcom.2004.12.046-Figure1-1.png",
        "caption": "Fig. 1. Orientation as input to digital world model of artifact.",
        "texts": [
            " Since the physical state of an artifact is usually changed through human manipulation, the position 0140-3664/$ - see front matter q 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.comcom.2004.12.046 * Corresponding author. Tel.: C43 732 2468 8555; fax: C43 732 2468 8426. E-mail addresses: ferscha@soft.uni-linz.ac.at (A. Ferscha), resmerita @soft.uni-linz.ac.at (S. Resmerita), holzmann@soft.uni-linz.ac.at (C. Holzmann). and orientation of the artifact are ideal candidates for enabling gestural interaction. In particular, orientation can be seen as input to the digital world model of an artifact, as depicted in Fig. 1. In this context, the present paper addresses the issues of gesture-based interaction for remote control, and the use of orientation sensors for gesture detection and recognition. The main objective is to speed-up practical realization of intuitive gestural interaction by providing application developers and sensor manufacturers with common specifications of information structures and operational requirements that will enable the use of various (different) types of sensors and artifact to control, by gestures, a wide spectrum of applications"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001389_robot.1994.351406-Figure9-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001389_robot.1994.351406-Figure9-1.png",
        "caption": "Figure 9: Experiment schematic",
        "texts": [
            " Instead, the contact force in the control loop is estimated by the virtual displacement according to the following equation and the SICC is compensated using this force in realtime. f = KT(2 - z d ) . (24) In the whole experiment, the Cartesian trajectory and end effector stiffness are preplanned according to the task. At the first experiment, the effect of the contact force on the the overall stiffness Characteristics of the manipulator is investigated. For a given virtual displacement of 0.02m along the normal direction of the environment surface as shown in Fig. 9, the virtual displacement is increased into the environmental surface and the contact force is measured. The KT is given as follows: KT = diag(200, 300) , (25) whose units are N / m . Particularly, y directional stiffness is set stiffer than that of I direction to lessen the sliding motion along the environment. According to the virtual displacement toward inner wall, we are supposed to read the contact forces proportional to the displacement. In the second experiment, a force sensor with flat surface is placed parallel to the x-y plane as shown in Fig. 9 and the manipulator is commanded to follow a circular trajectory with 0.01 m radius with an angular velocity of 0.1 Hz, which is low enough to neglect the inertial effect. Similar to the first experiment, the force sensor reads the force proportional to the virtual displacement of the constrained circle. In this experiments, the taskspace stiffness is given as (26) KT = diag(200, 200) . 5.3 Results & Discussions Figs. 10 and 11 are the results of the first experiment. In Fig. 10, the measured forces of noncompensated controller are a little smaller than that of compensated controller"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001978_robot.1992.220277-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001978_robot.1992.220277-Figure2-1.png",
        "caption": "Fig. 2 Symbols in the dynamic eqations of motion.",
        "texts": [
            " These are conditions in which we train a mobile robot in the push-a-box task. e = $2 - el. 3 Equations of motion Alexander and Maddocks [8] and many others have already proposed equations of motion for mobile robots. Barraquand and Latombe[S] derived a control law to multibody robots like a tractor and a trailer. We derive our equations of motion for the situation discussed in the previous section. The symols related in mechanical behaviors of a mobile robot, an object, and motors are shown in Fig. 2, which are briefly interpreted in the following paragraphs. 1. symbols related to a mobile robot v1 velocity of translation W 1 angular velocity of rotation 81 angle of the axis z1 from X D L , DR driving force of two wheels N ~ , L , N ~ , R frictional force from floor -F,, -Fy forces from a pushed object 4 moment of inertia Ml mass Nl 2 force from floor 2. symbols related to a pushed object 7 radius of a driving wheel v2 velocity of translation w2 angular velocity around 02 82 p2z F,, Fy 12 moment of inertia M2 mass N22 force from floor angle of the axis z2 from the axis X friction coefficient from floor to a box forces from a mobile robot 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000761_s0890-6955(97)00059-x-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000761_s0890-6955(97)00059-x-Figure2-1.png",
        "caption": "Fig. 2. Link with the disk counterweight.",
        "texts": [
            " The shaking force attributable to the inertia of moving links is considered in this study. The shaking moment is the sum of the inertial torques and the torques of the inertial forces with respect to (w.r.t.) the reference point. If agi and ai are the acceleration of the mass center and angular acceleration of link i, then the shaking force and shaking moment of the drag-link drive are F = 2 O6 i = 2 miagi (1) and MR = 2 O6 i = 2 (Rgi \u00d7 miagi + Iiai) (2) respectively, where Rgi is the position vector of the mass center of link i w.r.t. the reference point R(xr, yr). As shown in Fig. 2, if a disk counterweight whose mass and radius are mbi and rbi respectively, is added on link i, and its relative angular position and distance of the mass center relative to a pivot are bi and lbi, respectively, then the total mass is Mi = mi + mbi (3) The relative angular position and distance relative to the pivot of the total mass center are gi = fi + tan 2 1F mbilbisin(bi 2 fi) mili + mbilbicos(bi 2 fi) G (4) Li = mbilbisin(bi 2 fi) Misin(gi 2 fi) (5) respectively, and the total mass moment of inertia is Ii9 = II + 1 2 mbir2 bi + mip2 i + mbiq2 i (6) where pi = \u00ceL2 i + l2 i 2 2Lilicos(gi 2 fi) (7) qi = \u00ceL2 i + l2 i 2 2Lilicos(bi 2 gi) (8) In the following, design variables, objective function and constraints for the optimization are introduced"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003172_detc2005-84638-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003172_detc2005-84638-Figure2-1.png",
        "caption": "Fig. 2 - Schematic of dynamic model",
        "texts": [
            " (4) Then mesh point vector (x, y, z) is given by \u2211 \u2211 = == N i i N i iiy f fr y 1 1 , yxz FyFMx /)( += , xzy FxFMz /)( += , (5) while the mesh stiffness is defined as )/( 0eeFk totalm \u2212= , (6) where e and 0e are the loaded and unloaded transmission error in the line-of-action direction. A 14-degree of freedom lumped parameter dynamic model is used to study the effects of assembly errors on a face-milled hypoid gear dynamic response [9]. The model consists of a hypoid gear pair (i.e. pinion and gear), engine and load elements as shown in Fig. 2. Pinion and gear are modeled as rigid conical body. Shaft and bearing are simulated by a set of stiffness and damping elements [10]. Two local coordinate systems Sl (Xl, Yl, Zl) (l=p, g for pinion and gear respectively) are defined whose origins are at the centroids. Equation of motion can be expressed in matrix form as }{}]{[}]{[}]{[ FqKqCqM =++ . (7) The generalized coordinate is then given by {q} = { E\u03b8 , qp T, qg T, L\u03b8 }T, (8) T lzlylxllll zyxq },,,,,{}{ . \u03b8\u03b8\u03b8= , (subscript l=p, g) (9) ,(10) where [K] is the combined stiffness matrix of mesh stiffness km and stiffness of support structures like shafts and bearings"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002047_ecc.2003.7086447-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002047_ecc.2003.7086447-Figure1-1.png",
        "caption": "Figure 1: The geometrical scheme of the IMI planar manipulator.",
        "texts": [
            " For constant velocity, the steady-state friction torque is then given by: \u03c4fiss = gi(q\u0307i) sgn(q\u0307i) + fi(q\u0307i) (3) Different parameterizations are possible for functions gi(q\u0307i) and fi(q\u0307i): the first one is a nonlinear function of velocity, generally expressed by means of exponential terms, while the second one can be given by a simple linear viscous function or by a higher order polynomial function, when required for a better fitting with the collected experimental data. The considered robot is a planar two-arms manipulator, manufactured by IMI (USA), and sketched in Figure 1. The maximum extension of the links ( 1 + 2) is about 0.7 m, the angular limits being \u00b12.15 rad for both joints. The arms are driven by a couple of brushless NSK Megatorque direct drives. Two control modes are available, the Torque Mode and the Velocity Mode: on the basis of the resolver signals, a current loop is closed to regulate the torque in the first case, whereas a further velocity loop is added in the second mode. The basic mode is the Torque Mode, and it will be the only one used in this work to control the manipulator"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001455_50006-1-Figure5.49-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001455_50006-1-Figure5.49-1.png",
        "caption": "FIGURE 5.49 Cross section of stepper motor stator: (a) unenergized stator (rotor not shown); (b) energized stator (rotor not shown); (c) rotor at position of maximum drive torque; and (d) rotor rotated to position of zero drive torque.",
        "texts": [
            " Each coil is mounted on a soft-magnetic stator element that consists of two opposing toothed components and a flux return ring. The number of teeth on a stator equals the number of poles on the rotor. The drive coils are assembled by first sliding the coil and flux return ring on one of the toothed components and then inserting the remaining toothed element into the assembly in such a way that the stator teeth are equally spaced. A cross section of the interior of an assembled four-pole stator is shown in Fig. 5.49a. An \"unrol led\" perspective of an assembled stator element (without the coil) is shown in Fig. 5.50. 440 CHAPTER 5 Electromechanical Devices In the can-stack motor each rotation step is initiated by activating a single phase. Specifically, when one phase is activated (with the other phase off) the rotor experiences a torque that rotates it into magnetic alignment with that phase. The stator teeth of the two phases are offset from one another by half-a-tooth (or pole) pitch in an angular sense. Therefore, by sequentially activating the two phases the rotor can be repetitively stepped an angular measure equal to half a pole pitch. The torque developed by the motor can be understood by considering the activation of a single phase as depicted in Fig. 5.49'. The activation sequence is as follows: (a) the coil is unactivated (rotor not shown); (b) the coil is activated and a magnetic field is created in the stator cavity (rotor not shown); (c) the rotor is initially in a position where it experiences maximum drive torque that is due to the interaction of the radially directed stator field and equivalent current sheets of the rotor (surface currents exist at the transitions between neighboring poles); and (d) the rotor has rotated into magnetic alignment with the phase where it experiences zero torque. This occurs when the equivalent current sheets of the rotor are centered with respect to the gap as shown. When the rotor is in this position there is no drive torque because the stator field across the equivalent current sheets is parallel to the direction of rotation as shown in Fig. 5.49b. The alignment of the rotor to a given phase is enhanced by the lower reluctance of the rotor/stator circuit in the aligned position (Fig. 5.49d). When the rotor aligns with one phase it is in a position maximum torque for the other phase because the stator teeth for that phase are offset by half-a-tooth (or pole) pitch. Thus, the rotor can be continuously rotated (stepped) by activating the two phases in sequential fashion. In the following example, we derive an expression for the drive torque of a \"can-stack\" stepper motor. EXAMPLE 5.14.1 Derive an expression for the drive torque of the stepper motor shown in Fig. 5.48. Assume that the rotor is a radially polarized multipole cylinder with a magnetization M = _Mst, (5",
            " First, we obtain a field solution in the interior of an energized stator with no rotor present. Second, we reduce the rotor to an equivalent current distribution and then compute the torque on it using a Lorentz force approach with the stator field as an external field. Stator field: Let L and R s denote the length and inner radius of the stator, respectively. Each stator has Npolr teeth, which equals the number of poles on the rotor. The stator is enclosed by an n-turn coil and a flux return ring. A cross section of the interior of a four-pole stator is shown in Fig. 5.49a. Let dp, denote the angular span of each tooth and qSg denote the angular expanse of the gap between each tooth. These angles are related by the following equation, 2re ~b~ = q~,. (5.281) Npole We seek a field solution for the interior of the stator. To obtain an analytical solution, we assume that the stator is infinitely long. This assumption is not as radical as it might first seem because the stator tends to confine the flux and minimize leakage etc. In the interior of the stator, V x H - O ",
            " The angular span of the gap between neighboring teeth is q5~ = 9 ~ (q5~ = 2rc/Npole- q~t)\" There are two phases to consider, which are labeled 1 and 2, respectively. Recall that the stator teeth of the two phases are offset from one another by an angular span equal to one half of the pole pitch, which in this case is 18 ~ The drive torque Tz(O) for each phase is shown in Fig. 5.52. This plot shows the torque on the rotor as it rotates the angular span of one pole (0 <~ 0 <~36~ When 0=0, the rotor is positioned as in Fig. 5.49c and d for phase 1 and phase 2, respectively. In this initial position, phase 1 exerts almost maximum torque, and phase two exerts zero torque. The peak torque for phase 1 is 1500 #N. m, which occurs at 0 = 12 ~ When the rotor is rotated to 0 = 18 ~ (half a pole pitch) as shown in Fig. 5.49d, the torque of phase I is zero and the torque of phase 2 is near a maximum. For 18 <~ 0 <~ 36 ~ the torque of phase 1 reverses direction as shown. D In the previous sections we derived analytical lumped-parameter models for the analysis of various electromechanical devices. Such models can be developed for some devices, but certainly not all. Geometric asymmetries and /o r material nonlinearities often preclude a full analytical treatment. However, in such cases it is still possible to perform a lumped-parameter analysis using a hybrid analytical-FEM approach"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002082_iros.1999.811663-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002082_iros.1999.811663-Figure4-1.png",
        "caption": "Figure 4: A section of a snake model with 3 arcs of circle and 2 cubic polynomial curves between.",
        "texts": [
            " The mechanism is supposed to progress over a perfectly horizontal ground with vertical projections for the natural supports which are indispensable for the animal to brace the sides of its body to create necessary propulsive resulting force. Directions and magnitudes of propulsive forces are a pmori choosen. As a first approach, we consider the body form in 2 parts: the ones around the supports, where snake forms nearly the same curvature, as arcs of circle of fixed radius, and the rest of the whole body as cubic polynomial functions between the arcs of circle, illustrated in figure 4. Our cubic polynomial's representation is as follows: with a function parameter r and coefficie_nts a'o, a'l, a'2 and Z3. z ( r ) and y(r) are projections of f ( r ) to Cartesian coordinates. The below mentioned curve choices provide us a relative computing simplicity. These choices validity will be prooved by realistic snake forms in progression to be obtained from the forseen experiments observations. In order to obtain an initial configuration of the mechanism whose geometric scheme is described below, we consider a snake in pause, ready to move, in contact with its 3 supports, the required minimal number of simultaneous contact for a progression by lateral undulation [ l ] "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002185_ic00218a013-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002185_ic00218a013-Figure5-1.png",
        "caption": "Figure 5. Absorbance-potential curves in 0.1 M NaSCN and 0.1 M HC104 solutions with (A, B) and without (A\u2019, B\u2019) 2 mM Fe(II1) present (cell thickness 0.017 cm; sweep rate 2 mV s - \u2019 ) . Wavelength monitored: (A, A\u2019) 475; (B, B\u2019) 320 nm. Anodic switching potential: (1 , 1\u2019) +0.500; (2, 2\u2019) +0.520; (3, 3\u2019) +0.540 V.",
        "texts": [
            " A slight increase in absorbance at 475 nm could arise from the fact that the iron(II1)-thiocyanate solution has already faded partially. A large increase in absorbance at 320 nm is due to the electroreduction of SCN-. Curve d in Figure 4 shows the spectrum for the electrooxidized thiocyanate solution in the absence of iron ion. The electrooxidized thiocyanate solution exhibits a symmetrical peak at 320 nm and a small and broad peak at 420 & 5 nm.8 These peaks also disappear upon the electroreduction of the solution at 0.00 V, and the resulting spectrum is the same as that of curve b in Figure 4. Figure 5 presents the absorbance-potential curves in acidic thiocyanate solutions with and without iron ion present. These spectroelectrochemical experiments were carried out with the same conditions as Figure 1. The broken lines show the absorbance changes monitored at 475 and 320 nm in acidic thiocyanate solution in the absence of iron ion. The absorbance monitored at 320 nm (Figure 5 B ) increases as the anodic switching potential becomes more positive, reaches a maximum during the negative scan at potential near the zero-current axis on the thin-layer cyclic voltammogram, then decreases as the applied potential becomes less positive, and falls to zero upon which the cathodic current drops to an almost zero level. N o detectable change is observed on the absorbance monitored at 475 nm in acidic thiocyanate solution in the absence of iron ion, as shown in Figure 5A\u2019. The solid lines in Figure 5 present the absorbance changes monitored at 475 and 320 nm in acidic thiocyanate solution containing iron ion. In the presence of Fe(III), Fe(II1) in the OTTLE cell was previously reduced to Fe(I1) at 0.00 V, and then the absorbance-potential curves were recorded from 0.00 V to positive potentials. On the initial positive scan, Fe(I1) is oxidized to Fe(III), the absorbance at 475 nm increases and gives a broad peak during the negative scan, and then Fe(II1) is reduced to Fe(I1) with an absorbance \u201chalf-wave potential\u201d of +0",
            "32 V, where the absorbance \u201dhalf-wave potential\u201d means the potential at which an absorbance is equal to one-half of the maximum absorbance on the absorbance-potential curve observed during the negative scan. The absorbance monitored at 320 nm exhibits a sharp peak during the negative scan, and the oxidized species are totally reduced in a relatively narrow potential region (approximately 160 mV) with an absorbance \u201chalf-wave potential\u201d of +0.38 V. Although the absorbance-potential curves monitored at 320 nm in acidic thiocyanate solutions with and without iron ion present display an identical shape with a sharp peak, as shown in Figure 5 B, B\u2019, they are clearly different. The electrooxidized thiocyanate solution in the absence of iron ion is reduced in a wide potential region (approximately 250 mV) with an absorbance \u201chalf-wave potential\u201d of +0.34 V. If the absorption peaks at 475 and 320 nm for the acidic iron(II1)-thiocyanate solution are assigned to the same species, it could be expected that the absorbance-potential curves monitored at both 475 and 320 nm give the same absorbance \u201dhalfwave potential\u201d. The absorbance-potential curves monitored at 475 and 320 nm for the acidic iron(II1)-thiocyanate solution exhibit the absorbance \u201chalf-wave potential\u201d of +0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003918_cdc.2006.376701-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003918_cdc.2006.376701-Figure5-1.png",
        "caption": "Fig. 5. Ramp\u2013shaped saturation function \u03c82(v, \u03c8 \u00b1 2 ) with the limits \u03c8 \u2212 2 , \u03c8 + 2 depending on the new input v.",
        "texts": [
            " In view of (23) and with the above assumption \u2202\u03c81/\u2202\u03be1 > 0 the inequality y\u0308\u2212 2 \u2264 y\u0308\u2217 2 \u2264 y\u0308+ 2 can be written as y\u0308\u2212 2 \u2212 \u22022\u03c81 \u2202\u03be2 1 \u03be2 2 \u2202\u03c81 \u2202\u03be 1 \u2264 \u03c82(v, \u03c8\u00b1 2 ) \u2264 y\u0308+ 2 \u2212 \u22022\u03c81 \u2202\u03be2 1 \u03be2 2 \u2202\u03c81 \u2202\u03be 1 which yields the limits \u03c8\u00b1 2 = y\u0308\u00b1 2 \u2212 \u22022\u03c81 \u2202\u03be2 1 \u03be2 2 \u2202\u03c81 \u2202\u03be 1 . (24) Note that the limits \u03c8\u00b1 2 are not constant but depend on the coordinates \u03be1, \u03be2, and the output y\u2217 1 , in order to satisfy the constraints (18). Since no further output differentiation is required, a C0 ramp\u2013shaped function is sufficient to construct \u03c82(v, \u03c8\u00b1 2 ), see Fig. 5. The ODEs (21) and (23) form a dynamic system with the states \u03be1 and \u03be2 and the new input v. The output trajectory y\u2217 2(t) satisfying the constraints (17)\u2013(18) can be retraced algebraically from (19), (20), and (22) As mentioned in the previous section, the smooth saturation function \u03c81(\u03be1, \u03c8 \u00b1 1 ) has to be strictly monotonic, i.e. \u2202\u03c81/\u2202\u03be1 > 0. An appropriate setup is given by (see Fig. 4) \u03c81(\u03be1, \u03c8 \u00b1 1 ) = \u03c8+ 1 + \u03c8\u2212 1 \u2212 \u03c8+ 1 1 + exp [m \u03be1] (25) The parameter m influences the slope at \u03be1 = 0 and is chosen as m = 4/(\u03c8+ 1 \u2212\u03c8\u2212 1 ) which corresponds to the slope \u2202\u03c81/\u2202\u03be1 = 1 at \u03be1 = 0. The ramp\u2013shaped saturation function \u03c82(v, \u03c8\u00b1 2 ) in Fig. 5 is defined by \u03c82(v, \u03c8\u00b1 2 ) = \u23a7\u23aa\u23a8 \u23aa\u23a9 \u03c8\u2212 2 if v < \u03c8\u2212 2 \u03c8+ 2 if v > \u03c8+ 2 v else. (26) To incorporate the output constraint (17) in the feedforward control design, the BVP (10b) of the output y\u2217 2(t) is substituted by a BVP of the new system (21), (23) \u03be\u03071 = \u03be2, \u03be1(0) = \u03be1,0, \u03be1(T ) = \u03be1,T \u03be\u03072 = \u03c82(v, \u03c8\u00b1 2 ), \u03be2(0) = \u03be2,0, \u03be2(T ) = \u03be2,T . (27) Thereby, the remaining BVPs (10a), (10c) and the new BVP (27) are algebraically coupled by the new coordinates \u03be1, \u03be2 and the output variables y\u2217 2 , y\u0308\u2217 2 via the relations (19), (22)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001377_robot.1996.503846-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001377_robot.1996.503846-Figure2-1.png",
        "caption": "Figure 2: Lumped-parameter model of the experimental manipulator ADAM.",
        "texts": [
            " Each of motors 1-3 has an optical encoder for sensing the joint angle and a tachometer for sensing the angular velocity. None of the motors 4-7 has a tachometer, and thus, pulse signals generated by optical encoder are translated into velocity signals through F/V (Frequency to Voltage) converter. The parameters of each link of ADAM are presented in Table 1. Strain gauges are used to measure the link vibrations while a force sensor is used to measure thle contact force a t end-effector. 3.2 A lumped-mass spring model The arm under consideration is modeled by lumpedmasses and massless springs as shown in Fig. 2. Thie lumped masses are considered concentrated at the tip of respective links while the links are considered as massless springs with elastic and torsional properties as E313, E515 and G3 J3, Gs Js , respectively. 3.3 Control scheme We shall make use of a simple control scheme which represents our initial approach to the sophisticated control problem. More details on the control, such as sta.bility analysis, will be presented elsewhere. As ADAM is equipped with the velocity feedback servo motors, so joint motion is commanded by joint velocity command, and therefore joint torque cannot be controlled directly"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002564_2004-01-1307-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002564_2004-01-1307-Figure4-1.png",
        "caption": "Figure 4. Pressure distribution on the front wheels: (a) Base-model, and (b) Config. 1.",
        "texts": [
            " 2: a 3D front-wheel deflector, 50 mm in height and about 500 mm in length. The shape of the deflectors follows the end curve of the wheelhouse. The idea is to protect the wheel and the link arm from the upcoming flow, as well as to reduce the amount of flow into the wheel house. \u2022 Config. 3: a 3D front-wheel deflector, 50 mm in height and about 115 mm in length. The shape of the deflectors follows the end curve of the wheelhouse. The idea is to reduce the exposed area of the deflector, while still protecting the front-wheel from the upcoming flow. \u2022 Config. 4: a 3D front-wheel deflector, 25 mm in height and about 270 mm in length. The shape of the deflectors follows the end curve of the wheelhouse. Just as in Config. 1, the idea is to protect the wheel and the link arm from the upcoming flow, while reducing the exposed surface represented by the deflector by decreasing its height. \u2022 Config. 5: a 2D front-wheel deflector, 50 mm in height and 285 mm in length and 150-200 mm in front of the wheel-house. The objective is to protect the wheel and the link arm from the upcoming flow, and reduce the effect on the front lift coefficient",
            " The drag coefficient, Cd, is defined as: AU5.0 F Cd 2 x \u03c1 = , where Fx is the total force is the streamwise direction, A is the frontal area of the car, and \u03c1 and U have been defined previously. The results on Table 2 show that the deflectors of Configs. 1 and 4, Figures 3(b) and 3(e), respectively, are the best proposals regarding Cd values. However, there is a possibility for further Cd improvement by reducing the drag contribution of the deflector itself, as the results on Table 3 will show. Of all cases studied, Config. 4 gave the best results. Note that on Table 3 the values presented for the front and rear wheels include the contribution of the brakes, and that the floor includes both wheel houses. Note also that the values for the cooling package include the drag contribution due to the pressure loss through the condenser, radiator, charge air cooler, and fan. In Configs. 1 to 5, it is observed that the main effect of the front-wheel deflector is on the drag reduction of the front and rear wheels. Configs. 1 to 4 also cause a significant reduction of the drag contribution of the underbody and front suspension (except for Config",
            " Such a parametric study is not included in this work, rather, it is suggested as a wind tunnel analysis. A proper way to understand the values on Table 3 is in connection with distribution plots of non-dimensional static pressure, Cp, defined as 2 refs U5.0 pp Cp \u03c1 \u2212 = . Figures 4 and 5 show a comparison between the base-model and Config. 1 for the front and rear wheels, respectively. Of all deflectors investigated, Config. 1 and 2 give the highest drag reduction for the front and rear wheels, respectively. The deflector of Config. 1 is plotted in Figure 4 (b) and it shows the area of the front-wheel it protects. It is also visible by comparing Figures 4(a) and 4(b) that the front brakes also benefit from the inclusion of the deflector, as high-pressure areas have disappeared in Figure 4 (b). On the other hand, the deflector represents itself a region with high-pressure values that contribute significantly to drag increase. The plots on Figure 5 (a) and 5 (b) show that the high pressure area on the front side of the real wheels is greater for the base-model and for Config.1, explaining the results of Table 3. The inside of the rear wheels do not seem to be affected. Similar results to the ones shown in Figures 4 and 5 were obtained for the other four deflectors investigated, and therefore are not presented here",
            " The lift coefficient, Cl, is defined as: AU5.0 F Cl 2 Z \u03c1 = . It is, however, more relevant to divide Cl into front lift coefficient, ClF, and rear lift coefficient, ClR. These coefficients are defined as AU5.0 F Cl 2 ZF F \u03c1 = and AU5.0 F Cl 2 RZ R \u03c1 = , with Cl = ClF + ClR. The results of the lift coefficient are summarized on Table 4 for all cases studied. From Table 4 it is can be seen that all deflectors, with exception of the deflector in Config. 3 and 5, increase the front lift, ClF. The 25 mm deflector of Config. 4 causes a less dramatic increase compared to the other deflectors tested. A slight decrease in the rear lift is also observed with this deflector in comparison with increase ClR observed in other cases. The increase of front lift, can be attributed to the higher pressure areas created in front of the deflector as shown in Figure 7 (b) for the case of Config. 1. Greater or smaller higher pressure zones are created by the other deflectors studied and are reflected in the values of ClF. Results of numerical flow simulations of a detailed car underbody have been presented in this paper"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000901_932414-Figure15-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000901_932414-Figure15-1.png",
        "caption": "Figure 15",
        "texts": [
            " Thus, instead of computing the basic solutions one could represent directly the points corresponding to the coordinates Sk and Tk in a system of orthogonal axes. Proceeding in this way the diagrams represented in Fig. 14 and 15 are obtained. It is evident that also in this case a new system of coordinate axes is defined for the harmonic order k =1/2 (Fig. 14), indicating opposite contributions of cylinders +1 and -4 (increased contribution of cylinder #1 and decreased contribution of cylinder #4) and, respectively, +2 and -3. For the harmonic order k = 1 a new line is defined (Fig. 15) expressing in one direction the nonuniformity -1, +2, +3, -4 (increased contribution of cylinders#2 and #3 and decreased contributions of cylinders #1 and #4). In order to point out how these diagrams may be used, a nonuniformity was simulated by varying the MIP of the cylinders as follows: MIP#1 =0.72 MPa,MIP#2 = 0.78 MPa, MIP#3 =0.75 MPa,MIP#4 = 0.73 MPa. (32) Performing the computations it was found S1/2 = \u20133.90733 and T1/2 = 0.32124, representing point Q in Fig. 14 and, respectively. S1 = 5.90733 and T1 = 7.96166, representing point P in Fig. 15. The coordinates of these points, according to the divisions marked along the reference lines, led to the following system of equation: from which, assuming that the first cylinder operates at the median value of the MIP (\u2206x1 =0), the following results are obtained: \u2206x2 = 0.061, \u2206x3 =0.031 and \u2206x4= 0.01. These values show the fact that cylinders 2,3 and 4 have increased contributions with respect to the first cylinder, invalidating the hypothesis that cylinder number 1 operates at the median value of p"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002114_027836498600500208-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002114_027836498600500208-Figure2-1.png",
        "caption": "Fig. 2. Gear train coordinate systems.",
        "texts": [
            " Henceforth, we will use four coordinate systems: the fixed coordinate system So, with unit vectors i, j, and k, which is rigidly connected to frame 4; and the movable coordinate systems S3, Sg, and S,, which are connected to links 3, 8, and 7, respectively. We will consider three stages of transformation of rotation: (1) with carrier 3, (2) with carrier 8 while carrier 3 is at rest, and (3) rotation of gear 1 or gear 2 while both carriers 3 and 8 are at rest. 2.1. STAGE 1 Consider that carriers 3, 8, and all the gears are rigidly connected to each other and form a rigid body. This rigid body with carrier 3 is then rotated through the angle 03, about the YO-axis. The coordinate system S8 (with carrier 8) will take the position shown in Fig. 2A. 2.2. STAGE 2 Now consider that carrier 3 is fixed and carrier 8 is rotated about the z8-axis through the angle 883\u2019 Carrier 8 and gears 7, 6, and 5 form a rigid body in this motion. Coordinate system S8 will take the position shown in Fig. 2B. Gear 5 rotating through the angle 083 will rotate gear 2 through the angle 023 about the y~-axis, which coincides with the yo-axis. at UNIV ARIZONA LIBRARY on May 28, 2015ijr.sagepub.comDownloaded from 76 where N2 and N3 are the tooth numbers of gears 2 and 5. Similarly, we may show that gear 1 will be rotated by gear 6 through the angle 813 about the y3-axis, where Here: Nl and N6 are the tooth numbers of gears 1 and 6. 2.3. STAGE 3 Now consider that both carriers are at rest and gear 7 is rotated through the angle 878 about the j$-axis (Fig. 2C). This rotation of gear 7 can be performed just by the rotation of gear 2 or gear 1. At this stage we can consider that the gear train transforms rotation as a simple train with fixed planetary carriers. While gear 7 rotates counterclockwise, gears 1 and 2 rotate clockwise. It is evident that The absolute motion of gears 1 and 2 (with respect to the frame 4) is considered as a motion of the following components: (1) in rotation with carrier 3, and (2) in rotation with respect to carrier 3. The rotation relative to carrier 3 is performed: (a) by rotation of carrier 8 with gears 7, 5, and 6; and (b) by rotation of gear 7 while carriers 8 and 3 are at rest"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003858_j.measurement.2005.11.012-Figure12-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003858_j.measurement.2005.11.012-Figure12-1.png",
        "caption": "Fig. 12. Placement of floor sensor and \u2018\u2018VMS\u2019\u2019 and defining of covering area.",
        "texts": [
            " 220 V power supply cord with plug, fuse socket and computer interface socket named \u2018\u2018OUT\u2019\u2019 are placed back side of unit and not shown in the figure. Upper scale value of instrument is limited to 99 cm. The structure of laser operated vertical movement sensor \u2018\u2018VMS\u2019\u2019 is shown in the Fig. 11. Here 1\u2014the height adjustable support, 2\u2014the \u2018\u2018VMS\u2019\u2019 sensor. Height of this sensor is adjustable up to 1.5 m and can be connected with a flexible cable to the main device (connection cable is not shown in the figure). The place of sensors and creating of the covering (affecting) area with beams are shown in Fig. 12. The covering area of infrared beams is drawn by hatching here. The minimum dimensions are given here. A 220 V plug cord is connected to the socket placed back side of unit to supply power to the \u2018\u2018VMS\u2019\u2019 unit. The connection cable of laser operated vertical movement sensor is connected to the VMS socket on the front side of main unit. The connection cable of floor sensor is connected to the FS socket. Power cord plugged in the mains socket and then power switch is switched on. Display shows \u2018\u201800\u2019\u2019"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002738_j.jneumeth.2004.03.023-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002738_j.jneumeth.2004.03.023-Figure1-1.png",
        "caption": "Fig. 1. Construction of dual carbon fibre electrodes. (A) Schematic crosssection of electrode before pulling showing arrangement of empty and carbon-fibre filled glass blanks. (B) Schematic appearance of tip of electrode after pulling and spark etching.",
        "texts": [
            " All electrodes to be used for amperometry were subjected to a fixed potential (+ 300 mV versus Ag/AgCl) for at least 1 h when new, and for 30 min before each experiment, in artificial cerebrospinal fluid (aCSF, s 2 7 d e S t H w t w c v b t m a c o p 2 m p n t b m electrode with the carbon fibres separated at the tip by a few microns, quadruple glass blanks were prepared with carbon fibres placed in two of the blanks, the other two being left empty. The blanks were glued together such that the two empty blanks were closer together than those containing carbon fibres (Fig. 1A). When pulled as previously described for multibarrel iontophoresis electrodes (Armstrong James and Millar, 1979), the two empty barrels pulled to a smaller diameter than the barrels containing the carbon fibres. This gave the desired geometry with the two carbon-bearing barrels separated by 4\u20138 m at the tip (Fig. 1B). Attempts to trim these two carbon fibres using the normal forceps method were unsuccessful; unless the two carbon fibres were perfectly aligned to the cutting plane, a twisting moment was generated during the cut which tended to crack the glass insulation around the carbon. Instead the two carbon tips were individually spark-etched (Millar and Pelling, 2001). This involved burning away the excess carbon fibre using a high voltage arc, initially with pulsed voltages to get the correct length of exposed carbon tip, and then using a controlled d.c. high voltage source to obtain the final conical tip profile (Fig. 1B). This method gave superior results to the previously reported single stage etching process (Williams et ee below for composition). .1.1. Carbon monofibre microelectrodes Carbon monofibre microelectrodes with a diameter of m and a length of 30\u201350 m were prepared as previously escribed (Armstrong James and Millar, 1979). Briefly, the lectrode consists of a single carbon fibre (Courtaulds XA), 7 m diameter, encased in a cylindrical glass capillary ube. A borosilicate capillary tube (1 mm internal diameter, arvard Apparatus Ltd",
            " For instance, a potential of +200 mV versus Ag/AgCl is sufficient to oxidise DA and NA but not 5-HT. Conversely, a potential of +500 mV versus Ag/AgCl oxidises DA, NA and 5-HT. Thus, an amperometric electrode set at +200 mV should record only the catecholamine component of a monoamine mixture while one set at +500 mV would detect both catecholamines and indoleamines. The difference between the currents at +200 mV and +500 mV corresponds, in essence, to the indoleamine oxidation current. Using a dual electrode assembly (Fig. 1), with one electrode monitoring at +200 mV (channel A) and the other at +500 mV (channel B), it should be possible to measure catecholamines (channel A output) and 5-HT (channel B minus channel A) simultaneously and in real time. This electrical subtraction method is common practice to eliminate movement artefacts from multi-electrode electrophysiological recordings in freely moving animals. Moreover, the approach is very similar in principle to that previously reported by Burmeister and Gerhardt (2001) who successfully used the differences in the chemistry of two recording electrodes to identify and eliminate interfering signals from analyte responses when detecting glutamate at enzyme-modified surfaces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002463_robot.1990.126125-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002463_robot.1990.126125-Figure1-1.png",
        "caption": "Figure 1. Two-link serial chain",
        "texts": [
            " For link i , this matrix, Ii, is represented as follows: where Mi is a 3 x 3 diagonal matrix of the mass of link i , and I; is the 3 x 3 moment of inertia tensor at the origin of the ith coordinate system. The matrix Ii is symmetric and positcve definite, but not necessarily diagonal. The 3 x 3 matrix, hi, is equal to mi&, where mi is the mass of link i, and si is the position vector of the center of gravity of link i from the ith coordinate origin. Because Ii and si are defined in coordinate system i , the matrix Ii is constant. To illustrate the power of spatial notation in the formulation of dynamic equations, the basic dynamic equations for a simple two-link serial chain, as shown in Fig. 1, will be given. Several basic equations which will be useful in developing the Inertia Propagation Method will be presented to conclude this section. The two links of the chain have spatial link inertias of 11 and 12, respectively. The two links are connected by joint 2, with motion space 4 2 . In this brief analysis, it is assumed that the gravity, centripetal, and Coriolis forces are all zero. A spatial force, f1, is exerted on link 1. The spatial force which link 2 exerts on the environment is f"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001349_0954407011528095-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001349_0954407011528095-Figure4-1.png",
        "caption": "Fig. 4 Model geometry",
        "texts": [
            " They are (a) loading pressure model, element analysis technique and is beyond the scope of(b) viscous pressure model, (c) asperity contact model, this work.(d) squeeze- lm model, (e) drum dynamics model and The band tension distribution is computed on the basis(f ) heat transfer model. In the following section, the of a force balance. It is assumed that the band tensionsubmodels are described in detail. distribution varies quasi-statically in time. The drum angle is measured from the servo to the anchor counterclockwise. As shown in Fig. 4, the wrap angle \u00e1 is de ned3 MATHEMATICAL MODEL where a circumferential tangent of the band departs from that of the drum surface. The gure also illustrates vari3.1 Loading pressure ous forces exerted on a band segment between angles \u00f5 and \u00f5+d\u00f5. Since the oil lm thickness h is very smallWhen the shift event is initiated, the strut pulls one end throughout engagement, the Reynolds number for aof the band and creates a tension distribution around typical band system remains in the range of laminar ow.the drum. As illustrated in Fig. 4, when the drum turns For example, the Reynolds number is of the order ofin the same direction as the strut motion, the band ten10\u00d52 for a system with 5 cm drum radius and 0.1 mmsion rapidly increases toward the anchor owing to visoil lm thickness at 150 \u00dfC oil temperature, rotating atcous shear and asperity friction forces. This so-called 2000 r/min [15]. Assuming Newtonian ow, the viscous\u2018energizing\u2019 reaction enables the band system to produce shear at location \u00f5 at time t is described as follows:a large torque output with a small applied force. On the other hand, when the drum turns in the opposite direc\u00f4 vis( \u00f5, t )=\u00e8(t ) Ro \u00f6(t ) h(\u00f5, t ) (\u00f6f \u00d5\u00f6fs) \u00d5\u00f6fp h(\u00f5, t ) 2Ro qPvis q\u00f5tion, the band tension decreases toward the anchor and yields a smaller engagement torque. This is called a \u2018de(1) energizing\u2019 reaction. The model coordinates are de ned in Fig. 4. The gure where \u00f6f , \u00f6fs and \u00f6fp are the empirical shear stress fac- D05800 \u00a9 IMechE 2001Proc Instn Mech Engrs Vol 215 Part D at University of Birmingham on June 5, 2015pid.sagepub.comDownloaded from tors which represent the eVect of surface roughness and ~ F z =dN\u00d5(T +dT ) sinAd\u00f5 2 B\u00d5T sinAd\u00f5 2 Basperity contact on the oil ow [27, 28]. During the partial lubrication phase, the oil ow area is disturbed and \u00d5P a R o W d\u00f5reduced due to the increasing asperity contact area. The shear stress factors account for this eVect as discussed =0 (8) below"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003135_1.2389233-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003135_1.2389233-Figure4-1.png",
        "caption": "Fig. 4 Kinematic description of the belt element",
        "texts": [
            " 5 Free body diagram of driver band pack Transactions of the ASME 28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use s t a b f l t a f t d i r m J Downloaded Fr equently gives rise to variations in the band pack tensile force T , as illustrated in Fig. 5. As the belt traverses the pulley wraps, he compressive force Q between the elements builds up. In ddition to the normal and friction forces from the band pack, the elt element is also subjected to the normal and frictional forces rom the pulley, as depicted in Fig. 7. Since the belt slips along the ine AD refer to Fig. 4 , the friction force acts along this line and hus is composed of two components one in the axial direction nd the other in the rotational plane ABE . In addition to the orces acting on the belt, Figs. 6 and 7 highlight the forces and orques acting on the pulley. Similar free-body analysis can be one on a belt segment engaged with driven pulley under the nfluence of load torque, l. The constraint of inextensibility of the belt implies that the time ate of change of length of any infinitesimal element of belt s ust be zero, i",
            " Using this, the wrap angles can be found to be = \u2212 2 sin\u22121 r \u2212 r d = + 2 sin\u22121 r \u2212 r d 9 The relative velocity between a belt element and the pulley can be readily obtained as, v\u0304rel = r\u0307er + r se s = \u0307 \u2212 Also, tan = r s r\u0307 10 It is to be noted that the relative velocity, v\u0304rel, as given by Eq. 10 is not the actual sliding velocity of the belt element. It only rep- JANUARY 2007, Vol. 2 / 89 28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use r l s s p T o t I s d I t r p s e t t Q S n o M w f 9 Downloaded Fr esents the relative velocity between the belt element and the puley in the rotational plane ABE refer to Fig. 4 . Since the belt lides on the sliding plane refer to Fig. 4 , the actual or true liding relative velocity, vs, between the belt element and the ulley is, in fact, given by, vs = r\u0307 sec2 + tan2 , tan s = tan cos he absolute acceleration of the belt element, a\u0304, can be easily btained from the absolute velocity v\u0304 of the belt element, and is hus expressed as a\u0304 = dv\u0304 dt = r\u0308 \u2212 r\u03072 er + r\u0308 + 2r\u0307\u0307 e 11 n addition to the aforementioned assumptions, the following asumptions are also made in the analysis to aid the solution proceure: \u2022 Uniform pressure distribution dN /rd between the belt and the pulley; \u2022 Assume is negligible and \u0307 \u0307",
            "org/ on 01/ F normal force between band pack and the element I pulley rotational inertia N normal force between pulley and the element Q compressive force in the belt elements r nondeformed belt pitch radius R deformed belt pitch radius T tensile force in the band pack u axial width variation of the pulley sheaves z constant transversal width of the belt pulley wrap angle 0 half-sheave angle of the nondeformed pulley half-sheave angle of the deformed pulley s pulley half-sheave angle in the sliding plane s length of the infinitesimal belt element angle subtended by the belt, s, at its instanta- neous center angular location of the belt element on the pulley wrap center of the pulley wedge expansion amplitude of the pulley sheave angle variation slope angle of the belt radius of the curvature of the belt angular speed of the pulley b linear mass density of the band pack e linear mass density of the belt element sliding angle of the belt element a coefficient of friction between the element and the band pack b coefficient of friction between the element and the pulley bo maximum coefficient of the kinetic friction between the belt element and the pulley \u0304 Stribeck-effect/lubrication parameter fr parameter relating kinetic friction to the static friction coefficient in driver input torque l driven load torque Superscript driven side quantities Appendix In this section, detailed dynamic equations of motion of the metal V-belt CVT system will be derived. From the kinematic description of the belt refer to Fig. 4 , the following geometrical relationships can be derived: tan = 1 r r s = r cos 1 = cos r 1 \u2212 = s tan s = tan cos A1 The velocity of an infinitesimal belt element of length s can be expressed as v\u0304 = lim t\u21920 s t v\u0304 = lim t\u21920 s t v\u0304 = lim r2 + r 2 t t\u21920 JANUARY 2007, Vol. 2 / 95 28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use I a i K p e I b m m t S o F s I t U o a 9 Downloaded Fr v\u0304 = r\u03072 + r2\u03072 A2 ntroducing 6 and the coordinate transformation between n , nd er ,e , i.e., n = sin cos \u2212 cos sin er e A3 n the above expression for belt velocity, yields v\u0304 = r\u0307er + r\u0307e A4 nowing this, the relative velocity between a belt element and the ulley can be readily obtained, as mentioned in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001545_j.2161-4296.2000.tb00219.x-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001545_j.2161-4296.2000.tb00219.x-Figure1-1.png",
        "caption": "Fig. 1 Effect of Roll on GPS Measurement",
        "texts": [
            " This independence is due to the fact that the control algorithm uses only estimates of specific \u017dstates and not the measurements themselves assuming that, given its measurements, the estima.tor can produce the required state estimates . This flexibility allows for optimization of the GPS INS integration without affecting the control algorithm of the tractor. The major need for attitude measurements is created by the fact that the GPS antenna is located at the top of the cab of the tractor so that it will be visible to as many of the overhead satellites as \u017d .possible. As seen in Figure 1, vehicle roll creates lateral position errors due to the noncollocation of \u017d .the GPS antenna and the control point CP , which is located on the ground between the rear wheels. The lateral error at the CP is simply \u017d . \u017d .y h sin 1error where y is the lateral difference between theerror GPS position and the CP. Even if the terrain is fairly flat, small irregularities in the ground will lead to position errors and can even cause the controlled system to become unstable. Analysis has shown that for a typical \u017d "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001841_095440603321509711-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001841_095440603321509711-Figure1-1.png",
        "caption": "Fig. 1 Schematic of contact nite element modelling",
        "texts": [
            " Such a formulation provides a general nite element discretization, which may consist of an unstructured mesh and does not require some special form of \u2018contact elements\u2019 . In effect, the evolutionary contact shape optimization method presented herein does not necessitate a mating mesh of elements over the contact interfaces. However, a mating mesh usually offers higher computational accuracy and numerical stability [16]. The gap contact elements make the formulation considerably easier [17]. Therefore, without losing generality, a mating mesh with gap elements is adopted in this study for both the contact analysis and the design optimization. Figure 1 also illustrates a nite element (FE) discretization scheme, where the contact between two bodies is represented by a number of gap elements connecting potential or actual contact node pairs. These gap elements are designed to resist compression only and are automatically removed from the analysis if placed in tension. In the process of nite element analysis, the contacting bodies are modelled individually and the contact surfaces are separated by a very small gap. As indicated in Fig. 1, the contact node pairs are joined together by beam elements connected across the initial gaps between these two contact surfaces. At the C10902 # IMechE 2003 Proc. Instn Mech. Engrs Vol. 217 Part C: J. Mechanical Engineering Science at UNIV OF PITTSBURGH on March 16, 2015pic.sagepub.comDownloaded from initial condition, all the beam elements are neither in compression nor in tension. The initial gap lengths indicate the critical contact state. Any consequence of loading that makes the gap smaller would put the beam elements in compression and such beams need to possess an arti cially high axial stiffness to transfer the forces between the two bodies and to prevent one body from penetrating into another",
            " Based on the step modi cation of gap spacing, the total gap of the contact pair can be updated as gk j \u02c6 gk\u00a11 j \u2021 Dk j \u202613\u2020 or the coordinates of the corresponding design boundary as ak j \u02c6 ak\u00a11 j \u2021 Dk j \u202614\u2020 where the superscript k stands for the iteration step of the evolutionary procedure. It should be noted that the gap beam length would be changed with the coordinate modi cation of the nodes at both its ends. As mentioned earlier, the initial length of the gap element indicates the critical contact state. To implement this concept into the whole optimization process, a virtual thermal strain is introduced to the gap element whose nodes need to be modi ed. Taking a pair of nodes \u2026 jp, jq\u2020 with a higher stress level as an example (Fig. 1), the coordinate of node jp is moved apart from jq with a length of gj. In order to make the gap beam element contract in length equal to this coordinate modi cation, a ctitious tensile stress is introduced by giving the nodes at both ends of the gap beam element a temperature T k j (less than the reference temperature T ref j ) to provide a tensile deformation of gk j . This can be done by satisfying the equation k T k j \u00a1 T ref j \u00b1 \u00b2 L jnj \u02c6 \u00a1gk j \u202615\u2020 where L j is the initial length of the jth gap element and k is the coef cient of thermal expansion of the gap element\u2019s material"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001747_s0031-3203(02)00045-6-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001747_s0031-3203(02)00045-6-Figure1-1.png",
        "caption": "Fig. 1. Candidate new positions for an F particle (see text).",
        "texts": [
            " The two particles at each seed point are called free (F) particles. The growth system works as follows: For each F particle: (1) Compute the direction of the line that joins this F particle with its neighboring particle in the snake (note that an F particle has only one neighboring particle); we call this line the u line. (2) Find a 9xed number N of candidate new positions for the F particle. These positions are equispaced along a circular sector of radius hp and angular width , centered at the F particle and oriented along the u line (see Fig. 1). (3) The new position for the F particle is selected as the candidate position with highest M value. If more than one candidate position has the same value, the system selects the position that is closer to the u line. (4) The F particle is advanced to the new position, and a new intermediate (I) particle is placed in its previous position. During the growth process it is possible that two F particles meet (i.e., that their distance becomes smaller than a threshold 1). If this happens, the F particles connect and change their status to I particles, so that a longer snake is obtained"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001601_1.1619378-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001601_1.1619378-Figure1-1.png",
        "caption": "FIG. 1. Sketch of the different orientations. Note that the inclination of external field H0 is different from the inclination of the internal one, H, and they are both in the Oxz plane. Also the hydrodynamic torque changes sign when crossing the origin along Ox .",
        "texts": [
            " In this paper, we present in Sec. II determination of the velocity profile and flow rate of a MR fluid in a cylindrical channel, taking into account the inclination of the field relative to the channel axis. In Sec. III we describe the experiments, present the results, and compare them with the theoretical predictions derived in Sec. II. II. VELOCITY PROFILE IN THE ABSENCE OF AXIAL SYMMETRY Consider unidirectional flow in a cylindrical channel with velocity v 5 v(x ,y)iz directed along the z axis ~Fig. 1!. The uniform magnetic field ~of intensity H! inside MR fluid is situated in the xz plane and forms an angle u < p/2 with axis Ox . Hereafter angle u is referred to as the inclination angle. It should be noted that this angle is different from u0 that defines the direction of the external field H0 . Assume that aggregates take the form of linear chains with the length much larger than the particle diameter but much smaller than the channel radius R, so that the velocity gradient does not vary too much Redistribution subject to SOR license or copyright; see http://scitation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002404_iros.2000.894577-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002404_iros.2000.894577-Figure3-1.png",
        "caption": "Figure 3: The generated time trajectory and the corresponding arm motion in case that cy = 5n/4",
        "texts": [
            " From the table, we know that, the long motion time is necessary for the case that the manipulator arm moves into the postures where the joint velocities are fast increased, as shown in figure 2. The joint torques due to the joint velocities thus become so high that only a small room of joint torques is left for increasing the path-tracking velocities. The proposed minimum time path-tracking scheme does not behaves the function of preventing the increase of joint velocities. One example of the derived time-trajectory and the generated arm motion, where a = 5x/4, are shown in figure 3, and the corresponding torque profiles of joints 1 , 2 , 3 are shown in figure 4, respectively. As seen, two joints (a redundant joint plus one more joint) used their bound value all the time while the manipulator tracking the path in the maximal velocity, and the redundancy of the manipulator is effectively utilized to increase the path-tracking velocity. Figure 5 shows the boundary of the path that the manipulator can track by the proposed minimum time path-tracking control scheme, and the corresponding path-tracking motion times for the inclination angles a: 0, x/4,x/2,3x/4, 7r , 5~/4,37r/2,7x/4 [rad]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003500_iccis.2004.1460465-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003500_iccis.2004.1460465-Figure4-1.png",
        "caption": "Figure 4. Schematic diagram of a flcxibte transmission system",
        "texts": [
            " The effective way to increase the weight accuracy is to apply the average of weights in periods of time. It makes unwanted changes have no effect on system performance. V. SIMULATIONS To illustrate the above design technique, a flexible transmission system is considered. This system consists of - - 0 1 0 0 0 0 0 0 1 2k,r2 2k,rz f2 2k,r2 _-_- _- - J , J 2 J 2 J 2 A = 2k2r2 s3 0 -- -- 2k2r2 L J 3 J 3 J 3 - threc horizontal pulleys connected by two clastic belts. The schematic diagram of the systcm is shown in Fig. 4. The objective is to control the position of the third pulley which may be loaded with small disks. This can be done by measuring its position and applying the required forces using a dc motor to the first pulley. There are three main plant modcls depending on different loading; no-load, half-load (1 .XKg) and full-load (3.6Kg). Each model contains of two flexible modes (with damping factors of less than 0.05). The dynamics of the system can be described as [9] T B = [ o J,. 2klr2 0 O] , C=[O 0 1 01 (19) where x = [8* e2 8, 83]T and J, f, P and k represent the incrtial momentum, friction factor, radius of the pulley and stiffness of the belts between pulleys, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003631_icems.2005.202558-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003631_icems.2005.202558-Figure4-1.png",
        "caption": "Fig. 4. Flux distributions of different dc excitations",
        "texts": [
            " 3(b) can also be obtained as: Fdc, = FPM FPM d-- 2 J (9) Compared with (8) and (9), it illustrates that, for the machine with magnetic bridge, (Og+10g-)=4 only needs a small change in dc excitation, namely 25% of FPM during flux strengthening, and 12.5% of FpM during flux weakening, whereas 100% and 50% of FPM are needed in dc excitation of the machine without magnetic bridge. By using the 2-D FEM, the static characteristics of the machine are analyzed. In order to assess the performance of the proposed machine more accurate, its iron core and magnetic saturation, leakage flux and armature reaction are taken into account. Fig. 4 shows the flux distributions of the proposed machine under different dc wingding excitation currents. A. PM Flux Linkage and backEMF When the machine operates at a constant speed with no-load, the corresponding flux linkages with respect to the rotor position under different dc excitation currents are simulated as shown in Fig. 5. When the dc excitation MMF reinforces the PM MMF, this extra flux path will assist the effect of flux strengthening. On the other hand, if the dc field MMF opposes the PM MMF, this extra flux path will weaken the PM flux leakage"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003623_acssc.1990.523486-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003623_acssc.1990.523486-Figure3-1.png",
        "caption": "Figure 3. The cart-inverted pendulum system The \u2018cart\u2019 IS assumed to slide freely along the rod. The pendulum may swing through 3GO degrees without obstruction.",
        "texts": [
            " The approach is to determine a target \u2018next value\u2019 for v(yle( tk+l) using a convergence model with acceptable response characteristics, and then select a control which the network predicts will match this value ( P = 0). If the network model of the dynamics is accurate enough, tlie continidy of U ( .) will ensure tha t the actual value of the v(ye( tk+l)) will be less than v(y,( tk)) . The stability results are preliminary, and are based on s~ ro r ig assumptions concerning the existence of a control which can minimize the given function, U(.). 3 Test Problem The controller was applied to the problem of stabilizing the cart / inverted pendulum system, shown in figure 3. The equations of motion for this system are (in the absence of disturbance forces and torques): neurons. There were five input nodes ( U , 2, 6, i, i) a t t i ;, and four output neurons (i, 6, i, 6\u2019) a t t k + l . The off line training of the network first used \u201cglobal\u201d training data from the full nori-linear range of the problem (61 E {-3.75, 3.75}, and 61 E {-5, 5)). Control inputs were taken form {-loo, 100). Finally, the resulting network was \u201clocally trained\u201d, about the origin, with training da ta generated by taking two steps from t,he origin, with control inputs taken uniformly from {-IO> 10)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002627_bf02844050-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002627_bf02844050-Figure3-1.png",
        "caption": "Figure 3 Ball impact apparatus.",
        "texts": [
            " The final deflection of approximately 7 mm at the end of contact is thought to be due to the deformation of the pile and, to some extent, the shockpad which are slow to recover and remain deformed after the impact hammer had left the surface. Readers Grade A cricket balls were fired onto each of the test-beds, using a range of different dynamic conditions (three speeds, three spins and two angles). A modified JUGS bowling machine was used which allowed the balls to be fired at a narrow angle to the ground, from a short distance away from the impact area. The motion of the ball before and after impact was recorded using a high-speed video camera (Fig. 3) sampling at 240 Hz. Each firing condition was repeated five times. The range of dynamic conditions set on the bowling machine was designed to include that seen in \u00a9 2004 isea Sports Engineering (2004) 7, 121\u2013129 123 0 200 400 600 800 1000 1200 0 2 4 6 8 10 12 Time (ms) Time (ms) Time (ms) A cc el er at io n (m /s 2 ) -4 -2 0 2 0 2 4 6 8 10 12 V el oc ity ( m /s ) -15 -10 -5 0 0 2 4 6 8 10 12 D is pl ac em en t ( m m ) 0 200 400 600 0 5 10 15 Deflection (mm) F or ce ( N ) a) b) d) c) a normal game of cricket, from slow to fast speeds, shallow to steep trajectory and back spin to top spin"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002386_s0301-679x(01)00116-5-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002386_s0301-679x(01)00116-5-Figure5-1.png",
        "caption": "Fig. 5. Finite difference grid and control volume by RNM.",
        "texts": [
            " In addition, we propose a computer program dealing with the nonsymmetrical complexity geometry of film gap clearance between the bearing and steel shaft guide, which is Nomenclature a area of the restrictor, cm2 A1\u20135 coefficient of the mass flow rate equation B1\u20135 coefficient of the mass flow rate equation CL stiffness, kg/\u00b5m C1\u20133 coefficient of the mass flow rate equation C0 the orifice discharge coefficient D0 feed hole diameter, mm Ds precision steel shaft guide diameter, mm FL load capacity, kg g acceleration of gravity, m/s2 Gw groove width, \u00b5m hi,j film gap of the bearing at land region, \u00b5m h0 film gap of the bearing at land region in equilibrium position, \u00b5m Hg groove depth,\u00b5m mi, j, i+1, j+1 mass flow of gas in or out the reference area,kg/s M the division number of bearing in horizontal Min mass flow of gas through feed hole,kg/s N the division number of bearing in vertical Pa ambient pressure, kg/cm2 Ps supply pressure, kg/cm2 Pr the recess pressure, kg/cm2 Pi,j pressure distribution of the bearing r radius of the bearing, mm R gas constant, m/K s1, s2 the reference distance T absolute temperature, K y1, y2 the reference distance a declination angle, \u00b0 g declination angle, \u00b0 d declination angle, \u00b0 the gas exponent of heat insulation m coefficient of viscosity, kg s/cm2 r density of gas, kg/m3 \u03c8 the coefficient of orifice outlet flow q angular coordinate in resistance network method, \u00b0 Fig. 1. Traditional aerostatic linear guideway system. Fig. 2. PCB drilling station with mixed linear guideway. caused by the nonsymmetrical external forces. It can be seen that the misalignment effect between the bearing and steel shaft guide will reduce the bearing behaviors such as load capacity, stiffness etc. Fig. 5(a) shows the partial view of the proposed bearing with axial straight groove. To calculate the pressure distribution in the reference area, a computer program describing the continuity of mass flow rate is developed. The satisfaction of flow equilibrium in the reference area bounded by dotted lines in Fig. 5(a), can be described as mi+1 mj+1 mi mj 0 (1) Using the finite difference form, we can obtain the flow out of the reference area due to pressure as follows: mi+1 1 12mRT (Pi,j+1 Pi,j) 2 (Pi,j+1 Pi,j) s2 y2 y1 2 (2) Gw h3 i,j Gw(h3 i,j Hg)3 mj+1 1 12mRT (Pi,j+1 Pi,j) 2 (Pi,j+1 Pi,j) y2 Gw /2 (3) s2 s1 2 h3 i,j We can also obtain the flow into the reference area as follows: mi 1 12mRT (Pi,j Pi 1,j) 2 (Pi,j Pi 1,j) s1 y1 y2 2 (4) Gw h3 i,j Gw(h3 i,j Hg)3 mj 1 12mRT (Pi,j Pi,j 1) 2 (Pi,j Pi,j 1) y1 Gw /2 (5) s1 s2 2 h3 i,j where m is the viscosity coefficient, R is the gas constant, and T is the temperature. Substituting Eqs. (2)\u2013(4) into Eq. (1) and let s1 s2 s, y1 y2 y, we obtain P2 i,j in finite difference form as follows: P2 i,j (6) P2 i+1,j\u2217A1 P2 i 1,j\u2217A2 P2 i,j 1\u2217B1 P2 i,j+1\u2217B2 A1 A2 B1 B2 where A1 A2 [( y Gw)h3 i,j Gw(h3 i,j Hg)3] 2\u2217 s , (7) B1 B2 s\u2217h3 i,j 2\u2217( y Gw /2) Fig. 5(b) shows the bearing with the circumference arc type groove. The value P2 i,j can be obtained as follows: P2 i,j (8) P2 i,j+1\u2217A3 P2 i,j 1\u2217A4 P2 i+1,j\u2217B3 P2 i 1,j\u2217B4 A3 A4 B3 B4 where A3 A4 [( y Gw)h3 i,j Gw(h3 i,j Hg)3] 2\u2217 s , (9) B3 B4 s\u2217h3 i,j 2\u2217( y Gw /2) In a similar way, the value P2 i,j in the grooved bearings at the region can also be presented as: P2 i,j (10) P2 i,j+1\u2217A5 P2 i,j 1\u2217A5 P2 i+1,j\u2217B5 P2 i 1,j\u2217B5 2A5 2B5 where A5 y\u2217h3 i,j s (11) B5 s\u2217h3 i,j y Eqs. (6, 8) and (10) give the pressure distribution in the considered bearing which is subject to the following boundary conditions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003762_j.jappmathmech.2006.03.010-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003762_j.jappmathmech.2006.03.010-Figure1-1.png",
        "caption": "Fig. 1.",
        "texts": [
            " The constraints imposed on the control torque, which is applied to the pendulum at the suspension point, can be hard. In this case, bringing the pendulum into the upper unstable equilibrium position without oscillations about a lower equilibrium is not possible from all initial states. By linearizing the equations of motion of the pendulum about the upper unstable equilibrium position, it is possible to construct (analytically) the set of states, from which this equilibrium can be achieved. A single-link pendulum, to which an external torque L is applied at the fixed suspension point O, is shown in Fig. 1; is the angle of deflection of the pendulum from the vertical measured counterclockwise. The torque L is assumed to be positive and is directed counterclockwise. The equation of motion of such a pendulum is well known: (1.1) Here, m is the mass of the pendulum, b is the distance from the suspension point O to the centre of mass of the pendulum, r is the radius of inertia of the pendulum about the suspension point O and g is the acceleration due to gravity. The friction force in the axis of suspension is ignored"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003169_09544054jem552-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003169_09544054jem552-Figure1-1.png",
        "caption": "Fig. 1 Rotor and tool coordinate systems",
        "texts": [
            " Previously, Andreev [2], and more recently Xing [3], in their textbooks on screw compressors, gave the envelope condition in its general form to generate the tools for machining screw compressor rotors. Stosic [4] presents a general case suitable for the generation of helical rotors and their tools on nonparallel and non-intersecting shafts. This meshing condition, although derived specifically for generating screw rotor tools, is quite general and may be equally conveniently employed to generate other helical surfaces. The coordinate systems in which the rotor and tool geometry are defined are given in Fig. 1. The rotor and tool shafts are at non-parallel and non-intersecting axes, the angle between which is S. The envelope meshing condition of the helical rotor and its form tool is \u00f0C xh \u00fe p cot X \u00de xh @xh @t \u00fe yh @yh @t \u00fe p p# @yh @t C cot X @yh @t \u00bc 0 \u00f01\u00de where C represents the distance between the rotor and tool axis centre-lines. The helical surface of the screw rotor, from which the tool is calculated, is given in equation (2) in the fixed XhYhZh coordinate system. Its derivatives with respect to the rotor parameter t are given in equation (3) JEM552 IMechE 2006 Proc",
            " A revised value of u is then calculated from equation (1) and the procedure repeated until the difference between two consecutive values becomes sufficiently small. Once calculated, the distribution of u along the profile may be used to calculate the coordinates of the meshing tool point coordinates, as well as to determine the contact lines and paths of contact between the rotors their tools. Once the angle u is known, the meshing tool transverse plane point coordinates Rt and zt may be calculated from the layout presented in Fig. 1 by use of equation (2) Rt \u00bc xt sin t \u00fe yt cos t \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2t \u00fe y2t q \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi xh C\u00f0 \u00de2\u00fe yh cosS zh sinS\u00f0 \u00de2 q zt \u00bc yh sinS\u00fe zh cosS \u00f04\u00de The tool coordinates Rt and zt now fully define the tool surface from which the rotor surface is formed. In order to quantify the influence of the tool set errors, as well as the influence of the tool deformation and wear, a tool to rotor coordinate transformation is needed to obtain the rotor coordinates from the given tool coordinates. This transformation was originally derived by Stosic [4] for the more general case of a hobbing tool from which the meshing condition presented in this paper can be derived as a special case. Given the tool coordinates Rt and zt and their derivatives @Rt/@t and @zt/@t, the rotor profile point coordinates xh, yh, and zh can be calculated from the layout presented in Fig. 1 as xh,yh,zh\u00bd \u00bc Rt cost\u00feC,Rt sintcosS zt sinS,Rt sint sinS zt cosS\u00bd \u00f05\u00de for the angle parameter t which, following Stosic [4], is obtained numerically from Rt @Rt @t \u00fe zt @zt @t cos t \u00fe p\u00fe C cotS\u00f0 \u00de @zt @t sin t \u00fe p cotS C\u00f0 \u00de @Rt @t \u00bc 0 \u00f06\u00de These are then used to calculate the rotor transverse coordinates x and y from the inverse of equation (2) as x,y\u00bd \u00bc xh cos#\u00fe yh sin#, xh sin#\u00fe yh cos#\u00bd \u00f07\u00de where u \u00bc zh/p. This fully represents the rotors machined from their tools for which the coordinates are given"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002715_j.jcsr.2005.04.020-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002715_j.jcsr.2005.04.020-Figure1-1.png",
        "caption": "Fig. 1. Shape formation by post-tensioning in the bottom chord.",
        "texts": [
            " The condition of geometric compatibility between the initial and final configurations of a post-tensioned and shaped hypar space truss is that all the non-gap members remain of the same length (only deflection, without large strain) during the shape formation process. Also, distances between joints in which the shorter bottom chords are placed to create gaps must shorten to allow the post-tensioning operation. The main idea for the post-tensioned and shaped hypar space truss is idealized with the mechanism of Fig. 1. In this procedure, the gap sizes are determined by the shapes of structures. In general, for a post-tensioned space truss, certain methods are used in the shape-finding. These shapefinding procedures are simulated by computer analysis based on a geometrically nonlinear membrane or shell theory. For a given arbitrary plan, a flat membrane is subjected to uniform pressure, line or concentrated loads, and the desired shape can be generated by a computer-aided shape-finding process. As shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001882_1.1398549-Figure9-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001882_1.1398549-Figure9-1.png",
        "caption": "Fig. 9 Summary of the different film formation according to the kinematics conditions and the nature of the contacting surfaces. Under pure rolling, viscous boundary films are formed on each surface and both ensure a starved lubrication of the contact. The film thickness is half the steady-state value hl . When sliding is introduced by keeping the entrainment speed constant, shearing occurs at the interface between the film and one of the surface. Only one of the surface is covered by a homogeneous film. Experiments performed with a brass\u00d5 chromium contact and with steel\u00d5chromium contact show that the boundary layers are more adherent on the brass than on chromium surface and they are also more adherent on a chromium surface than on a steel surface.",
        "texts": [
            " In the case of drawing lubricants, the role of local concentration of lubricating phase in the inlet of the contact which is controlled by the flow rate is very important. The existence of such an optimal concentration of lubricating compounds in the inlet zone could be related to the existence of a critical speed below which the lubricant film cannot be formed. These assumptions on the wetting properties combined to hydrodynamic effects can give a global view of the mechanism of lubricating film formation with the drawing lubricant ~see Fig. 9! but have to be experimentally confirmed. The experiments performed on the EHL test rig have shown a new mechanism of lubrication with water-based lubricants having a microscopic lamellar structure. It has been found that boundary layers build-up on the contacting surfaces are responsible for the lubrication process under a starved regime. It appears that the viscosity of the bulk emulsion is too low to form an EHD film in the contact. The boundary layers that are formed in the EHD regime have high viscosity but cannot create a sufficient reservoir to supply the contact and lead to a fully flooded lubrication"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003139_12.539578-Figure16-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003139_12.539578-Figure16-1.png",
        "caption": "Figure 16. Wireless Temperature Sensor Integrated Bearing",
        "texts": [],
        "surrounding_texts": [
            "A remotely-powered wireless temperature sensor to measure cage temperature in real-time for the bearing health monitoring has been proposed and developed. The wireless sensor developed in this study is based on the principle of operation of an inductor-capacitor (L-C) tuned Colpitts oscillator. A pair of miniaturized temperature sensitive capacitors was integrated into a simple inductor-capacitor (L-C) oscillator as sensing elements, and the oscillator serviced as a telemeter circuit that transmits critical temperature data to a receiver via computer data acquisition system. The remote power for the sensor operation was supplied by radio energy induced from exciter coil outside into the sensor circuit. The sensor circuit described here provides an effective solution for the monitoring of bearing health. Dupont Kapton\u00ae thick film carrier and Surface Mount Devices (SMD) were used to fabricate the sensor. The sensor calibration shows that the first prototype sensor has good sensitivity, an almost linear response, and high stability. It is demonstrated that this wireless temperature sensor could provide an effective means for bearing health condition monitoring. Proc. of SPIE Vol. 5391 375 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/18/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx"
        ]
    },
    {
        "image_filename": "designv11_24_0001392_cdc.1998.757988-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001392_cdc.1998.757988-Figure1-1.png",
        "caption": "Figure 1: The n-trailer mobile robot.",
        "texts": [
            " Obviously, when the free space is large enough and the vehicle is not particularly cumbersome, our technique presents no significant improvement with respect to the standard path followers. The paper is organized as follows: in Section 2 the ntrailer system is modeled using the Frenet frames; in Section 3 local stability to a circular path is proved and in Section 4 the algorithm is applied to a car pulling two trailers. 2 Kinematic model and F\u2019renet frames Suppose we have the n-trailer system of Fig. 1. The nonholonomic constraints on the points Pi (below called nonholonomic points) originate from the assumption of rolling without slipping of the wheels. The dynamic equations are well-known (see [6]) and can be calculated recursively. The equation for the orientation angledi asafunctionofBi-1 a n d v i , i E { l , ..., n}is: (1) vi - e i ) Li ei = where the velocity of the i-th axle is: For the front axle we can write: A where ,& = 00 - 81 is the steering angle and vo is the longitudinal velocity of the front car"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002959_tmag.2005.846254-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002959_tmag.2005.846254-Figure1-1.png",
        "caption": "Fig. 1. Cross-sectional geometry of the test motor.",
        "texts": [
            " (2) where is the rotor displacement, is the flux density, is force, and and are the fundamental and whirling frequencies. Because of this frequency shift, the FRF of the harmonics are defined as (3) The modulation presented in (3) has to be taken into account when the response signal is divided by excitation signal, both in the frequency domain. III. RESULTS The application was tested for the four-pole 15-kW cage induction motor with open rotor slots at rated load (slip: %). The main parameters of the motor are given in Table I and its cross-sectional geometry is shown in Fig. 1. The motor was chosen because it has been equipped with the active magnetic bearings (AMB) for the force measurements. To validate the calculation methods presented in the paper, the AMB allows the accurate creation of the whirling motion and the force measurement. We have not measured the flux density harmonics itself. Figs. 2 and 3 presents the calculated harmonics of flux density harmonics in time domain and in complex plane in order to find out the behavior of the vector of the flux density harmonics during the simulation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003293_j.aca.2004.08.008-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003293_j.aca.2004.08.008-Figure2-1.png",
        "caption": "Fig. 2. Home-made cell for measurement of membrane impedance: PVC block (1) with cylindrical container (2), Pt electrodes (3), Pt wire contact to conductivity meter (4), contact opening (5), membrane to be tested (6) and bolts to connect PVC blocks (7). The left and right PVC blocks have a symmetrical buildup.",
        "texts": [
            " The column outlet was directed perpendicularly towards the sensitive membrane of the coated wire electrode in a flow cell (see [5]). The distance from the LC tubing outlet to the electrode was 100 m. The membrane potential was measured against an Orion 800500 Ross\u00ae reference electrode using a high impedance (1013 ) amplifier. The detection signals were recorded on a PC 1000 data acquisition system from Thermo Separation Products. The conductivity of the membranes was measured in a home-made cell (Fig. 2) by using a conductivity meter (type K610, Consort, Belgium), working at 66 Hz and 125 mV signal amplitude. 2.2. Chemicals All chemicals were of analytical grade. The eluent was prepared by dilution of a phosphoric acid solution, obtained from UCB. The eluent was passed through a 0.45 m membrane filter (Alltech) and constantly degassed. Organic acids were purchased from Merck, Acros, Aldrich, Fluka and Sigma. 1 \u00d7 10\u22122 M stock solutions of carboxylic acids were prepared in the 1 mM phosphoric acid eluent",
            " Membrane impedance testing t m e r w t t s o c a 2 t ( r P F 2 w A o a m ere diluted to the required concentrations when necessary. olutions of analytes were filtered using a 0.45 m memrane filter (Alltech), before injection. High-molecular mass VC was obtained from Janssen Chimica. The plasticizers oitrophenyl octyl ether (o-NPOE), bis(2-ethylhexyl)phtalate DOP), tris(2-ethylhexyl)phosphate (TOP) and tris(2thylhexyl)trimellitate (TOTM), and tetrahydrofuran (THF) olvent were purchased from Fluka. Membrane materials were placed in a home-made cell o estimate their impedance (see Fig. 2). For this purpose, embranes were made by the solvent casting technique (as xplained for the electrode coatings in Section 2.3), by evapoation in a suitable Petri dish. Membranes of 1.5 cm diameter ere cut from the 100 m thick membranes and placed beween the two plastic (PVC) containers (see Fig. 2). The conainers, with 10 mm diameter cylindrical holes at the contact ides, were filled with 0.01 M KC1. Two square Pt electrodes f 1 cm \u00d7 1 cm and 0.25 mm thickness were placed in the ell (Fig. 2). The cell constant was determined (1.07 cm\u22121), nd was taken into account. .5. Log P calculations For the calculation of log P values of analyte substances, he internet site http://www.logp.com from ChemSilico LLC Tewksbury, MA, USA) was used. Calculations of log P for eceptors were performed using Hyperchem for Windows, rofessional version-Rel 6.03 from Hypercube (Gainesville, lorida, USA). .6. Synthesis of the receptors Mass spectrometric characterizations were performed ith liquid secondary ion-mass spectrometry (LSIMS, MD 604 apparatus), or with matrix assisted laser desrption/ionization (MALDI, Kratos Analytical MALDI 4 pparatus)",
            " Electrodes incorporating lipophilic macrocyclic polyamines without urea groups (compounds 5, 6 and 7), and with an amide containing side group (compound 10), were also studied for comparison. 3.1. Optimization of the membrane compositions Although the podand urea receptor-based electrode materials revealed to be very sensitive, their practical use was hampered by noise pickup phenomena. It is typical behavior for membranes with low conductivity characteristics. Measuring the impedance of membrane materials in a setup as given in Fig. 2 (cf. Section 2.4) shows why this is the case. Quaternary ammonium compound MTDDACl clearly has a greater effect on the conductivity of the membrane than the studied compounds (Table 1). Especially the podand urea receptors performed badly in this respect (e.g. 3, Table 1). Addition of 0.2% MTDDACl to the membrane mixtures containing o-NPOE greatly enhanced the conductivity characteristics. The membranes described further will therefore either be a mixture composed of PVC/o-NPOE/podand urea r N s 0 3 s t l w d o T M M M M M M N N N N M M Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003613_20060621-3-es-2905.00064-Figure10-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003613_20060621-3-es-2905.00064-Figure10-1.png",
        "caption": "Figure 10. For a gain of K=0.56 the robotic arm hits the ball",
        "texts": [
            " The animation starts with a block diagram and overall system, a robotic arm and a graph which will be animated to show the effect of different gain values. By pressing the play button the robotic arm moves across the area and tries to hit the ball at different speeds. As we run through the animation as depicted, the arm tries to hit the ball with different motions and angles. On the first attempt, K2=0.9, the arm misses the ball completely (Figure 8) the second attempt, K1=0.65, it hits the ball but not properly due to angle error, but on the third attempt, Kbest=0.56, it hits the ball (Figure 10). This example will lead to better design and help the student to understand how different cases and requirements can be solved with control system engineering skills. The basic mechanisms that relate these and other phenomena, for example, the effects of sampling and non-linear elements, can be illustrated very effectively using these tools and enhance student learning of the topics to a high degree (Dormido, Control learning, 2003). So far, it has been demonstrated that these animations and multimedia tools are vital to visualization of these concepts"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001486_cca.1999.806179-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001486_cca.1999.806179-Figure2-1.png",
        "caption": "Figure 2: Hypersonic Glide Vehicle",
        "texts": [
            " The translational motion of the vehicle is obtained from Newton's equations. Pitch and bank are the two rotational degrees of freedom and are obtained from pitch and bank autopilot transfer functions which are characterized by simple lags. CADAC has been used extensively to test hypersonic vehicles and its equations of motion account for a spherical rotating earth. For display purposes, the CADAC-GLOBE plotting program is used to project the trajectory on the earth. The vehicle to be flown is the generic 400 kg hypersonic glide vehicle depicted in Figure 2. Its aerodynamic coefficients are given in Table 1. Lower and upper limits of Oo and 30' are imposed on angle of attack. During the exo-atmospheric flight phase, reaction jets provide stability until the dynamic pressure has reached a level sufficient for the six control fins to execute effective aerodynamic control. High bank angles produce tight turns but result in excessive loss of altitude; small bank angles produce shallow turns but unacceptably large turning radii. Sensitivity studies led to the enforcement of f70\u00b0 bank angle limits as a reasonable compromise"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002427_20.104551-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002427_20.104551-Figure2-1.png",
        "caption": "Fig. 2.",
        "texts": [],
        "surrounding_texts": [
            "INTRODUCTION\nThe capture of ultra-fine particles by HGMS collectors was described in a systematic way for the first time in 1983 by a theoretical model [1,2], supported by experiments [2,3]. The model developed was based on a single space dimension and time and was followed by further studies [4,5,6] in which interparticle forces, including hydrodynamic or electric double layer forces, were taken into account. A limitation of all of these previous studies is that the consideration took place only in one space dimension and time, which precludes the posibility of taking the fluid flow into account. This paper presents a generalization of thd theoretical model [1,2] by considering two dimensional HGMS capture including the effects of diffusion, magnetic traction force and fluid velocity drag force. The interparticle forces are disregarded here since the intention is to obtain a simplified two dimensional model which will highlight the main features of the time dependent retention of ultra-fine particles by a single wire collector. This will provide the first stage of the development of a complete analysis of HGMS collection of ultra-fine particles in two dimensions.\nTHEORY '\nHGMS diffusion equation Brownian motion has a significant effect upon the kinematics of particles suspended in a fluid if the particle size becomes smaller than the order of 1 pm. For a suspension of such particles, it is necessary to describe their retention on and about a magnetic collector by the diffusion equation [ 1,2]\n&/at = DVC - v . (UFC) , (1)\nwhich relates the action of the external forces F(r) to the time evolution of the particle volume concentration, c(r,t), where r is the position vector and t is time. The diffusion coefficient, D, is assumed to be isotropic and independent of the concentration, c. That is D = ukT, where k is the Boltzmann constant, T is the absolute temperature and U is the particle mobility, which for spherical particles can be written in Stokes' approximation as U = 1/(6qb), where b is the particle radius and r) is the viscosity of the fluid.\nTo describe particle collection on and about a cylindrical wire, it is convenient for reasons of symmetry to use polar coordinates (r,8). Furthermore, the normalized dimensionless space and time variables r, = r/a and r = Dt/az may be introduced, where a is the collecting wire radius, and equation (1) becomes\n- {?+ $-(G,c)+\nwhere G = aF/(kT) is readily determined once the contributions to the external force, F, are known.\nIt is assumed that only the magnetic traction force and the fluid velocity drag force are considered and that the magnetic field. H,, large enough to saturate the wire, is applied along the x-axis, while the background velocity, V,, of the potential flow makes an angle a with the x-axis, i.e. with H,. Then, using expressions in [7], the components of vector G = [G,, Go] are calculated as\nG, = G, ( r i 3 cos20+r;5KW) + Gvo(1-r;2)cos(0-a), (3a)\nG, = G, r;Ssin20 - GvO(1-r;2)sin(0-a) , (3b)\nwhere G,=-4rpdMHob3/(3kT), K,=M/(2H0), Gvo=-6qbV,,/(kT), x = x,, - xf is the difference between particle and fluid susceptibilities at temperature T and p, = 4 r x lO-'Hm-'.\nOther forces may be incorporated in this theoretical model by adding further G, and G, terms to expressions (3a,b).\nSolution of the HGMS diffusion equation Equation (2) cannot be solved analytically and therefore its solution is obtained by a numerical method. Since far a particular time r the concentrations c(r,, 8, r ) are known at any mesh point (r,, e), equation (2), which may be expressed as\n= f(c, r,, 8) , (4)\nrepresents an initial value problem that yields c for time r + dr. This problem is solved here by the Euler method, where the function f(c, r,, 0) is evaluated by using finite differences to approximate the partial derivative terms on the right hand side of equation (2). In this way the CPU times are relatively long but possible instabilities, associated with the use of higher quadrative methods, are avoided.\nSaturation As particle concentration increases interparticle forces will limit this concentration to a finite value. This process is rather difficult to model and therefore a simple deterministic approach is adopted.\nExperimental evidence [4] indicates that saturation occurs approximately at c = 0.1. This value is therefore used as a limit to the particle buildup concentration, and meshes with a concentration c > 0.1 are assumed to be saturated and are removed from the calculation.\nBoundary conditions at an impervious surface Calculation of the right hand side of equation (2) requires values of concentration for the four surrounding meshes. For a mesh at the wire surface, however, there are only three meshes available and hence the value of &/a7 cannot be determined using equation (2).\nIt is noted that whilst concentration is represented by a continuous parameter, it is actually a density and therefore a finite volume must be used to determine the particle concentration. Fig. 1 shows a rectangular parallelepiped FQRSTUVW with an impervious face PQRS. Considering the flow across face TUVW it is easy to show that the time rate of particle concentration for an impervious surface in the radial direction is given as\n(aC/a7),. = (1/6rn)(W%,) - (l/6r,)(Grc) (5a)\nand similarly for an impervious surface in the azimuthal direction.\n(ac /ado = (i/(r,6e))(ac/LM)-(l/(rn60))(Goc) . (5b)\n0018-9464/90/0900-1867$01.00 0 1990 IEEE",
            "1868\nRESULTS\nA number of simulations have been performed to model the capture of manganese pyrophosphate (Mn,P,0,.3H20) particles (b = 1.2 x in aqueous suspension on a thin stainless steel wire (a = 5 x m, M = 8.61 x lo5 A m-l). In all cases a magnetic field of H, = lo7 A m-1 and a fluid velocity of V, = m s-l have been used where appropriate with a concentration of particles entering the area of c, = 10-3. Results of particle retention for two different initial conditions are presented here.\nParticle retention for the initial condition c(r,, 0) = co\nr -- 0 in an area of homogeneous concentration c(r,,O) = c, will now be discussed.\nFirst, to compare with previous single space calculations and experiments [l-31, Figs. 2 and 3 show the results of calculations with the magnetic field H, = lo7 A m-l only, i.e. for V, = 0. These results exhibit similar characteristics as those presented in [ I -31, although it is noted that different data are used in each case.\nm, x = 2.03 x\nThe effects of switching the magnetic field on instantly at time\nThe derivation is carried out in metric coordinates and real time. The resulting particle concentration time rates, (sa) and (5b), are given in the normalized dimensionless variables ra, 8 and r.\nThe terms ac/ar, and ac/% have to be determined by using the mesh next to the surface and the neighbouring mesh. Expressions (5a) and (5b) are only terms which appear in equation (2) for %/a7 at the wire surface. Expression (sa), for example, is used for a mesh at the wire surface to provide the contribution in the ra direction. The appropriate terms in equation (2) are used for the 0 direction and therefore equation (2) is replaced by\nIn addition to using expression (5a) at the wire surface, a saturated region is modelled by assuming that it is impervious. Therefore, expressions (sa) and (5b) are used to provide terms for meshes next to saturated areas in both the radial and azimuthal directions.\nEarlier studies [ 1,2] used a different boundary condition, namely &/ar, = G,c, by setting the particle flow to zero at the wire surface. It is noted this is an approximation to expression (5a) since it may be also obtained by setting the left hand side of (5a) equal to zero. Hence, boundary conditions (5a, b) used here are dynamic conditions, whereas a l a r , = G,c used in [1,2] is a quasi-steady-state condition.\nOuter boundary conditions The numerical model of HGMS capture necessarily covers a finite area and therefore, for the same reasons as at the wire surface, it is necessary to provide boundary conditions at the outside edge of the area, where the calculation takes place.\nFor meshes where the flow is into the area of computation the concentration is determined by the conditions upstream. It is assumed that the concentration there is constant and therefore at the upstream boundary the concentration is fixed, that is c = c,,.\nAt the downstream boundary, where the flow is outward, it is reasonable to assume that the concentration parallel to the direction of flow is constant. This is, however, not congruent with the symmetry of the (ra,O) coordinate system. Therefore, a simplified boundary condition is assumed, namely that, whilst the azimuthal terms in equation (2) apply, the radial concentration gradient is zero, that is w a r , = 0.\nFig. 3.\nConcentration contour plot for V, = 0, r = 0.20 and initial condition c(r,,O) = c, =\n' -a :;yo/*7oo -9\n-10\nRadial concentration profiles for V, = 0, r = 0.20 and initial condition c(r,, 0) = c, =\nThe effect of flow velocity is -shown in Figs. 4 and 5, where concentration contours are plotted for H, = lo7 A m-l, V, = m s-1, r = 0.075 and 0.25, respec.:vely.",
            "1869\nParticle retention for the initial condition c(rar 0) = 0 m\ns-1 in an area of concentration c(r,,O) = 0 at T = 0 is shown in Figs. 6 and 7. These figures show contours for r = 0.075 and r = 0.25, respectively. It may be seen that the results are similar to those given in Figs. 4 and 6. However, the effect of transporting particles into a previously empty region is to introduce a delay in the buildup of particles, especially behind the wire. It is noted that for T = 0.075 there is no saturated buildup on the downstream side of the wire.\nThe effect of instantly switching H, = lo7 A m-1 and V, =\nDISCUSSION AND CONCLUSIONS\nA two dimensional theoretical model for the capture of ultra-fine particles on an HGMS collector has been developed. A full set of boundary conditions has been derived and in particular dynamic boundary conditions at the wire surface have been formulated. The results show areas of depletion, accumulation and saturation at intuitively expected locations of space after appropriate periods of time. The model gives pointers for future experimental work which is needed for its full validation.\nThe comparison between results shown in Figs. 4, 5 and Figs. 6,7 indicates that, for the cases investigated herr-, the particles retained at the downstream side of the wire are supplied by forces of diffusion and not by fluid flow. This is a valuable result since the origin of the rear capture is still a subject of discussion.\nREFERENCES\nR. Gerber, M. Takayasu and F. J. Friedlander, IEEE Trans.Magn. MAG-19 (1983) 21 15. M. Takayasu, R. Gerber and FIJ. Friedlander, IEEE Trans.Magn. MAG-19 (1983) 21 12. M. Takayasu, J.Y. Hwang, F.J. Friedlander, L. Petrakis and R. Gerber, IEEE Trans. Magn. MAG-20 (1984) 155. R. Gerber, IEEE Trans.Magn. MAG-20 (1984) 1159. J.P. Glew and M.R. Parker, IEEE Trans.Magn. MAG-20 i1984) 1165. D. Fletcher and M.R. Parker, J.Phys.D: Appl.Phys. 17 (1984) L119. R. Gerber and R.R. Birss, High Gradient Magnetic Separation, Chichester: RSP-John Wiley & Sons, 1983."
        ]
    },
    {
        "image_filename": "designv11_24_0003314_1.2180281-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003314_1.2180281-Figure1-1.png",
        "caption": "Fig. 1. The rotating frame. In the top view the unit vectors u and u correspond to and .",
        "texts": [
            " In this paper we show that the physical essence of the problem is the Coriolis torque; the latter yields a unified solution to all the variants of the problem and explains the appearance of a universal constant. Although the Coriolis torque acts on any spinning body in a rotating frame, we believe this example is one of the first in the literature where it is used to advantage. What forces the ball up? Let be the angular velocity of the ball about its center, and z, , its vertical, azimuthal, and radial components in cylindrical coordinates, respectively see Fig. 1 . While the ball is rolling down, 0 for inside rolling . If we can find a mechanism that reverses the sign of , then the ball will roll upward. The desired mechanism exists and it is the Coriolis torque. 497\u00a9 2006 American Association of Physics Teachers ject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 13 May 2014 07:23:28 This art Take a frame rotating with angular velocity around the axis of the cylinder in such a way that the point of contact between the ball and the cylinder appears to move only vertically along a \u201ccontact line"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001455_50006-1-Figure5.39-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001455_50006-1-Figure5.39-1.png",
        "caption": "FIGURE 5.39 Coil geometry: (a) top view of the stator; and (b) perspective of coil.",
        "texts": [
            "255) ~rA w where Nac is the number of active coils, Nturn is the number of turns in each coil, lw is the length of the wire in each coil, and r~ and A~ are the conductivity and cross-sectional area of the wire. In our case there are 4 active coils, Nac = 4. Notice that Eq. (5.255) constitutes one equation with three unknowns: Nturn, 1~, and A,,. Therefore, additional information is needed. One approach to obtaining the unknowns is to specify the orientation, shape, and dimensions of the coil. To this end, we specify the motor cavity height h, which puts an upper limit of h - t m on the height of the coils (Fig. 5.37). We choose the cross-sectional area Ac and mean length per turn l t (Fig. 5.39). Given the coil dimensions, we write the following additional relations, Nturn A., A c = (5.256) 5 and l w = f o N t u r n l , , (5.257) where fp is a wire packing factor and f~ is a geometric factor. For precision wound coils fp ,~ 0.69. The three unknowns Xturn , lw, and A w are obtained via the simultaneous solution of Eqs. (5.255), (5.256), and (5.257). 426 CHAPTER 5 Electromechanical Devices Once the orientation and geometry of the coils are known we compute the torque constant K t. To this end, consider the force on an infinitesimal segment of coil wire dl",
            " We assume that the rotor field is in the z direction and obtain dF = idl x B = i(dr~: + r d O ~ ) x B g~ A = iBo(rdO~: - drO?), (5.258) where By is the rotor field in the gap region. The torque is given by dT = r x dF, and if we substitute Eq. (5.258) and take the z-component we find that d T z = - i B g r d r . This is the torque imparted to the segment of the coil by the rotor magnet. Notice that only current in the radial direction contributes to the axial torque. If we consider a typical coil geometry, there are two sides that have an effective length l e in the radial direction (Fig. 5.39b). The torque on the rotor due to an active coil can be estimated as Tcoil-- 2 iN turnBeRl e, (5.259) where factor 2 takes into account the two sides of the coil and R is the mean radius of the magnet, ~ = R 1 + R 2 . 2 The effective length l e can be determined from the coil geometry. The total torque is simply Eq. (5.259) times the number of active coils, m Tto t -- 2iN,:,oNtu~nB~Rle. Therefore, the torque constant is K, - 2NacNturn B oRI e. (5.260) Furthermore, in the MKS system K e = K t. At this point, all the terms in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000664_1.521881-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000664_1.521881-Figure6-1.png",
        "caption": "FIG. 6. Inert gas shielding configurations used for top and bottom of welds.",
        "texts": [
            " Consistent welds are indicated by coupled and inconsistent and no welds are indicated by uncoupled. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 169.230.243.252 On: Thu, 18 Dec 2014 06:48:45 siderations, the threshold irradiances indicated in Fig. 4 are applicable to BOP and butt welds with good fitup and where fitup tolerances are small compared to beam spot size. The different gas shielding configurations illustrated in Fig. 6 were used to determine top shielding effects on weld appearance. The slightly different angles were necessitated by constraints in the experimental system and fixturing limitations but do not produce significant differences in results. Beam focus was located at the workpiece surface. The different cross jet configurations affect the plasma formation over the weld. The leading edge configuration tends to blow plasma to the to-be-welded location while the trailing edge and transverse direction configurations blow the plasma away from the to-be-welded location"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001765_1350650011543709-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001765_1350650011543709-Figure4-1.png",
        "caption": "Fig. 4 Picture of a battery-powered telemeter installed on the bearing cage",
        "texts": [],
        "surrounding_texts": [
            "In the remotely powered version, two types of inductor coil for power transmission were tested. The first used a surface mount technology (SMT) inductor coil as coil 2, while in the second a loop of copper wire wound all along the periphery of the cage worked as coil 2. The efficiency of power transmission between the two coils is a function of coupling between them. It was found that inductor coil 2 employing a loop of copper wire provided better coupling. The copper loop inductor was able to transmit 25 times more power than the SMT coil.\nThe telemeter mainly consists of a temperature-sensing element, the sensitive capacitor and other electronic components. The telemeter is built separately on a printedcircuit board (PCB) instead of building directly on the cage. The PCB was then installed on the cage using a glueing agent. This construction was adopted for ease of manufacture. The PCB serves as wiring and mounting pads as well as the support for the components. Photolithography was used to develop the PCB and discrete SMT components were mounted on it by soldering.\nPhotolithography was used to develop the pattern of the desired circuit on a flexible copper-coated polyamide circuit board, commercially available and known as Kapton1. The circuit board is available with multiple layers of copper with layers of insulating material separating multiple layers of copper. Because of the simplicity of the telemeter circuit designed for this study, single-layer Kapton was used. A Kapton1 circuit board with 0.3 kg of copper per square metre on a polyamide substrate 0.05 mm thick was used for the telemeter developed for this study.\nThe first step in the process is to design and develop the artwork or the pattern for the desired circuit representing a positive or negative image of the wiring and soldering pads\non a photographic film. While designing the artwork, large sizes of mounting pads are recommended to accommodate dimensional tolerances in the SMT components. To account for the non-uniform nature of the etching process that would follow, the separation between the copper regions in the pattern should be large enough to avoid traces of copper left behind in the etching process. At the same time, the width of copper regions forming connecting wires must be large enough to avoid breaks in the circuit. It was found that the minimum dimension for a width of wire or a gap must be at least 250 \u00edm. The quality of pattern generated depends on the sharpness of edges and lines of pattern on the photographic film. Therefore, the pattern is printed on the photographic film paper using a high-density 2510 dots=inch laser printer. Figure 3 depicts a picture of the circuit pattern prepared on the photographic film.\nThe next step is to transfer the pattern on to the circuit board. For this purpose, the circuit board is completely covered with a layer of an AZ-1518 positive photoresist, a substance that changes its chemical properties after exposure to light. A centrifuge is used to achieve a thin and uniform layer. In the next step called pre-baking, the layer of photoresist is baked in an oven at 60 8C for 30 min before allowing it to cool to ambient temperature for about 30 min. The circuit board is then exposed to ultraviolet light for 120 s through the photographic film, which has the desired circuit pattern. The photographic film acts as a light-blocking mask. The circuit board with the exposed layer of photoresist is now developed in a 1:1 solution of water and AZ developer, a solution of trisodium phosphate, silicic acid and sodium salt in water. Here the portion of the photoresist layer that was not exposed to light is dissolved. The board is then post-baked in the oven at 120 8C for 60 min. This process forms a hard layer on the circuit board in the form of the pattern that was printed on the photographic film. The preceding procedure is carried out under safe sodium light so as to avoid premature exposure of photoresist.\nThe board is then exposed to etching solution at elevated\nJ01201 # IMechE 2001 Proc Instn Mech Engrs Vol 215 Part J\nat Universitats-Landesbibliothek on December 16, 2013pij.sagepub.comDownloaded from",
            "temperature of 45\u201350 8C. The etching solution is a chemical solution of ferric chloride and hydrochloric acid in water, commercially known as electronic circuit etching solution. The part of the copper that is not under the photoresist layer is dissolved and the copper pattern as designed on the photographic film is generated on the board.\nThe SMT components are mounted on the circuit board using standard soldering techniques, although proper care needs to be taken when dealing with discrete size SMT components manually. The exciter coil for the remotely powered telemeter and a receiver antenna are fabricated in the form of loops made of copper wire and mounted on a support and installed around the bearing. Figures 4 and 5 show photographs of the fabricated and installed batterypowered and remotely powered telemeters respectively.\nThe output frequency is monitored using a radio-frequency spectrum analyser connected to the loop antenna. A data acquisition system collects the output from the spectrum analyser at small time intervals of 5\u201315 s.\nThe bearing used in this study for temperature monitoring is a Timken JM205149/JM205110 tapered roller bearing with internal and external diameters of 50 and 90 mm respectively. Tests were conducted with the full complement of rollers in the bearing and also when two-thirds of the 18 rollers were removed. The rollers were removed from the bearing in order to achieve higher contact stresses in the bearing for a given load.\nFigure 6 shows a schematic assembly of the test rig. The test rig is built on a rigid frame that supports an 11.2 kW a.c. motor on the top. The motor shaft turns the inner race of the bearing through a spindle assembly. The outer race of the bearing is fixed to the housing and is mounted on a torsion bar. The housing also contains an oil sump underneath the outer race to supply lubricant to the bearing. The housing and the torsion bar are mounted on a subframe that can be moved vertically along the guide pillars using a hydraulic jack. An axial load of 22 250 N will generate a Hertzian contact stress of 1.725 MPa at the race\u2013roller contact. The axial load is measured using a load cell.\nFigure 7 depicts the details of the torque measurement subassembly. The torsion bar located below the bearing was designed to allow measurement of torque transmitted through the bearing. Two arms 1808 apart extend from either side of the housing. Because of the torque generated in the bearing, the torsion bar twists. The tangential move-\nProc Instn Mech Engrs Vol 215 Part J J01201 # IMechE 2001\nat Universitats-Landesbibliothek on December 16, 2013pij.sagepub.comDownloaded from",
            "ment of the arms is measured with proximity sensors and is calibrated to measure the torque. This system allows for accurate torque measurements down to 0.11 N m.\nCalibration was performed by immersing the telemeter installed on the bearing cage in an oil bath. A hot-plate was used to increase the temperature of the oil bath gradually, while a thermocouple was used to monitor and record the temperature. A radio-frequency spectrum analyser with a\nloop antenna was used to pick up the telemeter output. Figure 8 illustrates a calibration curve for the telemeter used in this study. The results indicate that frequency is a linear function of temperature without any hysteretic effects.\nThe monitored parameters include speed, axial load, torque transmitted, housing temperature and cage temperature. The output from the load cell, proximeters and thermocouples are recorded in a computer using a data acquisition card. The speed is recorded using the frequency drive output while the telemeter frequency for the cage temperature is first analysed in a spectrum analyser and then recorded into the computer. The data acquisition software used in this study is Delphi1.\nThe test bearing is pool lubricated using SAE 30 weight oil. A reservoir underneath the bearing is filled until about 75 per cent of the bearing is submerged in oil at rest. During operation the tapered roller bearing pumps the oil upwards to the top of the bearing housing from where it is drained back into the reservoir underneath the bearing through holes in the housing. A constant supply of lubricant to all parts of the bearing is thus maintained.\nTests were conducted at shaft speeds ranging from 400 to 2400 r=min and axial loads from 2225 to 22 250 N with loads resulting in outer ring peak contact stresses of 1.21\u2013 1.72 GPa. Tests were conducted at constant load and speed, with the bearing initially at room temperature. The operating parameters were recorded during the tests at time intervals of 5\u201315 s. The parameters monitored included cage temperature (measured with the telemeter), housing temperature (measured with a thermocouple) and bearing torque as functions of time.\nJ01201 # IMechE 2001 Proc Instn Mech Engrs Vol 215 Part J\nat Universitats-Landesbibliothek on December 16, 2013pij.sagepub.comDownloaded from"
        ]
    },
    {
        "image_filename": "designv11_24_0003286_j.jmatprotec.2005.05.038-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003286_j.jmatprotec.2005.05.038-Figure8-1.png",
        "caption": "Fig. 8. Layout of the experimental rig spindle unit with variable preload (b).",
        "texts": [
            " When the spindle does not rotate, the axial force Pa causes the spindle deflection in the direction of the applied force. When the spindle speeds up to a high rpm, the centrifugal forces and gyroscopic moments acting on the balls cause the relative axial deflection of the springy constrained rings, i.e., it pushes the spindle slightly out of the housing. This effect we term a \u2018negative axial stiffness\u2019 of SU at high rpm. We performed an experimental study of the effect described using a rig intended for testing of high speed SUs (Fig. 8a). The spindle housing was mounted in an aerostatic bearing to reduce an influence of external disturbances. The spindle was driven by an adjustable motor via a belt trans- mission. The bearing preload was adjusted by a variation of air pressure (Fig. 8b). Spindle axial displacements were measured by checking the axial clearance \u2206x between the non-contact sensor (model TRK/2-5, Hettynger Co.) and the face of a measuring mandrel. The sensor signal was input to the amplifier (KWS-73, Hettynger Co.) and then into the spectrum analyzer (model 2031, B&K Co.). The sensitivity of the measuring system was 0.1 m. Experimental measurements were conducted under three different preloads: 65, 120, and 210 N. When accelerating the spindle up to 24,000 rpm, we switched off the belt drive and let the spindle rotate freely"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000808_0045-7825(94)90113-9-Figure13-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000808_0045-7825(94)90113-9-Figure13-1.png",
        "caption": "Fig. 13. Two member truss.",
        "texts": [
            " Whether a pixel in a scan is bone c,r soft tissue is decided based on a threshold for the gray value; those pixels with gray values greater than the threshold are considered to be bone and those below it are discarded. Since the threshold is more or less arbitrary (within a certain range), it can introduce uncertainty in the shape of the bone. It may be considered necessary in such cases, to compute the variability of the response due to the variability in the geometry of the structure. To illustrate this, we use a simple two-member truss, similar to the truss in [ 13] as shown in Fig. 13. The x coordinate of node 1 is a normal random variable with mean 20 and standard deviation I. It is desired to compute the mean and standard deviation of the x displacement of node l using a second order approximation. A second order Taylor series approximation of the nodal displacements about the mean value of xl is given by: u = u (\u00b0) + u(1)(xl -- ~l) + \u00bduC2)(xl -- ~l) 2, (15) where u c\u00b0), u ~), and u ~2) are obtained using a second order perturbation as described in [ 14]' uC\u00b0)fK-IF, (16) u \u00a2I) = -K-l(Kfl)u(\u00b0)), (17) u(2)= -K -l (2Kfl)u (1) + K(2)uf\u00b0)), (18) where K E R 2\u00d72 is the global stiffness matrix evaluated at the mean value of x~; K (I) and K c2) are the first two derivatives of K with respect to x~, u C\u00b0) E R 2\u00d7~ is the vector of nodal displacements at the mean value of xl and u (1) and u (2) are the first two derivatives of the nodal displacement vector with respect to xl. The mean and covariance of u can be obtained as follows: I-.-(2)n-2 (19) \u00a3 [ u ] = ~ = u ( \u00b0 ) + 2 . \" x~, Cov[ u] -- o\u00a2[ (u - a) (u - a)T] _ (U(1)) (U(IJ)To.2 ! _ I (U(2)) (U(2))To.4 (20) where o'z, is the standard deviation of xl. The global stiffness matrix for the problem in Fig. 13 is given by: where A is the area of cross-section of the member, E is the Young's modulus and LI and L2 are the lengths of the two members. The lengths are given by the formulae: L! = ~/(x2 -- Xl) 2 \"+- (Y2 - Yi) ~, L2 = ~/(x3 - Xl) '2 + (Y3 - Yl) 2 (22) 206 $. Chinchalkar/CompuL Methods Appl, Mech. Engrg, 118 (1994) 197-207 and ct =cos0t , st = sin0t, c2=cos02, s2 = sin02, (23) where O2=tan-1(Y~-Y-~), (24) The calculation of g (t) and K (2) requires tedious algebraic manipulations if their values are required in closed form"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003933_cdc.2006.376702-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003933_cdc.2006.376702-Figure1-1.png",
        "caption": "Fig. 1. Eye-in-hand visual feedback system.",
        "texts": [
            " We use the 4\u00d74 matrix gab = [ e\u03be\u0302\u03b8ab pab 0 1 ] (1) as the homogeneous representation of gab = (pab, e \u03be\u0302\u03b8ab) \u2208 SE(3) describing the configuration of a frame \u03a3b relative to a frame \u03a3a. The adjoint transformation associated with gab is denoted by Ad(gab) [14]. In this section, the brief summary of our prior work in [5] is given. An energy function and a stabilizing control law, which play an important role for a predictive visual feedback control, are derived. The visual feedback system considered in this paper has the camera mounted on the robot\u2019s end-effector as depicted in Fig. 1, where the coordinate frames \u03a3w, \u03a3c and \u03a3o represent the world frame, the camera (end-effector) frame, and the object frame, respectively. Then, the relative rigid body motion from \u03a3c to \u03a3o can be represented by gco. Similarly, gwc and gwo denote the rigid body motions from the world frame \u03a3w to the camera frame \u03a3c and from the world frame \u03a3w to the object frame \u03a3o, respectively, as shown in Fig. 1. The objective of visual feedback control is to bring the actual relative rigid body motion gco to a given reference gd. The reference gd for the relative rigid body motion gco is assumed to be constant throughout this paper, because the camera can track the moving target object in this case. The relative rigid body motion from \u03a3c to \u03a3o can be led by using the composition rule for rigid body transformations ([14], Chap. 2, pp. 37, eq. (2.24)) as follows: gco = g\u22121 wc gwo. (2) The relative rigid body motion involves the velocity of each rigid body"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002300_vib-48318-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002300_vib-48318-Figure2-1.png",
        "caption": "Figure 2. The Space Station Remote Manipulator System (SSRMS) \u2013 Canadarm2",
        "texts": [
            ", to check if we are finding the real solution not just something which satisfies the constraints. Currently, the only reliable, known method for this is to use accurate integration methods with appropriately small time steps. Another approach that has been believed to improve the accuracy is to apply so-called energy rate constraints. But, as was shown in [2], this could actually be quite misleading. As an example, we discuss the simulation of the seven jointed Space Station Remote Manipulator System (SSRMS) (Figure 2) when both of its ends (end effectors) are attached to interfaces on the International Space Station, and it forms a closed kinematic loop. The SSRMS was installed onto the space station in April 2001 and has since been used many times to assist in the assembly and operation of the space station. More detailed information on this robotic arm is available in [8], [12]. The scenario investigated here, where the closed-loop arm is subjected to loads similar to the ones observed during space shuttle docking maneuvers or space station attitude control"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001574_elan.200302717-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001574_elan.200302717-Figure1-1.png",
        "caption": "Fig. 1. Screen-printed pattern. The symbols, W and C, represent working and counter electrodes, respectively.",
        "texts": [
            " The amperometric technology was employed to detect the ethanol concentration variation. Moreover, the sensing behavior was also discussed in both the aspects of solid state and aqueous electrochemistry. Rectangular alumina strips (Al2O3) with a dimension of 10 mm 20 mm 0.635 mm were prepared for the substrate with the following cleaning process: in acetone to remove the organics and in deionized water (DI water) with an ultrasonic cleaner for 3 minutes. A two-electrodes pattern was designed with auto-CAD software as shown in Figure 1.Awire of Ag/AgCl in saturated potassium chloride solution was prepared as reference electrode. The nickel conductive paste (Electro-Science Laboratories Inc., type 2554) was screen-printed on the Al2O3 substrate as both Electroanalysis 2003, 15, No. 20 \u00b9 2003 WILEY-VCH Verlag GmbH& Co. KGaA, Weinheim DOI: 10.1002/elan.200302717 working and counter electrodes with alignment technology. This as-printed substrate was fired in the atmosphere of air with a BTUsystem and a Bruce 7354M control unit at 950 C for 20 min and then at 650 C for 15 min"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000602_mssp.1997.0092-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000602_mssp.1997.0092-Figure2-1.png",
        "caption": "Figure 2. A dual sensor system measuring rigid vibrations.",
        "texts": [
            " Whirling motion of shafts causes the centre of gravity of a shaft cross-section to move in an elliptical orbit (or a combination of elliptical orbits at different frequencies) around the centre of rotation. Whirl can also be described in terms of travelling waves progressing in a co-rotating direction (forward) or counter-rotating (backward). Backward whirl is usually encountered when the bearings and the support structure are anisotropic. This was demonstrated analytically by several researchers [5, 6] for a simple Jeffcott rotor model (Fig. 2). This analysis is given in Appendix A for reference and to assist in the derivation of the main results. It can be shown that backward whirl is excited for such a system by ordinary, forward-rotating unbalance (see Appendix A) [6]. Hence, separation of the whirling response into forward and backward components provides valuable information about the asymmetry of the bearing stiffness in the x- and y-directions. Under steady-state conditions when the speed of rotation, V, is constant, and when the only excitation is due to unbalance, the rotor will whirl at a single frequency and the response measured by s1(t) and s2(t) will have the shape of an ellipse",
            " The lateral motion of the shaft and the axial motion of the disc can be described by means of equation (4), where only a range of nodal diameter (and hence a range of wavelengths) is considered to contribute. This range is n= nmin \u00b7 \u00b7 \u00b7 nmax. su (t)= s nmax n= nmin pn (t) einu + p\u2212n (t) e\u2212inu (5) When only a shaft is considered, the effective range (as shown in Appendix B) is nmax = nmin =1 where for a rigid disc, the axial motion described by n=0 needs to be considered as well. We can write explicitly the expression for a signal measured on a shaft, as shown in Fig. 2 or on a disc in the z-direction, as shown in Fig. 4. su (t)= p1(t) eiu + p\u22121(t) e\u2212iu +C (5a) A rigid disc attached to a flexible shaft is depicted in Fig. 4. In this figure, the intersection of the disc with a plane parallel to the x\u2013y plane is seen to create a single nodal line. In what follows, two methods allowing us to extract the forward and backward whirl with amplitudes are outlined. 3.1.1. Method I: using a combined signal to separate forward and backward whirl for shafts Combining the response measured from s1(t) and s2(t) (see Fig. 2 and 7), to create a complex signal, s\u0303(t)= s1(t)+ is2(t) (6) we obtain, for a single frequency v: s\u0303(t)=Af eivt +Ab e\u2212ivt +C (7) where Af , Ab are the forward and backward vibration amplitudes respectively and C equals (x0 + iy0) and is constant. It is shown in Appendix B that the complex signal created in equation (7) can be substituted into equation (1) to obtain a double-sided spectrogram for which positive frequencies represent the forward whirl and negative frequencies represent backward whirl",
            " 8, a vector of measurements at time t, [s1(t) s2(t) \u00b7 \u00b7 \u00b7 sm (t)], is constructed from all m sensors. The decomposition of the different wavelengths necessitates the extraction of the coefficients in equation (5). Since the sensors are assumed to be spaced equally at an angle Du, the shortest wavelength that can be extracted, according to the Nyquist sampling criterion [10, 11], (expressed in terms of the equivalent number of nodal diameters) is: nnyq = p Du (12) For example, in the system depicted in Fig. 2, the two sensors spaced at 90\u00b0 can detect up to nnyq =180\u00b0/90\u00b0=2. Given the m discretely distributed sensors, a system of linear equations can be set up: su (t)= s nmax n=0 pn (t) einu + p\u2212n (t) e\u2212inu (13) for every u= kDu, k=1 . . . m and nmax =g G G F f m+1 2 m 2 m odd m even The solution for equation (13) consists of m coefficients pn (t) which are generally complex. When the number of wavelengths present in the response nmax is larger than nnyq (practically nmax is restricted by the number of sensors), spatial aliasing will occur and the estimate of the coefficients will be erroneous. This apparent difficulty can be resolved by using band-limiting constraints (wavelength-limited, when applicable) or by using a sufficient number of sensors. In any case the terms from the spatial aliasing can be identified since they appear at the \u2018wrong\u2019 frequencies so that physical understanding of the expected behaviour can be used to detect them. Wavelength-limited interpolation can be demonstrated for the shaft depicted in Fig. 2. As stated before, the two sensors spaced at 90\u00b0 can theoretically detect up to nnyq =180\u00b0/90\u00b0=2, but in this case we have only n=+1 and \u22121. Thus, we can force C2 =C\u22122 =0 which leads to the result described in equation (8) and in full in Appendix D. Therefore, we need use only two sensors (instead of four) while no information is lost. A similar procedure can be taken when the contribution of short wavelengths is very small. Then short wavelengths are neglected without greatly affecting the results",
            " It is important to note that this transformation is not possible unless the separation into a different number of nodal diameters has been performed. This is due to the fact that different wavelengths travel at different speeds and have different phase-shifts due to the rotation of the disc. In this section, some simulated and experimental examples are shown. Various aspects of the proposed method are demonstrated. 4.1.1. Separation of forward and backward components for a rotating shaft: Assume that two signals s1(t) and s2(t) are measured from the system in Fig. 2, and that the two measurements show the following time behaviour: s1(t)=Af cos (8f(t))+Ab cos (8b (t)) s2(t)=Af sin (8f(t))\u2212Ab sin (8b (t)) (21) Substituting equation (21) in (6), one obtains the forward\u2013backward representation: s\u0303(t)=Af e+i8f(t) +Ab e\u2212i8b(t) (22) The phase arguments, 8f(t) and 8b (t) are defined via their time derivatives [instantaneous frequencies computed according to equation (2)], as follows: 2pff(t)=vf(t)= d8f(t) dt =2p02+110 t tmax1 2pfb (t)=vb (t)= d8b (t) dt =2p0190\u22121740 t tmax1 2 1 (23) Processing the signals provides the results shown in Fig",
            " Intersection in the positive frequency region means the excitation of a co-rotating mode. In the negative frequency region, the intersection describes a backward whirl resonance. 4.2.1.1. Measured response and the computed Campbell diagram. In this section, experimentally obtained results measured on a rotating shaft are presented. The experimental rig consists of a DC motor coupled to a shaft supported in bearings. Also, a rigid disc is fixed to free end of the shaft (see Fig. 15). Two proximity probes (90\u00b0 apart) are arranged as shown in Fig. 2 and the only excitation forces are due to the inherent unbalance in the system. The conventional and the two-sided directional Campbell diagrams are shown below in Figs 13 and 14, respectively. In this example, an experimental rig was used to demonstrate the value of the proposed method. Two plots are shown, the first one is an conventional Campbell diagram where all the information is overlaid on the positive frequency range. The second plot shows separated positive-frequency (forward) and negative-frequency (backward) vibration components and the superior resolution of the directional Campbell diagram is clearly demonstrated",
            " S 1995 ASME, Winter Annual Meeting, October, Boston. Multi-dimensional directional spectrograms and Campbell (Zmod) diagrams for rotating machinery. 10. V. C. C 1988 Signal Processing\u2014The Modern Approach. McGraw-Hill. 11. P. A. J 1984 Deconvolution. San Diego: Academic Press. 12. I. B, P. S, D. A. R and D. J. E 1994 International Conference on Vibration Measurement by Laser Techniques, October, Ancona, Italy. A laser-based measurement system for measuring the vibration on rotating discs. The rigid rotor in Fig. 2 behaves according to the equation of motion: ITb + IpVa\u0307+Kbb=Mb (t) ITa\u0308\u2212 IpVb +Kaa=Ma (t) (A1) where: Kb = 1 2KxL2, Ka = 1 2KyL2. A conical unbalance, uu manifests itself as two moments: Ma (t)= uuV 2(It \u2212 Ip ) sin Vt Mb (t)= uuV 2(It \u2212 Ip ) cos Vt (A2) Therefore, neglecting the transient solution, we obtain: a(t)=A(V) sin Vt= uuV 2((Ip \u2212 It )Kb +V2(I2 t \u2212 I2 p )) D sin Vt b(t)=B(V) cos Vt= uuV 2((Ip \u2212 It )Ka +V2(I2 t \u2212 I2 p )) D cos Vt (A3) where: D=(I2 t \u2212 I2 p )V4 + (Ka +Kb )ItV 2 +KaKb. Backward whirl occurs when A(V)B(V)Q 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001349_0954407011528095-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001349_0954407011528095-Figure1-1.png",
        "caption": "Fig. 1 Typical band system surface is lubricated with the oil, this phase is called partial lubrication. The viscous torque and asperity",
        "texts": [
            " derived to describe the engagement process, including the self-energizing mechanism, asperity torque transfer,Knowledge obtained through a mathematical analysis enables potential improvements in band design and shift viscous torque transfer, squeeze lm, porous diVusion and heat transfer. Finally, the summary is given incalibration process. Little attention has been given in the past to model Section 4. the band engagement process. This is partly due to the high level of diYculty and partly due to the availability 2 ENGAGEMENT MECHANISMof high quality experimental data. Friction materials for band brakes are often tested in combination with various transmission oils to characterize engagement behaviour Figure 1 illustrates a typical band brake system. It con- sists of a band, a drum, an anchor and a servo assembly.[5\u201313]. However, an interpretation of experimental data can be diYcult without a basic understanding of the The inner surface of the band strap is lined with a porous friction material. Figure 2 shows a picture of a band andengagement process. Most design analyses have been limited to a static estimation of torque capacity based drum assembly. The drum is usually connected to a plan- etary gear set directly"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002263_pime_proc_1986_200_137_02-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002263_pime_proc_1986_200_137_02-Figure7-1.png",
        "caption": "Fig. 7 Variation of pressure difference uF with d$* and uE'L2/2n2Rb",
        "texts": [
            " By definition, which, by substitution of equation (21) and rearrangement, leads to Let the magnitude of the pressure variation, From equation (21), Pmax - P m i n 9 be F. This may be arranged to give whence This may be substituted in equation (22b). Rearrangement and integration leads to ' (4 (eaF - 1)} dy (25) = i I++ &z This equation has been evaluated numerically to give the relationship between a( =do/$*), aL2E'f2n2Rb and a(P,,, - a,) for various values of F = P,,, - Pmin, and the results are presented in Figs 7 and 8. 5 DISCUSSION 5.1 Magnitude of the pressure ripple Figure 7 gives the relationship between aL.?E/2n2Rb and either doll;* (Fig. 7b) or 1 -do/$* (Fig. 7a) for various values of the pressure ripple F( = P,,, - Pmin) in the range aF = 0.01 to > 3 . For a given surface, d o , L constant, and a given load, b constant, the pressure ripple increases as the surfaces move more closely together. The pressure ripples in an EHL contact thus behave in a manner similar to that already described under classical conditions (Section 2). The effects of asperity shape may be considered by varying the wavelength L, keeping the amplitude do constant. For a given separation of the surfaces, do/h* constant and a given load, a decrease in L results in a decrease in the magnitude of the pressure ripple-again, behaviour similar to that of classical conditions, as shown in Fig",
            "2, the description of slope is that appropriate to a parabolic rather than Hertzian pressure distribution; the slope consistent with a Hertzian distribution is a factor of two smaller in the immediate vicinity of the pressure maximum, but is not used because it cannot be expressed explicitly over much of the conjunction (16). The discrepancy in slope results in very little error in film thickness under piezoviscous conditions (Section 3.1), but it is expected to have a rather larger effect upon the magnitude of the pressure ripple because it will directly affect the quantity of flow. At worst, the lines for constant aF in Fig. 7 might be moved to values of aE'L2/2n2Rb lower by a factor of two, but this will be so only for aF < 3. Values of aF greater than this value all fall upon the same line, which thus represents an upper limit of ripple pressure and will be independent of the preceding considerations. The probable reasons for a limiting form of behaviour may be found in Fig. 8, which shows the way in which a(P,,, - fro) varies with aF[=a(Pmax - Pmin)] for various values of a(=do/fi*). As aF increases, the minimum value of pressure Pmin+ the average value 3, for all values of do/h*",
            " Proc Instn Mech Engrs Vol 200 No C5 lated to piezoviscous conditions then the limit becomes Aq e-d 'mim - e-UPmar This can be reached only if Pmin becomes zero or slightly sub-ambient, so a more convenient limit is Pmin = 0 An estimate of the conditions which lie outside the limit is most easily achieved by examining the inequality P O a( jo - Pmin) may be rearranged to give aF{ 1 - a(Pm,, - fio)/aF} and evaluated from Fig. 8, while aa0 may be found by substitution of . the Hertzian relationship po/b = E/4R in the group aL2E/2n2Rb. This leads to ap, = ~ ~ t L E / n R ) ~ / ( c r L ~ E / 2 n ~ R b ) and the inequality becomes The equation is evaluated in Fig. 9 of Appendix 2 and lines of equal aLE/nR are superimposed on Fig. 7. Conditions to the right of a given line are such that Pmin < 0 for that value of aEL/zR. It will be shown in the following section that typical values of aELInR are in the region 1-10; thus negative pressures occupy only a small region of the chart where values of aE'L?/2n2Rb are also in the region 1-10. Figure 9 shows that values of up, are low under such conditions so it is probable that this region of the chart represents classical conditions on the macro-scale which are not covered by this analysis",
            " Not all surfaces, however, have such a clearly defined periodicity and in many cases the autocorrelation function may be close to exponential. In this case Archard (20) @ IMechE 1986 at Harvard Libraries on July 11, 2015pic.sagepub.comDownloaded from ELASTOHYDRODYNAMIC PRESSURE RIPPLING IN CYLINDERS 345 has suggested that the main-scale wavelength of the surface is -lob* where /3*, the correlation distance, is the exponent of the exponential correlation function. With the value of L shown in Fig. 1, the group uE\u2018L/nR (Fig. 7) has a value - 5 for 3 inch steel discs run with a typical hydrocarbon lubricant. This value, together with the discussion in the previous section, indicates that the analysis is applicable provided u E C / 2n2Rb does not exceed -4. 5.3.2 Amplitude Equation (14) describes the effect of roughness on film thickness and it may be seen that roughness is expressed in terms of the standard deviation of the surfaces only. In order to have a similar effect, the standard deviation of the sine wave must be the same as that of the surface, uiz"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000635_s0039-9140(99)00134-4-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000635_s0039-9140(99)00134-4-Figure4-1.png",
        "caption": "Fig. 4. The trace depicts a stop flow assay. The buffer was stopped after 14 min for 11 min and restarted. Circulation medium: buffer containing 2.8 mg ml\u22121 TBO. Injection solution: 50 mM lactate and 30 mM NAD+.",
        "texts": [
            " The higher response of TBO with LDH compared to MB could be attributed to the efficient oxidation of NADH (produced locally on the CPG due to the LDH reaction) by TBO in close proximity of the RVC surface. In contrast, in the case of direct oxidation of NADH the proximity to the electrode is very poor. However, under a similar situation the oxidation by MB is very poor due to inefficient electron transfer on the RVC surface. 3.4. Stopped flow assay In order to investigate signal amplification in the presence of LDH a stopped flow assay was performed. This concept had been exploited earlier for enzyme assays [31]. Fig. 4 illustrates the profile of the stopped flow assay in the presence of LDH in the FIA mode. On stopping the flow there was a sharp rise in the current and the slope of this rise was approximately 0.024 mA min\u22121. This value denotes a zero or pseudo-zero order rate of conversion of L-lactate to pyruvate or NAD+ to NADH by LDH. As the flow was stopped at the peak, the entire substrate injected into the flow stream had reached the cell and reacted continuously with LDH leading to a signal amplification"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000847_70.833184-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000847_70.833184-Figure5-1.png",
        "caption": "Fig. 5. The multi-object-error-based worst-case and best-case configurations for a stationary three-link planar revolute manipulator with anticipation of a failure in any joint. The manipulator on the left has the largest cost-function value using the comprehensive measure for end-effector position (0.61, 1.92), and the manipulator on the right has the smallest. The curve to the far right shows the cost-function value parameterized by q .",
        "texts": [
            " The regions of interest ( , , and ) are line segments running the length of each link. The TABLE I D\u2013H PARAMETERS FOR THE RRC K-1207i interest density is a constant of , where the unit of length is , and the choice of point error is Euclidean distance with given by (3). For this example, a possible free-swinging failure in any of the three joints is anticipated. An appropriate cost function is . For this cost function, with an end point (0.61, 1.92), worst-case and best-case configurations are shown in Fig. 5, together with a curve showing the value of the cost function parameterized by . The gradient-projection technique [25], [26] was used to find both the worst-case (using the negative of the gradient) and best-case configurations. Fig. 5 illustrates the tradeoff that must be made when optimizing a cost function that includes the possibility of multiple joint failures. The best-case configuration would actually give greater motion after a joint-three failure than the worst-case configuration. However, this is more than compensated by the fact that the best-case configuration gives much less motion after a joint-one failure. From the worst-case to the best-case configuration, the value of is improved by more than a factor of five"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002920_0301-679x(81)90098-0-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002920_0301-679x(81)90098-0-Figure2-1.png",
        "caption": "Fig 2 Elastic conformity envisaged with real roughness would be preferential to certain asperity wavelengths. For convenience the figure shows only one compliant rolling element, whereas in practice i f materials o f similar modulus were employed the deformation would be shared",
        "texts": [
            " Elastic conformity of asperities Surfaces produced by modern finishing techniques have asperities which are low enough in magnitude and extensive enough in the spatial plane to elastically conform with a contacting surface. As Greenwood and Tripp I showed, we can create elastic conformity within the Hertz contact in a similar way to the Hertz contact itself. The effect postulated is depicted in Fig 1. In reality, we would expect the effect of conformity to be dependent upon a combination of the height and spatial width parameters of each asperity. This is depicted in Fig 2 which indicates conformity over asperities of wavelengths up to some limit, but non-conformity to those wavelengths we might describe as the Hertzian contact roughness. We require to know what surface feature wavelengths or spatial sizes, r, can elastically deform under any normal load. To achieve this we assume a model of an elliptical Hertz contact zone covered by a series of parallel ridges of circular cross-section (Fig 1). For an infinite roller on a flat plate, the contact width co ~3 is: a r e a = \" / r o b Iffg 1 Hertzian contact model used in developing elast& conformity parameter co = 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001370_amc.1996.509431-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001370_amc.1996.509431-Figure1-1.png",
        "caption": "Figure 1: Example of system wit,h time delay.",
        "texts": [
            "ystem in the industrial world have time delay greatly. For example, like Figure 1, since on the mechanism of system the sensor to detect control output is located apart from the point where we should put the sensor to know the accurate information, time delay appears between the accurate output to the sensor output. Now we often use Smith predictor method to control the system with time delay[l]. In Smith\u2019s method time delay element is taken out of a closed loop equivalmtly by using a plant model. Smith predictor control is very simple and useful. However, in Smith\u2019s method, when a disturbance adds to input side of plant in the system, we can\u2019t effectively control the disturbance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003135_1.2389233-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003135_1.2389233-Figure1-1.png",
        "caption": "Fig. 1 Pushing V-belt CVT arrangement",
        "texts": [],
        "surrounding_texts": [
            "1 i s s d s m t t i t o I o r a u d t\nm b c\nJ 2 A\n8\nDownloaded Fr\nNilabh Srivastava e-mail: snilabh@clemson.edu\nImtiaz Haque e-mail: imtiaz.haque@ces.clemson.edu\n106 EIB, Flour Daniel Building, Department of Mechanical Engineering,\nClemson University, Clemson, SC 29634\nTransient Dynamics of the Metal V-Belt CVT: Effects of Pulley Flexibility and Friction Characteristic A continuously variable transmission (CVT) offers a continuum of gear ratios between desired limits. The present research focuses on developing a continuous one-dimensional model of the metal V-belt CVT in order to understand the influence of pulley flexibility and friction characteristics on its dynamic performance. A metal V-belt CVT falls under the category of friction-limited drives as its performance and torque capacity rely significantly on the friction characteristic of the contact patch between the belt element and the pulley. Since the friction characteristic of the contact patch may vary in accordance with the loading and design configurations, it is important to study the influence of the friction characteristic on the performance of a CVT. Friction between the belt and the pulley sheaves is modeled using different mathematical models which account for varying loading scenarios. Simple trigonometric functions are introduced to capture the effects of pulley deformation on the thrust ratio and slip behavior of the CVT. Moreover, since a number of models mentioned in the literature neglect the inertial coupling between the belt and the pulley, a considerable amount of effort in this paper is dedicated towards modeling the inertial coupling between the belt and the pulley and studying its influence on the dynamic performance of a CVT. The results discuss the influence of friction characteristics and pulley flexibility on the dynamic performance, the axial force requirements, and the torque transmitting capacity of a metal V-belt CVT drive. DOI: 10.1115/1.2389233\nKeywords: CVT, metal V-belt, friction characteristic, pulley flexibility, inertial effects, belt-pulley inertial coupling\nIntroduction\nOver the last few decades, environmental concerns have made t imperative for the government of most of the nations to impose tringent regulations on the fuel consumption and exhaust emisions of the vehicles CAFE standards in the U.S., ACEA stanards in Europe, etc. . Lately, continuously variable transmissions CVT have aroused a great deal of interest in the automotive ector due to the potential of lower emissions and better perforance. CVT is an emerging automotive transmission technology hat offers a continuum of gear ratios between high and low exremes with fewer moving parts. CVTs are aggressively competng with automatic transmissions, and today several car manufacurers, such as Honda, Toyota, Ford, Nissan, etc., are already keen n exploiting the various advantages of a CVT in a production car. n spite of the several advantages proposed by a CVT, the targets f higher fuel economy and better performance have not been ealized significantly in a real production vehicle. In order to chieve lower emissions and better performance, it is necessary to nderstand the dynamic interactions occurring in a CVT system in etail, so that efficient controllers could be designed to overcome he existing losses and enhance vehicle fuel economy.\nThis paper outlines a detailed one-dimensional continuous odel of a metal pushing V-belt CVT considering the effects of\nelt-pulley inertial interactions, pulley flexibility, and friction haracteristic of the contact zone. The model gives a profound\nContributed by the Design Engineering Division of ASME for publication in the OURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 17, 006; final manuscript received September 28, 2006. Review conducted by Ahmed\n. Shabana.\n6 / Vol. 2, JANUARY 2007 Copyright \u00a9 20\nom: http://computationalnonlinear.asmedigitalcollection.asme.org/ on 01/\ninsight into the dynamics of a CVT system, which could be exploited further to design efficient controllers and reduce associated losses.\nThe basic configuration of a CVT comprises the two variable diameter pulleys kept at a fixed distance apart and connected by a power-transmitting device like a belt or chain. One of the sheaves on each pulley is movable. The belt can undergo both radial and tangential motions, depending on the loading conditions and the axial forces applied to the pulleys. The pulley on the engine side is called the driver pulley and the one on the final drive side is called the driven pulley. Figures 1 and 2 1 depict the belt structure and the basic configuration of a metal V-belt CVT. Torque is transmitted from the driver to the driven pulley by the pushing action of the belt elements. Since there is friction between the bands and the elements, the bands, like flat belts, also aid in torque transmission. Hence, there is a combined push-pull action in the belt that enables torque transmission.\nA sundry of research has been conducted on different aspects of a CVT, e.g., performance, slip behavior, efficiency, configuration design, loss mechanisms, vibrations, operating regime, etc. Most existing models of belt CVTs, with a few exceptions, are steadystate models that are based on the principles of quasistatic equilibrium. Gerbert 2 performed some detailed analysis on the slip behavior of a rubber belt CVT. Slip was classified on the basis of creep, compliance, shear deflection, and flexural rigidity of the belt. Micklem et al. 1 incorporated the elastohydrodynamic lubrication theory to model friction between the metal belt and the pulley and also studied the transmission losses due to the wedging action of the belt. Sun 3 did a performance-based analysis of a metal V-belt drive and obtained a set of equations to describe the belt behavior based on quasistatic equilibrium. Friction between\n07 by ASME Transactions of the ASME\n28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use",
            "t a t u m e d\np r fi t d l f s e e V s a p t u t b f I o m p S c b m p a\nJ\nDownloaded Fr\nhe individual bands in a band pack was also taken into considertion in the model development. Kobayashi et al. 4 investigated he torque transmitting capacity of a metal pushing V-belt CVT nder no driven-load condition. Their research focused on the icroslip characteristic of the V-belt due to the redistribution of lemental gaps in the belt and reported a simulation procedure for etermining slip-limit torque based on steady-state assumptions.\nCarbone et al. 5 developed a theoretical model of a metal ushing V-belt to understand the CVT transient dynamics during apid speed ratio variations. Nondimensional equations were dened to encompass different loading scenarios; however, the inerial coupling between the belt and the pulley was not modeled in etail. Carbone et al. 6 used two friction models, namely a Couomb friction model and a viscoplastic friction model, to model riction between the belt and pulley and to accurately predict the hifting dynamics during slow and fast maneuvers. Later, Carbone t al. 7 extended their previous work 5 to investigate the influnce of pulley deformation on the shifting mechanism of a metal -belt CVT. The authors suggested that in steady state, the presure and tension distributions were unaffected by pulley bending nd depended only on the thrust ratio. However, pulley bending layed a significant role in determining the transient response of he variator. Sorge 8 analyzed the mechanics of metal V-belts nder the influence of pulley bending. The flexural rigidity has remendous influence on the seating and unseating behavior of the elt. Rapid variation of curvature may change the direction of rictional forces, thereby, affecting the torque capacity of the CVT. de and Tanaka 9 also experimentally investigated the influence f pulley bending on the contact force distribution between a etal V-belt and pulley sheave. They observed that asymmetrical ulley deformation led to nonuniform contact force distribution. attler 10 analyzed the mechanics of a metal chain and V-belt onsidering both longitudinal and transverse stiffness of chain/ elt, misalignment and deformation of pulley. The pulley deforation is modeled using a standard finite-element analysis. The ulley is assumed to deform in two ways, pure axial deformation nd a skew deformation. The model was also used to study effi-\nournal of Computational and Nonlinear Dynamics\nom: http://computationalnonlinear.asmedigitalcollection.asme.org/ on 01/\nciency aspects of belt and chain CVTs. Bullinger and Pfeiffer 11 developed an elastic model of a metal V-belt CVT to determine the power transmission characteristic at steady state. Pulley, shaft, and belt deformations were taken into account. The frictional constraints were modeled using the theory of unilateral constraints. The belt dynamics was specified by separate longitudinal and transverse approaches. The transversal dynamics was modeled using Ritz-approach based on B-splines. The longitudinal dynamics was described by using Lagrange coordinates.\nSrivastava et al. 12,13 developed a transient dynamic model of a metal pushing V-belt block-type CVT considering the inertial interactions between the belt and the pulley in significant detail. The authors used a continuous Coulomb friction approximation to model contact between the belt element and the pulley. The interaction between the band pack and the belt element which has been neglected in a lot of previous models was also taken into account during the course of model development. The authors observed that not only the configuration and loading conditions, but also the inertial forces, influence the dynamic performance of a CVT, especially its slip behavior and torque capacity. The authors suggested that CVT, being a highly nonlinear system, needs a specific set of operating conditions, which can be found using an efficient search mechanism, in order to successfully meet the load requirements. They used a genetic algorithm GA to capture this feasible set and also highlighted its efficiency in capturing this set by comparing it to the results generated by design of experiments DOE . The optimization objective function was suitably chosen to maximize torque transmission capacity of the CVT. Srivastava et al. 14 also developed a metal pushing V-belt CVT model in steady-state to study its microslip behavior and to investigate its steady-state operating regime. They discussed the influence of torques and axial forces on belt slip. Slip is based on redistribution of gap among belt elements and formation of inactive arcs, as proposed by Kobayashi et al. 4 . The model is able to predict the maximum transmittable torque before the belt undergoes gross slip. The authors observed that the CVT operates in definite regime of axial forces and torques. They predicted the minimum axial force necessary to initiate torque transmission and also the maximum axial force that the CVT can sustain based on slip behavior and not on stress/wear/fatigue effects .\nAlthough the friction characteristic of the contacting surface inevitably plays a crucial role in CVT\u2019s performance, literature pertaining to the influence of friction characteristic on CVT dynamics is scarce 2,6,15 . Almost all the models, except a few, mentioned in the literature use Coulomb friction theory to model friction between the contacting surfaces of a CVT. However, depending on different operating or loading conditions and design configurations, the friction characteristic of the contacting surface may vary. For instance, in case of a fully lubricated CVT, the friction characteristic of the contacting surface may bear a resemblance to Stribeck curve 16 rather than to a continuous Coulomb characteristic. Moreover, very high forces in the contact zone may further lead to the conditions of elasto-plastic-hydrodynamic lubrication, which may yield a different friction characteristic. It has also been briefly reported 15 in the literature that certain friction characteristics induce self-excited vibrations in the CVT system. However, it is not clear whether such phenomenon is an artifact of the friction model or the real behavior of the system. It is, thus, necessary to study the influence of different friction characteristics on the performance of a CVT. It is also important to note that although an exact knowledge of the friction characteristic in a CVT system can only be obtained by conducting experiments on a real production CVT, these mathematical models give profound insight into the probable behavior that a CVT system exhibits under different operating conditions, which may be further exploited to design more efficient controllers.\nThe research reported in this paper focuses on the development of a detailed transient dynamic model of a metal pushing V-belt CVT. The goal is to understand the transient behavior of a belt\nJANUARY 2007, Vol. 2 / 87\n28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use",
            "e d t t t i c d\n2\ne i t i m d\np h e t t m\n8\nDownloaded Fr\nlement as it travels from the inlet to the exit on both driver and riven pulleys and also to evaluate the system performance under he influence of pulley flexibility and varying friction characterisics of the belt-pulley contact zone. The inertial coupling due to he radial and tangential motions of the belt over the pulley wraps s also taken into account. The modeling analysis and the results orresponding to the metal pushing V-belt model are discussed in etail in the subsequent sections.\nModeling of a Metal Pushing V-belt CVT The belt-CVT model presented in this paper is subjected to the xternal conditions of a constant driver angular speed, a constant nput torque applied to the driver pulley, and a constant load orque on the driven pulley. The model captures various dynamic nteractions between the belt and the pulleys as a belt element\noves from the entrance to the exit of the pulley. The model evelopment and analysis includes the following assumptions:\n\u2022 Elements and bands are treated as a continuous belt; \u2022 The center of mass of the element and that of the band pack\ncoincide; \u2022 Belt length is constant; \u2022 The belt is considered to be an inextensible strip with zero\nradial thickness and infinite axial stiffness; \u2022 Impending slip condition exists between the band pack and\nthe element; \u2022 Bending and torsional stiffness of the belt are neglected; \u2022 Line contact between the belt and the pulley is parallel to\nthe pulley axis.\nIt has been observed 7\u201311,17 that elastic deformations of the ulley sheaves significantly influence the thrust ratio and slip beavior of a belt CVT. However, instead of a detailed finitelement formulation of pulley sheaves, simple trigonometric funcions as outlined in 7,10,17 are used in this model to describe he varying pulley groove angle and the local elastic axial defor-\nations of the pulley sheaves. Figure 3 7 depicts the model for\nFig. 3 Pulley deformation model\nom: http://computationalnonlinear.asmedigitalcollection.asme.org/ on 01/\npulley deformation. The following equations describe the pulley deformation effects as introduced by the model in Fig. 3\n= 0 + 2 sin \u2212 + 2\nR tan = r tan 0 \u2212 tan \u2212 0 1\nIt is to be noted that although the amplitude of the variation in the pulley groove angle is small, it is not constant during shifting transients. Sferra et al. 17 proposed the following correlations for the variation and the center of the pulley wedge expansion, ,\nFig. 5 Free body diagram of driver band pack\nTransactions of the ASME\n28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use"
        ]
    },
    {
        "image_filename": "designv11_24_0000538_1.2834185-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000538_1.2834185-Figure1-1.png",
        "caption": "Fig. 1 Schematic of a singie asperity in contact with a smootli flat sur face in tlie presence of a continuous iiquid fiim when (a) tf) is iarge and {b) <f> is small",
        "texts": [
            " It is used to predict the stiction for disks with various roughness and for lubricants with various viscosities and thickness. 2 Single Asperity Model We first analyze a single asperity contact and then will extend it to multiasperity contacts. For the calculation of growth of the meniscus force with time for a single asperity contact, the asper ity is assumed to be spherical and all the roughness is assumed to lie on one surface. This can be modeled as a sphere contacting a plane, the plane being covered by a layer of lubricant, as shown in Fig. 1. Based on Gao and Bhushan (1995), the de crease in pressure inside the meniscus region created due to the formation of the curved meniscus causes a flow of lubricant into the low pressure area resulting in an increase in the wetted cross sectional area of the meniscus. This increase in the wetted meniscus area causes an increase in the meniscus force. The solution for the time dependent stiction then can be broken down into two parts: (1) determining the increase in the wetted meniscus area with time and (2) determining the increase in meniscus force with an in crease in the wetted meniscus area",
            ", 1975) 2K = d^hldr^ dhldr [1 + {dhldryy'^ r[\\ + {dhldrYV (5) As the disjoining pressure is assumed to be made up of the molecular contribution only, for nonpolar liquids, the expression for the disjoining pressure is n = 6-nh^ where A is the Hamaker constant (6) Now the gradient of the curvature exists only in the curved portion of the film as the film is flat elsewhere and so has zero curvature. Again the gradient of the disjoining pressure also exists only in the curved portion of the film as it is a function of film thickness and the film thickness is assumed to be con stant on the smooth surface. So the gradient of the driving force exists only in the curved portion of the film. For any portion in the curved film (Fig. 1) r = X, if XQ < r < Xo + R\\ dy^_ _ dt \u2014 l-KX - VlKy + n ] ir\\ ax (7) (8) The right-hand side of this equation is evaluated at the point where the curved film intersects the flat film (point A in Fig. 1(a)) . At this point x = Xo + /fi cos a,h = h\u201e and dhldx - 0. Here a is the angle subtended by the curved meniscus at its center as shown in Fig. \\{a) and is given by a = 90 -I- 61 - (\u0302 (9a) If the angle </> is small, as shown in Fig. \\{b), then a = 90 - 6 - 4) (9b) The angle 0 is the contact angle of the liquid and is the angle between the tangents to the surface of the sphere and the menis cus at the point of contact. In the case where the tangent to the sphere is above the tangent to the meniscus (Fig. 1(a)) Eq. 9(a) holds, while for the reverse case (Fig. 1(b)) Eq. 9(b) is valid. Fig. 1(a) shows the general case in which angle </> is not small. As the head asperities come in contact with the disk asperities in the presence of a very thin film, angle </> is small and the meniscus forms as shown in Fig. 1(b). For this case Eq. 9(b) applies and is used in the analysis. The angle </> used in Eq. (9) is given by cos (f) = Xo/R where R is the radius of the asperity and Xo is the distance from the vertical axis to the point of contact of the meniscus. As dh/dx = 0, the gradient of the disjoining pressure vanishes and the curvature gradient remains as the sole driving force behind the flow. Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 02/24/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use An expression of the film thickness h at any point x can be derived by simple geometry to be h = ha + Ri-^R\\- (R, cos a + xo - x)^ (10) ing rhy X and substituting for h from Eq",
            " (16) and (17) numerically using Newton's iteration method (Szidarovsky and Yakowitz, 1978). 2.2 Calculation of Equilibrium Time. The flow of the lubricant into the meniscus ceases when an equilibrium is at tained between the constituents of the driving flow. This hap pens when the disjoining pressure is equal to the Laplacian pressure (Mate, 1992). Thus equilibrium is attained when 11 = 2Ky. Using the expression for K and 11 from Eq. (12) and Eq. (6) and evaluating the expression at the point A in Fig. 1. A (1 + cos e)y Sirhl 2R (18) where {XQ),^ is the value of xo at the equilibrium time. Then, [(xoUV = 2R -6-n-hly(l + cos g) A (ho-D)\\ (19) where a = Ri\\-cos<t>)~^~^ ( l i e ) Z ZK Using the expression for Ru the expression for the curvature, Eq. (llfl) reduces to 2K -2x{\\ + cos 9) + (D + a - ho) cos a -I- Xo(l + cos 6) (D + a - ho}x (12) Using this curvature in the equation for the flow, Eq. (8) , and using the values of x and h mentioned earlier, simplification leads to dV _ 2nhly 1 H- cos g dt 377 D + a \u2014 ho (13) This flow increases the volume of the meniscus",
            " (19) is a function of normal load and the strength of the liquid film. After the time U^ the meniscus force will remain a constant and further growth of stiction will not occur. 2.3 Determination of Meniscus Force. To determine the meniscus force at a given time, we use the fact that the meniscus force is proportional to the projected meniscus area (TTXJ) be tween the liquid and the asperity (Gao and Bhushan, 1995). Again the meniscus force for a sphere in contact with a continu ous film on a flat surface (Fig. 1) at the equilibrium time will be equal to the equilibrium meniscus force given by (Gao et al., 1995) iU)^ = 2iTRy{\\ + cos 9) (20) The meniscus force at any time t less than the equilibrium time will be 2 f,At) = 2T,Ry{\\ + cos 61) Xo (^o)e( (21) Now meniscus force, / \u201e , at a certain time t can be obtained by solving Eqs. (16), (19), and (21) iteratively. These equations are solved numerically using Newton's iteration method. The iteration process is stopped when meniscus force, given by Eq. (21) is equal to the equilibrium value"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000476_s0045-7949(99)00201-1-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000476_s0045-7949(99)00201-1-Figure3-1.png",
        "caption": "Fig. 3. Geometry and material layout of the shallow shell element with positive directions of nodal displacements and rotations.",
        "texts": [
            " The position and the orientation of the local coordinate system (x ', y ', z ') are identi\u00aeed by the vector rb and the angle fb between the x '- and x-axes, respectively. The height of the shell from the reference surface is denoted by hs (see Fig. 2(b)). The distance between the neutral axis of the beam and the shell mid-surface is indicated by the eccentricity parameters z 0ec: The positive directions of displacement and rotation \u00aeeld in both elements are shown in Fig. 2(a). They will be discussed later in this section. The material lay-ups for both the shell and the stiffener components are illustrated in Figs. 3 and 4, respectively. As shown in Fig. 3, the shallow shell element is made of a layered composite laminate. Each layer is assumed to be homogeneous, elastic, and orthotropic with elastic moduli, E1 and E2; shear modulus, G12; and Poisson's ratio, n12. The subscripts ``1'' and ``2'' specify the longitudinal and transverse directions relative to the \u00aebers in the layer. Also, the pos- ition of each ply with respect to the element mid-plane is denoted by the local coordinate z-. As in the case of the shell component, the sti ener is also made of layered composite materials",
            " (10) lead to 0As XKs k 1 zk zk\u00ff1 d0eT sLQs 0esL d z d0As 0l XKb i 1 A i b d0eT bLQb 0ebL dA i b d0x 0 0As XKs k 1 zk zk\u00ff1 d0eT sN t 0ss d z d0As 0l XKb i 1 A i b d0eT bN t 0sb dA i b d0x 0 dWe \u00ff 0As XKs k 1 zk zk\u00ff1 d0eT sL t 0ss d z d0As \u00ff 0l XKb i 1 A i b d0eT bL t 0sb dA i b d0x 0 11 In accordance with Mindlin's theory [17], the incremental displacement components of the shell element, u, v, and w in the x-, y-, and z--directions, are expressed as us x, y, z us0 x, y zysy x, y 12a vs x, y, z vs0 x, y zysx x, y 12b ws x, y, z ws0 x, y 12c The functions u0 and v0 represent the in-plane displacements and w0 the out-of-plane displacements on the mid-surface of the shell element. The bending (normal) rotations about the x- and y-axes are denoted by yx and yy, respectively. The element coordinate system is chosen such that the positive x-axis points in the direction from node 1 to node 2 of the element. As shown in Fig. 3, the element reference plane coincides with the (x\u00b1y ) plane. The components of the incremental displacements and bending rotations at each node of the element, with positive sign conventions, are shown in Fig. 2(a). The variable z- is de\u00aened as z z\u00ff h x, y 13 where h(x, y ) describes the shallow mid-surface of the shell element. For the beam element, the displacements at a point are expressed based on the Timoshenko beam theory, which assumes constant transverse shear deformations across the thickness of the beam"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002193_87-gt-110-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002193_87-gt-110-Figure3-1.png",
        "caption": "Fig. 3 Pick-up location for radial shaft vibrations and speed measurement",
        "texts": [
            " Under running conditions the following values were measured: a) shaft speed and, if required, floating ring speeds b) oil inlet pressure and temperature c) rotor vibrations relative to the housing d) absolute bearing housing vibrations 2 Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use Radial vibration measurements were taken on the compressor end horizontally and vertically, using eddy-current pick-ups (see Fig. 3). After appropriate signal-conditioning (amplification filtering), the signals were recorded on magnetic tape. The vibration levels were plotted in real time vs rotor speed, and the relative shaft motion could be observed as Lissajou curves on an oscilloscope during controlled rotor acceleration runs. Upon completion of the testing a detailed spectral investigation of the recorded signals was conducted by means of a computer-controlled signal analysis system. This system converts sequential time intervals of the vibration signals into the frequency domain via the fast Fourier transform"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001275_03093247v263147-Figure9-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001275_03093247v263147-Figure9-1.png",
        "caption": "Fig. 9. Comparison of load capacities for same area of cross-section",
        "texts": [
            " A uniform sectioned disc spring with D, = 90, D i = 46, h, = 2, and t = 4.5 was replaced by a trapezoidal cross-sectioned disc spring with ti = 3.6 and t , = 5.4, JOURNAL OF STRAIN ANALYSIS VOL 26 N O 3 1991 (( IMechE 1991 at Purdue University Libraries on July 8, 2015sdj.sagepub.comDownloaded from keeping all other parameters and the area of crosssection constant. The load carrying capacity of the trapezoidal spring was about 6000 N greater than that of the uniform sectioned spring, as seen from Fig. 9. This indicates an increase of load carrying capacity of about 30 percent for the similar trapezoidal spring of equal crosssectional area. Disc springs can be combined in highly diverse ways for obtaining parallel stacks consisting of individual disc springs oriented in the same sense, or series stacks consisting of individual disc springs or of parallel stacks positioned alternatively. However, a deviation in the characteristic curve is reported (44) due to friction between the springs, the springs and guide rods, and the spring and external edges where the load is introduced"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001914_rob.10048-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001914_rob.10048-Figure3-1.png",
        "caption": "Figure 3. Assignment of the linear springs.",
        "texts": [
            " Given arbitrary approximation of the position vector PC and the orientation matrix [R] of the moving platform, the corresponding limb lengths can be computed from Eq. (3). However, the lengths computed in this way will not agree with the given ones. Consequently, the configuration error of the moving platform can be defined as: E = 6\u2211 i=1 ( l2i \u2212 l\u22172i )2 (8) where l\u2217i denotes the given length of the ith limb. The problem now becomes finding the optimal configuration of themovingplatform, such that E isminimized. To efficiently solve this problem, the limbs are first imagined as linear springs, as shown in Figure 3. The undeformed lengths of the springs are defined as the given lengths of the limbs, and, hence, they will exert either compression or extension forces on the moving platform for incorrect configurations, as shown in Figure 4. These imaginary spring forces are defined by: Fi = (l\u2217i \u2212 li ) ui (9) where ui is a unit vector that indicates the current direction of the limb, pointing from the base to the moving platform. Secondly, the moving platform is considered as a system of six particles of unit mass connected by massless rigid rods, as shown in Figure 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003141_tsmc.1982.4308921-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003141_tsmc.1982.4308921-Figure4-1.png",
        "caption": "Fig. 4.",
        "texts": [
            " A nonlinear matrix differential equation model can easily be obtained from (38) by inverting the GIM ('M). By the formulations given above a considerable redundancy has been removed from the modeling of open loop kinematic chains resulting in an efficient modeling technique. Table I presents a comparison of this method with other modeling procedures. Example: In order to demonstrate the power of the GIM method in comparison to other methods, dynamic description of an anthropomorphic industrial manipulator will be obtained by this method. The manipulator has three joints of the rotary type (Fig. 4). For the purpose of comparison it is neither necessary nor desirable to obtain again the complete set of dynamic equations of the manipulator by other modeling methods. Rather computation of a few typical coefficients or terms will suffice to illustrate the comparison. As stated previously modeling techniques based upon Lagrange's method are superior to those based upon Newton-Euler formalism or D'Alembert's principle. Consequently Uicker's method has been used to compute certain coefficients of the dynamic equations, and then to illustrate the advantages of the GIM method"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003006_tmag.2004.828994-Figure13-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003006_tmag.2004.828994-Figure13-1.png",
        "caption": "Fig. 13. The 2-DOF flying slider model in near-contact regime.",
        "texts": [
            " 1:0; S=S = 5:0; k = 5:0 10 [N/m]; k = 6:0 10 [N/m]). Fig. 12(a) and (b) show the experimental trailing edge vibrations of a commercially available slider just after touch down and before takeoff, respectively. A typical feature of the bouncing vibration is that the fundamental frequency is related to lower-mode pitch resonance and that the bouncing vibration contains many super harmonics, except for the case just after touch down. Simulation analysis was done for a 2-DOF flying slider model shown in Fig. 13, including friction force in addition to contact force with roughness and lubricant layer. Note that is the sum of and the attractive force. As a parametric study, contact force is changed by multiplying the contact force at 40 40 m pad area and 1-nm lubricant thickness shown in Fig. 9 with an integer. The effect of frictional coefficient and air-bearing stiffness are also examined. We assume that the waviness amplitude is zero. Fig. 14 shows the maximum spacing at the trailing edge versus nominal flying height (FH) when a displacement disturbance of from 1 to 50 nm is applied at each FH"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003766_0278364906061159-Figure12-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003766_0278364906061159-Figure12-1.png",
        "caption": "Fig. 12. Inner mechanisms of head unit.",
        "texts": [
            " As a result, Table 1. Tube Unit Specifications Diameter of tube 80 (mm) Length of tube 3000 (mm) at Virginia Tech on March 14, 2015ijr.sagepub.comDownloaded from at Virginia Tech on March 14, 2015ijr.sagepub.comDownloaded from Table 2. Head unit specifications Diameter 90 (mm) Weight 400 (g) Fig. 13. Head unit. extra wire will pile up at the end. To make the head unit follow the tube, it is necessary to wind up the excessive wire length. Therefore, we added a wire-rewinding device to the head unit (Figure 12). The head unit has a CCD camera. The specifications of the head unit are shown in Table 2. As shown in Figures 14 and 15, the hermetic case is composed of the following: 1. a winch; 2. a slip ring; 3. an air tank (hermetic case); 4. lock mechanism. The winch winds up the tube and wire simultaneously. The slip ring allows the supply of electricity to the outside through the wire wound up around the winch. The air tank contains the air supplied from the air compressor. The amount of tube expansion is controlled by the handle and lock mechanism"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002006_978-3-662-09769-4-Figure6.8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002006_978-3-662-09769-4-Figure6.8-1.png",
        "caption": "Figure 6.8: Angles of the aerodynamic forces and torques",
        "texts": [
            "4 Forces and torques which act on the body Weight: The weight of the rocket is: or Ffv=A~~\u00b7(O, 0, m\u00b7g)T =F~ (6.56) (6.57a) ( 1 ,B\u00b7sin<p-'1/J\u00b7cos<p,B\u00b7cos<p-:-'1/J\u00b7sin<p)T ( 0 ) Ffv = 'ljJ , cos <p , - sm <p \u00b7 0 , -{}, sin<p , cos<p m \u00b7 g and finally (6.57b) As the line of action of Fw meets the point C, Fw does not generate a torque with respect to C. Aerodynamic forces and torques: The absolute value of the velocity of the rocket is (6.58a) Then the following angles of the rocket are introduced (see Figure 6.8): vL sin\u00df ~ \u00df :~ _Q, V and 6.3 Model equations of a spinning rocket (three tr. DOFs, threerot. DOFs) 433 To obtaill formal expressiolls of the aerodyllamic forces alld torques, the fol lowillg parameterswill be illtroduced: cx('y), cy(\u00df), Cz(a) as the aerodyllamic force coefficiellts, dx('y,p), dy(a, q), dz(\u00df, r) as the aerodyllamic dampillg co efficiellts, Cxp('y,p), Cyq(a, q), Czr(\u00df, r) as the aerodyllamic torque coefficiellts, 1'\\,x, 1'\\,y, 1'\\,z as the force coefficiellts which depelld Oll the geometry ofthe rocket, alld 1'\\,P' 1'\\,q, 1'\\,r as the torque coefficiellts which also depelld Oll the geometry of the rocket"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002547_s10010-005-0011-3-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002547_s10010-005-0011-3-Figure2-1.png",
        "caption": "Fig. 2. Eigen-trajectories (x(t), y(t)) for \u2126/\u03c9R = 1.0, 2.0, 3.0; \u25e6\u2013initial point; the trajectory for \u03bb1 is oriented opposite to the direction of rotation, for \u03bb2 coincide the directions",
        "texts": [
            " In equations the tilde is dropped.) 2.4 Solutions to the linear system To become familiar with the system we calculate some results for the linear system, the system without the influence of the gear coupling effects, i.e. MF = 0 in Eq. 2. The free vibrations u = u\u0306 exp(\u03bbt) (13) lead to two (couples of complex conjugate) eigen-solutions (\u03bb, u\u0306)k , k = 1, 2, which depend on the speed \u2126 because of the gyroscopic effects. Table 2 contains the values of (\u03bb, u\u0306)k for \u2126\u0303 = \u2126/\u03c9R = 0, 1.0, 2.0, 3.0, ( j := \u221a (-1)); Fig. 2 points out the shape of the corresponding trajectories. The forced harmonic oscillations have for \u2126 = constant the form xu = x\u0302c cos(\u2126t)+ x\u0302s sin(\u2126t) = x\u0302 cos(\u2126t +\u03b1x) , yu = y\u0302c cos(\u2126t)+ y\u0302s sin(\u2126t) = y\u0302 cos(\u2126t +\u03b1y) . (14) Figure 3 shows the resonance curves x\u0302(\u2126), y\u0302(\u2126). \u2126/\u03c9R \u03bb1/\u03c9R u\u0306T 1 /eR \u03bb2/\u03c9R u\u0306T 2 /eR For the balanced rotor, eu = 0, follows from Eq. 2 the equation of motion Mu\u0308+ (D+\u2126 \u00b7G+ f(v) \u00b7C1) u\u0307+ (K+\u2126 \u00b7 f(v) \u00b7C2) u = ( kxax kyay \u2212 W ) . (15) In the balanced rotor does not exist any synchronisation between its rotation and its oscillations",
            " Diagram 8 shows the spiralling outward motion of bearing B (in the direction of the rotation), but now the angular velocity \u03a8\u0307(t) has diminished drastically, see diagram 5, its mean arrives at a value \u03c9p close to the eigen-frequency \u03c92 of the linear oscillations (cf. Table 2 and the legends to Figs. 6 and 8 below). Almost immediately an oval limit cycle, a periodic motion, is reached, see diagram 9. Its shape is comparable to that of the eigen-trajectory of the linear oscillation, see diagram 2 of Fig. 2, just a little tilted against the direction of the rotation. The half axes of the limit cycle have about the same magnitudes as the peak values of the resonant curves in Fig. 3. Figure 6 presents the coupling moments for the limit cycle, (M\u03c6x , M\u03c6y) \u2261 (M\u03d5x , M\u03d5y), cf. Eqs. 62, 67. To compare the phases of rotation, diagram 1 shows the orbit (x(t), y(t)) of the limit cycle, and o marks the initial point, o \u2192 + indicates the direction of motion. Diagram 2 shows the orbit of (M\u03d5x , M\u03d5y), it is a circle: the magnitude of the moment vector is constant (= MF/(1+ l3/l4), since tanh (v(t)/v\u2217) = 1)",
            "89 is about the lower critical speed of the (linear) rotor system (cf. the left peak in Fig. 3), and lies in the stable region of the perfectly balanced rotor. Figure 13 shows the orbits of the forced oscillations for eu = a \u00d7 euN , a = 1, 2.5, 5. The character of the orbits is similar to those in the right diagram of Fig. 12, except that here, because of the larger rotational speed, the coupling yields already at smaller eccentricities. (The oval orbit for a = 5 has about the slenderness of the eigen-trajectory in the left-hand diagram of Fig. 2.) 4.3 Unbalance oscillations in unstable regions Quite different is the character of the orbits at \u2126/\u03c9R = 1.11, Trot/TR = 5.6605, close to the second critical speed, slightly above the stability border of the perfectly balanced rotor, \u2126B/\u03c9R = 1.051, see Fig. 4. For the perfectly balanced rotor there exists a nearly circular limit cycle, its radius r = r(\u03a8) lies in the range 0.581 < r/eR < 0.587; its period Tp/TR = 5.6631 is just a tiny bit larger than Trot/TR. Thus, the centre circling rotor along the limit cycle stays just behind the rotor\u2019s rotation, the gear coupling does not stick"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000332_s0094-114x(96)00076-6-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000332_s0094-114x(96)00076-6-Figure1-1.png",
        "caption": "Fig. 1.",
        "texts": [
            " [1], which is written in standard form, and the directrix F is the striction curve of E and the parameter a is the arc-length of spherical image curve of the unit vector of the generator L. Meanwhile, the Frenet frame {rp, Et, E2, E3} of E is defined by equation (2) and the differential formula is as equation (3) in Ref. [1]. Then, another line L* with unit vector I* moves along the directrix F* and is adjoining to the line L in each position and traces another ruled surface E* in 0-0'k, we call the ruled surface E an original ruled surface and E* an adjoint ruled surface of E, shown in Fig. 1. Thus, E* can be represented by E*: R*(a,/~) = rp + rpA + pl*(a) (1) and rpA = XlEI + x,.E2 + x3E3, 1\" = ll*El + 13*E~. + 13\"E3, 1,2 +/3.2 + 13,2 = 1 (2) tThis project was supported by the National Natural Science Foundation of China. 433 where rpA is the vector from the striction point P to a point A on the line L* and (xt, x2, x3) are three components of rpA in frame {El, E_,, E3} respectively, rp is the vector of the striction point of Z. However, the vectors rpA and 1\" can be visualized as the functions of the spherical image curve's arc-length a of the generator's unit vector of the original ruled surface Z"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002996_anie.198307641-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002996_anie.198307641-Figure6-1.png",
        "caption": "Fig. 6. Film formation in anaphoretic coating (schematic).",
        "texts": [
            " Today, electrophoretic coating (also known as electrodeposition coating) is used, for example, on a large scale for priming vehicle bodywork. For this purpose the coating resin, present in aqueous solution as a polyelectrolyte, is deposited on an immersed metal part by applying a direct current (anaphoretic or cataphoretic coating). o d ~ [ ~ , ~ ] . 3.2.1. Anaphoretic Coating For the coating resin, anodic deposition requires a water-soluble polyanion which can be coagulated by protons on the workpiece connected as the anode in the circuit (Fig. 6). The protons are formed by electrolysis of the water. Suitable polyanions include, for example, low-molecular weight resins with carboxyl groups rendered water-soluble by neutralization with bases. After deposition on the workpiece, the solid film (thickness 1 2 0 pm) is crosslinked at elevated temperature in the presence of reactive compounds. 3.2.2. Cataphoretic Coating Cathodic deposition requires a water-soluble polycation which can be coagulated by hydroxyl ions on the workpiece connected as the cathode in the circuit"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001663_s0022112000002494-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001663_s0022112000002494-Figure1-1.png",
        "caption": "Figure 1. Streamfunction for a stokeslet situated at (0, 1) above a plate (corresponding to y = 0). (a) Stream lines corresponding to a Stokeslet at (0, 1). (b) Illustration of image system for a stokeslet near a rigid boundary.",
        "texts": [
            " In order to model the far-field flow generated by the beating of the flagellum we assume that it can be mimicked using a point force, Blake & Otto (1996). To determine the flow field arising due to the stokeslet we solve the Stokes equations forced by a delta function multiplied by the force vector, this is affected by three-dimensional Fourier transforms. The presence of the solid boundary generates an image system which comprises an image point force (to satisfy the condition of no normal flow) a Stokes doublet and a source doublet (to satisfy the condition of no-slip), see figure 1. We refer the reader to Blake & Otto (1996) and the work of Lorentz (1896). If the point of application of these stokeslets remains stationary then flows with closed streamlines will be obtained and this will not lead to any degree of mixing (other than by molecular diffusion, which we assume to be relatively weak). However, if the location of the stokeslet changes a mechanism for enhanced mixing is dispersion induced by the corresponding chaotic advection. In Blake & Otto (1996) and Blake, Otto & Blake (1998) some preliminary discussion has been given, stating that flows comprising two point forces operating at different spatial points with distinct periods of operation can lead to chaotic particle paths, leading to enhanced mixing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003209_1.2061007-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003209_1.2061007-Figure1-1.png",
        "caption": "Fig. 1 Specimens of tubesheet",
        "texts": [
            " 127, NOVEMBER 2005 Copyright \u00a9 rom: http://pressurevesseltech.asmedigitalcollection.asme.org/pdfaccess.as hydraulic tube-expansion strength are presented, which mainly focuses on the effect of circumferential grooves. The following effects on joint strength were investigated: 1. groove width with one groove 2. groove location with one groove 3. groove depth with one groove 4. spacing between grooves with two grooves Specimen. The experiments were performed using a carbon steel 10 tube and a low-alloy steel 16 Mn tubesheet, as shown in Fig. 1. The dimensions of the tube and tubesheet are listed in Table 1. Material Properties of Specimens. The properties of tube and tubesheet materials are given in Table 2. They were determined using an MTS 880 testing machine. Experimental Procedure. The surface of the tubesheet holes was finished to meet commercial specifications. The roughness value of the surface of the tubesheet holes is Ra12.5* m. Prior to tube expanding, preparation work for expansion was carried out first. It included numbering the tube and tubesheet, respectively, measuring and recording the original inside and outside diameters d1, d of the tubes, and the tubesheet hole diameter D"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002441_iros.2000.893186-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002441_iros.2000.893186-Figure1-1.png",
        "caption": "Figure 1: The friction cone at a grasping point.",
        "texts": [],
        "surrounding_texts": [
            "Theorem 1 Suppose that a n-finger fnctional grasp is given. Denote the convex hull of the primitive contact wrenches wi by H(W) . Assume that point P is an interior point of H(W). The ray from point P to the origin 0 of the wrench space R6 intersects H(W) in a point Q only. A form-closure grasp is equivalent to that the distance dl between points P and Q is strictly larger than the distance d2 between points P and O(Fig.2). The proof of this theorem can be found in [3]. The proposed qualitative test algorithm works on Theorem 1. To use the theorem, we must first find an interior point P of H(W) and then detect the intersection point Q of H(W) with the ray PO. A strictly positive convex combination of the primitive contact wrenches wi is an interior point of the convex hull H(W). In other words, if a point P has the following form: N N P = z a j w i , x a j = 1, aj > 0, i = 1 , 2 ,... N i= 1 i= 1 - 1224 - point P is an interior point of H(W). choose P as the centroid of the convex hull. Here we (5) To find the intersection of H ( W ) with the ray, we address a problem of finding the facet of the convex hull intersected by the ray PO, which is closely related to the following ray-shooting problem: Definition 2 Ray-shooting problem: Let M be a given set of points in Rd. Assume that the convex hull H ( M ) contains the origin. Given a ray emanating from the origin, find the facet of H ( W ) intersected by this ray. It is well known in Computational Geometry that the ray-shooting problem can be transformed to a linear programming problem based on the duality between convex hull and convex polytope. Note that a ray-shooting problem assumes that the convex hull contains the origin. However, it is not clear at present stage that whether the origin of the wrench space R6 lies inside the convex hull H ( W ) . By applying a coordinate translation of -P on points in R6, we readily change the origin to P, which lies exactly inside the convex hull. After the coordinate translation, the convex hull H ( W ) is dual to the convex polytope (wi - P ) T ~ 5 1 i = 1,2, ..., N . (6) Denote the direction vector of the ray PO by t . Based on the duality between convex hull and convex polytope, the ray shooting problem is equivalent to a problem of maximizing the objective function z = tTx (7) subject to the constraints in (6). Suppose that the optimal solution of the linear programming problem is e'= ( e l , e2, ... e6). According to the transformation T, the facet E of H ( W ) intersected by the ray PO is e121 + e 2 2 2 + e323 + e4x4 + e525 + e 6 2 6 = 1. ( 8 ) Then, the intersection point Q of H ( W ) with the ray PO is the intersection of the hyperplane defined by (8) with the ray PO."
        ]
    },
    {
        "image_filename": "designv11_24_0002972_1.2114947-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002972_1.2114947-Figure4-1.png",
        "caption": "Fig. 4 At different values of E1 /E3, E2 /E3, =1 nm, *=0.5 m, H3 /E3=0.05, h1 / =h2 / =10, H1=H2=H3, E3=100 GPa, \u201ea\u2026 profiles of contact pressures, contours of von Mises stresses on the surface, von Mises stresses on the max J2 plane, principal tensile stresses on the max t plane, and shear stresses on the max xz plane with pn /E3=1\u00c310\u22125, and \u201eb\u2026 variation of maximum pressure, fractional real area of contact, and fractional plastic area of contact with normal pressure pn.",
        "texts": [
            " The first two sets of simulations are designed to study the stiffness, thickness, loading, and meniscus effects. For various ratios of Young\u2019s modulus of the layers to that of the substrate, five structures are used, I: E1=E2=E3 homogeneous solid ; II: E1 /E3=E2 /E3=0.5 single layered solid with a compliant top layer ; III: E1 /E3 =E2 /E3=2 single layered solid with a stiff top layer ; IV: E1 /E3=1, E2 /E3=0.5 solid with a compliant interlayer , and V: E1 /E3=1, E2 /E3=2 solid with a stiff interlayer . Figure 4 a shows the pressure and stress distributions for various stiffness ratios of the layers to that of the substrate. Table 1 a summarizes the relevant data. Figure 4 b shows the maximum contact pressure, the fractional real area of contact, and fractional plastic contact area as a function of applied load for the five structures. At a given load, a compliant top layer II decreases the maximum local contact pressure, and the probable occurrence of plastic contact, but with increasing of the real area of contact, as compared to homogeneous solid I , whereas a stiff top layer III has the opposite effects. This agrees with common engineering experience and that presented by Bhushan and Peng 11 for a single layered model",
            " The increase of magnitudes of local contact pressure and real area of contact are moderate at the beginning, but become significant upon part of local contacts close to or reaching plastic regime. The change of real area of contact is more dramatic than the change of maximum contact pressure. The maximum contact pressure increases with the increase of the normal load until reaching the effective hardness. After that, plastic contact occurs and the maximum pressure remains. Figure 5 presents similar data to Fig. 4, whereas layer thickness is taken as h1 / =h2 / =1 instead of h1 / =h2 / =10. Table 1 b summarizes the relevant data. Similar observations are obtained, whereas the differences can be observed. The differences between the two sets of data shown in Figs. 4 and 5 are believed to be the Transactions of the ASME data/journals/jotre9/28738/ on 05/21/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F effect of layer thickness. Layer effects are observed to be amplified as layer thickness increases for these cases"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000555_s0890-6955(97)00031-x-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000555_s0890-6955(97)00031-x-Figure5-1.png",
        "caption": "Fig. 5. Stress distribution on the major flank and minor flank.",
        "texts": [],
        "surrounding_texts": [
            "To estimate the inner stress in a cutting tool, it is important to find the distribution of the contact load over the contact area on the rake face between tool and chip, and on the major and minor flank faces between tool and workpiece. However, obtaining the precise load distribution for a cutting tool is a very difficult task. Over the years, many investigations have been carded out to explore the load distribution over the cutting tool and several models have been developed for load distribution, such as linear normal distribution, exponent distribution and constant combined with exponent distribution, etc. The most fundamental model was proposed by Zorev [11]. He suggested that the normal and shear load on the rake face were distributed in the manner shown in Fig. 2. The normal load on the rake face decreases parabolically from a maximum value at the cutting edge Cutting tool fracture, Part I 1699 to zero at the end of the chip-tool contact zone. The shear load shows a more uniform distribution in the seizure region where the normal load is so high that seizure occurs between chip and tool materials and thus the shear stress becomes equal to the shear yield stress of the chip material. The shear load gradually decreases to zero in a relatively small region adjacent to the end of the contact zone. Apart from the model of contact load distribution on the tool faces, the contact load also depends on the., contact area of the tool with the chip and the workpiece. On the rake face, the contact area depends on the contact length between chip and tool rake face, lcr. On the flank face, the contact area depends on the theoretical chip width, b~, and the contact length between tool and workpiece, lcf. Since the flank wear, VB, exists almost throughout the whole lifetime in machining, the contact length between tool and workpiece is approximately equal to the major flank wear land. In this work, linear and constant stress distribution models were adopted for their simplicity. The models for load distribution are also supported by other investigators. 6.1. Load on rake face Cutting loads are assumed to exist on all contact areas between tool and chip. The image in Fig. 3 shows the contact area between the chip and the tool on the rake face at different feed rates. The contact area on the rake face can be formed in the area ABCDE, as shown in Fig. 4(b). The contact area is determined by the depth of cut, contact length and angle, a2. The angle a2 is actually determined by the feed rate and the tool nose radius, which can be estimated from the following expression: a2 = ~ + arct~m (34) where s is the feed rate and r is the tool nose radius. When the depth of cut is greater than the tool nose radius, along the x-axis, the whole contact area on the rake face can 1700 J.M. Zhou et aL be divided into two areas: a rectangular area and a segment area, as shown in Fig. 4(b). Along the y-axis, the contact area between the chip and the rake face can be classified into two areas: seizure contact area and sliding contact area. Therefore, the whole contact area is divided into four subareas and the contact load on each subarea is different. 6.1.1. Normal load on rake face. Based on Zorev's work, the normal load was assumed to have a triangular distribution on the rake face in the presented model, as shown in Fig. 4(a), which means that the load has its maximum value on the cutting edge and decreases linearly to zero at the separation point of the chip and tool. In the nose area, the maximum load along the cutting edge will decrease linearly to zero with increasing angle 012. More specifically, as shown in Fig. 4(b), for the contact area r < x < b~ and 0 < y < l . , the normal load is calculated from the following equation: / c r - - Y ~rr](x,Y) - - - Pr (35) l . For the contact area 0 < x < r and 0 < p < r - / c r ( 0 1 2 - - 01 ) /012 , the normal load is calculated from the equation (p + lc, - r)(a2 - a) Orr2(P,01) = 1cr012 Pr (36) where Pr represents the maximum load along the cutting edge. Accordingly, the normal force on the rake face and the normal contact load on the rake face have the following relationship: Icr b l \u00b0t2 NT=ffO'r,(X,y) dxdy+f i o'~z(P,01)pdpd01 0 r 0 0 l 2 _ 01 r -- lcr 01 lcr b l \u00b0t2 0 r 0 012 - 01 r - ~ r - - 012 = (bl - r) - 1-~ 012(7lcr -- 25r) le~ r ( P + ~ r - - ~ ( 0 1 2 - - 01) 1~r012 PPr dp dot (37) 6.1.2. Shear load on rake face. The shear load on the rake face can be resolved into the load in the axial direction and the load in the radial direction. The distribution of the shear load on the rake face is different from that of the normal load, as shown in Fig. 4(a). In the seizure contact area, the shear load is distributed uniformly due to the seizure occurring between chip and tool materials under high normal stress, which makes the shear stress equal to the shear yield stress of the chip material. In the sliding contact area, however, the load is distributed linearly, due to the reduced normal load on the rake face in this region, which allows the chip to slide along the tool face. The shear load, therefore, is calculated with different distribution models in four different zones. For zone I: r < x < b] and 0 < y < l J 2 , the shear load in the axial and radial directions has a constant distribution which can be calculated from Cutting tool fracture, Part I 1701 ~ ( x , y ) = ~ (38) ~ ( x , y ) = ~ (39) For zone II: r < x < bl and leer2 < y < ler, the shear load in the axial and radial directions has a linear distribution which can be calculated f rom 2(1\u00a2r -- y ) ~ (40) ~r2(X,y) -- lcr ~rr2(X,y) -- 2(/\u00a2r -- y ) ~ (41) /cr For zone III: 0 < 0 / < 0/2 and r - /cr(0/2 - 0/)120/< p < r, the shear load in the axial and radial directions has a linear distribution which can be calculated f rom rr3(P,0/) - 0/2 - 0 / ~ (42) 0/2 7 r 3 ( P , 0 / ) _ 0/2 --\" 0/ TR r ( 4 3 ) 0/;; For zone IV: 0 < 0/ < 0/2 and r - /er(0/2 - - 0/)[0/ < P < r - Icr(0/2 - - 0/)/0/, the shear load has a linear distribution in both axial and radial directions and can be calculated f rom rrr4(P,0/) = 2(p + lcr -- r)(0/2 -- 0/) ~ (44) /er0/2 rr4(P,0/) = 2(p + lc~ - r)(0/2 - 0/) ~ (45) 1cr0/2 where ~ and t R represent the m a x i m u m contact shear load along the cutting edge, respectively. Accordingly, the shear forces on the rake face and the contact shear load on the rake face have the fol lowing relationship: / c J 2 bl /cr bl a 2 f f f f 2(lcr-y) f i \u00a2 d x d y + i 2 C d x d y + 0 r l\u00a2r/2 r 0 0/2 -- 0/ r -- l c r - - 20/ 0/2 - - 0/ 0/2 0/2 0/ r - - / c r - - 0r2 20 / 0 0/2 -- 0/ r -- /or 0/ 2(p + lcr - r)(0/2 - a ) /cr0/2 ~ p dp d a = (46) 1, 49 ) (bl - r) + ~ a2r - ~ 0/2/cr lcrt~r and 1 7 0 2 J . M . Z h o u et al. lcr/2 b I TR:fft\"rdxdy 0 r /cr bl lcr/2 r ~2 t dy+ f 0 0/2 - 0/ r - lcr 20 / 0/2 ~ 0/ 0/2 ~p dp dot 0/2 - 0/ r - - l e t - - \u00b0t2 20 / +ff 0 0/2 - 0 / r -- lcr 0/ 2(p + lcr - 0(0/2 - 0/) 1cr0/2 tRp dp dot (~ 15 49 ) = (bl - r) + ~ azr - ~ 0/2lcr l c~ (47) 6.2. Load on flank face While the distribution of contact load over the rake face contact area must be explained on the basis of shear deformation and plastic flow of the machined material along the primary and secondary deformation zones, the development of contact load over the flank area can be attributed to the interaction between the workpiece (rather the machined surface) and the flank face of the cutting tool [17]. Besides the normal load acting on both the major and minor flank faces, two shear loads affect both the major and minor flanks, respectively. On the major and minor flank area, the shear loads in the tangential direction, Txy and ~'yx, are generated by the friction between the tool and workpiece associated with the cutting velocity. The friction between the tool and workpiece due to the vibration will generate a shear force in the radial direction. The shear load on the minor flank face in the axial direction is due to the friction between the minor flank face and workpiece caused by feed movement. However, compared with the shear load in the tangential direction, the shear load on the major and minor faces in the radial and axial direction is much smaller in normal cutting conditions because of the much smaller movement, therefore they can be neglected in FEM calculations. Normal loads on the major flank face and minor flank face are also assumed to conform to the uniform distribution, but in the nose area the maximum load will gradually decrease to zero along the nose edge, as shown in Figs 4(a) and 5. In the major flank area, normal stress and shear stress are calculated with the following equations: Cutting tool fracture, Part I 1703 O'n = pf (48) \"i'll = t f (49) In the comer region, the normal load distribution is more complicated. Through analysing the cutting forces measured from a wide range of cutting parameters, Sandqvist [14] found that the normal load along the nose area will decrease with increasing angle or2, and he suggests that the distribution of the contact stress on the flank face conforms to the following model: trf2 = cos pf (50) Similarly, the shear loads in the tangential direction on both the major flank side and the minor flank side are assumed to comply with a similar type of distribution, i.e. where pf and tf are the maximum normal load and shear load along the cutting edge, respectively. Therefore, the normal force and the shear force on the flank can be expressed by the following equations: 0 a2 N~= f f sin(dO cos(<),z,, d~ d~ = -- lcf 0 a2(40t 2 + 2\u00a2r sin a2) 4 ~ - rt a l e t P f (52) 0 bl 0 ~2 T~: f ft,~+ f fcos(~)rtedo,~=(O,,-r)+ ),o~f -- lcf r -- /cf 0 (53) 0 bl 0 a 2 ;,,A= f f flo, cos( ,)cos( 2)rpf (54) -- lcf r -- lcf 0 1704 J .M. Zhou et al. 7/\" COS 0/2) d0/dz = (bl -- r) + 2r0/2 4 - - 0 / ~ ~ lcrpf When the primary cutting force is 1 N, all the values of Pr, t~r, fir, Pf and tf can be obtained from the above equations: 1 2 0 ( 1 - ~ar) P r - (60(b~ - r) - 0/2(7l~r -- 25r))l , (55) 480q~AT(I -- q~A) = (56) (360(bl -- r) + (150azr -- 490/zlcr))l= 480q~r(1 - q~) fir - ( 5 7 ) (360(bl -- r) + (1500/2r - 490/zlcr))ler 4(0/2 - ~/2)(0/2 + 7r/2)q~Rq~RV Pf = r0/2(20/2 -- 7r sin 0/2)lcf (58) 4(0/2 - 7r/2)(0/2 + ' / r /2)~A~AT (59) Pf -- (2 (b I - r)(0/2 - \"/r/2)(0/2 + 7r/2) - ~r0/2 c o s 0/2)/of 27rq~r tf = (~r(bl - r) + r0/2)lcr (60) From Eqns (52) and (53), NA and NR have the following relationship: 2(b l - - r)(0/2 - 7r/2)(0/2 + 7r/2) -- Irr0/2 cos 0/2 NA = NR (61) (20/2 -- zr sin 0/a)r0/2 or NA = kNR (62) and (~A ~AT = ktpRq~T (63) where k is the ratio between the normal force in the axial direction and the normal force in the radial direction, k is a function of b~, r and lcr. When the insert is DNMA150608, the depth of cut is 3.0 mm and the undeformed chip thickness hi is 0.5 mm, then the calculated value of k is about 6, which agrees with the results from the experiment carried out in this work. The above equation means that the values of the load function q~ and q~T Can be determined from the values of q~A, ~AT and k. Therefore, for a certain type of cutting tool, its maximum related stresses are only dependent on ~AT, q~A, q>r, let, lee and bl. 7. FINITE ELEMENT CALCULATIONS 7.1. Geometrical model Different finite element models are required for different geometries of the cutting tool in the calculation of maximum related stresses. In this study, finite element models for the cutting tool, DNMA150608, with five different syntactic VB were then created for the same tool dimensions used in the experimental research. The five different synthetic VB are: 0.05 (simulating a sharp edge), 0.20, 0.40, 0.60 and 0.80 ram. Each tool was divided into 10 noded isoparametric tetrahedron elements. Since the contact length was only a Cutting tool fracture, Part I 1705 small portion of the total rake face, mesh grading was required. A fine mesh was chosen near the cutting edge with a coarse mesh far from the edge, the element size becoming coarser away from the edge, as shown in Fig. 6. This has the effect of reducing the total number of elements, and hence the computing time, without sacrificing the accuracy of the results, especially near the cutting edge. The entire mesh was oriented at the appropriate angles to the applied forces. For the tool with large flank wear, the total mesh nodes increased from 11,000 to 14,000. Other simplifications were also applied, including assuming the material of the insert to be homogeneous and isotropic. 7.2. Determination of load cases About 135 load cases were calculated for each geometry, and a total of 680 load cases were chosen for FEM calculations to obtain the corresponding maximum related stresses. The load values for each load case were obtained from the cutting experiments. Cutting parameters in the: experiment were: \u2022 chip thickness h, - from 0.1 to 0.6 mm with step 0.1; \u2022 chip width b, - from 0.5 to 4.0 mm with step 0.5; \u2022 cutting speed v - from 80 to 250 m/min; \u2022 experimental materials - AISI1045 and AISI4340. Fig. 7 shows the areas in which the values of the load functions q~AT, q~r and q~A were distributed when the above cutting conditions were employed in the cutting experiments. 1706 J.M. Zhou et al."
        ]
    },
    {
        "image_filename": "designv11_24_0000052_s0003-2670(99)00015-x-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000052_s0003-2670(99)00015-x-Figure1-1.png",
        "caption": "Fig. 1. (a) Flow diagram of the system. Vi three-way solenoid valves; WB temperature controlled water bath at 478C; B reaction coil of PTFE tubing (500 cm long; 1.6 mm i.d.); Det spectrophotometer at 548 nm; P peristaltic pump; x stopper made by cutting up polyethylene tubing (2 cm) and melting one end; y perspex junction point; S sample solution; Cs sample carrier stream \u00b1 water at 2.0 ml min\u00ff1; R reagent solution \u00b1 10% (m/v) NaIO4 plus 0.36 mmol l\u00ff1 MnO\u00ff4 in 0.5 mol l\u00ff1 H3PO4; Air \u00b1 air flow at 2 ml min\u00ff1. W waste. (b) Timing course of the solenoid valves. ti timing course of the valve Vi. Higher level valve switched on; lower level valve switched off.",
        "texts": [
            "0 mmol l\u00ff1 MnO\u00ff4 stock solution was prepared in 0.1% (v/v) phosphoric acid medium. Reagent solutions containing 2.5, 5.0, 7.5, 10.0, 15.0, and 20.0% (m/v) NaIO4 were prepared in different concentrations of H3PO4 (0.1, 0.5, 1.0, 2.0, 3.0, and 4.0 mol l\u00ff1). These solutions were prepared without permanganate and containing 0.16 or 0.36 mmol l\u00ff1 MnO\u00ff4 . Soybean samples were mineralized by employing the nitric/perchloric digestion procedure, such as described elsewhere [19]. The \u00afow diagram of the system is shown in Fig. 1(a). All valves are switched off such that only the carrier solution (Cs) \u00afows through the analytical path. The analytical cycle starts when the microcomputer sends a set of electric pulses to the solenoid valves according to the sequence indicated in the valves timing course of Fig. 1(b). Valves undergo an on/off switching sequence, allowing insertion of sample and reagent solution aliquots into the reaction coil (B) sandwiched between two air bubbles. In the \u00aerst step, valves V1 and V2 are switched on during the time interval tw, thus the carrier stream is halted and sample solution \u00afows to \u00aell the conduit connecting valve V1 with point y. In the second step, valves V2 and V4 are switched on during the time interval ta to insert an air bubble into the reaction coil B. As indicated in the valves timing course, in the third and forth steps, the valves V2 and V3 and afterwards V2 and V1 are switched on during the time intervals tr and ts in order to insert into the reaction coil B several reagent slugs intercalated by sample slugs",
            " In conventional procedures employing stopped \u00afow [3] or zone trapping [4] approaches, the sample throughput would be impaired in order to attain the necessary residence time. The correlation between absorbance and concentration was ascertained by running a set of reference solutions with concentration ranging from 5 to 40.0 mg l\u00ff1 Mn2 and the obtained linear response can be expressed by the equation: Absorbance 0:470 0:0473 Mn2 ; r 0:999: The performance of the proposed \u00afow procedure was veri\u00aeed by analyzing a set of acidic soybean digests. Sample solutions were processed by running the \u00afow network as indicated by the valves timing course (Fig. 1(b)) and establishing the following operational conditions: oxidizing reagent solution containing 7.5% (m/v) NaIO4 plus 0.36 mmol l\u00ff1 MnO\u00ff4 in 0.5 mol l\u00ff1 H3PO4, 2.0 ml min\u00ff1 \u00afow rate, 160 ml air bubbles, and a loading cycle with 25 steps. Each step comprised sampling times of 0.9 s for sample and 0.5 s for the reagent (ts and tr intervals, respectively). Results obtained for the analyzed samples are shown in Table 1. Accuracy was assessed by comparing results with those obtained by induced coupled plasma atomic emission spectrometry and no signi\u00ae- cant difference was observed at 95% con\u00aedence level"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002369_095440602760400977-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002369_095440602760400977-Figure3-1.png",
        "caption": "Fig. 3 Angle of attack for nodal load and overlapping distance Fig. 4 Contact node velocity",
        "texts": [
            " 2, this condition is converted to the following: the maximum distance of all the overlapping nodal points with respect to the four active anks of the two pairs of teeth is less than a prede ned value in the deformed state. Here, the body of the driving and driven gear is denoted by gp and gg respectively. The overlapping distance, dg, m, for a nodal point, ug, m , is de ned as the distance between the actual nodal point and the rim of the opposite gear in the direction of the applied normal force, as illustrated in Fig. 3. In addition, due to the restriction of load only for overlapping nodes, an algorithm is derived in order to detect whether a node is overlapping or not and thereby if the presence of the nodal load is permissible or not. C04602 # IMechE 2002 Proc Instn Mech Engrs Vol 216 Part C: J Mechanical Engineering Science at RICE UNIV on November 23, 2014pic.sagepub.comDownloaded from Consider the nodal point ug, m belonging to the outer rim of the driving gear, with the coordinates xg, m, Zg, m , where m 1, 2, , n as shown in F ig",
            " F inally, by shifting the index p to g and vice versa, equations (6) and (7) are expanded in order to be valid for an arbitrary nodal point up, k located on the driving gear. The friction force is modelled using the Coulomb friction model and therefore the coef cient of friction, m, can be included as a contribution to the angle of attack. The statement that the normal forces acting on nodes must be true normal loads in the deformed state leads to the relation fpast i, k fprior i, k arctan mi, k , as shown in Fig. 3. This relation is valid for a nodal load f i, k acting in nodal point k , where fpast i, k and fprior i, k are two succeeding angles of attack. Expanding the relation by introducing a geometrical consideration leads to arg f i, k \u00b1 \u00b2 arg ui, k \u00a1 ui, k\u00a11 arg ui, k 1 \u00a1 ui, k p 2 \u00a1 arctan mi, k , 0 arg u 4 2p 8 The local friction coef cient mi, k +m depends upon the tangential relative velocity vector of the two mating surfaces, and is positive if the friction force acts in a counterclockwise direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002082_iros.1999.811663-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002082_iros.1999.811663-Figure5-1.png",
        "caption": "Figure 5: Curve deformation in 3 steps.",
        "texts": [
            " I f the first module is in a certain proximity of a support, Progress over an arc of circle of fixed radius. Else If the first module has in its sight a new support to take, Compute the required cubic polynomial and progress on it. Else, Compute the symetric of the last cubic polynomial as an a priori path and progress on it. While there is a new support t o be engaged, Begin the Step by step deformation process in order to Below described Step by step deformation algorithm is also illustrated in figure 5 for a 3 steps case. 1. Compute the required step number for the deformation. 2. Compute the next cubic polynomial and deform the present curve to get the new pace. 3 . If the first module is in a certain proximity of the new support, Quit this deformation algorithm and return to the main loop. Else, Go to 2. With Dm, diameter of one module, Nstep , step number, and M N , distance between M and N , step number of deformation is obtained as the integer part ' of the following division: N, tep = MN / Dna At each step, parameter \"r\" is being incremented of Dm for the computation of the parameters of an intermediate cubic polynomial curve"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000191_s0957-4158(96)00021-9-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000191_s0957-4158(96)00021-9-Figure1-1.png",
        "caption": "Fig. 1. (a) Photograph of the planar four-bar linkage under study\u2022 (b) Schematic diagram of the linkage\u2022",
        "texts": [
            " Furthermore, the rotor speed could be measured by the digital tachometer [12-15]. The position and speed data were then fed back to the PC/AT 386, thus closing the loop. As shown in section 2, the external moment T4 applied on the output link (link 4) referred to the input link is equal to T4h 4. For easily implementing such an external moment in experimental study, the external moment T4h4 seen by the motor was generated by software. The link parameters of the planar linkage under study, as shown in Fig. 1, are tabulated in Table 2. 5.2.1. Estimation of the parameter variation of the motor drive. The m o t o r drive wi thout load f rom the input vol tage to the shaft angular velocity (7.5 volt/3000 rpm) was exper imental ly de te rmined by a digital signal analyzer DSA-3562. By means of the curve-fi t t ing capabil i ty o f the analyzer , the exper imental t ransfer funct ion of the 946 MING-CHANG LIN and JIAN-SHIANG CHEN system from the input voltage (V) to the angular displacement (rad) was approximated by 2706 Gp(s) ~- s(s + 6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002845_0141-6359(82)90003-4-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002845_0141-6359(82)90003-4-Figure1-1.png",
        "caption": "Fig 1 Structure (a), shown modif ied (b)",
        "texts": [
            " These problems associated with friction damping have received serious study. Linear analysis 22'23 has been shown to give useful and meaningful results and joint surface preparations 28'29 have been found giving good energy dissipation without instigating serious fretting corrosion. Beards 3\u00b0 suggested that in any structure certain joints should allow frictional damping to occur under controlled conditions. These joints should be located so that the function of the structure is not impaired by their slight!y increased flexibi l i ty (Fig 1 ). The inherent damping of a structure so equipped will be much increased and hence the dynamic performance improved. Results have already been published 22'23'31'32 on the energy dissipation and frequency response of structures equipped with joints allowing controlled interfacial slip. PRECISION E N G I N E E R I N G 0141-6359/82/040185-06503.00@ 1982 Butterworth & Co (Publishers) Ltd 185 The investigations of Earles, Brown, and Earles and Philpot 16-18 were concerned with energy loss resulting from the relative slip at a flat metallic interface resulting from elastic elongation of the joint members with respect to each other"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001130_bf00353103-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001130_bf00353103-Figure1-1.png",
        "caption": "Figure 1 Schematic diagram of (a) cold mould, and (b) hot mould (all dimensions in mm).",
        "texts": [
            " T a b l e I I I lists the h y d r o g e n c o n - tents o b t a i n e d f r o m L e c o ana lys i s o f the a l loy samples . Front view Side view 3. R e s u l t s a n d d i s c u s s i o n 3.1. T h e r m a l a n a l y s i s Three pairs of thermocouples (Chromel-Alumel, type K), were each placed in the two moulds at positions from which samples for metallographic observations were prepared. Each pair consisted of two thermocouples separated by a 5 mm distance. Fig. 2a-c shows the temperature-time curves obtained from small (S), medium (M) and large (L) samples, respectively, taken from the positions shown in Fig. 1. In all three cases, the arrest corresponding to the Alloy H2 fl 0.22 f2 0.25 f3 0.20 f5 0.25 f6 0.31 f7 0.31 f8 0.25 hl 0.06 h2 0.52 h3 O.49 h4 0.13 h5 0.57 h6 0.12 h7 0.13 h8 0.45 sl 0.28 s2 0.24 s4 0.23 s5 0.26 s6 0.21 s7 0.21 s8 0.29 1245 500 120 (c) T ime ( s ) 25 0 20 9 'Q 15 E z _ ~ - - - ~ . . ~ 8 . 0 cm 7.5cm ~ Solidus 140 160 180 200 220 10 Figure 2 Continued. 5 20 (a) i i t k i i / 40 60 80 100 t20 140 160 Graduation in focus adjustment 55 650 P 2 600 O . E 550 180 Specimen Thermocouple Solidification Solidus velocity, position (cm) ~ time, ts (s) V~ (cm s- 1) Small (S) 3.0 12.5 0.450 3.5 Medium (M) 8.0 25.2 0.360 7.5 Large (L) 8.0 70,9 O. 114 7.5 a Height as measured from the bottom of the mould. 4\" 0 ' ' I I L I 60 80 100 120 140 160 Graduation in focus adjustment 3 . 2 . I m a g e a n a l y s i s As shown in Fig. 1, three samples termed small (S), medium (M) and large (L) were cut from each casting, and their upper surfaces polished for measurements of porosity. The porosity was quantified using a Leco 2001 image analyser, in conjunction with an optical microscope (Olympus PMG3). The accuracy of pore size and pore density measurements using image analysis depends on four parameters: focus, illumination, grey level and the number of images analysed per sample. Focus is one of the most important parameters for precise determination of pore shape and size",
            " Grain refining (through the addition of A1-5 wt % Ti-1 wt % B) reduced both per cent of 1248 surface porosity and pore size. It resulted, however, in a more uniform distribution of pores (see also [19, 20]). 3. Increasing the local solidification time or reducing t he so l idus ve loc i ty i n c r e a s e d b o t h the p o r e size a n d p e r c e n t o f sur face p o r o s i t y . evaluation P la t e s for r a d i o g r a p h i c e x a m i n a t i o n w e r e cu t as s h o w n s c h e m a t i c a l l y in Fig. 1. B o t h sur faces were p o l i s h e d p r i o r to tes t ing . T h e m a i n o b s e r v a t i o n s a re s u m m a r i z e d in T a b l e X I a - c for the t h r e e g r o u p s , i.e. Fe, H a n d Sr, respec t ive ly . T h e s y m b o l s c a n d h ind i - ca te a co ld o r a h o t m o u l d , respec t ive ly . T h e effect o f i n c r e a s i n g the h y d r o g e n c o n t e n t f r o m 0.06 to 0.57 ml 100 g - 1 AI o n e n h a n c i n g p o r o s i t y f o r m a t i o n is e x e m p l i f i e d in Fig",
            " Moderate grain; moderate to heavy gas cavities near top half of slice; moderate segregation. Coarse grain; moderate porosity; moderate segregation. m i n i m u m hydrogen level used with the highest stront ium concent ra t ion (300 p.p.m) is abou t 0.25 ml < 0.25 ml 100 g - 1 A1). S t ron t ium contr ibutes considerably to bo th poros i ty vo lume fraction and pore size [-19], as exemplified in Fig. 8. Micros t ruc tura l observa t ions were made on polished, unetched surfaces of the samples corresponding to small (S), med ium (M) and large (L) shown in Fig. 1 (and denoted by the letters S, M, L accordingly, in the alloy sample designations given in the tables). Fig. 9a, b shows the effect of soldification t ime for a degassed alloy (in the absence of Sr or grain Figure 6 Radiographs corresponding to (a) hl, and (b) h5 alloys. Figure 7 Radiographs corresponding to h6 alloy. 1251 1252 refiner addition). While it was rather difficult to observe any pores in the small sample, Fig. 9a, a few irregular/elongated pores could be observed for the large sample, Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001383_iros.1998.724803-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001383_iros.1998.724803-Figure3-1.png",
        "caption": "Figure 3: (a) The uniform discretization (Aq, = AqJ results in different Cartesian movements Ax, f Axl when different joints i, j are moved. (b) The optimal discretization results in equal maximum Cartesian movement Ax, = Axl when diflerentjoints i, j with distance I,, 1, to the endeffect m moved. [Beeh971 Aq, = Zarcsinj MaxMove 21, 1 ,",
        "texts": [
            " With a reasonable joint resolution of one degree, the uniform discretization result in huge C-spaces. For example, a discretization of the Puma260's joints with Aq = (lo, I\", I\", lo, lo, 1\") results in a C-space with 2.13*10\" states. To avoid the huge search space of uniform discretization, usually a heuristic discretization is applied. Here, reasonable Aq, are estimated by the user to balance the resulting Cartesian movement Ax, when the different joints i are moved for A4,. The underlying problem is illustrated in Figure 3a. For the Puma260, one may choose A4 = (lo, 2\", 3\", 4\", 5\", 6\") . In this way, generally, the nearer a joint is to the base the finer the discretization resolution is for the corresponding joint angle. Instead of having a uniform or a heuristic resolution along each configuration coordinate, an optimal discretization can be calculated. Therefore, the resolution along each coordinate is set according to the maximum movement of the robot endeffect at each step the robot moves along this coordinate. The result of this discretization is illustrated in Figure 3b. Analytically, this can be achieved by setting * Here, denotes the next smaller integer of x. where 1, is the distance between the center of joint i to the farthest point the endeffect can reach, and MaxMove is a pre-set distance the robot may move at one step along the coordinate [Qir196b].~ Altogether, the optimal discretization results in Cartesian movements Ax, of joint i which meets the condition Ax,,,, I MaxMove, where Ax,,, = max(hr, , V i }, For MaxMove = 10 mm of a Puma260, the optimal discretization equals to Aq = (0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000368_rnc.4590040110-Figure13-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000368_rnc.4590040110-Figure13-1.png",
        "caption": "Figure 13. Comparison of frequency response bounds for nominal and MSW compensation - longitudinal axis",
        "texts": [],
        "surrounding_texts": [
            "If a crossfeed is doing its job properly, then the off-axis frequency responses of the family of configurations will be substantially attenuated over the frequencies of concern \u2018w i \u2019 . The array of off-axis response magnitudes for each of the \u2018j\u2019 configurations are obtained at these \u2018i\u2019 frequencies and denoted by Moff,i,j in dB. The magnitude of the off-axis response is conveniently normalized relative to a baseline on-axis response to yield a measure of relative decoupling. The choice of which configuration to use for this baseline is arbitrary since we are mostly concerned with comparative improvements in decoupling for various strategies. In this paper the nominal configuration (# 1) is established as the baseline configuration, and is denoted by Mon,i,l dB at each frequency \u2018w i \u2019 . The decoupling at each of the five frequencies \u2018averaged\u2019 over all of the configurations is expressed (for each axis) by the metric: 5 5 JAVG = C C (Mon,i,l -MOB,; , j ) / 2 5 dB C o n f j = l w I = 1 The decoupling performance results for the uncompensated case and the two crossfeeds of the previous section (static and low-order) are shown in Table 11. The baseline pitch decoupling for lateral inputs with no crossfeed is obtained by using the data from Figure6 for the uncompensated off-axis response M0ff,i, j . The on-axis roll response data from configuration # 1 (Mon,i , l) is obtained from Figure 3. Using these data, the baseline decoupling with no crossfeed is JAVG, u~~~~~ = 29.8 dB, or a linear attenuation factor of roughly 30 dB. In other words with no crossfeed, the pitch response coupling is about 3 per cent of the on-axis roll response in the frequency range of concern. This high level of decoupling reflects the action of the mixer box (included in the bare airframe model) which decouples the control moments. The mixer box is effective for the pitch axis which has low relative aerodynamic damping specific moments owing to the high relative pitch inertia. The static gain crossfeed G( # 1 static) does little to further improve the decoupling. If nominal crossfeed compensation G k ( # 1 ~ 0 ) is implemented, then the Moff,i, j values would be taken from the plots in Figure 9 instead of from Figure 6 to compute JAVG, # 1 LO = 43 - 7 dB. There is a large improvement in decoupling when the low-order fit to the \u2018ideal\u2019 nominal crossfeed is used. The results for the roll axis decoupling for longitudinal inputs are also shown in Table 11. Here the uncompensated coupling is significant (15-0 dB = 18 per cent owing to the lower roll 174 D. R. CATAPANG. M. B. TISCHLER AND D. J . BIEZAD axis inertia. The static crossfeed solution actually worsens the overall cross-coupling (12.2 dB) while the nominal lower-order crossfeed shows an improvement in decoupling JAVG = 17-8 dB (13 per cent), although the coupling is still significantly above desired levels (25 dB z 5 per cent). This metric is easily extended for a large number of configurations and strategies. A computer program was developed to automatically scan configuration frequency files and tabulate the results. A single value of the metric may even be used (cautiously) to summarize decoupling performance for more than one axis (the average, for example). The safest procedure, however, is to apply the metric individually to each degree of freedom. Choosing a strategy. In the previous examples, the \u2018target\u2019 crossfeed values used in the fitting process were chosen based on the \u2018ideal\u2019 crossfeed solutions for configuration # 1 (nominal). The average decoupling performance metric using this strategy, JAVG, # 1 LO, was improved relative to the static crossfeed, JAVG, # 1 Static for both the pitch and roll cases. Many heuristic strategies for selecting appropriate target values were also considered in this study. Referring to Figure 11, one obvious method would be to select target values based on the average or centroid of each crossfeed template. The heuristic strategy recommended in this paper, which balances simplicity of implementation with excellent decoupling performances is called \u2018mean-square weighting\u2019 (MSW) decoupling. The first step in this strategy is to find a \u2018target\u2019 crossfeed point (gainlphase location) on each template that is a weighted-average which favours a cluster of points within a given template. Then, the lower-order fitting technique is used to design a crossfeed to best match these target points. Weights in the fitting program are chosen so that the crossfeed design matches more closely the target points associated with the templates having a smaller size - where the proper choice of desired target value is well defined and should be ensured. When the template is large in size, the weights are reduced since the exact location of the crossfeed is not as well defined. This is illustrated in Figure 12 for a set of artificially constructed templates. To implement the MSW strategy, first determine the average gain and phase point (dB and degrees) for each template I G(avg) I and L G(avg). The difference between the average gain ROBUST CROSSFEED DESIGN FOR HOVERING ROTORCRAFT 175 and phase of a template in the template gives the the template frequencies ~ and the \u2018ideal crossfeed\u2019 gain and phase for each configuration ( j ) gain and phase deviations for the template \u2018i\u2019. Now looping over all gives arrays as a function of i and j : A M i , j = ( l G ( # j ) l - IG(avg)Ili dB (13) (14) A4i , j = ( L G( # j ) - L G(avg))i degrees The mean-square weight for the point (i,j) is defined as: 11 1 w. .- \u201d\u2019 - min [ \u2019\u2019 [AM?, j + 0.017 45(A4i, j)\u2019 where the weighting of 7.6\u201d of phase to 1 dB is adopted as recommended in practice. l7 The MSW \u2018target\u2019 crossfeed point for the template \u2018i\u2019 is defined as: C Wi.j Conf j The lower-order \u2018fit\u2019 to the above \u2018target\u2019 crossfeed points is found by using the following weights in the NAVFIT program at frequency \u2018i\u2019: 11 1 0 k a g . i + 0.01745(a2 phase, i) 176 D. R. CATAPANG. M. B. TISCHLER AND D. J. BIEZAD where &as.; =- c 1 ( 1 G ( # j ) I - I G(avg) 1): and &ase,i 5 C O n f j = l , S c [ L G ( # j ) - LG(avg)J? (18) A sample calculation of weights is provided in Table I11 for the artificial data in Figure 12. Template 2 has the highest relative weighting because the template points are more highly clustered than the other templates. 1 5 C o n f j = l , S =- ANALYSIS Mean-square weighted decoupling improvement The \u2018mean-square weighting\u2019 (MSW strategy) was applied to design pitch and roll crossfeeds which are robust for all five configurations. The following low-order MSW crossfeeds are obtained: - 0*0272(24.5) &loo (4 * 62) w., (MSWLO 1 = (19) ROBUST CROSSFEED DESIGN FOR HOVERING ROTORCRAFT 177 These crossfeeds may be compared with those in Table I which approximated only the nominal 'ideal' crossfeed. The weighting did not change the pitch decoupling crossfeed significantly, which already exhibited satisfactory decoupling. The MSW roll decoupling crossfeed has been considerably adjusted relative to the earlier result. The performance improvement of the three crossfeed approaches (static, nominal, MSW) are compared in Table IV. Here the results are referenced to the uncompensated decoupling performance to highlight the differences between the decoupling strategies. In Table IV a value of OdB would indicate no relative improvement over the uncompensated case. As shown before, the static crossfeed slightly improves the robust decoupling in the pitch axis, but degrades the decoupling in the roll axis. With the MSW crossfeeds, significant performance improvements are achieved. The pitch rate decoupling improves by 4-6dB relative to the nominal crossfeed, yielding an overall relative attenuation of 18.6 dB. An even larger 178 D. R. CATAPANG, M. B. TISCHLER AND D. J. BIEZAD improvement in roll rate decoupling is shown. The MSW result is 8.5 dB improved over the nominal crossfeed for an overall relative attenuation of 11 - 3 dB. Absolute decoupling of both axes (pitch axis decoupling = 48.4 dB; roll axis decoupling = 26.3 dB) are within the desired goal of 25 dB. Figures 13 and 14 show a carpet plot of the off-axis longitudinal and lateral frequency responses for all five configurations using the MSW crossfeeds. In both axes, the improved performance of the MSW crossfeeds are clearly apparent. Most of the improvement is gained for frequencies of 1-3 rad/s which is the critical range for reducing the cross-coupling impact on the bandwidth of the feedback loops. The improvement in roll axis decoupling is especially significant (20 dB) in the crossover frequency range (1-3 rad/s). Off-axis control activity commanded by the MSW crossfeed is shown in Figure 15 for the doublet input to the primary axis. The MSW crossfeeds are seen to command smooth and low bandwidth cross-coupled inputs. These commands would be practicable for implementation."
        ]
    },
    {
        "image_filename": "designv11_24_0000847_70.833184-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000847_70.833184-Figure4-1.png",
        "caption": "Fig. 4. To find the object error for object rigidly attached to D\u2013H frame k, the weighted point error squared is integrated over the object.",
        "texts": [
            " Let be the object rigidly attached to frame , and let be a possibly time-varying weighting function for which there exists some (preferably small) integer such that it can be decomposed as follows: (5) This decomposition will allow a reduction in computation by eliminating the need for online integration. The object-based measure is established by integrating the product of and over (6) where is a differential volume, area, or distance element when is a solid, surface, or curve, respectively. This concept is illustrated in Fig. 4, where is a solid. When is Euclidean distance, (6) corresponds to the object norm of Kazerounian and Rastegar [28]. Equation (6) is in general a computationally expensive calculation that cannot be performed online. This calculation has been identified as a potential drawback of Kazerounian and Rastegar\u2019s method [8], [29]. However, it will be shown below that for the given assumptions, there exists a set of integrations independent of the joint variables that can be performed only once, and the results used in lieu of integrating each time step"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003996_tase.2005.846289-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003996_tase.2005.846289-Figure8-1.png",
        "caption": "Fig. 8. Sphere coordination system.",
        "texts": [
            " To implement this algorithm, the package GAlib from MIT was used [27]. This software has a C library with GA objects. The common genetic operators, such as crossover and mutation, are defined and implemented in this package. The library includes tools for using GAs to perform optimization in C programs using any representation and genetic operators. Hence, it can be easily embedded into and can interface with specific user applications. According to (19), putting the direction vector in the following coordinate system shown in Fig. 8, we have: (20) For every element in the solution space, which is represented as two real numbers in the genome under (20), Construct a real-type genome that comprises of two real numbers and and apply (10) as the objective function for the GA module. the GA module calculates according to the mapping relationship listed in Table I for all facets in the STL model. Apply them to the objective function and the fitness value (i.e., the error, as defined in (10), can be obtained for . Evolving after several generations, when the termination condition specified by the user is satisfied, this algorithm terminates and the best genome is thus output"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002332_1.1510593-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002332_1.1510593-Figure6-1.png",
        "caption": "FIG. 6. The schematic diagram to calculate the induced magnetic flux density: ~a! the radial component of the net eddy-current density Jr8 ~b! Ampere\u2019s law for the contour ca .",
        "texts": [
            " For an accurate result in the high angular velocity region, the net magnetic flux density BZ is obtained in a lumped way, instead of solving a magnetic diffusion equation. Actually, it is very difficult to solve the magnetic diffusion equation. The induced magnetic flux density is calculated from the eddy-current density by using Ampere\u2019s law.11 Since the tangential component of the eddy-current density is expected to be smaller than the radial one in the pole projection area, it is ignored for simplicity in considering the induced magnetic flux. The schematic diagram to calculate the induced magnetic flux density is represented in Fig. 6. The radial component of the eddy current Ir8 expressed in a lumped way in the pole projection area is obtained simply from Eq. ~23! as follows Ir85adCnormBzv . ~24! Then, by assuming the induced magnetic flux intensity Hi in the electromagnet is zero, Ampere\u2019s law for the contour ca in Fig. 6~b! can be expressed as 2lgHi5Ir8 . ~25! Therefore, the induced magnetic flux Bi has the form of Simply, the net magnetic flux density BZ can be considered as the summation of the applied and the induced magnetic fluxes in a vector form as BZ5Bz1Bi . ~27! Figure 7 shows the simplified distributions of the magnetic flux density. When the angular velocity of the disk v is zero, the net magnetic flux density distribution BZ is the same as Bz since Bi50. As v increases, however, the distribution of BZ looks like the one in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002463_robot.1990.126125-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002463_robot.1990.126125-Figure2-1.png",
        "caption": "Figure 2. Serial-link manipulator",
        "texts": [
            " In the new algorithm, the operational space inertia matrix of a partial chain is propagated across a connecting joint structure using a spatial articulated transformation, and combined with the spatial inertia of the next link to form the operational space inertia matrix of the augmented chain. This recursive process begins at the base member and progresses out to the last link where the operational space inertia for the entire chain is formed. The following analysis will be based on the simple configuration shown in Fig. 2. The new recursive algorithm is valid whether the base of the chain is constrained or unconstrained, as long as the appropriate inertial properties are known at the base member. By definition, the operational space inertia matrix of an i-link manipulator, A,, is the matrix which relates the spatial acceleration of link i and the spatial force vector exerted on the tip of link i. Thus, we may write: (20) A . . - -f. ,a, - *+1, where, according to our convention, f;+l is the spatial force exerted by link i on a constraining body or link. We will begin our analysis by examining this relationship at the base of the chain shown in Fig. 2. The spatial free-body dynamic equation for an unconstrained base member (link 0) is: IOW = -f1. (21) For this same member, Eq. (20) has the form: A0 a0 = -f1. (22) These two equations imply that A0 = Io (23) for an unconstrained base, where Io is the spatial link inertia of the base member. If the base member is fixed to the inertial frame, then Eq. (23) still holds, but in this case, IO is the sum of the spatial inertia of the base member and the spatial inertia of the earth, which is considered to be infinite"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001762_s0022-460x(88)80375-4-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001762_s0022-460x(88)80375-4-Figure2-1.png",
        "caption": "Figure 2. Harmonic forces on ring and each spring when system vibrates at one of its natural frequencies.",
        "texts": [
            " The problem under consideration is a free floating non-axisymmetric ring with attached radial springs at arbitrary locations, as shown in Figure 1. A similar problem with only one radial spring attachment was formulated in a previous paper by the authors [23]. In this paper, the problem is extended by formulating it for the general case of L arbitrarily spaced radial spring attachments. The modal expansion and receptance methods are used to formulate the problem. It will be shown that effects appear that were either not found when studying a single spring attachment or could not be recognized in their general form. In Figure 2, the systems B and A, represent the ring and the Ith radial spring, respectively. The analysis is based on the assertion that the undamped natural frequencies and modes of the ring are known either by an analytical method or by an experimental procedure. It is also assumed that the radial springs are attached to the neutral axis of the ring and RINGS WITH RADIAL SPRING ATTACHMENTS 549 the ring by itself is axisymmetric. The interaction forces between the ring and radial springs, when the system is vibrating at one of its frequencies, are harmonic forces, F:1 e jw \" in the radial direction. Displacements II: and lie are in the z and e directions. The radial springs attached to the ring can be replaced by L harmonic radial forces, as shown in Figure 2. For the ring, the radial displacements and the forces are related by 11: 1 f311 f312 f3IL F:1 11:2 f321 F:2 \" z3 f331 F:3 (1) lI:L f3L1 f3LL F:L where f3il is the receptance of the ring [23] (a list of nomenclature is given in Appendix B). The displacements and forces of the grounded springs are related by { \": 1 } rail1I.:2 = \":L \u00b0 \u00b0 ]{ -F:t} -F:2 al-L -1:L ' (2) where all are the receptances of the grounded springs. Both matrices are symmetric and only the diagonal terms of [a] are non-zero. At the point of contact, two conditions are already enforced in equations (1) and (2), namely the force and the displacement continuity conditions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000424_3.21149-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000424_3.21149-Figure1-1.png",
        "caption": "Fig. 1 Distributed parameter autonomous system consisting of a rigid hub with four cantilevered flexible appendages.",
        "texts": [
            " For a distributed parameter system the dynamics are described by a hybrid set of ordinary and partial differential equations. For such a system, the sorting out of the maximum invariant set is not a trivial task. In such a situation it is useful to apply the theorem in Ref. 1 so as to comment on the asymptotic stability of the system. The distributed parameter system consisting of a rigid hub with one or more cantilevered flexible appendages has appeared in the technical literature quite frequently (see Refs. 4, 5, 6, and 7). The system described in Fig. 1 consists of four appendages that are identical uniform beams conforming to the Euler-Bernoulli assumptions. Each beam cantilevered rigidly to the hub is assumed to have a tip mass. The motion of the system is confined to the horizontal plane and the control torque is generated by a single-reaction wheel actuator. Under the assumption that the system undergoes antisymmetric motion with deformation in unison (see Fig. 2), a class of rest-to-rest maneuvers was considered in Ref. 4. For the particular Lyapunov function considered, the best choice of the control input only guaranteed the negative semidefiniteness of the derivative of the Lyapunov function"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001378_0020772021000046289-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001378_0020772021000046289-Figure1-1.png",
        "caption": "Figure 1. Coordinate systems.",
        "texts": [],
        "surrounding_texts": [
            "The core of a FL controller is set of the FAM rules that correlate a fuzzy input set to a fuzzy output set of the FL controller. These rules establish linguistically how the control output should vary with the control input. A FAM rule is a logical if\u00b1then type statement: such as `if these antecedent components (group of fuzzy inputs) occur then this consequence (fuzzy output) should be used\u2019. Given a set of control inputs, the controller applies appropriate rules to generate a set of control outputs. The FAM rules can be derived based on one\u2019s sense of realism, experience and expert knowledge about the process. Fuzzy set and fuzzy logic theories are applied to quantify the control inputs, FAM rules and control outputs. Usually, a human operator uses the di erences (errors) between the system outputs and the desired values and the rates of changes in the errors as the antecedents to derive the consequence based on the knowledge (not necessarily very precise) about the process from the experience. This type of control strategy is very simple and generic. E ective control actions can be generated very quickly. Humans have been using it e ectively for a very wide range of processes or systems for a long time. The process considered in this paper is the dynamic positioning of a drill ship in an environment with a mean current under the controlled actions of rudder angle \u00afR, increase in thrust of main propeller TP and lateral bow thrust TB. Two coordinate systems (frames) are used to describe the motion of a drilling ship in the horizontal plane (\u00aegure 1). Frame O \u00a1 xoyo is \u00aexed at the centre of gravity of the ship and Frame O \u00a1 xy is the ground-\u00aexed coordinate system. With use of the concept of state space representation of a system, the position and orientation of the ship is uniquely determined by \u2026xg; yg; \u00c1; u; v; r\u2020 referred as the state space variables, where xg, yg are the x- and y-coordinates of the ship\u2019s centre of gravity in the ground-\u00aexed coordinate system O \u00a1 xy, \u00c1 is the yaw angle (or heading angle) of the ship, the angle between Oxo axis and Ox axis, u and v are the velocity components of the centre of gravity in Oxo, and Oyo directions, respectively, and r is the yaw rate, r \u02c6 d\u00c1=dt. The rudder angle \u00afR is measured from the ship\u2019s centre plane to the plane of the rudder, positive de\u00afection corresponding to making the ship turn right with the rudder located at the stern. The propeller thrust D ow nl oa de d by [ L ak eh ea d U ni ve rs ity ] at 0 6: 04 1 2 M ar ch 2 01 3 always points to the Oxo direction, and the bow thrust points to the opposite direction of Oyo axis. In other words, a positive bow thrust will make the ship turn right. The objective of the fuzzy logic control is to use available control devices to counteract the environmental forces and maintain the ship as close as possible to the desired position \u2026xd; yd \u2020 and heading \u00c1d. The FL controller receives the measurement of the state space variables \u2026xg; yg; \u00c1; u; v; r\u2020, compares them with the desired values and generates the control commands. The present FL controller is designed to mimic a human operator. A human operator usually would observe the di erences between the state space variables of the ship and their desired values relative to the vessel\u00aexed coordinate system. We therefore use the following quantities as the inputs to the FL controller: . \u00a2y \u02c6 \u2026xg \u00a1 xd \u2020 sin \u00c1 \u00a1 \u2026yg \u00a1 yd \u2020 cos \u00c1: o set of the ship relative to the desired position in the ship-\u00aexed system; \u00a2y is positive when the desired position is on the starboard of the ship and is negative when the desired position is on the port side. . \u00a2\u00c1 \u02c6 \u00c1 \u00a1 \u00c1d: angle between the actual heading \u00c1 and the desired heading \u00c1d. . r: yaw rate. . R\u00c1 \u02c6 ~R \u00a2 ~\u00c1d: projection of the vector of the distance from the centre of gravity to the desired position onto the direction of the desired heading. ~R \u02c6 \u2026xd \u00a1 xg; yd \u00a1 yg \u2020 is the distance vector from the centre of gravity to the desired position; ~\u00c1d is the unit vector in the direction of the desired heading, and R\u00c1 is R\u00c1 \u02c6 \u2026xd \u00a1 xg \u2020 cos \u00c1d \u2021 \u2026yd \u00a1 yg \u2020 sin \u00c1d. . Vd \u02c6 \u2026 ~Vd \u00a1 ~Vg \u2020 \u00a2 ~R=j ~Rj: projection of the relative velocity of the desired position to the ship\u2019s centre of gravity onto the straight line from the centre of gravity to the desired position. The quantity re\u00afects how fast the ship approaches the desired point. When the coordinate system is the ship-\u00aexed coordinate systern and ~Vd \u02c6 \u20260; 0\u2020 then, Vd \u02c6 \u2026 ~Vd \u00a1 ~Vg \u2020 \u00a2 ~R j~Rj \u02c6 \u00a1 ~Vg \u00a2 ~R j~Rj \u02c6 \u2026u cos \u00c1 \u00a1 v sin \u00c1\u2020\u2026xg \u00a1 xd \u2020 \u2021\u2026u sin \u00c1 \u2021 v cos \u00c1\u2020\u2026yg \u00a1 yd \u2020 \u2026xg \u00a1 xd \u20202 \u2021 \u2026yg \u00a1 yd \u20202 q : The above \u00aeve quantities are normalized as \u00b7\u00a2y \u02c6 \u00a2y YL ; \u00b7\u00a2\u00c1 \u02c6 \u00a2\u00c1 \u00c1L ; \u00b7r \u02c6 r rL ; \u00b7R\u00c1 \u02c6 R\u00c1 RL and \u00b7Vd \u02c6 Vd VL \u20261\u2020 using corresponding scaling factors YL, \u00c1L, rL, RL and VL whose values are to be chosen based on particular process. Similarly, the three control outputs, \u00afR, TP and TB are normalized as \u00b7\u0304 R \u02c6 \u00afR \u00afRL ; \u00b7TP \u02c6 TP TPL ; \u00b7TB \u02c6 TB TBL ; \u20262\u2020 where \u00afRL, TPL and TBL are scaling factors. The normalization makes the design of the FAM rules easier because it allows use of the same ranges of fuzzy sets and membership functions for di erent normalized inputs or outputs, and the outputs of similar e ects may be derived using the same FAM rules. Another advantage of the normalization is that the same FL controller developed in the normalized space can be easily implemented in di erent vessels by applying the simple scaling factors. Therefore, the fuzzy control of the vessel will thereafter be dealt with in the normalized space for the rest of the paper. To generate control commands, the FL controller proceeds through the following steps (Kosko 1992 and Parsons et al. 1995)."
        ]
    },
    {
        "image_filename": "designv11_24_0003930_ut.2004.1405575-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003930_ut.2004.1405575-Figure2-1.png",
        "caption": "Fig. 2 Model of Twin-Burger with 2-link manipulator",
        "texts": [
            " I , and a Resolved Acceleration Convol (RAC) method are described. Next. since the coordinate action between manipulator and AUV is required. the routing algorithm considering the dynamic manipulability of the robot is proposed. To verify the effectiveness of the RAC method and the routing algorithm computer simulation is performed. The simulation result shows the good control performance. -277- 0-7803-8541 -1/04/$20.00 @ZOO4 IEEE. 11. KINEMATICS AND DYNAMICS A. MODELING The underwater robot model used in this paper is shown in Fig. 2. Assumptions a?d symbols used in this paper are as follws: In this model, the robot base considers as the Twin-Burger. [assumptions1 1. The motion of the robot is limited in the horizontal surface, and the motion to the venical direction is supposed to be not carried out. 2. There is supposed to be a system in the stationary fluid. 3. The system is supposed to have stopped in the initial state. Er, : inertial coordinate frame [Symbols] : ith link coordinate frame (i = 0,1,2; link 0 means base) : coordinate transformation matrix from E"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002866_016-Figure10-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002866_016-Figure10-1.png",
        "caption": "Figure 10. Experimental arrangement for testing the combination of fibre and sensing polymer.",
        "texts": [
            " The first experiments rapidly showed that the attempts to measure ellipsometrically the index of water-saturated films had been unsuccessful. Hence the tests described here on index control and pH sensitivity had to be carried out with nominally dry films. To investigate index control we chose to coat the sensing material onto a fibre designed to be phase matched with a cladding index just below that of the dry undyed films as measured in Q 4. The coating index was then fine tuned by controlling the dye concentration. Figure 10 shows the experimental arrangement. He-Ne laser radiation was focused onto the cleaved end of the unclad fibre. Light was thus launched into both rod and tube waveguides, and also into unwanted modes of the inner cladding. The first mode stripper (a commercial thermoplastic with index 1.72) removed light from the tube guide and the inner cladding, so that light propagated only in the rod waveguide as the fibre entered the sensitive region. Any light coupled in that region from the rod to the tube was subsequently removed by the second mode stripper, so that the detector measured only the intensity of light emerging from the rod"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002473_s0020-7225(03)00241-6-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002473_s0020-7225(03)00241-6-Figure8-1.png",
        "caption": "Fig. 8. Comparison of r33 for different ns and m \u00bc 0:25.",
        "texts": [
            " The effect of using (6) for different values of n and the rate constitutive model (45) on true stress components are shown in Figs. 5\u20138 for m \u00bc 0:25. From Fig. 5 it is seen that r11 is symmetric relative to c, and for n \u00bc 1, r11 is bounded to E=\u00f01 2t\u00de\u00f01\u00fe t\u00de. For n < 0, r11 < 0 which is physically unacceptable. Also, from Fig. 6, for n \u00bc 1, r22 is bounded to E=\u00f01 2t\u00de\u00f01\u00fe t\u00de when c increases. In Fig. 7 s12 is anti-symmetric relative to c for all ns and coincide for n and n. For all the Cauchy stress components, there is very good agreement between Eq. (6) for n \u00bc 0, and Eq. (45). Finally, Fig. 8 reveals that r33 is symmetric relative to c while anti-symmetric relative to n. For n \u00bc 0 and the rate constitutive model, r33 is zero. The use of hypo-elastic constitutive equations for large strains in numerical applications usually require special considerations, as the strain does not tend to zero upon unloading in some elastic loading\u2013unloading closed cycles. Furthermore, they require objective rate tensors and incrementally objective algorithms for numerical integration. Hyper-elastic constitutive equations, on the other hand, do not require these considerations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000944_s0094-114x(96)00075-4-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000944_s0094-114x(96)00075-4-Figure4-1.png",
        "caption": "Fig. 4.",
        "texts": [
            " Based on the axodes, we discuss the instantaneous geometrical properties of a point trajectory by means of the moving frame approach in differential geometry [24]. 6.1. The moving frame of a point trajectory in spatial motion In order to examine the geometrical properties of a point trajectory, we set up a moving frame {RA, el, e2, e3} of a point trajectory FA at first. The origin of the moving frame is at point A on FA, and the axis el is the tangent line of FA at point A. By the equation (12), there exists a unique normal line APA which passes through the instantaneous screw axis and is perpendicular to ~f), shown in Fig. 4. This line APA has so much to do with the geometrical properties of FA and axodes, that it is taken as the third axis e3 of the moving frame, which is the unit vector of line APA; e2 can be determined by the dextral set of axes el, e2, e3. That is: el - - I R ; . I - R g~lf) \"~ /~* g(3f) - - - - g(2f) e2 = -- Rr - ~ ,-,2 ] R;, x E~ fl x2 ~ f ) + x3 ~ f~ e, - f R;, x ~')1 - - 9 - ,~2 9 - (22) 426 De Lun Wang et al. where R = [a,2 + fl,2r2]l/2 ' r = (x~ + x23) l'z The differential of arc-length s of FA can be derived by the first expression of equation (22): ds = R da (23) Thus, the differential formulas of the moving frame {RA, el, e2, e3} can be written as de,ds - k"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000488_21.156590-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000488_21.156590-Figure1-1.png",
        "caption": "Fig. 1 . Planar redundant manipulator",
        "texts": [
            " In summary, the proposcd approach for the numerical solution of inverse kinematics problem has the properties that, 1) the adjustment of the damping factor, according to the proposed scheme, is theoretically justifiable, and 2) that it is computationally faster than the procedure and scheme presented in [20]. V. SIMULATION RESULTS Here, the (17) using the numerical procedure described in the previous section is first tested for a simulated three degree of freedom planar redundant manipulator [28] shown in Fig. 1. The following task is considered. Given an initial end effector position: [ . r ~ ( t , , ) . . / \u2019 ~ ( t , , ) ] = [0.991421. 1.441421] with a corresponding initial configuration (rads.) [28] specified by [ H , ( t , ) . H , ( t , ) . H i ( t , ) ] = [O .O. l . . j T O T 9 G . -O.T8539S]. I t is required to move the end effector along a straight line with constant speed for t f G 10.0 s. to the final position: [.ri ( t f ) . . , . z ( t / ) ] = [0.0.2.330] with a corresponding singular configuration given by [HI(tf)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001914_rob.10048-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001914_rob.10048-Figure7-1.png",
        "caption": "Figure 7. Schematic diagram of the general stewart platform.",
        "texts": [],
        "surrounding_texts": [
            "Based on the two-stage algorithmpresented in the last section, a computer program for solving the direct kinematics problem of the two LAP types is developed. The program is written in Fortran 77 and executed on a 650MHz Pentium III personal computer. Two numerical examples are presented in this section todemonstrate the characteristics of theproposed method. The manipulators used for the examples are the general Stewart platform and the Hexaglide, as shown in Figures 7 and 8, respectively. The geometric dimensions of the two manipulators are given in Tables I and II. The dimensions of the general Stewart platform are identical to those presented by Innocenti and Parenti-Castelli.5 Example 1. To demonstrate the efficiency and stability of the proposed method, 100 sets of driving joint variables, randomly generated within the workspace of the robots, were given the program to solve for the corresponding configuration of the moving platform. The initial approximation of PC and [R] for all of the problems was assigned to: PC = 0 and [R] =  0 0 1 1 0 0 0 1 0   where 0 is a null vector. The convergence criterion is designated to \u03b5 = 10\u22128. It turned out that all of the problems were solved without any difficulty. The average computation time for solving one problem is about 0.36 second for the general Stewart platform, and about 0.37 second for the Hexaglide. To illustrate the typical convergence property of the method, the objective function value versus the iteration steps of an arbitrarily selected problem of the general Stewart platform is plotted in Figure 9 by using linear and logarithmic scales. The figure indicates that when the feasible configuration search algorithm tends to slow down as it approaches the solution, the NR algorithm takes over and gives the quadratic convergence rate. Example 2. This example demonstrates the ability of the proposedmethod for findingmultiple direct kinematic solutions. The values of the driving joint vari- ables for the general Stewart platform are given as Qd = [7.141, 7.348, 7.141, 6.403, 9.165, 5.000]t, and for the Hexaglide are given as Qd = [9.5, 12.0, 9.5, \u22129.5, \u221212.0, \u22129.5]t. To find the multiple solutions, the programwas executed recursively 100 times, and the initial approximations of PC and [R] were randomly assigned for each execution. The convergence criterion is alsodesignated to \u03b5 = 10\u22128. The total execution time for the case of the general Stewart platform is about 27 seconds, and that of the Hexaglide is about 81 seconds. Table III shows the six distinct real solutions found for the general Stewart platform, which are exactly the same solutions reported by Innocenti and Parenti-Castelli.5 For the Hexaglide, a total of 12 distinct real solutions were found. These solutions were distributed symmetrically above and below the base plane. The six solutions that are above the base plane are given in Table IV."
        ]
    },
    {
        "image_filename": "designv11_24_0000337_20.539484-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000337_20.539484-Figure3-1.png",
        "caption": "Fig. 3 Cross section ofthe guideway",
        "texts": [
            " The dynamic simulation presented in this paper is regarded as the preparation for experiments and the results will support subsequent measurement. 11. SYSTEM CONFIGURATION The maglev system dealt with here adopts the articulated bogie system and the bogies are located between the adjacent vehicles. A bogie has four SCMs on each side shown as Fig. 1, and they are magnetized with different polarities alternately. This paper deals with the dynamics of this bogie. On the other hand, levitation coils are arranged shown as Fig. 2 and Fig. 3 on the guideway and connected with other ones on the opposite side of the guideway shown as Fig. 4. When the SCMs pass in front of these levitation coils, induced current flows in these coils and an upward electromagnetic force is generated. Manuscript received Febraury 28, 1996. Akio SEKI, Yutaka O S D A Jun-ichi KITANO, Shigeki MIYAMOTO, phone 81-3-3274-9542, fax 81-3-3274-9550. P I 0.45111 111. FORMULATION A. Electromagnetic Force The electromagnetic force FscM between an SCM coil and a levitation coil is expresseld in terms of their current Ism and Aev as"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000031_physreve.60.2404-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000031_physreve.60.2404-Figure1-1.png",
        "caption": "FIG. 1. Geometry of the corrugated surface.",
        "texts": [
            " For small deviations of the nematic director from the plane of the surface, we write the anchoring energy in the RapiniPapoular form @5# *Permanent address: Dipartimento di Fisica and Unita\u0300 INFM, Politecnico di Torino, C.so Duca degli Abruzzi 24, I-10129 Torino, Italy. PRE 601063-651X/99/60~2!/2404~4!/$15.00 V5E dr' 1 2 W~n\u2022n!2, ~1! where n is the unit vector normal to the undulating surface and r' is a generic point of the (x ,y) plane. Expressing the nematic director in terms of the zenithal angle u with respect to the (x ,y) plane and of the azimuthal angle f with respect to the grooves\u2019 direction x, n5(cos u cos f,cos u sin f,sin u) ~see Fig. 1!, and keeping in Eq. ~1! only terms up to second order in u and f , and to second order in e , we arrive at the following anchoring energy V5E dr' 1 2 W$u2@12e2 sin2~q0y !#1f2e2 sin2~q0y ! 12ufe sin~q0y !%. ~2! This expression holds for small deviations of the surface director from the grooves\u2019 direction and for small inclinations e of the undulating surface. In Fourier space, the total free-energy F of the system, which is the sum of the anchoring energy ~2! and of the bulk Frank elastic free-energy @6# Fe5 1 2E dr@K1~\u00b9\u2022n"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002386_s0301-679x(01)00116-5-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002386_s0301-679x(01)00116-5-Figure7-1.png",
        "caption": "Fig. 7. Finite difference grids.",
        "texts": [
            " 6, can be expressed as follows: Min mCE mCW mAN mAS (12) where Min is the input mass flow expressed as, Min ac0 ps RT0 (13) In a inherently compensated restrictor, the area through which air flows out should be expressed as a = pk(h + Hg) which the diameter of a feeding hole is smaller than the width of a groove. In this case that the diameter of a feeding hole is larger than the width of a groove then a = (pd 2Gw)h + 2Gw(h + Hg). Under subsonic and supersonic conditions y can be calculated as follows: (14) 2g k k 1 ( pr ps ) 2 k ( pr ps ) k+1 k , pr ps ( 2 k 1 ) k k 1 2g k k 1 ( 2 k 1 ) 2 k 1, pr ps ( 2 k 1 ) k k 1 where Pr is the recess pressure, is the gas exponent of heat insulation and g is the acceleration due to gravity. Fig. 7 shows the finite difference grids, in which the external boundary conditions at end of the axial direction are P|1,N 1 (15) The circumferential periodicity conditions and due to the symmetry geometry can be describe as P|p 6 , 5p 6 1 (16) Eqs. (6, 10, 13) and (14) with the above boundary conditions can be solved using an over-relaxation approximation method. The flow chart of the simulation procedure by RNM. is shown in Fig. 8. Integrating the pressure distribution Pi,j over the area considered, the load capacity FL was calculated where FL (Pi,j Pa) dq dy (17) The stiffness (CL) is the derivative of load capacity with respect to the eccentricity or deflection and can be described as: CL FL h (18) The air film will be identical everywhere between the shaft and bearing when there is no load"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001921_20.43960-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001921_20.43960-Figure1-1.png",
        "caption": "Fig. 1 : a switched reluctance motor outline.",
        "texts": [
            "ist of symbols A magnetic vector potential B flux density : normal component Un \" \" : tangential component Ft magnetic force G Green function J current density L self-inductance 1 boundary element shape function N finite element shape function n outside normal to the boundary T torque W weight function r boundary of the studied region Q studied region \ufffd magnetic permeability Introduction Due to the recent developments in power electronics the switched reluctance motor (SRM) appears to be an attractive solution in the domain of industrial variable speed drive applications [1). An outline of a SRM is shown on figure 1. (*) Work supported by I.R.S.l.A. III such a machine the stator pole number is different from rotor pole number and the reluctance is strongly dependant on angular position of the rotor when a current is supplied to one stator winding pair. The motor torque appears due to the tendency of the rotor to take a position which minimises the reluctance. Optimization and smoothing of this torque is obtained with an appropriate current supply sequence. So the magnetic flux distribution must be computed for every angular position of the rotor and with any winding current sequence, to be able to estimate the influence of different design parameter values on global performances",
            " l=l =1 j\ufffd 6x Sx By By J l and for the boundary contribution \ufffd 1 J1 1 SA t=1\ufffd=l[-1 \ufffdMlllmd\u00bb 1 (6n)1 Resolution (16) (17) The assembly of equations (9) and (12) associated with continuity conditions and outer boundary conditions gives a global algebraic system to be solved ; M.X=F (18) The unknowns (X) of the problem are the potential at internal nodes of saturable region s. the potential and its normal deri vative along interfaces. the potential or its normal de\ufffdivative along outer boundaries. Due to saturation effects the system (18) is non linear. A New ton-Raphson method is used to solve it . Application The described method is applied to the SRM as shown in figure 1. With such a method the stator and the rotor only have to be meshed. An example of mesh is g iven in figure 4 where the current is supplied to one stator winding pair . In 4 (a) the position of the rotor corresponds to the maximum inductance value, while in 4 (b) thi s value is minimum. No mesh distorsion occurs when the rotor position is modified and in that case the angular value only has to be changed into the dataset. In the representation of figure 4 the solid shaft has been taken into account with boundary elem ents, neglecting saturation effect in that part "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002619_095440605x31481-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002619_095440605x31481-Figure3-1.png",
        "caption": "Fig. 3 Generating a CV1-gear in a single-indexing cycle by two cutter heads, fed transversely at the same rate in opposite directions, N \u00bc 30, R/m \u00bc 11, and f/m \u00bc 12",
        "texts": [
            " The other set has inside-cutting straight edges that are oppositely inclined and generate the convex flanks with an identical tooth trace. Thus, a CV1-gear has equal circularthickness teeth, and a pair of such gears will mesh in line contact. Still, there is a possibility of crowning the teeth by making the radius to the outside cutters larger than it is to the inside cutters. One common single-indexing cycle will do if the two cutter heads were made to operate diametrically opposed relative to the gear blank as shown in Fig. 3. Generating-rolling motion is obtained by blank rotation and equal, opposite transverse feeds of the two cutter heads between their end positions (drawn in solid and dashed lines). Operation in the C01505 # IMechE 2005 Proc. IMechE Vol. 219 Part C: J. Mechanical Engineering Science at UNIV OF VIRGINIA on July 12, 2015pic.sagepub.comDownloaded from reverse sense every next run will shorten the idle time. The parameters of Fig. 3 are such that, at the end of a cutting run, the outside-cutting tools just clear the gear blank at the four edge points. The actual involute generation ends earlier, but the blank could not be indexed unless the feed continued or the cutter heads were every time retracted, which scheme is not preferred for reasons of sustaining accuracy. This sets an upper bound on the number of teeth to be cut. The limitation due to the insidecutting tools is seen to be less tight. With a cutter tip slightly narrower than that of a full cutting-rack tooth, a dedendum/module ratio of 1",
            " Three decades later, Jury [38] reinvented the same gears and their generating method and machine according to the original concept of Wingqvist, using a cutter head with one pair of cutters. The present author [14] did the same after another two decades; he retrofitted a milling machine with continuous-indexing and differential mechanisms to validate the process. In two of his more relevant patents, Forster [39, 40] presented a method of generating CV5-gears using two opposed cutter heads on two parallel spindles; one to cut the concave flanks and the other for the convex ones. For some non-obvious reason, a rather straightforward scheme \u2013 analogous to that shown previously in Fig. 3 \u2013 was not adopted. The new concept, shown in Fig. 9, was based on fixing both spindle axes and imparting to the gear blank a feed rate v \u2018into\u2019 one of the cutter heads and \u2018out of\u2019 the other, in addition to its rotation at v. The tangential velocities of the blank relative to the cutter heads will thus be different; vr+ v, and it will be in the same ratio that the two spindles must rotate. Dividing these speeds by the circular pitch gives the number of teeth passing by the cutter heads per second, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000861_177424.177987-Figure11-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000861_177424.177987-Figure11-1.png",
        "caption": "Figure 11: Splitting a chain into two separated chains",
        "texts": [
            " Then the polygonal chain corresponding to T can be morphed with O(1) parallel moves to separate it into two linearly separated su bchains joined by a single edge, corresponding to splitting T at e. Proofi The children of the spine above e are all positive. Let T. be the subtree of T rooted at the bottom of e. T, corresponds to a microstructure disk D. in the reduced form. If we erase all the microstructure disks that contain D,, we obtain a mostly-convex chain with disks at its vertices (the only possible nonconvexity is at D.). See Figure 11. We coalesce all the disks except D, together by parallel moves (because T is valid, none of the requisite edge-shortenings causes a collision between chain edges.) This essentially leaves a two-vertex valid chain, whose finite edge can be stretched arbitrarily. \u2022l Consider the case in which the sequence of weights 11,... 11 k!x)y!rl)...)rj can be split into two subsequences, each with a valid sum, without separating x and y. Without loss of generality assume the split is to the right of some 1,"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002995_robot.2003.1241715-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002995_robot.2003.1241715-Figure6-1.png",
        "caption": "Fig. 6. Model of agents",
        "texts": [
            " Analyzers for collected objects . High energy system and energy charge system for . Communication capability agents . Omni directional passive wheel The roles of the mother ship are to observe agents to notify positions of agents and to hold materials gathered by the agents. L I Ftg 5 mother ship 111. CONTROLLER OF AGENTS A. Model of Agents We need to control not only a position of an agent hut also an angle of arm in order to move to any directions when an agent is docking to the mother ship. The model of agents is given in Fig. 6, and the notations are defined as follows: (%,Yo) : Coordinate of a finger of an agent - ( X , , Y,) : Coordinate of the center of the shaft of wheels d : Length from the center of agent to the center of the shaft . D : Length from the center of agent to the finger . D2 : Length from the center of the shaft of wheels to . 0, : Angle of the shaft - el : Angle of the arm The inputs are the velocity of right and left wheels U,, U, and angular velocity of the turret u a and a control vector U is defined as U = [U,, U , , uaIr ",
            " We consider two formations to transport the mother ship with multiple agents. One is parallel formation and the other is inline formation in Fig. 7 and Fig. 8. Features of parallel formation are . increase in the loadable payload on the mother ship, improvement of the speed, . easy to control onentation of the mother ship, requirement of low stifhess of agents' hands. When agents transport the mother ship, we fix e2 = rr/2 in order to simplify the system. Then state variable, input and output of each agent defined in Fig. 6 are changed to x = [ X , , I'l,Ol]r, u = [ u r , U , ] ~ andy=[Xo,Yn]Trespectively and the state space model is modified to = h(x) . (6) When three agents transport the mother ship as in Fig. 7, A. Parallel Formation state space models of each agents are i n =g(xn)~n (7a) .tl = &-(XI )U1 (7b) i 2 = d 4 U 2 ' (7c) and constraint between agent 0 and agent 1 is ~~ and constraint between agent 0 and agent 2 is where L, is length between agents' grubbing position of the mother ship. Differentiating (8)(9) by time, we obtain a velocity constraint as J, P1 X I = o 1x21 Assuming a norm of constraint forces is small, we obtain a model introducing a constraint term as "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003978_robot.2006.1641773-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003978_robot.2006.1641773-Figure1-1.png",
        "caption": "Fig. 1. Monitoring possibilities change based on sensor panning.",
        "texts": [
            " For each factor, for each relevant range of values, we assign a cost. For instance, Table I shows an example of a set of such assignments, for a hypothetical robot. The first column (attribute) marks the sensor attribute in question\u2014distance, field of view, or panning angle. The second column (range) marks the values (ranges of values) for which we wish to specify costs. The costs are noted in the final column. Note that several ranges may be possible for each attribute, which may differ in their costs or range of values. Figure 1 shows the Type 1 robot using its single sensor at different pan angles. Each curved subregion denotes monitoring areas with different costs. The two arcs differentiate distance limitations. The numbered squares denote other robots. Figure 1-a, for instance, shows the robot panning straight ahead (at 0\u25e6). Square 1 shows a robot that is outside of the distance range of the monitoring, regardless of panning angle or field of view. The bottom right robot (square 3) cannot be monitored given the current pan and field of view. The remaining robot (square 2) is currently within the central field of view. Figures 1-b,c show all robots in the same positions, but with different panning angles for the sensor. To contrast alternative sensing possibilities, we will edges from the monitoring robot to the other (monitored) robots",
            " For instance, based on Table I, the leftmost field-of-view range covers the arc [\u221250 + \u221290,\u221230 + 90] = [\u2212140, 60] degrees. We then locate robots within each region. For each, we create a directed edge from the monitoring robot. Since the positions of vertices in the multi-graph correspond to geometric positions in the formation, the distance between to robots corresponds to the length of the line connecting them, and the angle between any two robots can be computed relative to the initial pose. For instance, In Figure 1 the left top robot is outside of the distance range of the monitoring. Thus there would be no edge from the monitoring robot to this left top robot. Figures 1-a,b, show multiple ways in which the robot ahead of the monitoring robot (and slightly to the left) can be monitored\u2014within the central field of view (when the pan angle is set to 0\u25e6) and within the left field of view (pan angle set to 30\u25e6). Thus two edges to it would be created. Finally, we compute the weight of each edge, as a function of the costs of the distance, field-of-view and pan ranges involved"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002387_robot.1997.619348-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002387_robot.1997.619348-Figure1-1.png",
        "caption": "Figure 1: Schematic representation of the NonContact Impedance Control (NCIC)",
        "texts": [
            "Rmxm are the desired joint inertia, viscosity and stiffness, respectively; and dB = 6 - e d E %m is the deviation vector between the joint angle 8 and the equilibriumjoint angle 6 a . Also, the matrix r E Wxn can filter out the joint torque in such a way that the filtered joint torque has no effect to the end-effector motion [Il l : where ( J ) + denotes the pseudoinverse of J . It should be noted that the end-effector impedance remains to be the desired one given by (2). r = I - J ( J ) + , (8) 3 Non-Contact Impedance Control Figure 1 shows a schematic representation of the non-contact impedance control. Let us consider the case that an object approaches a manipulator. In order to consider t he interaction between the whole a r m and the object without contact, a number of virtual spheres with radius ~ ( ~ ) ( i = 1 , 2 , . . . , n) are used, where each center of the sphere is located on a link or a joint of the manipulator as shown in Fig. 1 (a). Then, when the object comes into the interior of the virtual sphere i, the normal vector from the surface of the sphere to the object is given as d X p = xp - T(9u(y (9) where X:) = X o - X ( i ) is the displacement vector from the center of the sphere X ( i ) E X' to the object X , E 8'. Also the vector E 8' is defined as where IX!i)I denotes the Euclidian norm of X $ i ) . When the object is in the virtual sphere, IX!i)l is less than di). Then the virtual non-contact impedance is considered between the object and the center of the virtual sphere as shown in Fig. 1 (b), where Bp) and I(?) represent the virtual inertia, viscosity and stiffness matrices associated with the i-th virtual sphere, respectively. Using the non-contact impedance and the displacement vector d X p ) , the virtual external force FLi) E 3' exerted from the object to the center of the sphere is defined as Mii)dXii) + B P ) d X b i ) + I.6i)dXbi) F'i) = { lx$i)l < dill IX$Z)( >_ T ( i ) . (11) From (10) and ( l l ) , Fji) becomes zero when the object is not in the virtual sphere or the object exists at the center of the sphere"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003814_12.601652-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003814_12.601652-Figure1-1.png",
        "caption": "Figure 1. DMD process with active height controller.",
        "texts": [
            " Recent advances in laser-based SFF manufacturing have made possible the \u201cone-step\u201d fabrication of useful tools for the metals and plastics industries directly from metal powders. Closed Loop DMD is a synthesis of multiple technologies including lasers, sensors, Computer Numerical Controlled (CNC) work handling stage, CAD/CAM software and cladding metallurgy. Direct Metal Deposition (DMD), developed in the Center for Laser Aided Intelligent Manufacturing (CLAIM) at the University of Michigan [1], is a laser-cladding-based process that makes fully-dense freeform metallic parts layer by layer (Fig. 1). The key characteristic of DMD process, which distinguishes it from other similar laser-cladding-based SFF processes, is the integrated feed back system which actively maintains a uniform deposition thickness, thus saving precious post-machining time. In DMD process, sensors collect the light from the interaction zone and use it as a feedback to control laser power and other process parameters. Closed Loop Direct Metal Deposition (DMD) process is creating considerable contemporary interest due to its capability to deliver \u201cCAD to Part\u201d"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002211_bf01560628-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002211_bf01560628-Figure2-1.png",
        "caption": "Fig. 2.",
        "texts": [
            " Articulated lattice system expandable along two direc- tions on a cylindrical surface Let us take a pair of equally long rectilinear rigid elements, pin-jointed at 0 (fig. 1.a), sketched as in fig. 1.b and called element X. From the connecting of N elements X with turning pairs in A 1 and B 1 (i = 1, 2, 3, . . . , N), one can obtain a kinematic chain, sketched as in fig. 1.c. By varying h, the chain can undergo compaction or expansion. Let us now analyze element X. The geometric relations are ([ 12] and Fig. 2): A H = HA ' = a sen O = p sen @ B K = KB' = b sen 0 OH = a cos 0 (1.1) OK = b cos 0. 1 0 6 M E C C A N I C A One gets = arctg a sen 0 - - n sen 0 a c o s 0 + b c o s 0 and being n = a/b n - - 1 = a r c t h - - tg0 n + l (1.2) In the case of n varying from element to element, there arises the possibility of building a kinematic chain that, for a given value of h, would set points A 1 along a line of variable curvature (fig. 3) and such that the polygonal line made up of a segments joining points A 1 would draw away from the curve less than a pre-set value",
            " Because of the given size of element X 1, specified by 2, n 1, h, all the possible settings of points A ' 2 t occur in the circumference $4 having its centre in B 1 and radius 2 (same length Of all rods); likewise, all possible t points B'2 lie on the circumference S B having centre A 1 P and radius 2. It becomes therefore possible to place A 2 on any curve going through A 1 and A ' 1 and crossing circumference S A . Being length s the same for all rods, and having set the distance between A and O equal to that between O and A ' (fig. 2), the length BO is equal to OB', a n d A B = A 'B ' . Theret fore (fig. 4), having set A 2 on curve C, it shall be sufficient r t to place B 2 at a distance from A 2 equal to that between t A 1 and B] in order to obtain the peculiar ratio n 2 = a2/b 2 of element X 2. By subsequent repetition, the ratio n i of all elements of X i of the chain are brought about. For a set h, one can then set all points A i on the given curve. I f the rods are sufficiently small, points A i on the curve are so near one another that the camber among the sides of and therefore n + l 0 = arctg ~ tg q~ (1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000319_1.869880-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000319_1.869880-Figure1-1.png",
        "caption": "FIG. 1. A sketch of the fluid release mechanism.",
        "texts": [
            " Prior to starting an experiment, the glass surface was cleaned in a consistent sequence with paper toweling and two solvents, listed as being infinitely soluble by one manufacturer, namely xylene and trichloroethylene. ~A second solvent was used in the hope that it would complement the other.! Afterward the angle of decline was set and checks were made with a sensitive spirit level to ensure that the table was not tilted in the lateral direction. The oil was placed in an unattached trough, sealed at each end, with a somewhat v shaped cross section, as shown in Fig. 1. One of the edges was convex instead of straight ~the piece was actually brass edging for stairs! and this side was placed against the glass. After it was ascertained that the trough was also level, it was slowly rotated along the glass and raised so that the contents spilled out onto the plate toward the upper end. In this way the oil volume, from 40 to 120 cm3, was uniformly distributed across the plate without having any appreciable initial velocity. ~In the Silvi and Dussan V experiments the liquids were contained behind a dam that was raised at the beginning of the experiment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002571_bfb0035233-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002571_bfb0035233-Figure2-1.png",
        "caption": "Figure 2 The MIT VES-II and the impact device",
        "texts": [
            " When the manipulator moves or when it makes a contact with the environment, the resulting interaction forces and moments between the manipulator and its supporting structure are measured with the force/torque sensor. Using a computer dynamic model of a free-floating or flexible manipulator supporting structure is calculated under the measured toad. Then the platform is commanded to reproduce this spatial six degree of freedom motion in real time. The VES can also be used to emulate the motion of space manipulators in micro-gravity conditions [7]. An impact device has been built to study impulsive contacts between the system and its environment (see Figure 2). The device is a pendulum with a steel hammer head. It is equipped with a piezo-electric sensor to measure the impact force and an encoder to be able to calculate the velocity of the impact head before and after impact. In our experiments, the impact device hits the tip of the manipulator end-effector which is wrapped in a soft material. Results are presented for experiments with the manipulator base fixed and the VES emulating the motion of a flexible long-reach system. In each case, three manipulator configurations and three sets of joint control gains are tested"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003281_s00419-006-0021-0-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003281_s00419-006-0021-0-Figure5-1.png",
        "caption": "Fig. 5 Kinematical structure of the direct drive arm (DDArm) manipulator",
        "texts": [
            "1825, Jxx2 = 3.8384, Jxx3 = 23.1568, Jxy1 = Jxy2 = Jxy3 = 0, Jxz1 = \u22120.0166, Jxz2 = 0, Jxz3 = 0.3145, Jyy1 = 0.4560, Jyy2 = 3.6062, Jyy3 = 20.4472, Jyz1 = 0, Jyz2 = \u22120.0709, Jyz3 = 1.2948, Jzz1 = 0.3900, Jzz2 = 0.6807 and Jzz3 = 0.7418 kgm2; \u2022 distance: axis of rotation\u2212mass center: px1 = 0.0158, py2 = \u22120.0643, py3 = \u22120.0362, pz1 = 0.0166, pz2 = \u22120.1480 and pz3 = 0.5337 m; \u2022 length of link: l2 = 0.462 m; \u2022 angle \u03b1 : \u03b11 = \u03b12 = \u221290\u25e6 and \u03b13 = 0\u25e6. Kinematical scheme of DDArm manipulator is given in Fig. 5. For simulation a fifth-order polynomial in joint space was chosen to generate the desired trajectory. Start points are (with index i): \u03b8i1 = \u22127/6 \u2217 \u03c0 , \u03b8i2 = 269.1/180 \u2217 \u03c0 , \u03b8i3 = \u22125/9 \u2217 \u03c0 rad, and final points (with index f) \u03b8 f 1 = 2/9 \u2217 \u03c0 , \u03b8 f 2 = 19.1/180 \u2217 \u03c0 , \u03b8 f 3 = 5/6 \u2217 \u03c0 rad, with time duration t f = 1.3 s. Maximal peak velocity was \u03b8\u0307kmax = 6.29 rad/s for each link, and maximal acceleration \u03b8\u0308kmax = 14.91 rad/s2 (for k = 1, 2, 3). The assumed trajectories are similar as in [1]. For NQV and UQV cases the appropriate programs were coded in MATLAB with the fixed step size 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003162_iros.2005.1545603-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003162_iros.2005.1545603-Figure3-1.png",
        "caption": "Fig. 3. The two types of compliant sections, shown as the dotted lines. O is shown in light gray, P in dark gray. (a) A straight line compliant section. (b) A circular shaped compliant section.",
        "texts": [
            " A section i \u2208 I defined on the domain s \u2208 [is, ie] is called compliant with obstacle l = (v0, v1) \u2208 L if \u2200s | d(\u03c4(s), l) = ro. In this case l is called the compliant edge. If the closest point is either v0 or v1 for the whole domain, then this vertex is called the compliant vertex. A noncompliant section is a section where O does not touch any l \u2208 L. From the definition it follows that there are two types of compliant sections: a straight line compliant section that is compliant with an obstacle edge and a circular compliant section that is compliant with an endpoint of an obstacle edge. Both types are shown in Fig. 3. Since we assume that O and P are in contact for all s \u2208 [0, 1], we define the push plan \u03c3 for P as \u03c3 : [0, 1] \u2192 [0, 2\u03c0). The push plan \u03c3 defines the position of P for a corresponding position on the trajectory \u03c4 . Definition II.3 (push position). At position s on the path, the position of P is denoted by \u03c3(s). \u03c3(s) is an angle relative to the center of O. At position s, the world coordinates of P are: \u03c4(s) + ( cos(\u03c3(s)) sin(\u03c3(s)) ) (ro + rp). For the desired object path \u03c4 our goal is to calculate a corresponding push plan \u03c3 such that if P complies to this path, it pushes the object along \u03c4 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000803_s0924-0136(00)00614-2-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000803_s0924-0136(00)00614-2-Figure4-1.png",
        "caption": "Fig. 4. Simulation of the development of a \u00afaw (shearing and surface notch) during two-stage injection forging.",
        "texts": [
            " At the \u00aenal stage of the forming, the friction resistance of the die surfaces to the \u00afow of material is almost fully established, and it would, therefore, be dif\u00aecult to effect material deformation to enable \u00aelling of the corners. The forming-pressure is limited largely by the limitation of tool strength. Under\u00aelling, invariably, results in notches on the component surface, similar phenomenon also being identi\u00aeed during double-ended injection forging (d3 in Fig. 3). Another type of notch was also identi\u00aeed during a twostage forming \u00d0 type d4 in Fig. 3, when a preforming procedure was employed (Fig. 4). It was observed that a discontinuity of material \u00afow occurred when second-stage injection was initiated (Fig. 4(c)), as a result of which a notch was caused. It was realised that rotation of the issuing material, die-de\u00afection and unloading, temperature change during loading and unloading, would contribute to the initiation of the notch. Thinning (e1 and e2 in Fig. 3) of the \u00afange is a prevailing phenomenon during injection forging, and occurs, mostly, in injection upsetting or in the free-forming of the \u00afange. Thinning may occur asymmetrically, this occurring in the form of unevenness of the \u00afange thickness along the circumference (e3 and e4 in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002466_iros.1993.583931-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002466_iros.1993.583931-Figure3-1.png",
        "caption": "Fig. 3 Determination of relative-vector",
        "texts": [
            " Figure 2 shows tlic top view of t,hc two robots. Tlic t,lirec pliotodctcctors of t,lic stay-robot gciicratc pulscs Sensor construction for two robots after bcing hit by tlie laser beam from tlie inovc-robot. Tlie stay-robot first approxiiiiatcly deteriniiics tlie direction in which tlic niovc-robot cxists by chcclting tlie ordcr of tlicse pulses. Then, it deteriniiics the relative-vector to tlic movcrobot using the time intervals betwcen each pair of pulscs. The principle of this process is shown in Fig. 3. In Fig. 3(a), the center of tlic tlirce photodctectors A, B aiid C of the stay-robot coiiicidcs with tlie origin of the zy-axis, and, in particular, photodctcctor A is on the zaxis. Tlic move-robot is reprcsciited by tlic point D which indicates tlie rotatioil axis of the rotating laser beam. If the lascr beam rotates in the clocltwise direction in the figure, tlie order of tlie pulscs genciatcd by the photodetectors is A + B + C. In this case, the stay-robot first dctcrinincs that tlie move-robot exists in tlie shaded area of Fig. 3(b). Tlie stay-robot then deteriniiics the relative-vcctor to tlic move-robot which is indicated by the polar coordinates (I, a ) of point D. Tlic angle betwccn lines DA and DB is callcd 81 aiid tlie anglc between liiics DA aiid DC is called 02. 81 is obtained by multiplying the timc interval between pulscs of photodetectors A aiid B by the angular s p e d of rotation of tlie laser beam. 8 2 is obtained similarly by using the tiiiic interval between pulses of photodetectors A and C. We set the distance I,., to 1 between each pliotodetcctor and the origin for simplicity. Then, hold among 81, 8 2 and ( 1 , a ) . Tlie stay-robot can invcrsely cdculate the polar coordinates (1, a ) from the angles el , 82 by means of the above equations. In the following subsection, the ineasureniciit crror of the relative-vector is estimated. 3.2 Error estimation in determining the relative-vect or Deterinining the relativc-vector cquals calculating the polar coordinates (1, CY) of D in Fig.3(a). Tlie coordiiiatcs are inversely calculated by Eq. (1) using 81 aiid 8 2 . Tlicsc anglc values are obtained by multiplying tlie time interval betwccii pulses of photodetectors by the angular spccd of the lilscr beam rotating around the move-robot. In this paper, errors in tlie ii~easureinent of dl aiid 8 2 are assuiiicd to bc the inaiii errors in tlie determination of the relative-vector. Hercafter, we set tl = tan61, t 2 = tan62 for siinplicity and tlic errors includcd in these values arc iegardcd as nieasurcnieiit errors",
            " The iiiaxiiiiuln values for At1 and At2 in the problcm are obtained by multiplying the niaximun error values ep and et by the angular spced ( of tlie rotating lascr bcanl and by the dcrivative (1 / cos2 6) of tan B. (Ax, Ay) givcs the crior vcctor 1\u2019 that is included in tlie rclativc-vcctor measurcd by tlic stay-robot. Tlic inaxiniuii value T\u2018lnax for this vector is deiivcd by putting thc iiiaxiiiiuiii values of At1 aiid At2 into Eq.2; sec Fig.B for tlie maximuni iiieasurcl~~cnt crror of rclational positions. In Fig. G, tlie liorizoiital axis represents the distancc 1 of point D from tlie origin (indicatcd in Fig. 3(a)). Tlic vcrtical axis rcprcseiits the absolute value of error vcctor F:\u2019,,,,. Both axcs arc normalized by thc arm lcngth l,,,,, which supports c,zcli of the photodctectors. Oiic linc clcpcnds 011 incasnrciiicnt erior ep aiid tlie otlicr clcpcnds on el. The sliadcd arcas + indicate values calculated for all siiglcs a of the polar COO^diiiatcs of point D. The parameters used in Fig. G are sliowii in Table 1. Tliesc values (except for those notcd by *) are quoted from the spccificatioii of a rotating laser unit manufactured by a Ja"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000803_s0924-0136(00)00614-2-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000803_s0924-0136(00)00614-2-Figure1-1.png",
        "caption": "Fig. 1. Process model of injection forging of solid billets.",
        "texts": [
            "low-dependent forming defects were identi\u00aeed for the injection forging of solid billets with reference to several process con\u00aegurations with a view to de\u00aening the process range of injection forging. The mechanism of initiation of the defects was analysed based on which the identi\u00aeed defect-forms were classi\u00aeed. # 2000 Elsevier Science B.V. All rights reserved. Keywords: Metal forming; Injection forging; Forming defects Injection forging is a process in which the work-material retained in an injection chamber is injected into a die-cavity in a form which is prescribed by the geometry of the exit (Fig. 1). To-date, several names have been used to describe this con\u00aeguration \u00d0 injection forming, injection upsetting, radial extrusion, side extrusion, transverse impact extrusion, lateral extrusion and injection forging. The name injection forging is used throughout this paper. Injection forging is characterised by the combination of axial and radial \u00afow of material to form the required component-form. In the 1960s some interest was generated in injection upsetting, which was developed with a view to extruding complex component-forms"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002864_0301-679x(87)90042-9-FigureI-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002864_0301-679x(87)90042-9-FigureI-1.png",
        "caption": "Fig I Three-lobe journal bearing configuration",
        "texts": [],
        "surrounding_texts": [
            "A study of elastohydrodynamic effects in a three-lobe journal bearing\nK, Prabhakaran Nair, R. Sinhasan and D.V. Singh*\nThe effect of flexibility of bearing liner on the static and dynamic performance characteristics of a three-lobe journal bearing was studied. The threedimensional Navier-Stokes and the continuity equations governing the lubricant flow in the clearance space of the journal bearing, and the threedimensional elasticity equations governing the displacement field in the bearing liner, were solved by using the finite element method and an iteration scheme. The static and dynamic performance characteristics were calculated at various eccentricities for a wide range of values of deformation coefficients which take into account the flexibility of the bearing liner.\nKeywords: elastohydrodynamics, journal bearings, deformation\nThe current trend in the design of high speed rotating machinery is to have smaller weight and size with maximum efficiency and stability. In such applications, multilobe journal bearings are often used to obtain better dynamic stability than a system with plain cylindrical journal bearings. In the last two decades, investigations in the field of tribology have been directed to elastohydrodynamic (EHD) analysis because significant changes in the bearing performance characteristics are observed with flexibility of bearing liner under heavy load. Therefore, to obtain an optimum design of a journal bearing system, the flexibility of bearing liner must also be considered along with the bearing geometric and operating parameters, and a coupled elastohydrodynamic problem should be analysed. In the present work, the effect of bearing liner deformation on the performance of a three-lobe journal bearing system was studied.\nExtensive literature on EHD analysis is available for plain cylindrical bearings 1-4 . However, EHL data for a three-lobe journal bearing system is scarce. So, it is felt that there is a need for the recomputation of three-lobe journal bearing performance characteristics including the effect of bearing deformation.\nIn the present work, the finite element method and an iteration scheme were used to solve the three-dimensional Navier-Stokes and the continuity equations in cylindrical coordinates for the lubricant flow field and the threedimensional elasticity equations for the bearing liner deformation. The Reynolds boundary condition at the trailing edge of the positive pressure zone and the equilibrium locus of the journal centre position for the vertical load support were established using nested iterative schemes.\n*Department of Mechanical and lndustrial Engineering, UniversiO~ of Roorkee, Roorkee- 24 7667, India\nTo account for the flexibility of the bearing liner, a dimensionless deformation coefficient ~ as a function of journal speed, geometry of the bearing, viscosity of the lubricant, modulus of elasticity of liner material, and the thickness of the bearing liner, is defined. The results of static performance characteristics (load capacity, attitude angle, end leakage and power loss) and the dynamic performance characteristics (stiffness coefficients, damping coefficients, critical journal mass, threshold speed, and damped frequency of whirl) are presented at various eccentricity ratios, for ellipticity ratio ~-p = 0.5 and an aspect ratio LID = 1.0, for a wide range of values of deformation coefficients.\nAnalysis\nThe momentum (neglecting the local and convective inertia terms) and the continuity equations governing the laminar flow of incompressible lubricant in the clearance space of a finite journal bearing system are written in the following dimensionless form:\nY 30 -f-2 O0 ~2\n- a~ = V2 2 aft F R ~ - r\nwhere\n~2 aO ~2 (l)\n3 2 1 a 1 3 2 1 3 2 V2 =( a~ - - - T + ~ r r \u00f7 z ~ ao ~ + # 2 a~2 )\n1 3~ OF f 1 3 ~ - - - + ( + ~ - ) + ( =o (2)\nTRIBOLOGY international 0301-679X/87/030125-08 $03.00 \u00a9 1987 Butterworth & Co (Publishers) Ltd 125",
            "I RLIII\nThe following boundary conditions pertinent to the flow field are prescribed on nodal pressures, pressure gradients, and velocity components.\n~ = 0 a t 0 = 0 , 0 r L\n/ 5 = 0 a t E = \u00b1 /\nu = v = w = 0 a t T = R + h ~ = 0 a t r = R (3)\na = l - - - e c c o s O + - - s i n 0 a t T : / ~ # #\nF - e c s i n 0 - _ c o s 0 a t Y = R R\nThe solution of Eqs (1) and (2), using the boundary conditions (3), gives velocities u, v. w and pressure distribution p.\nUsing the finite element formulation based on Galerkin's technique and applying boundary conditions at the etement equation stage, element equations are assembled to get the following dimensionless global system equation s\n[G] ( ' I '}= (RA) + ~ {Rs} + ~ {Rw} (4)\nThree-dimensional 20-node isoparametric elements in which there are 20 nodes for velocity and 8 corner nodes for pressures are used for discretization of the positive pressure fluid film region of the clearance space. The positive pressure fluid film region of each lobe is discretized into 40 elements (10 elements in the circumferential direction, 4 in the axial direction, and one in the radial direction).\nTire complete bearing liner is discretized into 180 elements (45 elements in the circumferential direction, 4 in the axial direction, and one in the radial directkm). Eight-noded hexahedral isoparametric elements are used, in which displacements are assumed to vary linearly.\nTire following boundary condition is used for bearing liner analysis. The bearing shell is assumed to be contained in a rigid housing as shown in Fi:~ 1.\n126 June 1987 Vol 20 No 3",
            "il (Vz, l where I is the global number of nodes on the bearing and rigid housing interface.\nUsing the potential energy theorem, a set of algebraic equations is obtained in terms of nodal displacement vector { d} = [ Vo, Vr, Vz ] T for the displacement field of the bearing liner6'7 :\n[2] ( d ) = \u00a2 {F) (6)\nwhere { F) ; the force vector, is the result of surface traction force caused by hydrodynamic pressure acting on the fluid and bearing liner interface, and the deformation coefficient\nis given by\n~ = (poCoj/E) (R j/c) 3 (th/Rj)\nEqs (4) and (6) were solved itcratively. The solution scheme adopted is shown in Fig 2. The matched steady state solutions for nodal pressures, obtained for the modified film geometry, were used to determine the static and dynamic performance characteristics 5 .\nResults and discussions\nTo check the validity of the computer program and solution algorithm, performance characteristics were computed for a three-lobe journal bearing, taking the deformation coefficient ~ as zero. The static and dynamic performance\ncharacteristics obtained for Vp = 0.5, e-c = 0.3 and ~ = 0, were compared with published results 8'9. These results compare well.\nFig 3 shows the computed displacements of the interface of the fluid film and bearing liner and corresponding pressure distributions for deformation coefficients f = 0.1 and\n= 0.5 and e-c = 0.3. The pressure curves in each lobe indicate that peak pressure decreases with increase in deformation coefficient, and the positive pressure zone increases at low deformation coefficients. However, at the large deformation coefficient the positive pressure zone is reduced. A similar trend was observed by Carl 1\u00b0 in his experimental investigations for circular journal bearings.\nThe effect of bearing deformation on load-carrying capacity of a three-lobe journal bearing is presented in Fig 4. The results show that at any eccentricity ratio the value of load-carrying capacity decreases with increase in deformation coefficients, and the reductions are appreciable at large deformation coefficients. It is seen that the load support decreases by 89.8% for e-c = 0.2, 91.8% for ~-c = 0.3,\n_ _ . .\n0 O.l 0.2 0.3 0.4\n' \u00b0 \u00b0\nr-- / \\ ' o . '\nI0 o 0 \u00b0 ~ \u00a2 i\nFig 5 Effect of eccentricity ratio on attitude angle\nT R I BO L O G Y i n t e r n a t i o n a l 127"
        ]
    },
    {
        "image_filename": "designv11_24_0003205_020-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003205_020-Figure2-1.png",
        "caption": "Figure 2.",
        "texts": [
            " I 1 = j 1 + J ( A - B ) t L2 x { [ 1 + 2 R 2 + a 2 7 J 1 + [ ( R - a ) / L I 2 x ( J 1 + [ ( R + a) /LI2+-) R 2 + a 2 L ] K ( k ) 1 1-41 + [ ( R - a ) / L J 2 +2 - ( R +a)\u2018 J 1 + [ ( R - a ) / L ] Z , ( , ~ , r , 2 , k ) ] + I o L2 1594 A H Cook and Y T Chen where Io = { :R2\u20192a 5 rra Ja + [ ( a + R ) / L ] * - - d l + [ ( a - R ) / L ] * J 1 + [ (a + R ) / L ] Z + J l + [ ( a - R ) / L I 2 when a 3 R when a s R k = 1 - J 1 + [ ( a - R) /LI2 l + J l + [ ( a + R ) / L ] \u201d f f 2 = K ( k ) , E ( k ) , ll($.rr, k , k ) and I I ($rr , a2, k ) are the elliptical integrals of the first, Equation ( 9 ) is the formula for the point in the end plane of the cylinder but with the ( 1 1 ) where L is the length of the cylinder and [ is the distance of the point Q from the end plane of the cylinder as shown in figure 1 . In Heyl\u2019s experiment, the test mass was in the middle plane of the cylinder (see figure 2 ) so the attraction, according to equation ( 1 1 ) is ( 1 2 ) If ( < 0 in figure 1 , according to the superposition principle, equation ( 1 1 ) will become second and third kind respectively. superposition principle of gravitation the formula for an arbitrary point is F ~ / ~ G P = Cy( L - l, R, a 1 + Cy(l, R, a 1 FL2\u2019 = 2FL\u201d = 4GpCy(tL, R , a) . Fa/2Gp=Cy(L+IlI ,R, a ) - C y ( l l l , R , a ) . ( 1 3 ) The radial Newtonian gravitational force of any complex co-axial cylinders will not be difficult to obtain from the following sum Heyl measured the period of the torsional pendulum in the near position and far position from a pair of cylinders (see figure 2 ) . He had paid great attention to the details of his experiment, so that although it was performed a long time ago (1930 and 1942) his result is still regarded as one of the most accurate results and quoted very often in the literature. As a check on Heyl\u2019s approximate formula used in his calculations, the following comparison is an example. To illustrate the convergence of his series, Heyl calculated the attraction of a cylinder upon a point at the centre of its lateral surface, a = R = t L = 10 cm",
            " He kept eleven terms of his formula, the result is Ff\u2019/.rraGp = 1.535 5797. The radial Newtonian gravitational force 1595 According to equations (12) and (9), this number is - = t [ & K ( k ) - - E ( k ) ] Fa\u2019 2 = 1.535 5784. lraGp T JJ- 1 We notice that this result is independent of the numerical value of a and R. It is clear from equation (9) that the motion of a test particle in the field is highly nonlinear, even though the displacement is very small. Consider the equation of motion of a pendulum with the cylinders in the near position (figure 2). For simplicity the mass of the beam is neglected and the mass m of the ball is taken to be unity. In the ideal case without damping, the Lagrangian function of the pendulum is (15) where Z is the moment of inertia of the whole pendulum, T is the modulus of torsion of the filament, assumed constant with respect to 8. V ( 8 ) is the potential energy in the field produced by the cylinders and can be obtained from the result in \u00a7 2 and the geometrical relation to figure 2. Then (16) 3 = ;zi2 - v(e) --$e2 av/ae = 8GpCy(tL, R, a ) ( b f / a ) sin 8. Thus the Lagrangian equation of motion becomes Ze+~8+8GpC,(iL, R, a ) ( b f / u ) sin 8 = O . (17) The function Cy(iL, R, a ) is a function of 8. To show the nonlinear character of equation (17) when 8 is much less than 1, we expand C,(iL, R, a ) around the equilibrium point a. 1596 A H Cook and Y T Chen so that the equation of motion with damping will be z ~ i + 2 ~ t j + +*e +pe3 + ,,e5 +. . . = o where a = ~ G P (bf lao) cy(%, R, ao) Comparing the two coefficients a and P, the ratio is It is very easy to prove that so that the third term in the bracket of equation (21) is positive as well"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001812_amp-120018903-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001812_amp-120018903-Figure8-1.png",
        "caption": "Figure 8. Schematic diagram of free surface and weld pool geometry used for calculating u1 and u2.",
        "texts": [
            " A model of the welding process, in which an experimentally generated free surface was used as a boundary condition, supported the results by showing similar trends. Conclusively, free-surface deformation caused by varied gravitational orientations needs to be considered for a precise estimation of the weld-pool geometry, specifically during high-heat input welding. It is possible that the microgravity environment of space or the low gravity environment of Mars will alleviate free-surface deformation, reducing the impact of gravitational orientation on weld-pool shape. A simple geometry of the free surface and weld pool is considered (Fig. 8) to aid in support of the claim that the measured free surface at the end of the weld track is comparable to the free surface in situ. Once the arc is extinguished, the free surface will recover to a new equilibrium state in the absence of arc pressure (which earlier supported the deformation). If the solidification-front velocity can be shown to greatly exceed the free-surface-front velocity (and the distances of the two fronts from the center of the pool are of the same order), then the solidification front can be expected to overcome the freesurface front, ultimately capturing it and preserving its shape"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000386_bf00435723-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000386_bf00435723-Figure1-1.png",
        "caption": "Fig. 1.",
        "texts": [],
        "surrounding_texts": [
            "the following substitute problem subject to fo e mi_n fo(s, 9, fl) ds (16) V,q ~(o) = o, ~(se) = o. Epui(Pi(v, {t, P), 7\"min,i, Z-max,i) ~ \u2022u,i, i = 1,2 . . . . , n. (17) EpU0@, Vmax(8, P)) ~< 5uO. (18) EpUT(T(q,p) - xe) ~< ~T, 0 ~< s ~< Se, (19) where q in (19) is the solution of (12) with initial values q(0) = (t(0) and q(0) = 0. In the problem (16)-(19) we have to calculate Epui, Epuo and EpUT. The numerical calculation of the expected values is usually very difficult because ui, u0 and u r can be complicated functions of p. By means of Taylor expansion with respect to p the expectations can be determined approximatively. Since q in (19) depends on p too, the above derivatives (t (k) ok - = ~ ( t ( s ) , p ) are needed to approximate EpUT. If ~ and ft are discretized, the substitute problem (16)-(19) is reduced to a nonlinear finite-dimensional parameter optimization problem, which can be solved, e.g., by mathematical programming methods."
        ]
    },
    {
        "image_filename": "designv11_24_0003768_j.mechmachtheory.2005.10.010-Figure22-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003768_j.mechmachtheory.2005.10.010-Figure22-1.png",
        "caption": "Fig. 22. Grinding process by ball end grinder.",
        "texts": [
            " 21(b) shows the grinding process of the sun-worm tooth profile, the CBN grinder is driven by high speed motor and the movements is the same like the manufacturing process. In the abovementioned process, the fly-blade and the CBN grinder are designed according to the normal tooth profile of the sun-worm and the sun-worm tooth profile generated by conical, cylindrical and spherical rollers can be manufactured. But for the spherical roller meshing, the grinding manufacturing for sun-worm tooth profile is fulfilled by the ball-end grinder illustrated in Fig. 22. In the grinding process, the grinding speed mP = 0 at point P. This causes the grinding manufacturing problem for the spherical roller enveloping. This results in the special concern for the design of the fly-blade while manufacturing the sun-worm tooth profile generated by the spherical roller. The stationary internal gear tooth profile can also be manufactured by the method similar to that of the sun-worm tooth profile. This paper contributed to the study of the toroidal drives by focusing on the comparative study of meshing characteristics based on different meshing rollers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003136_1.2125967-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003136_1.2125967-Figure1-1.png",
        "caption": "Fig. 1 \u201ea\u2026 An overview of the high-pressure c plungers.",
        "texts": [
            " The tested lubricants in this work are a POE polyol ester oil, POE diluted with the nonchlorinated HFC hydrofluorocarbon refrigerant R-134a, the naphthenic mineral oil, and the mineral oil diluted with chlorinated HCFC hydrochlorofluorocarbon refrigerant R-22. Compressibility data for the tested lubricants are fitted to the Jacobson and Vinet model. The results for mixtures are compared with pure oil and earlier presented results from other authors. The compressibility measurements presented in this paper are done in the high-pressure chamber developed and described by Jacobson 7 and further described by St\u00e5hl and Jacobson. An overview of the high-pressure chamber can be seen in Fig. 1 a , with the high-pressure cylinder 3 and the plungers 7 in Fig. 1 b . In the compressibility test the lower plunger is fixed while the other is movable. The test lubricant is placed in the cylinder between the plungers when the lower plunger is in position in the cylinder. The sample cavity must be kept at a pressure of at least 0.7 MPa to be able to supply the oil/refrigerant sample. Therefore, the lower plunger is modified with a hole through the plunger and provided with a one-way valve also functioning as seal. This allows filling of lubricant when both plungers are in place"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002887_01483918108064817-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002887_01483918108064817-Figure1-1.png",
        "caption": "FIGURE 1",
        "texts": [],
        "surrounding_texts": [
            "FURFURAL IN BACTERIAL CULTURES 287\na c i d i f i e d s a m p l e w a s m i x e d w i t h 1 m l o f d i e t h y l e t h e r i n a c a p p e d t u b e a n d l e f t a t c o l d room ( q S C ) u n t i l t w o p h a s e s were c l e a r l y s e p e r a t e d .\ni ~ o n a g u e o u s p h a s e was d e c a n t e d i n t o a n o t h e r c a p p e d\nt u b e a n d e v a p o r a t e d a t 3 5 D C . An a p p r o p r i a t e a m o u n t o f t h i s s a m p l e w a s r e d i s s o l v e d i n t h e c o r r e s p o n d i n g m e t h a n o l s o l v e n t f o r HPLC a n a l y s i s a n d t h e o t h e r i n d i s t i l l e d w a t e r\nf o r s c a n n i n g o f U V s p e c t r o p h o t o m e t e r . A n a l y s i s b y U V S p e c t r o p h o t o m e t e r a n d HPLC -___ ___-_ -____ ----- _-____--_______--- P r e p a r e d s a m p l e s were s c a n n e d w i t h i n t h e r a n g e o f 2 1 0 nm t o 3 3 0 nm i n w a v e l e n g t h b y P e r k i n - E l m e r M o d e l 1 3 9\nUV-VIS s p e c t r o p h o t o m e t e r ( H i t a c h i , L t d . , T o k y o , J a p a n ) .\nO p e r a t i o n a l c o n d i t i o n s of HPLC ( W a t e r s A s s o c i a t e s\nI n c . , b i i l f o r d , M a s s . 0 1 7 5 7 , USA) were a s f o l l o w : c o l u m n , p - B o n d a p a k C 1 8 ; s o l v e n s , m e t h a n o l / w a t e r (100/0, 7 0 / 3 0 , 5 0 / 5 0 , 1 0 / 9 0 ) ; f l o w r a t e , 1 . 0 m l / m i n ; d e t e c t o r , U V M o d e l 4 4 0 , 2 5 4 nm; i n j e c t i o n , 1 0 ~ 1 ; t e m p e r a t u r e , room t e m p e r - a t u r e . M e t h a n o l s o l v e n t s ( f o r c h r o m a t o g r a p h i c g r a d e , M e r c k ) were d e g a s s e d a n d f i l t e r e d t h r o u g h M i l l i p o r e f i l t e r p r i o r t o u s a g e .\nG r o w t h o f P s e u d o m o n a s FS1 w a s o b s e r v e d i n t h e c u l t u r e\nm e d i u m c o n t a i n i n g y e a s t e x t r a c t a n d f u r f u r a l a s a c a r b o n s o u r c e . A s i m p l e m e t h o d t o d e t e r m i n e t h e q u a n t i t y o f f u r f u r a l a n d p o s s i b l e a m o u n t of i t s m e t a b o l i t e ( s ) i n t h i s b a c t e r i a l c u l t u r e was n e e d e d . F u r f u r a l i s a n a r o m a t i c , : o i . : pound a n d h a s U V a b s o r b a n c e a t 2 7 7 nm o f w a v e l e n g t h ( 5 ) . 'i'tie m e t a b o l i t e ( s ) w o u l d b e e i t h e r f u r a n d e r i v a t i v e s s u c h\na s 2 - f u r o i c a c i d a n d 2 - f u r f u r y l a l c o h o l ( 3 ) or g l u t a m a t e w h i c h d o e s n o t h a v e U V a b s o r b a n c e ( 6 ) .\nI f m e t a b o l i t e s a r e f u r a n d e r i v a t i v e s , i t i s c e r t a i n",
            "288 HANG, HAN, AND C U E\nt h a t i t h a s UV a b s o r b a n c e . I n o r d e r t o r e s o l v e a b o v e p r e s u m p t i o n s U V s c a n n i n g w a s c a r r i e d o u t a n d t h e r e s u l t s a r e s h o w n i n F i g u r e 1.\nT h e p e a k a t 2 7 7 nm w a s t h e f u r f u r a l (A,B) a n d s h o w e d\nt h e g r a d u a l d e c r e a s e ( A , B , C , D ) . I n a d d i t i o n a new p e a k a t 2 4 5 nm a p p e a r e d a f t e r 1 2 h r o f g r o w t h a n d t h e r e a f t e r d i s a p p e a r e d . H s u b s t a n c e w h i c h p e a k s a t 2 4 5 nm ( E 2 4 5 ) s eems t o b e a m e t a b o l i t e f o r m e d e x t r a c e l l u l a r l y . T h e y u r i f i e d E 2 4 5 s u b s t a n c e w a s i d e n t i f i e d a s 2 - f u r o i c a c i d when c o m p a r e d w i t h a s t a n d a r d 2 - f u r o i c a c i d b y I R s p c c t r o - p h o t o m e t e r . 2 - V u r o i c a c i d w a s p r o d u c e d d u e t o t h e o x i d a - t i o n o f f u r f u r a l b y a n e x o e n z y m e ( 7 ) .\nFor s i m u l t a n e o u s d e t e r m i n a t i o n o f f u r f u r a l a n d\nU V s c a n n i n g s p e c t r a o f c u l t u r e f i l t r a t e d u r i n g t h e g r o w t h o f P s e u d o m o n a s FSl. ( A ) a p e a k of f u r f u r a l i n c u l t u r e m e d i u m , ( B ) ( C ) p e a k s a f t e r 1 8 h r a n d 3 0 h r of g r o w t h , r e s p e c t i v e l y , ( D ) d i s a p p e a r a n c e o f t w o p e a k s a f t e r 5 5 h r of q r o w t h .",
            "FURFURAL IN BACTERIAL CULTURES 289\n2 - f u r o i c a c i d i n b a c t e r i a l c u l t u r e s , c u l t u r e f i l t r a t e w a s p r e p a r e d t o b e a n a l y z e d b y HPLC w i t h d i f f e r e n t m o b i l e p h a s e s o f m e t h a n o l a s s h o w n i n F i g u r e 2 .\nF u r f u r a l a n d 2 - f u r o i c a c i d c o u l d b e s e p a r a t e d w e l l\nw h e n s o l v e n t s o t h e r t h a n a b s o l u t e m e t h a n o l were u s e d . T h e o p t i m u m c o n d i t i o n f o r r e t e n t i o n t i m e o f e a c h m o b i l e p h a s e o c c u r r e d o n l y w h e n 7 0 % m e t h a n o l w a s u s e d .\nT h u s , t r a n s f o r m a t i o n o f f u r f u r a l i n t o 2 - f u r o i c a c i d\na n d t h e u t i l i z a t i o n o f 2 - f u r o i c a c i d d u r i n g t h e c u l t u r e\nd e v e l o p m e n t o f P s e u d o m o n a s F S 1 c o u l d b e d e t e c t e d b y HPLC, u s i n g 7 0 % m e t h a n o l s o l v e n t .\nP a i r s o f p e a k s i n c h r o m a t o g r a m s i n F i g u r e 3 d e m o n -\ns t r a t e d t h e g r a d u a l i n c r e a s e a n d d e c r e a s e o f 2 - f u r o i c\n1 2 1 I\nI I I I J 0 4 8 12 16\nMINUTES\nF I G U R E 2\nC h r o m a t o g r a m s o f 2 - f u r o i c a c i d ( 1 ) a n d f u r f u r a l ( 2 ) a t v a r i o u s c o n c e n t r a t i o n s o f m e t h a n o l s o l v e n t . ( A ) 1 0 % m e t h a n o l , ( B ) 5 0 % m e t h a n o l , ( C ) 7 0 % m e t h a n o l , (D) 1 0 0 % m e t h a n o l ."
        ]
    },
    {
        "image_filename": "designv11_24_0003956_tia.2005.863899-Figure18-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003956_tia.2005.863899-Figure18-1.png",
        "caption": "Fig. 18. Flux distribution of synchRel under the no-load condition (with flux barriers).",
        "texts": [
            " The readings near the no-load condition have been considered in order to minimize the effect of flux barriers, as the effect of flux barriers was not modeled initially. This can be explained using stator voltages and currents under no-load (VtnL and IanL, respectively) and full-load (VtfL and IafL, respectively) conditions are shown in Fig. 6. For a synchronous machine under the no-load condition, \u03b4nL is low. With the polarized section of the rotor lying almost right below the poles of the rotating magnetic field, the influence of flux barriers is minimal (compare Fig. 17 with Fig. 18). In the case of the synchRel, the sample calculations of case 1) k = 2 and m = 1 are given as follows: L0 and L2 can be obtained by considering fundamental space harmonic. Using (15) and (16) Ld =Ll + 1.5[L0 + L2] Lq =Ll + 1.5[L0 \u2212 L2] (17) where L0 = 2\u03c0\u00b5orlaog(a2 1s/2) and L2 = 2\u03c0\u00b5orla2g(a2 1s/4). Substituting the values of various quantities in (17), we have[ 0.2158 0.0188 0.0779 0.1566 ] [ D Q ] = [ 342.4 172.5 ] . (18) Solving (18), we have d = 1 D = 0.6418 mm q = 1 Q = 3.0724 mm. (19) A similar procedure has been adopted to compute the effective air gaps of the synchronous motor when run as a synchRel (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002131_0094-5765(87)90031-2-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002131_0094-5765(87)90031-2-Figure1-1.png",
        "caption": "Fig. 1. A schematic diagram of the space station supported tethered subsatellite system with threedimensional offset of the attachment point and thruster-momentum wheels control.",
        "texts": [
            " of ordinary and partial nonlinear, nonautonomous and coupled differential equations that account for: (1) three-dimensional rigid body dynamics (librational motion) of the station and subsatellite; (2) swinging inplane and out-of-plane motions of the tether of finite mass; (3) offset of the tether attachment point from the space station's centre mass as well as controlled variations in it; (4) transverse vibrations of the station; (5) longitudinal and transverse vibrations of the tether; and (6) external forces due to aerodynamic drag and solar radiation effects. The Lagrangian formulation procedure is adopted in deriving the equations of motion. Figure 1 shows the schematic diagram of a two body tethered system with an offset of the attachment point denoted by the vector dA. The offset is measured relative to the centre of mass of the plate. The magnitude and direction of the offset can be varied by means of the boom-trolley arrangement. The boom and trolley masses, being small compared to that of the platform, are neglected. The librational motions are measured from the orbital frame F0 to the body frames Fa, Fb, and F~ attached to the station, subsatellite and tether, respectively as shown in Fig. 1. As the mass of the station is much larger than that of the tether and subsatellite, the overall centre of mass is considered coincident with that of the station. The system under consideration has nine generalized coordinates: three corresponding to the platform librations (,,a, pitch; /?A, yaw; YA, roll); three representing the subsatellite rotations (~B, pitch; /~B, yaw; ~'B, roll); two defining the inplane (~c) and out of plane (~c) swing angles and one corresponding to the instantaneous length of the tether (7)",
            " Controllability of the system was established by a numerical technique that utilizes the Householder's transformation [2]. The aforementioned linear, coupled, nonautonomous equations can be written in matrix form as ~c=Ax+ Bu, where x is the (n x 1) state vector made up of the six generalized coordinates and their corresponding velocities, and u is the (r x 1) control vector, corresponding to forces from the three orthogonally placed thrusters and moments from three momentum wheels as shown in Fig. 1. A and B are the system characteristic and control influence matrices, of di- (a ) 2 4 2O 1 6 g - b 1 2 \u2022 8 4~ 4 0 -4 I 0 A b -I -3 -4 1 5 A 1 0 5 0 S at eL Li te p ar am et er s dx A = 2 0 m dy A : 2 0 m tiz zy = 2 0 m P ~ = lO O m PB = '} 2 0 m T et h er p ar am et er s in = lO O m = 0 .0 1 In tt io L co nd iti on s 0 4 (0 } = 0 ,~ (0 ) :0 ,% (o } = # ,~ to )= o T A ( O ) = y ~ ( O ) = 0 a c (0 ) = 0 .0 1 , a c' (O ) = 0 7\"c (0 ) = yc '(O ) = 0 ,~ ( 0 )= ~ '( 0 )= 0 I I 1 0 2 0 8 ( ro d io n s) Fi g"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002049_ivs.2002.1188016-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002049_ivs.2002.1188016-Figure5-1.png",
        "caption": "Fig. 5. Kieneke model - longitudinal force - dry asphalt",
        "texts": [
            " This formulae is a reference in wheel-ground contact forces estimation domain. The formulae uses longitudinal slipping to determine longitudinal forces by: and side slip angle to calculate transversal force: Iv. MODELS COMPARISON A . Methodology To compare the different models, the first step is to generate forces for the seven ground types over the plan P defined by: P=gl=[-1;1] ,6=[-10;10] (15) where side slip angle is in degrees. hypothesis of constant load F, = 4500 N . 4 for longitudinal force and figure 5 for transversal force. hy direct difference. All simulations are done with MATLAB software under Results of simulation for dry asphalt is shown on figure When totality of forces is generated, comparison is made Kiencke and Ben Amar models are directly compared. Then they are compared to Pacejka model. This could shown adaptability of the two first models to \"magic formulae\". To do this comparison, \"magic formulae'' coefficients are identified with optimisation methods such as gradient or simplex"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003361_j.jmatprotec.2004.12.017-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003361_j.jmatprotec.2004.12.017-Figure2-1.png",
        "caption": "Fig. 2. (a) Contact area in flange forming. (b) A sector of contact between the tool and the tube.",
        "texts": [
            " This is changed after the tool continues to be pushed outwards until it leaves that contact finally at step 7. Stage 3 (steps 9\u201310): at which the tool reaches its end contact with the specimen. The area of contact decreases until reaching zero at the end, leaving the flange. To determine the contact area during the indentation phase o a all geometry of the specimen other than contouring of the top surface. The process of deformation, the contact area between the forming tool (ball) and the workpiece in flanging of tubes are shown in Fig. 2a and b. Assumptions were made to simplify the calculation as follows: the centerline of the ball coincides with the outer diameter of the tube; the thickness does not change. Consider an arbitrary portion of the deformed flange contacting with the form tool in position one. When the forming tool advances in the radial direction by the value of the outward feed, the contact area will be obtained by the tool movement path when it moves from the first to the second position. The acting contact area, however, is approximately a half segment of a sphere along arc AB at the front of the forming ball while the other half of the sphere along the arc BL at the rear of the form tool is free from contact. From Fig. 2b, BC2 = AC2 + AB2 \u2212 2AC \u00b7 AB cos\u03b8 (4) cos\u03b8 = ( AC2 + AB2 \u2212 BC2 2AC \u00b7 AB ) (5) \u03b8 = cos\u22121 { AC2 + AB2 \u2212 BC2 2AC \u00b7 AB } (6) y = AC \u2212 AC cos\u03b8 + twp (7) A o y C f the process, the movement of the displaced volume is ssumed to cause only an insignificant change in the over- C = Rwp in + Rball (8) r = (Rwp in + Rball)(1 \u2212 cos\u03b8) + twp (9) L = 2AC sin\u03b8 and C\u2032L\u2032 = 2AC sin\u03b8 + 2twp = 2(Rwp in + Rball) sin\u03b8 + 2twp (10) Area = (\u03c0 4 ) {C\u2032L\u20322 + 4(y + v)2} (11) Aactive = 0.5 (\u03c0 4 ) {C\u2032L\u20322 + 4(y + v)2} (12) where Rball, ball radius; Rwp in, inner workpiece radius; twp, workpiece thickness = flange thickness"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000602_mssp.1997.0092-Figure15-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000602_mssp.1997.0092-Figure15-1.png",
        "caption": "Figure 15. Shaft\u2013disc system and the electromagnetic exciter.",
        "texts": [
            " 12), because at those speeds, the excitation due to unbalance coincides with a natural frequency. Intersection in the positive frequency region means the excitation of a co-rotating mode. In the negative frequency region, the intersection describes a backward whirl resonance. 4.2.1.1. Measured response and the computed Campbell diagram. In this section, experimentally obtained results measured on a rotating shaft are presented. The experimental rig consists of a DC motor coupled to a shaft supported in bearings. Also, a rigid disc is fixed to free end of the shaft (see Fig. 15). Two proximity probes (90\u00b0 apart) are arranged as shown in Fig. 2 and the only excitation forces are due to the inherent unbalance in the system. The conventional and the two-sided directional Campbell diagrams are shown below in Figs 13 and 14, respectively. In this example, an experimental rig was used to demonstrate the value of the proposed method. Two plots are shown, the first one is an conventional Campbell diagram where all the information is overlaid on the positive frequency range. The second plot shows separated positive-frequency (forward) and negative-frequency (backward) vibration components and the superior resolution of the directional Campbell diagram is clearly demonstrated",
            " This is an initial implementation of the method to a more complicated system. The experimental and display routines are constantly being improved, and thus the presented example is an intermediate result and is likely to be refined in the future. In many real-world situations, a fixed-in-space excitation force is exerted on a rotating disc. This force can result from the interaction between the stator and the rotating disc, or in the laboratory it can be supplied by an electromagnetic exciter depicted in Fig. 15. A fixed-in-space, force, F0 eivt, was applied by an electromagnetic exciter. More information about the experimental set-up can be found in [11]. The experimental rig described here was used to test the proposed method for disc vibration. In this case, the disc modes for which the number of nodal diameters is greater than 1, cannot be excited by unbalance in the system, and so an external excitation has to be provided to generate a response in the required mode. The force experienced by the disc is modulated by the disc modes, thus the excitation of a specific modal pattern is achieved by the constant (DC) part of the excitation inevitably existing in the magnetic exciter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002627_bf02844050-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002627_bf02844050-Figure1-1.png",
        "caption": "Figure 1 Accelerometer impact apparatus.",
        "texts": [
            " Many of the materials used within the pitch systems are polymers and therefore have complex properties, being visco-elastic and nonlinear in nature. Accelerometer impact tests were carried out on the four surface test-beds. A Clegg impact hammer was used with a 0.5 kg cylindrical mass attached to an accelerometer (Clegg, 1976). The impact face was flat, as used in previous studies, although it has been shown that this is more susceptible to irregular contact at the edge, when the impact deviates from the normal, compared with rounder hammers (Carr\u00e9 et al., 2004). This apparatus can be seen in Fig. 1. Normal impacts were carried out from two drop heights, 0.30 m and 0.55 m. The drop heights were chosen based on previous experience of cricket pitch testing (Baker et al., 1998). For a 0.5 kg hammer, this gives a range of kinetic energies at impact of approximately 3 to 5.5 J and it is known that the loading phase of an impact is controlled by the initial kinetic energy (Carr\u00e9 et al., 2004). In comparison, the vertical component of kinetic energy for a typical fast-medium cricket ball impact is approximately 7",
            ", 1999). Each test was repeated five times. Normally, instrumentation within the Clegg apparatus samples the accelerometer signal and a digital display on the impact hammer indicates a value of peak deceleration in g (gravities). However, for these tests the raw, unfiltered data output from the hammer\u2019s linear accelerometer was amplified and fed through an analogue/digital converter (Picoscope ADC-100, 12-bit resolution), sampling at a rate of 23.3 kHz and finally stored on a laptop computer (see Fig. 1). This gave a complete time history of the acceleration of the mass during impact with the surface. A typical unfiltered acceleration signal as sampled during the testing is shown in Fig. 2(a) (from Pitch C, drop height of 0.55 m). Note: The sign convention used is positive displacement downwards and time t = 0 at the point of first contact. 122 Sports Engineering (2004) 7, 121\u2013129 \u00a9 2004 isea Knowing the velocity before impact (based on previous calibration of the impact hammer), this signal was integrated over time using a step-by-step method with time period 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001899_robot.1994.350908-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001899_robot.1994.350908-Figure2-1.png",
        "caption": "Figure 2: Grasp parameterization",
        "texts": [
            " The purpose of this search procedure is to locate points on the object\u2019s surface which are suitable places to position the robot\u2019s fingers . At each step of the search procedure, a candidate grasp is evaluated and compared to the best grasp previously located. If the grasp is superior, i t is recorded as the best grasp. Otherwise, attention advances to the next grasp candidate. The system continues searching in this manner until all eligible candidate grasps have been evaluated. Each grasp is parameterized by a line in the image (see Figure 2). This line represents the direction along which the gripper\u2019s two fingers will approach the object. The grasp line is defined by a pair of values, I and 0. I represents the distance from the center of mass of the object to the grasp line, while 0 represents the angle between the x axis and the projection of the center of mass onto the grasp line. 0 is measured with the center of mass as the origin. The search scans incrementally through the possible values for I and B within the bounding box surrounding the object"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002175_1.1515333-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002175_1.1515333-Figure1-1.png",
        "caption": "Fig. 1 Brush parameters of large diameter cup brush",
        "texts": [
            " Within the literature little is available on the characteristics of mechanical brushes, with the exception of the work of Stango et al. @2\u20134#, Shia and Stango @5,6# and Cariapa et al. @7#. The majority of this work, however, is based on circular filamentary brushes and applications within autonomous deburring and honing systems. Such brushes are designed for high speed machining operations and so they are of very limited interest to the investigation of brushes in sweeping applications where brush speeds are usually much lower. Large diameter cup brushes ~Fig. 1! are commonly found on street sweeping vehicles and Stango et al. @4# have made an initial investigation of small brushes with similar properties. The sweeping characteristics of a brush change according to the operating geometry, applied brush load, and rotational speed. Any model developed to analyze the parameters of a brush must therefore take into consideration all these aspects. Stango et al. @4# have already investigated the effect of centrifugal forces, although the characteristics of a vertically loaded rotating brush do not appear to be documented",
            " This will then be used to predict the steady-state charac- Contributed by the Dynamic Systems and Control Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the ASME Dynamic Systems and Control Division, November 2000; final revision, May 2002. Associate Editor: Y. Hurmuzlu. Copyright \u00a9 2 rom: http://dynamicsystems.asmedigitalcollection.asme.org/ on 08/16/201 teristics of the brush as the tines deflect. It should be noted, however, that the model developed in this paper is for the case of the brush running horizontally on the road, i.e., w50 in Fig. 1. Adopting the notation of Stango @4#, a typical large diameter cup brush, as shown in Fig. 2, is manufactured by forcing groups of brush bristles, or tines, into a mounting board at an angle f. The tines have a common length L and constant flexural rigidity EI throughout their length. If there are nt tines mounted in a given brush, then they may be described such that ng tines are each housed in nm mounting points. The mounting holes in turn are split with nri groups of tines mounted about set radii Ri r , the free end of the tines being at radii Ri t "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003013_tia.1986.4504803-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003013_tia.1986.4504803-Figure4-1.png",
        "caption": "Fig. 4 shows the circuit of the brushless self-excited threephase synchronous motor for low-speed drive. Compared with Fig. 1, the diode which had been inserted into the statorwinding is taken away. If the voltages expressed by the following equations are supplied to the motor by a PWM inverter, self-excitation can be achieved.",
        "texts": [],
        "surrounding_texts": [
            "I. INTRODUCTION\nFOR A SYNCHRONOUS motor, the simple brushless structure is desirable from the viewpoint of low maintenance. Many brushless excitation schemes have been proposed so far. Some use the ac exciter and rotating rectifier and others use the claw pole which is excited directly from the stator side. However, all of these schemes have disadvantages: complicated structure and large machine size. The permanent-magnet type of synchronous motor with a capacity of several kW is now available due to the progress of magnet materials. However, there is a disadvantage in that the magnet can be demagnetized when the motor is started or overloaded.\nIn 1958, Nonaka had reported that it was possible to construct a brushless self-excited single-phase synchronous motor [ 1] by connecting a diode in series with the fieldwinding on the rotor and by utilizing the backward-rotating field caused by single-phase magnetomotive force.\nMoreover, in 1958, Nonaka proposed a brushless selfexcited three-phase synchronous motor [2], [3]. In the motor, a stationary magnetic field was superimposed on the revolving field by connecting a diode in series with one phase of the stator winding. The rotor has the same structure as the brushless single-phase motor. The voltage of the fundamental frequency induced in the rotor winding is rectified to yield an exciting current. Although the field current pulsates heavily, the flux linkage of the field winding is kept constant.\nPaper ^TC 85-1 1, approved by the Industrial Drives Committee of the IEEE Industry Applications Society for presentation at the 1985 Industry Applications Society Annual Meeting, Toronto, ON, Canada, October 6-11. Manuscript released for publication March 19, 1986.\nS. Nonaka is with the Department of Electrical Engineering, Kyushu University 36, Hakozaki, Fukuoka 812, Japan.\nH. Takami is with the Department of Electrical Engineering, Yamaguchi University, Ube 755, Japan. IEEE Log Number 8609874.\nWhen this motor is driven by a voltage source inverter [4], [5], the dc component of the stator current circulates through the inverter and feedback diodes, and it does not flow into the power source transformer of the converter. Therefore the transformer core is not biased by the dc current [4]-[6].\nThis motor has been applied successfully to a brushless selfexcited commutatorless motor [6].\nFurther, in 1966, it was pointed out that a brushless selfexcited three-phase synchronous motor [7] was possible by harnessing the harmonic fields produced by the squarewave voltage of the voltage source inverter-the 6th harmonic voltage induced in the rotor winding. Several years later, Chalmers et al. proposed a self-excited synchronous motor based on the same principle [8]. However, the output capacities of these motors were limited because the harmonic fields produced by the square-wave voltages were too weak.\nRecently a scheme for excitation control of a similar brushless synchronous motor which utilizes the harmonics contained in the output voltage of the sinusoidal PWM inverter was proposed [91. But the scheme did not provide for controlling the excitation. The forementioned motors do not fit in low-speed drive because the induced voltage in the rotor winding becomes lower as the speed decreases.\nThis paper presents a new method in which the higher-order harmonic component is superimposed on the sinusoidal fundamental current in the stator windings of the motor by a PWM GTO inverter. It is feasible to synthesize these waveforms using a microcomputer-based PWM technique. By this technique the control of brushless excitation can be attained, the torque characteristics are enhanced, and smooth operation becomes practicable for the low-speed drive [10], [ 1]. Experimental results are provided in the following discussion.\nII. PRINCIPLES OF THE BRUSHLESS SELF-EXCITED THREE-PHASE SYNCHRONOUS MOTOR\nA. Strategy for Superimposing the Stationary Field\nFor the normal-speed drive, the circuit of the brushless selfexcited three-phase synchronous motor, as shown in Fig. 1, has been reported [3], [4]. Diode D is inserted into one phase of the stator winding and then the stationary magnetic field is superimposed on the revolving field, so ac voltages of the fundamental frequency are induced in the field windings on the rotor revolving at synchronous speed. The voltages are half-\n0093-9994/86/0900-0847$01.00 \u00a9 1986 IEEE",
            "IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. IA-22, NO. 5, SEPTEMBER/OCTOBER 1986\nI\"ab 0\n20 _\ni1b r1:I -4-,\n20A 20\nzic f\nf% -\\ ~-r\n/1%\n12a 20AI -\nU2b 2 0 A \u00b0 \\%,-\nC 2ypiA\nwave rectified by diodes D2b and D2C connected to the field windings, and the rotor field is excited by the rectified currents. By this means the simple brushless self-excitation is achieved [2]-[5]. The structure of the rotor may be cylindrical or salient-pole [4], [5].\nIn the cylindrical rotor, the balanced two-phase or threephase field-windings are provided, and various types of halfwave rectified circuits can be composed with diodes mounted on the rotor [1], [21, [4]. This motor is driven at variable speeds with a voltage-source inverter without a feedback loop. The typical waveforms of the motor are shown in Fig. 2. The stator current il, forms a halfwave rectified current since diode D is connected to a phase-a stator winding. The rotor currents i2b and i2, flowing through diodes D2b and D2C are interrupted in a complicated way, due to the presence of fundamental voltage induced in the field-winding by the stationary field and of 6th-harmonic voltage produced by the square-wave inverter voltage.\nFig. 3 shows the load characteristics at the speed n = 1500 rpm and the terminal voltage Eab = 100 V, where I,, is the average value of the stator currents and i2a is the dc component of the phase-a rotor current. The stator current increases with the load, and consequently, dc components of the rotor field currents also increase with the load. This yields a selfexcitation effect similar to that of a dc-series motor.\nB. Strategy for Superimposing the Harmonic Field\nand c, respectively. a is the modulation index of the fundamental voltage and t is the modulation index of the v-thorder harmonic voltage. The v'-th harmonic component of the supply voltage produces a high-speed revolving field with v' times synchronous speed. So ac voltages with (v T 1) times fundamental frequency are induced in the field-windings on the rotor revolving at synchronous speed, where the minus and plus signs are applied for forward and backward rotations of the v'th harmonic revolving field, respectively. The voltages are\n848",
            "NONAKA AND TAKAMI: LOW-SPEED-DRIVE SYNCHRONOUS MOTOR\nhalfwave rectified by diodes D2b and D2C, and the rotor field is excited by the rectified currents.\nMoreover, the harmonic field superimposed on the fundamental field is almost cancelled by the ac components of the rotor currents. As the fundamental revolving field rotates smoothly by PWM technique, the torque pulsation is very small.\nIII. DRIVE SYSTEM\nFig. 5 is a diagram of the PWM GTO inverter that drives the brushless self-excited three-phase synchronous motor. The microcomputer (Intel 8086 microprocessor) generates directly the three-phase PWM waves in real time by comparing the triangular waveform with the reference waveform (expressed in (1)), which is coupled to the GTO thyristors of the inverter through amplification and isolation circuits.\nIV. EXPERIMENTAL RESULTS\nThe test motor was a 1.0-kW, 1l0-V, four-pole woundrotor-type three-phase induction motor. The experimental results were measured at no-load with a superimposed forward-revolving t-th harmonic field.\nFig. 6 shows the experimental waveforms of the brushless synchronous motor at frequency f = 5 Hz, fundamental modulation index a = 0.3, harmonic modulation index t = 0.3, and harmonic order v = 23. Each waveform shows terminal voltage Eab, stator currents i, ilb, ilc, and rotor currents i2a, i2b, i2., respectively. currents t2a, t2b, t2c, respectively.\nThe 23rd-harmonic currents produce the magnetic field rotating in the forward direction at 23 times the speed of the fundamental revolving field. Therefore the 22nd-harmonic voltages (fr =110 Hz atf = 5 Hz) are induced into the rotor windings. Fig. 7(a) gives the waveforms of both the terminal voltage Eab and the stator current il, under the same conditions as Fig. 6. Fig. 7(b) shows the expanded waveforms of Fig. 7(a) and Fig. 7(c) shows expanded waveforms of the rotor currents. These figures show clearly that the harmonics themselves are pulsewidth modulated to form quasi-sine waves.\nIn Fig. 8, Ila is the rms value of the stator phase-a current and i2, i2b and i2c are dc components of the rotor currents. From Fig. 8(a), it is clear that Ila increases with a, but i2a, i2b, and i2,. remain almost constant. On the other hand, Fig. 8(b) shows that i2, i2b, and i2 are nearly proportional to t. From both figures, the stator currents and the rotor currents can be controlled by a and t, independently.\n0.3, = 0.3, v = 23. (a) Upper: voltage Eb 50 V/div; lower: current i, 10 A/div; horizontal: 50 mS/div. (b) Upper: voltage Eab 50 V/div; lower: current i, 10 A/div; horizontal: 5 mS/div. (c) Current: 4 A/div; horizontal: 5 mS/div.\nIn Fig. 8(c), Ia, decreases linearly and i2,, i2b, and i2c decrease slightly as the frequency f increases. This is caused by the increase in induced EMF according to increase in frequency. As shown in Fig. 8(d), IIa decreases as v increases. The rotor currents decrease slightly with v increase in the region of v greater than 11, but decrease again with v decrease in the region of v smaller than 11. This means that it is undesirable to decrease the value of (v - 1)f under 50 Hz.\nBy the way, i is not equal to i2, for the following reasons. Field currents i2b and i2, are periodically interrupted due to effect of the circuit resistance and the forward voltage drop of the diode. In addition, the currents through diodes D2b and D2C are\n849"
        ]
    },
    {
        "image_filename": "designv11_24_0002162_s0022-460x(02)01256-7-Figure9-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002162_s0022-460x(02)01256-7-Figure9-1.png",
        "caption": "Fig. 9. Overlap of zones of instability for different values of internal damping (hashed zones indicate instability; ~,Civ \u00bc 0;\u2019, Civ \u00bc 1:00 10 3; m, Civ \u00bc 1:00 10 2).",
        "texts": [
            " Note that for small values of external damping Cext; the combination zones are wider than the principal zones, but as Cext increases the trend reverses (this was also noted by Mazzei et al. in Ref. [1]). Next the lab model is examined. Fig. 8 shows the instabilities for the lab model for the case where internal damping is zero (z1 \u00bc 0:0012; z2 \u00bc 0:0007). Note that in the lab model parametric instabilities due to rigid and flexible modes occur for practical rotational speeds (vo2; i.e., 5360 r.p.m.). The effect of increased internal damping is observed in Fig. 9. The figure shows an overlap of zones of instability for the following values of internal damping: Civ \u00bc 0 \u00f0z1 \u00bc 0:0012; z2 \u00bc 0:0007\u00de; Civ \u00bc 0:001N s=m \u00f0z1 \u00bc 0:0016; z2 \u00bc 0:0009\u00de and Civ \u00bc 0:01N s=m \u00f0z1 \u00bc 0:0053; z2 \u00bc 0:0030\u00de: (In Figs. 8\u201310 the external damping is given by Cext \u00bc 1:0 10 3 N= \u00f0m=s\u00de). Note that, as in the automotive example, parametric instabilities are reduced when internal damping increases. For the example, a value of Civ \u00bc 0:001N s=m \u00f0z1 \u00bc 0:0016; z2 \u00bc 0:0009; same as external damping) produces a small stabilizing effect on the system, whereas a value of Civ \u00bc 0:01N s=m \u00f0z1 \u00bc 0:0053; z2 \u00bc 0:0030; an order of magnitude higher than external damping) has a more pronounced stabilizing effect",
            " 11, Civ \u00bc 5:0 N s=m is always stabilizing. However it is conjectured that since DE shows a linear decrease (in contrast to ABC) there will be a value of v above which destabilization occurs (when DE intersects the horizontal asymptote ABC; this value is not pursued here, since it would be outside the practical range of operation). Note that it has been numerically observed that the straight-line behavior occurs when the internal damping is dominant. In the case of the lab model similar behavior was observed. It is seen in Fig. 9 that flutter instabilities diminish for increasing values of internal damping. However, destabilization occurs when a value of Civ \u00bc 0:15 N s=m \u00f0z1 \u00bc 0:0629; z2 \u00bc 0:0353\u00de; for example, is used (compare Figs. 8\u201310). Here the increase of internal damping leads to an increase in the flutter instability zone. Note that for this case instabilities occur for all points in the torque\u2013speed space that have speeds above v \u00bc 1:5 (approximately 4000 r.p.m.) which is below the upper speed boundary for this shaft and consequently can create unstable conditions inside the range of operation",
            " For this case increasing the internal damping can be destabilizing. For the lab model an overlap of flutter instability zones is shown in Fig. 14. (In both Figs. 14 and 15 external damping is given by Cext \u00bc 1:0 10 3 N=\u00f0m=s\u00de:) The cases shown are: Civ \u00bc 0 \u00f0z1 \u00bc 0:0012; z2 \u00bc 0:0007\u00de; Civ \u00bc 0:001 N s=m \u00f0z1 \u00bc 0:0016; z2 \u00bc 0:0009\u00de and Civ \u00bc 0:01 N s=m \u00f0z1 \u00bc 0:0053; z2 \u00bc 0:0030\u00de: It is seen that flutter instabilities decrease over the range observed when internal damping is increased. (This is the same trend observed in Fig. 9 which was obtained utilizing the monodromy method.) Simulations using the eigenvalue analysis and involving still higher values of internal damping led to increased flutter instabilities for this model (as shown by the monodromy method, for example, in Fig. 10). Consider the overlap plot shown in Fig. 15. In the plot P1 is a point that lies below the first critical speed and is stabilized by an internal damping increase (from Civ \u00bc 1:50 to 3:0 N s=m i.e., z1 \u00bc 0:6183; z2 \u00bc 0:3464 to z1 \u00bc 1:2354; z2 \u00bc 0:6922), whereas P2 is a point above the first critical speed that is destabilized by an internal damping increase (note however that the associated z values are probably too high to be attainable in practice)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002873_69.1.71-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002873_69.1.71-Figure8-1.png",
        "caption": "FIG. 8. The solutions \u03d5(\u03b8; 0, p) and \u03d5R(\u03b8; 0, p) for t+ < |t\u2212|.",
        "texts": [
            "13 Assume t\u2212 < 0 < t+ with t+ < \u2223\u2223t\u2212\u2223\u2223 in (3.1). Consider the reversible equation dx d\u03b8 = t+ |x | \u2212 1 \u2212 r cos \u03b8 (4.13) and let P and PR be the Poincare\u0301 maps associated to (3.1) and (4.13) respectively. Then PR(p) P(p). Proof. We consider different cases depending on the sign of p and the number of crossings of the solution \u03d5(\u03b8; 0, p) of (3.1) with the segment S, as stated in Remark 4.5. If p > 0 and \u03d5(\u03b8; 0, p) 0, then the equality P(p) = PR(p) is obvious. If p > 0 and \u03d5(\u03b8; 0, p) crosses the segment S at the points \u03b81 < \u03b82 < \u03b83, see Fig. 8, then we have \u03d5R(\u03b8; 0, p) = \u03d5(\u03b8; 0, p) for \u03b8 \u2208 [0, \u03b81] where \u03d5R(\u03b8; 0, p) is the solution of reversible equation (4.13). Since t\u2212 < \u2212t+, from Lemma 4.12 we have \u03d5R(\u03b8; 0, p) < \u03d5(\u03b8; 0, p) for \u03b8 \u2208 (\u03b81, \u03b82] and different cases arise depending on the behaviour of \u03d5R(\u03b8; 0, p). (a) If \u03d5R(\u03b8; 0, p) crosses S again, it must do at \u03b8 = \u03b82R > \u03b82 and from the nonintersecting property of solutions, we have that \u03d5R(\u03b8; 0, p) crosses S again at \u03b8 = \u03b83R < \u03b83 with \u03d5R(\u03b8; 0, p) < \u03d5(\u03b8; 0, p) for \u03b8 \u2208 [\u03b82, \u03b83], and so \u03d5R(2\u03c0; 0, p) < \u03d5(2\u03c0; 0, p) that is, PR(p) < P(p)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001469_robot.1994.351186-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001469_robot.1994.351186-Figure3-1.png",
        "caption": "Figure 3:",
        "texts": [
            " Example Using an example that was implemented in real-time, the need for normalizing the performance criteria and the effectiveness of the weighting schemes presented will be shown. In this example, the manipulator is required to track a specified trajectory without exceeding a joint limit or colliding with an obstacle. Since optimizing either the joint limit criterion or the collision avoidance criterion forces the manipulator to exceed the other monitored physical limitation, an acceptable solution can only be generated by balancing the requirements of both. Tbe workspace obstacle and end-effector trajectory for this example are shown in Figure 3. Figures 4 and 5 present the collision avoidance criterion and the joint limit avoidance criterion for the case when only a single performance criterion is optimized. From the plots, it can be concluded that optimization of a single performance criterion results in the manipulator\u2019s reaching either a joint limit or colliding with an obstacle. Figures 6 and 7 present the collision avoidance criterion and the joint limit criterion, respectively, obtained during multiple criteria optimization using the different weighting methods"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003858_j.measurement.2005.11.012-Figure11-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003858_j.measurement.2005.11.012-Figure11-1.png",
        "caption": "Fig. 11. Structure of vertical movement sensor \u2018\u2018VMS\u2019\u2019.",
        "texts": [
            " The front side of the main unit is shown in Fig. 10. A main power switch, \u2018\u2018RESET\u2019\u2019 button, \u2018\u2018VMS\u2019\u2019 connection socket, floor sensor connection socket and two digits display are placed on the front panel of the unit. 220 V power supply cord with plug, fuse socket and computer interface socket named \u2018\u2018OUT\u2019\u2019 are placed back side of unit and not shown in the figure. Upper scale value of instrument is limited to 99 cm. The structure of laser operated vertical movement sensor \u2018\u2018VMS\u2019\u2019 is shown in the Fig. 11. Here 1\u2014the height adjustable support, 2\u2014the \u2018\u2018VMS\u2019\u2019 sensor. Height of this sensor is adjustable up to 1.5 m and can be connected with a flexible cable to the main device (connection cable is not shown in the figure). The place of sensors and creating of the covering (affecting) area with beams are shown in Fig. 12. The covering area of infrared beams is drawn by hatching here. The minimum dimensions are given here. A 220 V plug cord is connected to the socket placed back side of unit to supply power to the \u2018\u2018VMS\u2019\u2019 unit"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002512_026635118700200301-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002512_026635118700200301-Figure5-1.png",
        "caption": "Fig. 5. Building formed with two 90\u00b0 modules joined on their ends.",
        "texts": [
            " It should be clear that the flexibility of the device leads to a large array of possible building forms and it is worthwhile illustrating some of these. Fig. 3. Partially unfolded and completely folded models. 132 wide, 2\u00b74m high, 3\u00b739m internal clear width, and each module would cover 1\u00b754m length. The shortcoming is that the clear head room would be just 1\u00b77m. One way in which the head room problem can be improved is to make a longitudinal field joint between two modules joined side by side as shown in Fig. 5. Clearly, the structure shown here could not be folded up without disassembly of this joint. The critical dimensions of this structure (assuming the' maximum cube side of 2'4m) would then be: width 8\u00b787 m, height 4\u00b744 m, internal clear width 8\u00b719m, head room at centre 4\u00b710 m, and length of module 1\u00b767m. The braces shown in this illustration are included to ensure that the device is a structure and not a mechanism. Earlier, it was mentioned that the element with 120\u00b0 apex angle had some intrinsically appealing properties",
            " 7 CONCLUSIONS In this paper it has been demonstrated how the well known Yoshimura buckle pattern can be adapted to form a system of demountable, portable structures. These structures can be folded through a sequence of hinges into a flat compact form which is ideal for transportation and storage. To date almost all of the development work has been performed on models. However, one structure of reasonable size has been built with 90\u00b0 elements and an element length (long side) of 1\u00b729m. The modules were made of 3 mm plywood. A building of the form shown in Fig. 5 was erected on a windy day by just an adult and a 14-year-old youth. The only problem with this particular building was that the thin ply was very flexible. Thus the outer edges of the panels tended to bend. This problem added an extra complexity to the erection and could lead to an instability in an erected structure. However, it was found that once erected and anchored to the ground, this prototype building was quite sturdy in the windy conditions in spite of the panel flexibility. I. YOSHIMURA, Y"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003130_1146816.1146830-Figure9-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003130_1146816.1146830-Figure9-1.png",
        "caption": "Figure 9. Repulsion of puck and mallett.",
        "texts": [],
        "surrounding_texts": [
            "ACM Computers in Entertainment, Vol. 4, No. 3, July 2006.\nThe gear reduction ratio of the servomotor is 410:1. The maximum torque that can be presented is 6.4 [kgf-cm]. The torque necessary for bending a joint of the arm unit is 0.69 [kgf-cm], which is a torque that can be operated easily by adults or children.\nThis RUI is a haptic display. We changed the current value input to the servomotor and measured the torque that can be presented in this system. The power supply for the servomotor drive is DC6V.\nFigure 7 shows the results of torque measurement, that the torque is proportional to the current value, and that its range is from 0.7 to 2.7[kg-cm].\nFor computer simulations of kinematics, it is necessary to solve the equation of motion via discrete mathematics. To solve the kinematics and dynamics of our physical model we use Euler\u2019s method, which is suitable for real-time processing.",
            "ACM Computers in Entertainment, Vol. 4, No. 3, July 2006.\nFor our experimental system, we developed an AirHockey game, in which the puck is represented as a thin disk that moves and rotates in a two-dimensional surface. In the simulation, there is a mallet on the circumference of the circle, the center is the root of the arm, and the radius is its length. The mallet moves according to the value of the potentiometer in the servomotor that actuates the arms of the RUI. The motor has a proportional control.\nWhen the mallet collides with the puck, haptic information is displayed to the user. The structure of this RUI arm is two orthogonal links, and it performs in a way that enables the display of one-dimensional haptic information. The reflection forces of the mallet and the puck are calculated by the simulation and applied to the set point of the servomotor.\n2\n2\ndt xdm dt dvmmaF === (1)\n2\n2 dt dI dt dIrFz \u03b8\u03c9 ==\u00d7 (2)\nThe equations of motion for the puck are arrived at by solving Eqs. (1) and (2), and Eqs. (3) to (8) are then obtained. These equations of motion are used for dynamic simulations of the puck in this AirHockey game.\ndttvxtxdttx )()()( +=+ (3)\ndttvytydtty )()()( +=+ (4)\ndt m\nFtvxdttvx \u03b8cos)()( +=+ (5)\ndt m\nFtvydttvy \u03b8sin)()( +=+ (6)",
            "ACM Computers in Entertainment, Vol. 4, No. 3, July 2006.\ndtttdtt )()()( \u03c9\u03b8\u03b8 +=+ (7)\ndt I\nrFztdtt \u00d7==+ )()( \u03c9\u03c9 (8)\nIn the simulation the puck is a rigid body, and when it collides with a wall or a mallet, it rebounds. There are various previous methods for consideration as the collision simulation algorithm for rigid body dynamics simulation systems. Barraff [1989] proposed to analytically calculate the forces between rigid bodies with a method that solves for contact forces in respect to momentum conservation and shows the characteristics of rigid bodies that don't mutually invade. However, when a lot of contacts occur at the same moment, the resulting computation takes a long time. Mirtich and Canny [1995.] reported a method in which the reaction force is calculated according to the impulsive force between two objects at the time of collision. Collisions between two objects are sequentially processed. In this method, the computation for processing one collision is not so great, but when many collisions occur within a short period, processing collisions sequentially requires a lot of computation. McKenna and Zeltzer [1990] presented a method using spring-damper models. The contact force is calculated from the amount of penetration, and hence this method is called the \u201cpenalty method.\u201d Penalty methods put multiple spring-damper models for multiple contact points, and multiple contact forces are solved at once. Because the contact force is calculated directly from the spring-damper model, the penalty method takes a linear computational complexity. Short computation times for each time step are important for real-time simulations. The Barraf, Mirtich, and Canny methods sometimes need a lot of computation, or indeed various computations, and thus aren\u2019t suitable for real-time simulations. On the other hand, penalty methods are simple and suitable for real-time simulations, so we chose a penalty method for this experimental system.\nUsing the penalty method, a high update rate of motion simulation is necessary. If the update rate is low, it causes a lot of penetration between objects, which receive a large reflection force, and the haptic information can\u2019t be stably displayed.\nLove and Book [1995] reported that an update rate of 1 [kHz] is necessary to display haptic information in a stable manner. Moreover, in a high update rate haptic simulation, the presence of a hard object becomes possible. We aimed for an update rate of 10 [kHz], with at least 1 [kHz] to stably display and present hard objects."
        ]
    },
    {
        "image_filename": "designv11_24_0001234_0022-4898(91)90013-v-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001234_0022-4898(91)90013-v-Figure2-1.png",
        "caption": "FIG. 2. D i s t r i b u t i o n s of s t resses a long t i r e - s o i l con tac t surface at s ide sl ip angle of 20\u00b0: s l ippage: - - = - 2 9 . 7 % , - 12 .2%, - . . . . . 66 .8%.",
        "texts": [
            " The time from a sampling of a certain channel to the next sampling of the next channel was 25/zs. These converted digital signals were processed by a computer program and 6 7 5 , , \\ 8 9 1. vari-speed motor, 2. rpm sensor, 3. potentiometer, 4. 3-axial force sensor, 5. test wheel, 6. linear vari-resistance, 7. 4-1ink parallelogram, 8. rpm sensor, 9. vari*speed motor, 10. carriage, I1. chain F la . 1. Schemat ic f igure of test appara tus . the results such as figures of stress distributions were shown on a CRT and drawn by an X-Y plotter. T E S T R E S U L T S As an example Fig. 2 shows the measured normal, longitudinal and lateral stress distributions along the tire-sand contact surface at three slippages of -29.7, 12.2 and 66.8% when the tire ran with a right side slip angle of 20 \u00b0. It is set that the stress is positive when the stress curve is outside of a circle which represents the tire, and it is negative in the circle. The normal stress showed a parabolic distribution along the contact surface, that is the same as past measurements. The longitudinal-tangential stress was always positive in a front region of the contact surface, but it became negative in a rear region of the contact surface when the slippage was negative"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001788_bf02459024-Figure9-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001788_bf02459024-Figure9-1.png",
        "caption": "Fig. 9. M the limiting cycle. P",
        "texts": [
            " c) i-th arc o f a n-th order p a t h ( l < i < n - 1 ) is the curve y ( x o = +_ x~, . . . , x i , x) . For xo = - x~, the arc is descending (x~+l < x < xi, Yi+l < Y < Yi) i f / is even, and ascending (x~ < x < xi+l, y~ < y < y~+l) if i is odd. On the contrary, for x0 = x~, the arc is descending (x~+~ < x < xi, y~+~ < y < y~) i f / i s odd, and ascending (x~ < x < xi+~, Yi < Y < Yi+I) if i is even. The function (20) y~ ~--- ( X 0 = - - X s , X 1 = a), - xs <- a <. x~, represents the ascending branch of the limiting cycle (fig. 9). The function (21) Yab ---- ( X 0 ---- - - Xs, Xl ---- a, x2 = b ), - x~ <~ b <~ a <- x , , represents the family of the first-order descending reversal curves at tached to the ascending branch of the limiting cycle at the point (a, y~). See fig. 9. Le t us define the Evere t t function by (22) F ( a , b) = (y~ - y~b)/2. Let us now consider a theorem which links the existence of the GPM with , ) N : ascending branch of the limiting cycle. N- -~ M: descending branch of > M: first-order descending reversal curve. r simple properties of the y vs. x curves of the HT. Let us recall that by HT we mean static hysteresis transducers whose y vs. x relationships satisfy properties 1-9 of the previous section and the symmetry property (17) of this section"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003903_iembs.2006.259950-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003903_iembs.2006.259950-Figure3-1.png",
        "caption": "Fig. 3. CAD drawing of the prototype FlexCVA. In this version, the worm gear is split with the top half connected to the front sprocket and lower half connected to the back sprocket. Belt tensioners with linear Hall Effect sensors send belt position to the controlling electronics. Springs in the tensioners automatically reduce the drive ratio as the load increases.",
        "texts": [
            " Many variations of linear and rotary FlexCVAs are possible and are the subject of several pending patent applications. The driver does not need to be a motor-driven cam but can be any technology that can deliver a repetitive deflection force including, for instance, a piezoelectric actuator. The brakes can be implemented with friction brakes, electrostatic brakes, or any other technology that can produce a braking force. For unidirectional CVT applications, the brakes can be implemented with simple mechanical one-way clutches. Figure 3 shows a CAD drawing of the first prototype dual-belt FlexCVA. The movement of each braking pulley is restricted by the worm gear acting as a brake or clutch. One brake is engaged while the other brake allows or forces the second braking pulley to advance in the direction of the output movement. The belts have enough slack to allow a driver to deflect the belt between the brake and load end of the belt. The output is advanced by activating one brake while its driver deflects the top or bottom of the belt to advance the output in the desired direction",
            " This graph shows measurements taken in the middle of the full performance range that extends to 34 Nm of torque and over 100 deg/s of speed. In the range of this graph, as the torque demanded by load increases, the input to output gear ratio increases from 675:1 to 3000:1. This automatic ratio adjustment gives a much wider performance range than a conventional DC motor with a fixed gear ratio. Figure 6 shows a photo of the current prototype. This prototype includes enhancements added as a result of initial testing of the device. The largest change from the design shown in Figure 3 is the addition of cam followers which roll against the cams and have sprockets to engage and deflect the chain. This change eliminates the friction of the chain against the cam and improves the actuator efficiency by allowing the use of quality bearings or bushings for all moving elements. Efficiency is also maintained by taking advantage of the CVT properties to run the brushless DC motor within its most efficient operating speed range. High efficiency is important to allow the use of small, lightweight batteries in portable active orthotic devices"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003190_05698190500414391-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003190_05698190500414391-Figure2-1.png",
        "caption": "Fig. 2\u2014Geometry of the journal bearing.",
        "texts": [
            " The Reynolds equation is not used to calculate the pressure distribution. Instead, the viscosity, \u00b5, the shear rate, and fluid velocity are calculated for 20 discrete positions across the film, assuming a linear variation of shear stress across the film. The pressure gradient, and thereby the distribution of shear stress, is adjusted at 1,000 discrete locations along the flow path so that volume flow rate is conserved (Bair (28)). Normal stress differences are ignored. The geometry and nomenclature for the bearing are shown in Fig 2. The film thickness, h, is specified as a function of angular position \u03c6, radial clearance c, and eccentricity D ow nl oa de d by [ N or th W es t U ni ve rs ity ] at 1 5: 44 2 1 D ec em be r 20 14 \u03b5, in the usual way (Cameron (29)): h(\u03c6) = c (1 + \u03b5 cos \u03c6) [12] For all calculations, the bearing radius is 15 mm, c = 15 \u00b5m, and the rotation rate is 4775 revolutions per minute. The Reynolds boundary condition (Cameron (29)) is employed where p = dp/d\u03c6 = 0 at \u03c6 = \u03c6\u2217, a position at which the volume flow is known"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003889_s0022-5193(80)80032-4-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003889_s0022-5193(80)80032-4-Figure4-1.png",
        "caption": "FIG. 4. Schematic diagram (derived from Fig. 2 in Chwang & Wu, 1971). Showing relative positions in unit time apart of a tranverse section of the helical wave-propagating flagellum of a swimming cell in steady motion in a viscous fluid. The flagellar cross-section shown at the top of the first broken circle rotates about the x-axis (perpendicular to plane of the page at the circle's centre) through 0 radians with an apparent angular velocity to-fl counterclockwise while the cross-section rotates about its own centre (in clockwise direction indicated by small arrow) with angular velocity ~. This motion has a component 0~ radians due to angular velocity of wave propagation to which does not involve rotation of the surface particle shown (dark spot) about the flagellum centre, and a component 02 radians due to induced angular velocity of cell and flagellum as a whole fl which involves rotation of the surface particle shown through 02 (fl) radians around the flagellum's centre. Rotation of the surface particle about the flagellum centre occurs at the same rate and in the same sense (clockwise) as rotation of the cell, but in opposite direction to wave propagation.",
        "texts": [
            " The structure of the basal body of the sheathed fagellum of P. stizolobii has been found to be identical to that of the basal body of E. coli, with two pairs of rings being connected by a rod element (Fuerst, 1975). The basal body of the sheathed flagellum of V. metschnikovii appears to comprise at least an upper double disc and lower single disc (Vaituzis & Doetsch, 1969) and that of the sheathed flagella of Photobacterium fischeri at least two discs or sets of discs (see Allen & Baumann, 1971, Fig. 4). It seems likely therefore that sheathed flagella of membranous type possess basal bodies of a structure similar to those of the sheathless flagella of E. coli and compatible with the features required of a flagellar basal body in the rotary motor model, derived from properties of sheathless flagella. In membranous sheathed flagella, however, the postulated function of the outer pair of basal rings, that of serving as a hushing required for passage of the rod through the cell wall (Berg, 1974), may require modification,at least with respect to passage through the outer membrane",
            " This cross-section will also rotate about the latter axis in a direction opposite to head rotation; this does not involve surface particle movement with respect to the flagellum centre, however. Movements of such surface particles and BACTERIAL SHEATHED FLAGELLUM MECHANISM 771 the sense of their ro ta t ion with respect to the head of the swimming, spinning organism can be clearly der ived f rom Fig. 14 (c) and (d) of Gray (1953), Fig. 7 of Keller (1977) and Fig. 2 of Chwang & Wu (1971), and a simplified version of the latter figure is shown in Fig. 4 of this paper. F r o m these considerat ions, it would seem that in the case where the sheath wavepropagat ion , core- ro ta t ion model for the shea thed flagellum applies, observat ion of a latex bead a t tached to the flage'llar sheath of a swimming wild-type organism will reveal a rota t ion of the bead only in the same sense as that of the cell itself. In the al ternate mode l where the sheathed flagellum rotates as a whole relative to the cell, o n e would expect an at tached bead to rota te in a sense opposi te to that of the cell 's rota t ion in addition to its rota t ion due to the spin of the whole system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002371_elps.200305362-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002371_elps.200305362-Figure1-1.png",
        "caption": "Figure 1. Schematic of the FIA-CE connection. A small contact area, depicted in the middle, connects the lower level to which the FIA flow enters and the upper level where the CE electrolyte flow is introduced. Both flows leave the connection through the waste capillary. Upper left shows a photo of the two-level cross (95 m ID). Upper right shows a photo of the graphite/polyimidecoated CE column inserted into the PDMS connection. Lower right shows a photo of the connection between the PDMS channel and a sharpened fused-silica capillary.",
        "texts": [
            " The ends of the large-dimension capillaries were carefully cut. Two of these setups were crossed on top of each other creating a two-level template for the fabrication of PDMS microchannels. A four-way channel cross was achieved by simply casting Elastosil 601 (Wacker Kemi AB, Stockholm, Sweden) onto prearranged fused-silica templates in a predrilled small petri dish. After curing the PDMS in an oven at 60 C for 60 min, the capillaries were pulled out of the mould leaving a well-defined microfluidic network, seen in Fig. 1. A microscope, Olympus AX 70 (Olympus Optical AB, Malm\u00f6, Sweden), was used for examining the definitions in the connection directly after manufacturing and later after long-term usage. After preparing integrated electrodes onto both CE capillary ends (see Section 2.2), chemical modification of the inside of the CE capillaries was performed to produce a positive charged surface for MS applications. A method using 3-aminopropyl-trimethoxysilane was applied as described by Moseley et al. [13]. In the CE-UV experiments bare fused silica was used",
            " The manufacturing of the liquid flow-CE interface resulted in a structure with 95 m ID channels in the center of the cross. Each channel in this center cross is about 5 mm in total length before it broadens out to a channel with 360 m in diameter. The broader channels make a suitable connection for conventional used fused-silica capillaries with 360 m OD. Such capillaries with 50/25 m ID were used to ensure a tight connection to the thinner channels. A schematic figure and photos of the resulting setup is shown in Fig. 1. The transparent feature of the material also allowed visual monitoring of the flow profiles in the connection by use of a dye. The chosen combination of flow rates and inner diameters of the CE column and the waste capillary directed both the CE electrolyte and the FIA flow to leave the connection through the waste capillary. The overpressure in the connection was very low, if present at all, assuming no hydrodynamic flow through the CE column. The CE performance was therefore not affected by the flow rates in the interface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000861_177424.177987-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000861_177424.177987-Figure4-1.png",
        "caption": "Figure 4: Translating an edge",
        "texts": [
            " The reduced form of P is based on a process of elim- inating P\u2019s edges one by one. Consider an edge e of polygon P whose endpoints u and v are shared with adjacent edges eti and ev. If we translate e parallel to itself while keeping the rest of the polygon fixed, u and v move along the lines supporting eti and ev, lengthening or shortening those edges as well as e itself. We can translate e so that at least one of e, e~, and eu gets shorter. One of the edges will eventually be reduced to zero length, if e does not hit another part of P first. See Figure 4. We show in Lemma 1 below that every polygon can be morphed with 0(1) edge translations (amortized) so that at least one edge is reduced to zero length, while keeping the polygon simple. In this case we can iteratively reduce the polygon to a triangle: at each of n \u2013 3 steps, we eliminate one edge of P by translation. For certain degenerate polygons, it is possible that the elimination process will terminate with a parallelogram instead of a triangle. This case does not pose any additional difficulties for our algorithm, and so we will ignore this possibility from here on"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000967_a:1013901228979-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000967_a:1013901228979-Figure4-1.png",
        "caption": "Figure 4. KAMRO (Karlsruhe Autonomous Mobile Robot).",
        "texts": [
            " Formal metrics to evaluate the progress made have to be developed. In our Institute several experiments have been made with the mobile two-arm robot system KAMRO (Karlsuhe Autonomous Mobile Robot). The robot consists of a mobile platform with an omnidirectional drive system using MECANUM wheels and two PUMA manipulators with 6 degrees of freedom mounted in a hanging configuration. It is also equipped with a multitude of sensors: one over-head camera, two hand-cameras, force/torque sensors on each manipulator and ultrasonic sensors on the mobile platform (Figure 4). The experiments made with the mobile manipulations demonstrate the principles of the communication between human and robots at the physical level. An operator guides the two manipulators of KAMRO by moving manually the endeffectors with his arms. The operator has just to concentrate on positioning the endeffectors, whereas the robot takes care of the collision avoidance between the two manipulators. Besides, the mobile platform must ensure that the two manipulators are always in a region of optimal configuration [18]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002386_s0301-679x(01)00116-5-Figure9-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002386_s0301-679x(01)00116-5-Figure9-1.png",
        "caption": "Fig. 9. Schematic geometry of the misaligment between the guideway and bearing.",
        "texts": [
            " Integrating the pressure distribution Pi,j over the area considered, the load capacity FL was calculated where FL (Pi,j Pa) dq dy (17) The stiffness (CL) is the derivative of load capacity with respect to the eccentricity or deflection and can be described as: CL FL h (18) The air film will be identical everywhere between the shaft and bearing when there is no load. If the shaft axis is not tilted in the bearing, the film gap is a function of q only. This allows the film thickness to be expressed as [6]: h h0 e cos q (19) The complex gap variation between the bearing and shaft should be modified to include angular misalignment is because of the nonsymmetrical load \u201cF\u201d as shown in Fig. 9, where g indicates the incline angle on the X\u2013Z plane, d is the bias angle on the Y\u2013Z plane and a displays the tilt angle on the X\u2013Y plane of the nonsymmetrical load, respectively. Then, the cross section of bearing on X\u2013Y plane is a sectional ellipsoid. Here S is the distance from the center of shaft to the rim of the cross-section of every bearing in the figure. The procedure for calculating the air gap will be described in Appendix A. Fig. 10 describes the gap variation of the spindle with misalignment angle; in which d g 0",
            " Increasing the groove width and depth enhances load capacity. 3. The initial stiffness is proportional to gap film, and increasing the film gap beyond the criteria point results in lower stiffness, while decreasing the groove width results in greater stiffness. 4. Decreasing the initial gap clearances results in greater load capacity. 5. The complex gap variation should be considered due to the nonsymmetrical load, and the angular misalignment reduces the load capacity. Using the elliptic coordinate axis X1\u2013Y1, then the values of xEM and yEM in the Fig. 9 are: xEM xd cos(a) z tan g (A1) yEM xd sin(a) z tan d (A2) e is the angle between the X axis and the X1 axis. Therefore, tan e tan d tan g (A3) The short elliptic axis can be expressed as follows: b r Ds 2 (A4) The long elliptic axis can be obtained as follows: a r2 w2 (A5) where w r tan b (A6) tan b tan2g tan2d (A7) a r 1 tan b r 1 tan2g tan2d (A8) The ellipse equation can be described as x2 1 a2 y2 1 b2 1 (A9) Through coordinate translation, we can obtain the ordinary equation in the primary coordinate system X\u2013 Y as y x tan a (A10) x c13 c23 tan a c11 2c12 tan a c22 tan2a \u00b1 c13 c23 tan a a 2c12 tan a c22 tan2a 2 (A11) c33 a 2c12 tan a c22 tan2a where c11 (b2 cos2e a2 sin2e) (A12) c12(b2 a2) \u00d7 cos e \u00d7 sin e (A13) c22 b2 sin2e a2 cos2e (A14) c13 yEM cos e \u00d7 sin e(b2 a2) xEM(b2 cos2e (A15) a2 sin2e) c23 xEM cos e \u00d7 sin e(a2 b2) yME(b2 sin2e (A16) a2 cos2e) c33 cos2e(b2x2 ME a2y2 ME) 2yMExME \u00d7 cos e sin e(a2 b2) (A17) sin2e(b2yEM a2xEM) a2b2 From Fig. 9 we know S x2 y2 (A18) The air gap can be represented as Eq. (A19) h(q,z) Ds 2 S(q,g,d,z). (A19) [1] Chen MF, Wu CS, Hsieh MC. The modal analysis and testing of the aerostatic linear guide for PCB drilling machine. In: The 16th National Conference on Mechanical Engineering (in Chinese), Taiwan, 1999. [2] Kogure K, Kaneko R, Ohtani K. A study on characteristics of surface-restriction compensated gas bearing with T-shaped grooves. Bull JSME 1982;25(210):2039\u201345. [3] Nakamura T, Yoshimotof S. Static tilt Characteristics of aerostatic retangular double compound restrictors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002157_027836498900800302-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002157_027836498900800302-Figure3-1.png",
        "caption": "Fig. 3. The distance between two convex h ulls.",
        "texts": [
            " (1) and (2), we can restate (3) as For brevity, we will define d* = d(n*). - at UNIVERSITE DE MONTREAL on June 20, 2015ijr.sagepub.comDownloaded from 34 Note that a positive distance results if the objects are disjoint, and a negative distance results if the objects intersect. Physically, the distance is the magnitude of the smallest pure translation which will bring the two objects into contact. We can define a distance vector d* = d*n*, which is the shortest translation vector to move K; into contact with Kj. The above definitions are clarified in Fig. 3. Maximizing d(n) is a standard problem of optimizing a function. The distance d* = d(n*) is a local minimum or maximum if The problem is considerably simplified if we consider only convex polyhedral objects. Convex polyhedra can be specified concisely and unambiguously by simple boundary representations, and the minimization problem can be discretized and simplified. Let us represent objects K;, Kj, by their respective sets of vertices Yl, t~. 3.2. The Separating Distance for an Arbitrary Normal Assume we are given a normal n and a corresponding tangent point ri E Kl"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003817_1.2214736-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003817_1.2214736-Figure3-1.png",
        "caption": "Fig. 3 Fluctuations in Fb and Fc c",
        "texts": [
            " 4 , the fastener tension will increase at a faster rate. The slope of the fastener tension-elongation curve becomes unity beyond the separation point. Accordingly, the fastener tension increases by the full amount of the increase in the separating force when the joint begins to separate. In the case of a harmonic separating force, such as the case of head bolts in an internal combustion engine, the increase in the fastener tension Fb and the reduction in the clamping force Fc, given by Eqs. 2a and 2b , will become harmonic as well 5 . Figure 3 shows fluctuations in Fb and Fc that correspond to the NOVEMBER 2006, Vol. 128 / 1329 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use fl f j f l m r w l e N i e r s j a l F s P t t z r a 1 Downloaded Fr uctuations in the separating force Fe. Under cyclic loads, the atigue strength must be considered for both the fastener and the oint. It is to be pointed out that the harmonic components of the orce would raise the mean tensile stress in the fastener, and will ower the mean compressive stress in the joint"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002037_iecon.1995.484167-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002037_iecon.1995.484167-Figure2-1.png",
        "caption": "Fig. 2 The &-pole system",
        "texts": [
            " CONTROL DESIGN FOR A CART-POLE SYSTEM Ln this section, we propose a method based on FLC and SMC for deriving the fuzzy control rule of the cart-pole system by a systematic way. The method is; Merent from traditional FLC approach and obtains a drastic reduction in the number of fuzzy rules which are necessary to control a 4th-order system. The proposed scheme can easily obtain a set of control rules with a minimal amount of prior information about the environment. In addition, the chattering effect via sliding mode can be handled effectively [7]. The control design is investigated as following subsections. A . Description of the Inverted Pendulum System Fig. 2 shows the schematic diagram of an inverted pendulum. The inverted pendulum system is composed of a rigid pole and a cart on which the pole is hinged. The pole is hinged to the cart through a joint such that it has only one degree of freedom. The cart travels in one axis along a finite-length track. The goal of this control problem is to make the pole upright and regulate the cart to a specified position. The model and the corresponding parameters of the cart-pole balancing system for our computer simulation are adopted from [ 151 with the consideration of friction effects"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003841_j.humov.2006.01.001-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003841_j.humov.2006.01.001-Figure1-1.png",
        "caption": "Fig. 1. (A) Diagram of the experimental setup. Participants towed a light weight distance meter during walking. All data were sent and received by telemeter. These data were converted to digital data at a 200 Hz sampling rate and analyzed with a computer. (B) The vertical movement effect was calculated by means of a trigonometric function equation with the radius of rod length (r) and the angle between the platform surface and rod (h), which was measured with a goniometer. Therefore, for example, the horizontal movement (x component) of the distance meter from point A 0 to point B 0, which was derived by measuring the participant\u2019s vertical movement (y component) from point A to point B, could be calculated as the difference between the coordinates of each point (A 0 and B 0). (C) An example of the cycle speed calculation during walking. The raw speed represents data measured by the distance meter. The real speed was calculated by eliminating the artificial speed (vertical factors) from the raw speed data.",
        "texts": [
            " Stride length was represented as the distance covered in one gait cycle. Cycle speed was calculated as the mean speed of one gait cycle. In order to measure cycle duration, we obtained the right heel striking time using a force-sensing transducer as foot switch. Accordingly, cycle duration was measured using the signals from this foot switch. To measure the precise moving distance, participants were asked to tow a light weight distance meter, which was attached to the participant\u2019s waist with a hard belt and a straight aluminum rod (Fig. 1A). The distance meter consisted of two wheels and a rotary encoder (OMRON E6C2-CWZ). The weight of this device was 2.2 kg. The wheel\u2019s circumference was 310 mm. The axis of the rotation of the encoder was coupled with a pulley on the wheel axle by a pulley belt. As a consequence, one wheel rotation produced one rotation of the encoder. The rotary encoder had an output of 600 pulses per rotation. Pulse data of the encoder were sent to a pulse counter which had a built-in math function (OMRON K3NR) to calculate the moving distance",
            " We measured the rod angle changes by means of a goniometer that was set on a flexible parallelogram housed in the frame of the distance meter throughout the experiment. Because the vertical action to the end point of the rod produced a slight circular movement in the entire rod as a radius, it caused extra movement in the forward direction and additional horizontal movement in the measuring device (distance meter). Therefore, the value of the rod angle to the horizontal axis was measured as the opposite angle in the parallelogram (Fig. 1B). The position shift of the distance meter caused by vertical movement was calculated by means of the following trigonometric function equation x \u00bc r cos h and y \u00bc r sin h; where x = the horizontal element (position of the participant to the distance meter), y = the vertical element (vertical position of the waist from the platform surface) and h = the angle formed by the platform surface and the rod of the distance meter. Thus, the real moving distance could be obtained by the successive subtraction of artifacts (produced by the vertical movement) from the raw position shift data measured by the distance meter. From the moving distance data, stride length was calculated as the real moving distance per gait cycle. We recorded the instantaneous speed using the real moving distance data throughout the experiment. In this manner, cycle speed was calculated as the mean speed per gait cycle from this record (i.e., the speed calculated from the displacement every 5 ms (digitalized data at 200 Hz)). Fig. 1C shows an example of the speed calculation of one gait cycle. In addition, we confirmed the reliability of this original technique as follows. Photocell switches were set at every 5 m on the platform and the time taken to pass through each limited section was measured. Using this distance/time operation, we obtained additional walking speed data. Throughout the experiment, we constantly monitored the difference between our original technique and the additional speed data as measured by means of the photocell switches"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000811_1.2834592-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000811_1.2834592-Figure3-1.png",
        "caption": "Fig. 3 Verification of the nonlinear model: a tapered land thrust bearing",
        "texts": [
            " This function feeds directly into the evaluation of normalized error function E{Az, Az). E is further normalized by the root-mean-square (RMS) value of the largest term within the perturbation space. In this case, the largest term is {dldX)[hl{dF^Mrbtildx)'\\. Contour plots of Snorm are generated from the error function. 3 Applications, Results, and Discussion The linear dynamic coefficients generated from a second or der nonlinear dynamic model are compared to the published results to verify the reUability of the present model. Figure 3 600 / Vol. 120, JULY 1998 shows the normahzed steady-state load, hnear stiffness, and Unear damping coefficient of a tapered land thrust bearing at different central film thicknesses (Someya and Fukuda, 1972). Steady-state load W^, stiffness k^, and damping coefficient b; in this figure are normalized as W, = {W^e^l^S),\\ = (k^e^ta/ fiiiiS), and hi = {bie^roljiS), respectively. Here, e = 10\"' is a constant, uj is runner angular velocity, S is sector pad area, /x is lubricant viscosity, and r\u201e is pad outer radius"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003387_s00604-005-0362-3-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003387_s00604-005-0362-3-Figure1-1.png",
        "caption": "Fig. 1. Cyclic voltammograms of the ( )1-ferrocenylethylamine modified platinum disc electrode in 50 mM phosphate buffer (pH 7.4) at s scan rate of (a) 20, (b) 60, (c) 100, (d) 200, and (e) 400 mV s 1",
        "texts": [
            " Peak identification was performed by standard addition. In this study, ( )-1-ferrocenylethylamine was used as a novel electron transfer mediator which can shuttle the electron from the active center of GOx to the electrode surface. The introduction of the electron transfer mediator in the fabrication of the electrochemical glucose biosensor involves the occurrence of a coupled catalytic reaction. It is of great interest to investigate the electrochemical behavior of ( )-1- ferrocenylethylamine. Figure 1 shows the cyclic voltammograms of a ( )-1-ferrocenylethylamine modified platinum electrode in 50 mM phosphate buffer at a scan rate of 20, 60, 100, 200, and 400 mV s 1. A set of well-defined quasi-reversible peaks are observed, exhibiting the electrochemical behavior of the derivatized ferrocene=ferricinium redox couple. The cathodic and anodic peak currents were almost equal. The peak-to-peak potential separation ( E) was greater than 59 mV at a scan rate of 20 mV s 1 and increased with the scan rate",
            " So the redox reaction process at the ( )-1-ferrocenylethylamine modified platinum electrode can be illustrated as follow: Figure 2 shows the cyclic voltammograms of the glucose biosensor in an unstirred 50 mM phosphate buffer containing 0, 10, 15, and 20 mM glucose at a scan rate of 100 mV s 1. Without glucose, the GOx electrode only shows a pair of well-defined peaks (Fig. 2a). They can be attributed to the redox reaction of the derivatized ferrocene=ferricinium redox couple on the electrode surface because the peak potentials are in good agreement with that in Fig. 1c. Figure 2 illustrates that addition of glucose to the buffer solution results in a dramatic change in the cyclic voltammograms with an increase in oxidation currents and concomitant decrease in reduction current. The catalytic current increases with the concentration of glucose. The fact that the reduction current does not increase along with the oxidation current indicates the GOx dependent catalytic reduction of the derivatized ferricinium ion. Figure 3 shows the typical current-time response of the glucose biosensor to successive additions of glucose using a constant applied potential of \u00fe0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002351_s0263574700006093-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002351_s0263574700006093-Figure4-1.png",
        "caption": "Fig. 4. Configuration of the locomotion mechanism.",
        "texts": [
            " Moreover, more than one joint can be chosen, either at the same time, or successively. In the following section we describe the simulation of some of these cases. 5. SIMULATION RESULTS A software package, specially developed for locomotion mechanisms2'3 was used for all simulations. First, the nominal dynamics was synthesized by a prescribed synergy method and then simulation of the mechansism's behaviour at the level of perturbed regimes is performed. The mechanical configuration considered is shown in Figure 4 and its parameters are given in Table I. The whole system has 20 DOF and two of them (those formed in contact of feet with the ground, i.e. rotations around X and Y; the rotation around axis Z is assumed to be prevented by a sufficiently high friction coefficient) are unpowered. A joint with more than one DOF is replaced by a kinematic chain having the same number of simple rotational joints as the real joint has DOF. The links of such a chain are considered light and with no length i.e. r,k = 0 (because of certain algorithm characteristics we put in the computer program riik = e, e = 000001 (m))"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002744_j.optlaseng.2004.03.006-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002744_j.optlaseng.2004.03.006-Figure2-1.png",
        "caption": "Fig. 2. Photograph of the bearing under test.",
        "texts": [
            " In other words, it continuously measures the time of every 4000 periods without dead time, calculates the frequency and stores the 1000 values in memory. The sampling period of the counter is approximately 1.5ms at the beat frequency of 2.7MHz. Another electronic frequency counter (model TA1100, manufactured by Yokogawa Corp., Japan) measured the rest frequency, frest (Hz), using an electric signal supplied by a photo diode embedded inside the He\u2013Ne laser. The measured data was low-passed filtered by assigning to every point the average of the eleven nearest neighbors. The averaging period is approximately 15ms at the frequency of 2.7MHz. Fig. 2 shows the photograph of the linear bearing under test. Metal parts and the corner cube prism are attached to the moving part. The total mass of the moving part shown in Fig. 2 is 1.946 kg. The bearing is fixed on a tilting stage whose tilt angle is adjustable. The range of the moving part is approximately 80mm, the maximum weight that can be tolerated by the moving part is approximately 200 kg. The total mass of the moving part can be set to 1.946, 3.595 kg or 5.238 kg by attaching masses as shown in Fig. 1. In the experiment, six measurements are conducted for each value of mass, 1.946, 3.595 kg or 5.238 kg. Fig. 3 shows the data processing procedure. For this case, the mass of the moving part, M, is 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002058_iros.1997.649050-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002058_iros.1997.649050-Figure2-1.png",
        "caption": "Figure 2: Motion and deformation of rodlike object",
        "texts": [
            " Finally, some numerical examples are shown in order to demonstrate how the shapes of deformed rodlike objects are computed using the proposed approach. 2 Modeling of Rodlike Object Deformation 2.1 Geometric Representation of De- In this section, we will formulate the geometrical shape of a rodlike object, which moves and deforms dynamically in three-dimensional space. Let L be the length of the object, s be the distance froin one endpoint of the object, along it, and t be the time. Let us introduce the global space coordinate system and the local object coordinate system at individual points 3n the object and at each time, as shown in Figure 2, LD order to describe the motion and the deformation 3f a rodlike object. Let 0-zyz be the coordinate system fixed on space znd P(s,t) - (qC be the coordinate system fixed on zn arbitrary point of the object at distance s and Lime t . Select the direction of the coordinates so that h e <-axis, qaxis, and C-axis are parallel to x-axis, yw i s , and z-axis, respectively, in natural state where the object neither move nor deform. Theii, the moion and the deformation of the object are represented 3y the relationship bet ween the local coordmate sys,ern Pjs,t) - Jq( and the global coordinate system 3-zyz"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002426_robot.1993.291880-Figure8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002426_robot.1993.291880-Figure8-1.png",
        "caption": "Figure 8: Graphical depiction of the blending described by Equation (54). See the text for a description.",
        "texts": [
            " This implies that it is possible to blend the angular velocities utilizing Equation (14), and obtain the incremental rotations from the value of the instantaneous angular velocity. 5.3 Angular Velocity Blending for Orientation As was discussed in the last section, the incremental rotations of an orientation blend may be approximated by uti- lizing the instantaneous angular velocity provided by Equation (14). Thus, the orientation of the target frame can be computed by utilizing Equations ( l ) , (4), (7), (8), and (14): m \"R(s,) = \" 2 0 n \"'R [w(s~)As] sn = n / N , AS = 1/N n = O (54) where N is the total number of steps for the complete blend. Figure 8 provides a graphical depiction of this blending method. Before the blend, there is motion away from the orientation of the previous frame, Fi-1, and toward the intermediate orientation, a = Fi. The constant angular velocity before the blend is wa. The blend begins at orientation 0. For each interval after 0 , a rotation is constructed and applied according to the angular velocity blending provided by Equation (14). After the normalized blend time s has become unity, the commanded angular velocity will be W b "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000771_0890-6955(93)90096-d-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000771_0890-6955(93)90096-d-Figure2-1.png",
        "caption": "FIG. 2. Machine set-up for hob relief grinding with a pencil-type grinding wheel.",
        "texts": [
            " The normal vector of the hob tooth flank is defined by the equation: n(h h) = k h \u2022 a s inO-c . (Pv\" s inO+b, cosO) 1 / --kh\" a- cosO+c \u2022 (pv- cosO-b \u2022 s in~)] / a.b J (4) where: doe a = 1--p~. drh b = rh+p\" (O-dAe) drh ktf+kh kh\" + tgv c - dza drh Zp- tgv 618 V. SIMON d~h _ reh sin7 drh ~ COS(T+~0h) \" The term Pv is the variable relief grinding parameter. 2.2. Grinding wheel profile for hob relief grinding The geometry and kinematics of the relief grinding set-up for the conical or dishedtype grinding wheel are given in Fig. 1, and for the pencil-type grinding wheel in Fig. 2. The setting angles are \"r and ~ for the conical or dished-type grinding wheel, while tilt angle, ,rp, is used in the case of the pencil-type grinding wheel. The relative motion of the hob to the grinding wheel consists of the helical motion (with angular velocity and axial velocity k h ~ ) , and their radial approach of velocity pt~. The calculation of the grinding wheel profile for hob relief grinding is based on two conditions. (1) The normal vector of the hob tooth flank at the point of the processed cutting edge must intersect the grinding wheel axis, This condition is expressed by the equation: c ",
            " The vector e h of equation (5) can be expressed as: C~h ~) = m32\" (az--kh\" 6 - - r h ( 3 ) ) - - m 33 \u2022 ( - a x \" sin6+ay \u2022 COS6--rh(2))] m33\" (ax \" c o s 6 + a y \" s i n 6 - - r h ( 1 ) ) - m 3 1 \u2022 (az--kh\" 6- - rh (3 ) ) / rh(1)\" m32--rh(2) \"m31 + ax\" sinx- cos 'q-ay, simq _l (9) where: ax = rgwo \" COS'q+ xM--px\" 6 az = rgwo\" cos'r \u2022 sinxl. ay = h-rgwo\" sinx- sin'q The profile of the conical or dished-type grinding wheel tz to) rt\u00a2)~ is defined by the ~. ga ~ ga / following equations: z(c ) = . ( c ) tg(3) = ~v/([rgtl)] +[rg~2)] ) rtg~) (c) 2 (C) 2 #gc) ..(c) (e) = m h g rh (10) The values of parameters ~ and pv, needed in equations (10), are calculated by iterations from equations (5) and (6). 2.2.2. The profile of the pencil-type grinding wheel. In the case of pencil-type grinding wheels (Fig. 2), the coordinate transformation from system Kh into system Kg is given by the equation: rg =M~h~)'rh (11) where: M(h~ ) COS(Tp+~) -s in(Tp+O 0 h'sinTp--(XM--p~). COSTp sin(%+~) cos(xp+~) 0 --h'coS'rp--(XM--Px~)'sinTp 0 0 1 -bg+kh'~ 0 0 0 1 b g ---- Zp \u2022 rpgwO \u2022 COSOJoh. In the case of the pencil-type grinding wheel for the vector Ch of equation (6), it follows: sin(Tp+~) \u2022 ( kh. ~+rh(3)--bg) ] COS(Tp-t-~) \u2022 (k h \u2022 ~+rh(3)--bg) -- rh( 1 )\" sin(xp + ~ ) - rh(2) \u2022 COS( \"fp + ~ ) + (X M --Px~ )sinxp + h\" cos% ) c~hP) = (12) The axial profile of the pencil-type grinding wheel (~Pa), xtP)~sa, is defined by equations: x ( P ) = "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002398_robot.1991.131855-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002398_robot.1991.131855-Figure1-1.png",
        "caption": "Figure 1:Direct drive manipulator with Variable Impedance Machine",
        "texts": [
            " Section 4 briefly presents the theory of the constrained motion control of McClamroch and Wang (19881, followed by experimental results obtained from the implementation of the control, 1645 CH2969-4/91/0000/1645$01 .OO 0 1991 IEEE and a discussion of these results. Section 5 concludes the paper. 2. Experimental Set-Up A two degree of freedom direct drive robot has been constructed using Yokogawa d.c. brushless motors, for experimental research in manipulator contact task control. The experimental facility includes a one degree of freedom linear translational device, referred to as a Variable Impedance Machine (VIM), to simulate object contact. Figure 1 shows this experimental equipment. The manipulator and VIM operate in the horizontal plane, hence the effects due to gravity are not considered. robot manipulator and VIM. The VIM is driven by a direct drive motor through a large pulley. The motor has a proportional and derivative control law applied to give the following closed-loop dynamics, with respect to task coordinates 1 b r2 + (c + - + k,,)i + kpx 0 mass of linear translational carriage polar moment of inertia of motor and variable inertia of motor (altered by adding steel plates to pulley) radius of pulley damping due to linear motion of carriage damping due to motor derivative feedback gain proportional feedback gain Pulley J\u2018 (a) F"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002482_tcsi.2002.808218-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002482_tcsi.2002.808218-Figure1-1.png",
        "caption": "Fig. 1. Illustration of the cutting hyperplane algorithm. In each iteration, we either improve the lower bound as in the left-hand figure or we improve the polyhedral approximation by adding a hyperplane as in the right-hand figure.",
        "texts": [
            " Let us, for simplicity, consider the case when is the positive orthant or defined by a collection of linear constraints, see [17] for a discussion on how the problem can be reduced to this form in more general cases. If the optimization problem subject to has positive objective value, then (26) is feasible; otherwise it is not. Hence it is enough to decide the sign of the optimal objective value and this can be done using the algorithm described in [17]. We explain this algorithm briefly. Let be the \u201cthe minimal spectral value.\u201d The idea is to approximate this concave function with a polyhedral function, which is successively improved until convergence. In Fig. 1 we illustrate the main idea behind the algorithm. In the left hand side we have generated a test point below , i.e., . We then have a new lower bound . In the right-hand side the test point is above and we generate a new hyperplane, which improves the polyhedral approximation. The new hyperplane may go through the test point , but we will show below that it is sometimes possible to obtain a deeper cut as is illustrated in Fig. 1. In this way we iteratively add new test points until either the lower bound is positive in which case the problem is feasible, or until the polyhedral approximation is below in which case the problem is unfeasible. Convergence can easily be proven under weak assumptions. The performance of the algorithm is dependent on how the test point is generated. Two examples are as follows. 1) Use some point between the maximum of the polyhedral function and the lower bound, see [17]. This is the simplest possible choice since it can be obtained by solving a linear program",
            " With the solution (29) the value of the integral in (27) becomes , where is defined as in iiic) in Theorem 3. For every unit length eigenvector corresponding to a negative eigenvalue of we can generate a cutting hyperplane. This is done in the following way. Assume and . Define for . Then, for any and in particular we have . We can now remove the halfspace from consideration. This formula was derived under the assumption that is included in . If we explicitly include then we can show that the following halfspace should be removed, see the right-hand side of Fig. 1 where we can see that this is a deep cut. Eigenvalue Optimization in Fourier Domain Analysis of harmonics in a system using the IQC (13) leads to a criterion that cannot be given an exact state\u2013space realization due to the involvement of the projection operators and . It is then most convenient to do the optimization in the Fourier domain. Before we discuss how this can be done, we state a result that will be useful in our numerical examples in the next section. Recall from Section V that we have to modify [without any restriction since by assumption we consider signals satisfying ] the performance IQC to be (30) in order to verify ( ) in a convenient way"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003435_icma.2005.1626569-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003435_icma.2005.1626569-Figure1-1.png",
        "caption": "Fig. 1 The measurement system of the 3-D motion of the pelvis.",
        "texts": [
            " Through the measurement in 20 healthy young adults, the data of 3-D displacement of the pelvis are present and a model is constructed to calculate the medial-lateral and vertical displacements of the pelvis for any able-bodied walking. II. EXPERIMENTAL METHODS During each experiment session the subjects are required to walk naturally on a motorized treadmill on the base of the treadmill level with the floor. The line ends of liner wire encoders (precision is up to 0.0003) placed on a frame are hitched on the marker N at the place of a subject\u2019s rump bone. The measurement system of the 3-D motion of the pelvis is simply described in Fig.1. The following sign convention is adopted for reporting: X: fore-aft direction (+X is always directed towards the back of the subject\u2019s body.); Y: medial-lateral direction (+Y is always directed towards the right side of the body.); Z: vertical direction (+Z is always directed in the superior direction.). The origin of coordinate O is showed in Fig.1, and the sensors\u2019 coordinates are S1 (p 0 0), S2 (0 \u2013q/2 w), S3 (0 q/2 w). As part of study, the lengths l1, l2 and l3 showed in Fig.1 are determined during a subject naturally walking through an interface card which transmits the sensors\u2019 output signals to a computer. Then the displacements (DF, DL and DV) of the pelvis in fore-aft, medial-lateral and vertical directions are calculated using (1). ( ) . 24 2 24 2 2 3 2 2 2 \u2212\u2212\u2212= \u2212= \u2212+\u2212\u2212= cceddDV qllDL pcceddwbaDF 1 Where ( ) 2 1 2 3 2 2 2 llla \u2212+= . 222 4 pwqb \u2212+= . 221 pwc += . wpwbad 2)( 2 \u2212\u2212= . ( ) 2 2 2 2 2 2 22 3 2 2 4 )( 4 lbap p ba q ll e \u2212+\u2212+ + + \u2212 = . DF is the displacement of the pelvis in fore-aft direction; DL is the one in medial-lateral direction; and DV is the one in vertical direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003882_s0007-8506(07)60477-6-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003882_s0007-8506(07)60477-6-Figure4-1.png",
        "caption": "Figure 4: Runout measurement via probing of two single points with a small probe sphere, corresponding to pitch measurement. Source: [7], edited.",
        "texts": [
            " Actually, this type of runout measurement is applied for fast manufacturing inspections using a simple dial indicator and leading to a high measuring uncertainty. mean value. The pitch of a bevel gear is defined in [5],[6] as the arc length between all consecutive left or right flanks of one gear, measured at the pitch diameter d in a distance R from the apex of the reference cone. This measurement position is equal to that of the runout. Therefore, CMM manufacturers tend to save measurement time by using the points obtained during the pitch measurement to evaluate the runout. Thus, measuring strategy described in section 2.1 loses its importance. Figure 4 shows the principle of pitch measurements, where both probe movements sample pitch points at all left and right flanks, respectively. Figure 5 illustrates the difference between the sampling points obtained by pitch measurement and the direct runout measurements of a spiral bevel gear. For the latter method, the contact points of the ball probe with the left and the right flanks are on different z-positions, whereas the pitch points are on the same z-level. For helical cylindrical gears, this fact is less critical, because the involute flank form is mathematically well defined as a continuous surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002396_cca.1998.728598-Figure3.1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002396_cca.1998.728598-Figure3.1-1.png",
        "caption": "Fig. 3.1 The ball and beam system.",
        "texts": [
            " The process of p -synthesis, on the other hand, is to design a controller K(s) such that the closedloop system M has a small upper bound of y with respect to the given structure of A which includes the performance and the plant uncertainty blocks. An existing algorithm for p -synthesis is the D-K iteration algorithm 1141, which consists of the p - analysis (D-Step) and the H , optimization (K-Step). Although the D-K iteration algorithm usually does not give an optimal solution, it has been satisfactory in many applications [6,13]. 111. The Ball and Beam Problem I n Fig. 3.1, Y is the position of the ball, 6 the angular position of the beam, and z the torque applied to the beam. The ball is assumed to roll without slipping on the beam. Let the mass and moment of inertia of the ball be M and J,>, respectively, the moment of inertia of the beam be J , the radius of the ball be R, and the acceleration of gravity be G. Define the state vector Then the ball and beam system can be represented by the following model [23], x=[x , x, x, x,]' = [ u i e 61' (3- 1) x = j (x) + g(X)u 3' = 12 (x) with f (x )=[xz B ( x , x ~ -Gsinx,) x4 0IT g(x) =io 0 0 11' h(x) = x, (3-2a) (3-2b) ( 3 - 2 ~ ) (3-2d) the torque where ~=2MxIx,x,+MG~,cosx,+(Mx~ J+J, , )u (3-2e) (3-20 B := M /(J,> / R 2 + M ) The objective of the ball and beam control problem is to design a controller so that the position of the ball will follow a tracking signal that represents the desired trajectory of the ball"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000616_1.1285908-Figure12-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000616_1.1285908-Figure12-1.png",
        "caption": "Fig. 12 Mechanistic description of the creping process",
        "texts": [
            " Further work is necessary to extend the speed range beyond 250 meters per minute and validate this conclusion. The creping process was observed with the help of a video camera under a microscope to understand the sequence of events leading to the creped structure. Hollmark @1# made similar observations and proposed a creping mechanism that was simply a summation of what was observed. We describe the creping mechanism in mechanistic terms that is useful in developing an analytical model. The observations under a microscope are described schematically in Fig. 12. Based on such observations, the following phenomenological mechanistic description of the process is presented: \u2022 As soon as the sheet hits the blade, stresses develop in the sheet and in the adhesive layer. \u2022 As the yankee dryer rotates, the paper-adhesive interfacial shear strength is exceeded and a crack develops releasing the energy due to web compression. This results in a portion of the sheet becoming detached from the dryer and simply lying on it. \u2022 The crack continues to propagate until the free segment of the web becomes unstable and buckles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002697_j.1751-1097.1987.tb04788.x-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002697_j.1751-1097.1987.tb04788.x-Figure3-1.png",
        "caption": "Figure 3. Voltammograms for the BLM (PCIPE) with FeS and FeSiCu deposited layers: (a) FeS deposited layer, the scanning range 5400 mV, (b) Cu layer deposited on one side of the membrane and FeS layer deposited on its other side, the range of scanning up to 2600 mV, the membrane resistance falling below 10' ohm for applied voltage exceeding t200 mV.",
        "texts": [
            " Open circuit potential (&,J measurements showed Nernstian dependence on Cu2+ concentration. This serves as another evidence that copper deposition onto the BLM takes place. Nonetheless, CuS could also be present in an inner layer (see Fig. 5a). FeS deposition When FeC13 was used in 2.5 mM concentration on one side of the BLM (nat. lecithin) while 0.2 mM Na2S was present on the other side, a silvergray layer was deposited onto the membrane surface whereupon considerable stability of the membrane was seen. It is shown in Fig. 3a that voltammograms for the above system could be recorded in the range from +400 mV to -600 mV with maximum current reaching 2 x A. However, no peak was observed in the voltammograms. The membrane with deposited FeS lasted up to 5 h without break- ing. Due to the fact that no shining mirror was observed and no good agreement with the Nernst law has been found, one can state that deposition of FeS rather than metallic Fe occurred. Combined CulFeS deposition Cu and FeS were deposited on both sides of the BLM (PCIPE), first by adding CuS04/Na2S couple, then after the first layer formed Na2S/FeCI3 couple was added. Extremely stable membranes were obtained yielding characteristic voltammograms; very flat in their middle part (high membrane resist- ance R , = lo8 ohm) and showing rapidly increasing current when +200 or -200 mV was exceeded ( R , falling below 10\u2019 ohm (Fig. 3b)). CdS deposition Point five millimolar CdC12 and 0.2 mM Na2S solutions were used to obtain the layer coating the BLM (PCIPE) surface in the same way as in previous experiments. As a result, a bluish coating of the membrane was observed but almost flat voltammograms were recorded giving evidence that no significant change in the membrane resistance occurred. Open circuit potential E,, = +160 mV (measured in the inner compartment) was registered but no agreement with the Nernst law was found. Obtained results indicate that CdS deposition rather than metallic Cd deposition took place"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000017_s0043-1648(99)00148-9-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000017_s0043-1648(99)00148-9-Figure2-1.png",
        "caption": "Fig. 2. Two discs test rig.",
        "texts": [
            " In most cases, convergence is reached after a few itera\u017d .tions; thus the shear stresses are calculated by Eqs. 20a,b and the solution advances to the next column iq1 until the whole contact width is covered. Finally coefficient of \u017d . \u017d .friction is calculated by Eqs. 21a,b and 23 . As men- tioned all three values should be identical; otherwise the achieved approximation is not satisfactory and a denser grid has to be used. In order to experimentally determine the friction coeffi\u017d . w xcient a two discs test rig was used Fig. 2 11 . The two discs have a diameter of 100 mm, a face width of 10 mm, and are made of case hardened steel 20MoCr4 and Ck15. For the experiments of this paper the oil jet temperature was kept constant at 608C and the maximum applied contact pressure was 600 MPa. Sliding velocity was varied from 1 to 5 mrs and the rolling velocity from 3 to 7.5 mrs. The disc surface bulk temperature was obtained by extrapolating measured values in 3, 6, 9 and 12 mm depth. The calculated central film thickness was determined to vary between 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003973_icsmc.2004.1401192-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003973_icsmc.2004.1401192-Figure1-1.png",
        "caption": "Figure 1. a planar 3 degree-of-freedom redundant parallel mechanism.",
        "texts": [
            " If the actuator singularity occurs, the rank of Jacobian decreases, i.e. runk (J) = r < n . It can be proofed as 3. If h.(JrJ)=X , denotes the set of the singularities here by B , and denotes the set of all the end-effector singularities got in step 2 by A , then the set of complex singularities is B - A . singularity analysis of a planar 3 4 follows degree-of-freedom redundant parallel manipulator r = r u r t k ( ~ ) = m i k ( ~ ~ ~ ) (9) A planar 3 degree-of-freedom parallel manipulator is showed in Fig.1, which is rebuilt on the base of a general parallel mechanism presented in literature [9 ] . Slider A, and .slider A, drive links AB2 and A$, when they slide along the vertical guide ways. Links A,B, and A,B, are two driven extensible struts with one end joined with the movable end-effector at point E, (E4), and the other end For J T J is a ii x 11 matrix, i f r 2 1 1 , then de/( JT J ) = 0 4216 joined with the driven sliders A, and A,, respectively. The moving end-effector is driven by sliders and extensible strut to motion with three degrees of freedom. Assuming the manipulator design parameters are: 12, I , , I , , I , , /, and dl with ll,14as two of actuated inputs, where l5 = I , = I l a n d I z + l l ~ d , . Obviously, the number of the input vector parameters is m = 4 , and the number of the output vector parameters is n = 3 , m i n , this mechanism is a redundant parallel mechanism. Taking out the links 45, or A4B, , the mechanism will become a general mechanism. As illustrated in Fig. 1, a reference frame !I1 : o - yz is fixed to the base, and moving reference frame 14' : i -ii is attached to the moving end-effector, where 0' is the paint to be positioned by the manipulator. The angle a! is the rotation angle from 'H' : 0' - y'z to !I1 : o - yz . Vectors r4 and r8, ( i = 1 ,\"., 4) are defined as the position vectfxs of points 4. and the position vectors of points 5, ., respectively. The geometric parameters of the manipulator are A$, =I, ( i = 1,2,3,4) . The position of point 0' with respect to the fixed frame ",
            "1 The actuator singularity singularity occurs, then Notice that 4,o and A, are collinear, then 0, = IT + 0, I According the discussion in section 3, if the actuator substitute it (24) we Will obtain - det ( JT J) (771 sin (0, - e, ) sin (0, - e, ) sin (a - e,) sin (a -e, ) (25) - \\--I +a&:12)(all -'21)' +2(a31a4i -a3!a41)2 = O To make above equation reasonable, it must be a = 0, , a = 0, - K Solving equation (22). two possible solutions are obtained as follows 0, = i~ + 0, 4.1.1 The first possible solution. a,, = 0 2 1 3 Y Y - d i (23) -=- 2-2, 2-2, It means that 4.0' and A, are collinear, for the sake of simplicity, we denote (see Fig 1) y-16sina z - I, cos a - zI sine, = 4 cos@, = 4 4.1.2 The second possible solution. = a4, = 0 3 Y ( Y - 4 ) (26) tana=-- -- ( 2 - 2 , ) ( 2 - 2 4 ) From tan a = - , we can deduce that A , , B, and 0' are collinear, and from tan a = - ( Y - ~ ) ,we can (Z-ZI ) ( z - 2 , ) deduce that A, , B4 and 0' are also collinear , hut because of the mechanical limitation of the mechanism, this case will not happen. Summarize the above two possibilities, the actuator singularities can be written in the form of a set 421 8 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003625_1-84628-269-1_7-Figure7.7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003625_1-84628-269-1_7-Figure7.7-1.png",
        "caption": "Figure 7.7. Illustration of initial sensor candidate locations (left) and time-variant dynamic impact on the bearing assembly due to defect\u2013rolling element interactions (right)",
        "texts": [
            " Input to the test bed, a bearing defect-induced vibration, was modeled as a transient dynamic force (Fb) of 2,860 N (10% of the bearing\u2019s dynamic load rating) with 1 ms duration, and is applied radially to the test bearing. The noise load was chosen to be 1/10 in magnitude of the excitation input (transient dynamic force). The static force load represents the preload applied to the bearing, when the hydraulic cylinder pulls the bearing housing. To model the time-variant defect position within the bearing as it rotates with the shaft, eight equal-distance positions (Pos 1 through Pos 8 in Figure 7.7) around the bearing periphery were selected. The arrangement was made in consideration of the trade-off between modeling accuracy and computational complexity. A transient dynamic force Fb was applied successively at each of the eight representative defect positions, to simulate the time-varying, impulsive interactions between the rolling element and the defect. Given the presence of background noise, selection of the optimal sensor locations need to consider nodal responses to both the signal input Fb",
            " and the noise input Fa. Certain locations, while showing large nodal displacement response to defect-induced signal input in the simulation, may also be sensitive to noise input, resulting in an overall low signal-to-noise ratio that renders the specific location unfavorable. To address this issue, the NSNR as defined in Equation (7.5) was used to form the FIM, instead of using nodal displacements excited only by signal input. A total of 68 nodes on the bearing housing, as marked by the dotted lines in Figure 7.7, were selected as the initial candidate sensor locations. The housing plate contains three structural recesses machined for sensor placement comparison. Each two adjacent nodes were separated from each other by a 5\u201310 mm space. These initial nodal locations and separations were chosen based on the geometrical dimension of commercially available accelerometers. For each of the 68 candidate locations, nodal displacement along the Y directions was computed. The resulting nodal-signal-to-noise-ratio (NSNR) for the 68 nodes were compiled as a column vector di. Given there are eight possible defect positions (Pos 1 through Pos 8), i = 1, 2, \u2026 8, resulting in a total of eight 68\u00d71 vectors. These eight column vectors were then integrated into the nodal displacement matrix D with a dimension of 68\u00d78. On the MATLAB\u00ae platform, the 68 candidate sensor locations were ranked using the EfI method. The eight nodal locations with the highest eight EfI values are listed in Table 7.3. As shown in Figure 7.7, the eight locations can be grouped as two individual (nodes 612 and 1431) and three cluster locations (represented by nodes 2071/2076, with 5 mm separation, nodes 1995/2074, 10 mm separation, and nodes 2132/2139, 5 mm separation). Given the geometrical closeness of these nodes to each other, it was considered sufficient to place one sensor at each of the three clusters. Thus, each cluster can be viewed as a candidate sensor location. Based on the EfI values in Table 7.3, the five candidate sensor locations are ranked as follows: (1) node group 2071/2076, within the bearing static load zone, (2) node group 1995/2074, located within the recess on top of the bearing, 900 counterclockwise from the load zone, (3) node 1431, along the bottom edge of the housing plate, (4) node 612, top edge of the housing plate, and (5) node group 2132/2139, within the recess opposite the bearing load zone"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003184_j.saa.2004.12.029-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003184_j.saa.2004.12.029-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of the FIA manifold used for the l-dopa determination. Pp: perictaltic pump; Iv: injection valve; D: detector; R: reaction coil; S: carrier stream; Ss: sample solution.",
        "texts": [
            " The 1 cm quartz uvette was applied for spectral analysis. The used dioderray spectrophotometer was supplied with a series of 328 ndividual photodiodes. The spectrophotometer instrumental orking conditions were: integration time (1 s), spectral band idth 2 nm and spectrum scan 0.1 s. Computer Pentium II 333 MHz, 64 MB RAM equipped n Grams/32 software package Version 5.2 (Galactic, USA) as used for generation of the derivative spectra. .1.1. FIA assembly The finally proposed single-channel FIA manifold is hown in Fig. 1. The carrier solution (S) (1 \u00d7 10\u22124 M hyrochloric acid), was aspirated by the Gilson (model Minilus 2) peristaltic pump (Pp). The sample solution (Ss) was njected into the carrier stream via a Rheodyne injection valve tandard solution was stored in dark bottle at 4 \u25e6C. Working olutions (5 \u00d7 10\u22126 to 5 \u00d7 10\u22124 M) were prepared freshly very day by an appropriate dilution of stock solution with ouble distilled water. Benserazide hydrochloride (BEN) \u2013 Sigma\u2013Aldrich, SA: the stock solution of benserazide hydrochloride 0",
            " Simultaneously, the benserazide content in capsules was assayed. The relative error of determination versus declared value did not exceed \u00b17%. Results of benserazide determination in pharmaceutical are shown in Table 6. Next the elaborated derivative spectrophotometric method of determination l-dopa and benserazide hydrochloride was combined with FIA system. The use flow analysis allows increasing the number of analyzed samples with better precision. For this purpose the single-channel \u2013 FIA manifold was chosen (Fig. 1). Sample solution was injected directly into carrier stream of 1 \u00d7 10\u22124 M hydrochloric acid and sample segment was transported trough reaction coil (R) into flow cell (D). When sample reached the spectrophotometer flow cell, the peristaltic pump was stopped and the spectrum was recorded. Next, it was converted into derivative spectrum using optimal mathematic parameters, selected previously for m 4 r p fl p a H l o c fl 6 a Using the optimal parameters of derivative spectra generation, selected previously for batch conditions, calibration graphs for determination of l-dopa and benserazide were drawn at analytical wavelengths as a function of the concentration of each compound alone"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000332_s0094-114x(96)00076-6-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000332_s0094-114x(96)00076-6-Figure3-1.png",
        "caption": "Fig. 3.",
        "texts": [
            " [1] for spherical motion if the moving frame of a point trajectory for spherical motion is coincident with the Frenet frame of a line trajectory for spatial motion. Since i is a unit vector, we can write out the components of I on each axis of the Frenet frame of the moving axode Em by equation (8) or (10): l~ = cos ~b, 12 = sin (p cos 0, 13 = sin q~ sin 0 (36) where ~p is the inclination angle between ! and ~m~, while the angle 0 is formed by ~m~ with respect to the plane comprised of i and ~\"~) shown in Fig. 3. Substituting the above equation into equation (28), we have sin 0 + f l * sin q~ cos q~ (37) sin 2 ~b By equation (40) in Ref. [1], the line 00g is located by the center 0 of the unit sphere and the geodesic curvature center 0~ of C~ and forms an angle 6 with respect to I, shown in Fig. 4, which is represented by ctg6 = p ~ - 1 _ fl~ (38) P~ Pg or : /s in 0 ) tg 0k--~-- + cos q~ sin q~ = sin: 4~ (39) Equation (39) shows the relationship between the spherical image curve C~ which is corresponding to a line trajectory, and its osculating cone at any instant, see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003814_12.601652-Figure15-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003814_12.601652-Figure15-1.png",
        "caption": "Figure 15. H13 sample with 0.5in. Channel. Radiographed image of the sample using X-rays Consistent diameter throught.",
        "texts": [],
        "surrounding_texts": [
            "Our initial work on the development of the DMD process was driven by industrial needs. The main foci were: (a) to provide aluminum components with low enough oxidation that it retains mechanical properties [95] and (b) to provide mechanically sound H13 tool steel components. The emphasis is the demonstration of the strength of the DMD technique. Both were successfully demonstrated [1, 96, 97]. Mechanical properties of aluminum and H13 tool steel components fabricated by DMD were found to be almost the same as the wrought materials [1, 95]. The cooling rate can be varied by varying deposition layer thickness and adjusted specific energy [2]. Control of cooling rates enables one to control the dendrite arm spacing and microstructure refinement. Within the power, velocity and powder mass flow rate study, the wall profile roughness averages were found to vary between 13 and 51 microns, while the wall maximum peak to valley distances ranged from 75 to 275 microns [2]. These roughness were found to both be directly related to the layer thickness. The wall roughness can be reduced significantly by making the deposition layers thinner. The reason the wall surface gets rougher as the layer thickness increases is due to the beam diameter variation due to defocusing. As the layers become thicker, the beam diameter has a longer distance to diverge. Therefore, the width of cladding is larger at the bottom of the cladding pass in comparison to the top of the cladding pass. By reducing the layer thickness, this beam diameter variation is also reduced and therefore the specimen wall roughness is minimized. In cases with higher deposition velocities, there was a problem with wall quality. With higher velocities, the cladding at the sample edges sometimes was not able to catch as much powder as the internal sample cladding. Eventually, the cladding was unable to build up fast enough to compensate for this condition, creating gaps in the cladding passes at the sample edges. By reducing the traverse speed of the deposition around the outline of the part, there is enough time for the clad to build to the required height eliminating any defects. The three sensor systems proved to be effective in reducing the surface roughness average of the fabricated parts by approximately 14 percent. In other words, from an average of 7 different specimen sets (5 different build patterns and 2 more with higher pass overlap), the three sensor configurations reduced the profile roughness average from 44 microns to 38 microns. And at the same time reduced the average maximum profile roughness height from 270 microns to 210 microns, or a 22 percent improvement. As was stated before, the maximum profile roughness height is the maximum surface peak to valley measurement. It has been demonstrated that a wide range of deposition rate and geometrical resolution may be possible by DMD by controlling the laser power and beam quality. With CO2 laser lateral resolution of 500 micrometer and vertical resolution of 25 micrometer have been achieved. Fig. 13 shows an IMS-Tl sample fabricated with H13 tool steel using DMD. This is a benchmark design used to validate any rapid prototyping process. Interfacing of DMD laser systems with CAD/CAM systems for one material or two materials in sequence e.g., copper cooling channels and heat sinks in injection molding die in Fig. 14 has also been demonstrated. As shown in Fig. 14, conformal cooling channel, along with copper heat sink has the Figure 13. IMS-T1 sample process parameters IMS-T1 Sample Process parameters: Material: H13 Laser power: ~1000W Deposition rate: ~5 gr/min Slice thickness: 0.01\u201d Total height: ~2.93\u201d (293 slices) Traveling speed: ~30\u201d/min Real laser-on processing time: ~50 hrs Total processing time: ~100 hrs Stress relieving time: ~24 hrs (6 x 4 hrs) Total time:~124 hrs Proc. of SPIE Vol. 5706 51 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/12/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx potential for improved thermal management and theoretical calculation shows that the time cycle can be reduced considerably. used for the \"fuse cover die\". Theoretical calculation shows potential time savings of 26%. A benchmark experiment carried out by one of the users showed 9% saving without any optimization of the flow. Potential time saving increases with the complication of the shape as shown in Table 4. This type of macrostructure design has already attracted considerable industrial interest. The Closed Loop DMD opens up a new horizon of designed materials when integrated with \u201cHomogenization Design Method\u201d and Heterogeneous CAD. This methodology of producing performance based \u201cDesigned Materials\u201d has the potential to change the manufacturing paradigms. This methodology will provide materials with properties that do not occur in Mother Nature. Fig. 18a shows an example of a designed material with negative co-efficient of expansion using Homogenization Design Method (HDM) [76]. Fig.18b shows the component fabricated by homogenization DMD technique using a combination of Nickel and Cycle Time\u2026. Injection time Packing time Freezing time Clamp Open time Up to 75% Cooling Time Cooling time = Freezing time + Packing time (Injection time \u2013 Time to reach the node) Figure 16. In an injection-molding die, 75% of the cycle time is devoted to cooling. 52 Proc. of SPIE Vol. 5706 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/12/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx Chromium. Fig.19 shows a designed component similar to a turbine blade that has 50% less mass but has the similar mechanical strength when compared to conventional blade designs. Fig.20 shows creep test data for a component fabricated with Inconel 738. Implication of 50% reduction in mass in a turbine is proportional reduction in fuel lost. Integrated Design and manufacturing: Imagine the impact of \u201cDesigned Materials\u201d on society and in the environment. On can foresee is new paradigm of manufacturing where it is driven by customer\u2019s desire instead of the best available practice. Fig. 21 illustrates the synergy this methodology can create compared to present day practice. Remote Manufacturing: Modern communication methods are improving the Internet\u2019s capability to transfer large volume of data in a relatively short time. Mathematical and optical methods of data compression are enhancing this capability even further. This will enable seamless communication between design and manufacturing teams in industry. It is conceivable that a design team can send their design data electronically and observe the fabrication from a remote site and even edit it on line [99]. Of course, to Proc. of SPIE Vol. 5706 53 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/12/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx realize this scenario, synthesis and enhancement of various technologies are needed. Fig. 22 shows the process already made possible at POM Group Inc. This has the potential for becoming a global manufacturing platform. An advantage for such platform will be paperless technology transfer across the globe. At the same time it will protect the intellectual property of the inventor by reducing paper trail. Electronic data transfer can be encrypted and thus reduce the potential for exposure to unwanted eyes. 54 Proc. of SPIE Vol. 5706 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/12/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx"
        ]
    },
    {
        "image_filename": "designv11_24_0001318_s0045-7825(02)00238-4-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001318_s0045-7825(02)00238-4-Figure2-1.png",
        "caption": "Fig. 2. Elliptical orbit of the shaft center.",
        "texts": [
            " The new coefficients are as following: G1i \u00bc A0i RT ; \u00f015\u00de G2i \u00bc P0iLi RT ; \u00f016\u00de G3i \u00bc Rsi\u00fe1 Rsi _q0i\u00fe1l10i\u00fe1 p \u00f05 4S0i\u00fe1\u00de c 1 c 1 P0i\u00fe1 1=c \u00fe Rsi\u00fe1 Rsi _q0i\u00fe1 P0i P 2 0i P 2 0i\u00fe1 \u00fe _q0i P0i P 2 0i 1 P 2 0i \u00fe _q0il10i p \u00f05 4S0i\u00de c 1 c 1 P0i P0i 1 P0i \u00f0\u00f0c 1\u00de=c\u00de ; \u00f017\u00de G4i \u00bc Rsi\u00fe1 Rsi _q0i\u00fe1l10i\u00fe1 p \u00f04S0i\u00fe1 5\u00de c 1 c 1 P0i\u00fe1 P0i P0i\u00fe1 1=c Rsi\u00fe1 Rsi _q0i\u00fe1 P0i\u00fe1 P 2 0i P 2 0i\u00fe1 ; \u00f018\u00de G5i \u00bc _q0il10i p \u00f04S0i 5\u00de c 1 c 1 P0i P0i 1 P0i \u00f0\u00f0c 1\u00de=c\u00de _q0i P0i P 2 0i 1 P 2 0i ; \u00f019\u00de G6i \u00bc Rsi\u00fe1 Rsi _q0i\u00fe1 Cri\u00fe1 _q0i Cri : \u00f020\u00de Substituting the perturbation parameters into the momentum equation we obtain X1i oV1i ot \u00fe X1i V0i Rsi oV1i oh \u00fe A0i Rsi oP1i oh \u00fe X2iV1i _q0iV1i 1 \u00fe X3iP1i \u00fe X4iP1i 1 \u00bc X5iH1: \u00f021\u00de The coefficients of this equation are X1i \u00bc P0iA0i RT ; \u00f022\u00de X2i \u00bc _q0i \u00fe \u00f02\u00fe ms\u00desr0iasi\u00f0Li \u00fe d\u00de V0i \u00fe \u00f02\u00fe mr\u00desr0iari\u00f0Li \u00fe d\u00de \u00f0Rsix V0i\u00de ; \u00f023\u00de X3i \u00bc ss0iasi\u00f0Li \u00fe d\u00de P0i sr0iari\u00f0Li \u00fe d\u00de P0i \u00fe _q0il10i p \u00f04S0i 5\u00de c 1 c 1 P0i P0i 1 P0i \u00f0\u00f0c 1\u00de=c\u00de \u00f0V0i V0i 1\u00de _q0i P0i P 2 0i 1 P 2 0i \u00f0V0i V0i 1\u00de; \u00f024\u00de X4i \u00bc _q0il10i p \u00f04S0i 5\u00de c 1 c 1 P0i 1 P0i 1 P0i 1=c \u00f0V0i V0i 1\u00de \u00fe _q0i P0i 1 P 2 0i 1 P 2 0i \u00f0V0i V0i 1\u00de; \u00f025\u00de X5i \u00bc _q0i Cri \u00f0V0i V0i 1\u00de msss0iDh0iasi\u00f0Li \u00fe d\u00de2 2Li\u00f0Cri \u00fe Bi\u00de2 \u00fe mssr0iDh0iari\u00f0Li \u00fe d\u00de2 2Li\u00f0Cri \u00fe Bi\u00de2 : \u00f026\u00de 4. Periodic solutions of first order equations Considering periodic elliptical orbit of shaft center, we obtain the solution of continuity and momentum equations. Elliptical orbit given in Fig. 2 has a major axis of length 2ea, a minor axis of length 2eb. The coordinates of shaft is centered at A\u00f0x; y\u00de and center point 0 which has coordinates \u00f0x0; y0\u00de. Then we can write x0 \u00bc ea cosXt; y0 \u00bc eb sinXt: \u00f027\u00de In the first order continuity and momentum equations the pressure P1i and circumferential velocity V1i can be taken as solution functions. Then one can write the term as P1i \u00bc P\u00fe ci cos\u00f0h \u00fe Xt\u00de \u00fe P\u00fe si sin\u00f0h \u00fe Xt\u00de \u00fe P ci cos\u00f0h Xt\u00de \u00fe P si sin\u00f0h Xt\u00de \u00f028\u00de and V1i \u00bc V \u00fe ci cos\u00f0h \u00fe Xt\u00de \u00fe V \u00fe si sin\u00f0h \u00fe Xt\u00de \u00fe V ci cos\u00f0h Xt\u00de \u00fe V si sin\u00f0h Xt\u00de: \u00f029\u00de In the matrix form P1i \u00bc \u00bdS fP1ig; fP1ig \u00bc P\u00fe ci ; P \u00fe si ; P ci ; P si T ; \u00f030\u00de and V1i \u00bc \u00bdS fV1ig; fV1ig \u00bc V \u00fe ci ; V \u00fe si ; V ci ; V si T : \u00f031\u00de Using these solution functions, the continuity and momentum equations can be written as fDg \u00fe G3ifP1ig \u00fe G4ifP1i\u00fe1g \u00fe G5ifP1i 1g \u00bc \u00bdafB\u0302g \u00fe bfC\u0302g \u00f032\u00de and fEg \u00fe X2ifV1ig _q0ifV1i 1g \u00fe X3ifP1ig \u00fe X4ifP1i 1g \u00bc \u00bdaf^\u0302Bg \u00fe bf ^\u0302Cg : \u00f033\u00de where fDg \u00bc P\u00fe si G1i X \u00fe V0i Rsi \u00fe V \u00fe si G1i P0i Rsi P\u00fe ci G1i X \u00fe V0i Rsi V \u00fe ci G1i P0i Rsi P si G1i X \u00fe V0i Rsi \u00fe V si G1i P0i Rsi P ci G1i X V0i Rsi V ci G1i P0i Rsi 8>>>>>< >>>>>: 9>>>>>= >>>>>; ; \u00f034\u00de fEg \u00bc V \u00fe si X1i X \u00fe V0i Rsi \u00fe P\u00fe si A0i Rsi V \u00fe ci X1i X \u00fe V0i Rsi P\u00fe ci A0i Rsi V si X1i X \u00fe V0i Rsi \u00fe P si A0i Rsi V ci X1i X V0i Rsi P ci A0i Rsi 8>>>>>>< >>>>>: 9>>>>>>= >>>>>; ; \u00f035\u00de fB\u0302g \u00bc G6i 2 ; G2i 2 V0i Rsi \u00fe X ; G6i 2 ; G2i 2 V0i Rsi X T ; \u00f036\u00de fC\u0302g \u00bc G6i 2 ; G2i 2 V0i Rsi \u00fe X ; G6i 2 ; G2i 2 V0i Rsi X T ; \u00f037\u00de f^\u0302Bg \u00bc X5i 2 ; 0; X5i 2 ; 0 T \u00f038\u00de and fC\u0302g \u00bc X5i 2 ; 0; X5i 2 ; 0 T : \u00f039\u00de (32) and (33) show that there are eight linear equations for each seal cavity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002458_tencon.1999.818739-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002458_tencon.1999.818739-Figure3-1.png",
        "caption": "Fig. 3. (a) Appearance and (b) Block Diagram of ForceFX Joystick.",
        "texts": [
            " The reflected force toward obstacles is the force to recover to original state. We defined the reflected force vector F, as the average vector value of detected sensor data. The method to calculate the F, using the distance between robot and obstacle is as follows. where (xr, yJ: x and y position of robot. (xo, yo): x and y position of each obstacle B. FORCE REFLECTION JOYSTICK The joystick in the experiment of force-reflection algorithm is ForceFX from CH Products Corporation and is one of the virtual reality products. Fig.3 shows the its internal block diagram. This joystick has master-slave architecture to realize the force-reflection[7], [81, [9] . CH Products Corporation offers the I-FORCE APVSDK for program development. We have used those functions, which generate the force with vector units to Xaxis and Y-axis[7]. C. SHARED CONTROL BY GAUSSIAN CURVE TABLE If the system uses only virtual elasticity region concept as a force-reflection method, its concept prevents the mobile base from entering the door. Suppose the situation like Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000281_s0005-1098(98)00047-8-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000281_s0005-1098(98)00047-8-Figure1-1.png",
        "caption": "Fig. 1. Crane in R3.",
        "texts": [
            " For systems with classical state representations, rank conditions were given for the solvability by quasi-static state feedback of the decoupling problem (Delaleau and Fliess, 1992) and of the disturbance rejection problem (Delaleau and Fliess, 1994; Delaleau and Pereira da Silva, 1994). In those references it was also shown for these classical systems that, if they can be solved, both problems can always be solved by a quasi-static feedback of a classical state (see Delaleau and Pereira da Silva, 1998 for a survey). In Delaleau and Rudolph (1995) it was shown that for differentially flat systems feedback linearization can always be achieved by a quasi-static state feedback. Consider the overhead crane, schematically shown in Fig. 1. The Cartesian coordinates (X, \u00bd, Z) of the load are given by X\"R sin h cos t#D x , (9a) \u00bd\"R sint#D y , (9b) Z\"R cos h cost. (9c) Here R is the length of the rope, D x and D y are the horizontal positions of the trolley, which is represented by point I. From Newton\u2019s law one gets mX\u00ae \"!\u00b9 sin h cost, (10a) m\u00bd\u00ae \"!\u00b9 sint, (10b) mZ\u00ae \"!\u00b9 cosh cost#mg. (10c) where m is the mass of the load and \u00b9 is the tension in the rope. Eliminating \u00b9 from these equations and choosing u\"(D x , D y , R) as the input, x\"(h, RhQ cost, t, RtQ ) as the state, and y\"(X, \u00bd, Z) as the output yields the (generalized) state representation: xR 1 \" x 2 R cosx 3 , (11a) xR 2 \" x 2 x 4 tanx 3 R "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000104_1.1286168-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000104_1.1286168-Figure4-1.png",
        "caption": "Fig. 4 Volume removed",
        "texts": [
            "12, 20.6% and therefore, no motion towards the exterior occurs. However, on that same surface, at the opposite side at qo 5$q3 L ,q4510,q551.8p%, the eigenvalues are $37.9, 0.027, 0% which is an indefinite form. The indicator s5224.18 is different in sign from the nonzero eigenvalues, therefore admitting motion; i.e., this surface, although it does not admit motion along some regions, it does on another region interior to the manifold. The complete boundary to the manifold is identified and shown in Fig. 4. Consider the motion of the same cutting tool represented in the introductory example by a cylindrical surface such that a 5-parameter verification will be developed. The machining operation will sweep the cylindrical surface first along the curve given above to yield the accessible set now called G ~Eq. ~39!! such that G~q3 ,q4 ,q5!5F 10 cos q3 cos q5120 sin q31q4 sin q3 210 sin q5 220 cos q32q4 cos q3110 cos q5 sin q3 G (42) The first will be a rotational motion of G and the second will be a translation along an axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000334_1.555334-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000334_1.555334-Figure1-1.png",
        "caption": "Fig. 1 Engine speed and vehicle drive torque in a typical up-shift of an automatic transmission passenger car",
        "texts": [
            " The gear shifts are performed by the transmission without involving the driver and handled by wet clutches that are included in the transmission. The clutch for the lower gear is disengaged, and the clutch for the higher gear is engaged, simultaneously. The control of these engagements is often predetermined without taking into consideration the friction characteristics and dynamic performance. Through better control of these engagements it is possible to increase the smoothness and other aspects of clutch performance, such as temperature rise and clutch life. In Fig. 1, a typical upshift of an automatic transmission car is shown, for example from first to second gear. The drive torque on the driving wheels of the car is the sum of the torques of the two gears during the gear shift. When the clutch for the 1st gear is disengaging, the torque on the gear decreases down to zero. At the same time the clutch for the second gear engages and an increasing amount of torque is transferred over on this gear. Before and after the gear shift the drive torque on the driving wheels is approximately constant and equals the engine torque (corrected by the gear ratio)",
            "1 s and constantly equal to approximately 3000 N after that. The brake torque due to friction when the clutch faces are pressed together, acquires a characteristic shape with a torque peak at the end of the engagement due to the static friction characteristics, which increase toward slower speeds. After the clutch has stopped, the brake torque decreases and only the constant applied torque from the hydraulic motor remains. The shape of the clutch torque curve is quite similar to the latter part of the gear shift torque of Fig. 1, i.e., the torque of the higher gear. The engagement can now be controlled in two ways, either by the normal force or the drive torque. The normal force can be controlled in different ways. One way is to decrease it by a ramp at the end of the engagement, as in Fig. 4. This will give a smooth decrease in the brake torque and eliminate the torque peak at the end of the engagement. The maximum brake torque has decreased significantly compared with the reference engagement. The engagement time is approximately the same and no other characteristics are greatly influenced be- Transactions of the ASME s of Use: http://www"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001359_s0020-7683(99)00190-0-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001359_s0020-7683(99)00190-0-Figure3-1.png",
        "caption": "Fig. 3. Multilayer shell: Pro\u00aele and geometric quantities.",
        "texts": [
            " Physical interpretation of the coupling terms that appear in the equations of motion is given. For truly large deformation in which the thickness of the shell is deformable, we refer the readers to Vu-Quoc and Ebciog\u00c6 lu (2000a) for multilayer beams. We will report the result for multilayer shells with deformable thickness in a future paper. The basic kinematics for geometrically-exact multilayer shells is presented in this section, together with some preliminary results that will be used in subsequent sections. 2.1. Basic kinematic assumptions and con\u00aegurations We present in Fig. 3, the pro\u00aele of a multilayer shell in the material con\u00aeguration B. Let x 2 B designate a material point having the material coordinates fx1, x2, x3g, and fE1, E2, E3g be the associated basis vectors, as shown in Fig. 3. We denote the reference layer as layer (0); the kinematics of deformation of all other layers are referred to layer (0). In the present formulation, the number of layers in the shell is arbitrary, and so is the layer thickness. Any layer can be chosen as reference layer. Shown in Fig. 3 is an example of a \u00aeve-layer shell, with the second layer from bottom chosen as the reference layer (0). Below, we will describe the notation adopted for various kinematic quantities. Once the reference layer (0) is chosen, layers above Layer (0) are numbered with positive integers, and layers below Layer (0) with negative integers. Let ` 2 Z designate a layer number.2 When both the 2 Z f0; 1, 2, 3, . . .g is the set of non-negative integers. L. Vu-Quoc, I.K. Ebciog\u00c6lu / International Journal of Solids and Structures 37 (2000) 6705\u00b16737 6707 upper layer ` and the lower layer \u00ff` are present, we often refer to both of these layers by s`), where s 21 designates the sign (positive for upper layers, and negative for lower layers)",
            " The surface s` A is at the distance s` h from the top of layer s`), and at s` h\u00ff from the bottom of layer s`). The thickness of layer s` is given by s` HM s` h s` h\u00ff s` h s s` h\u00ffs, 4 with s` h 6 s` h\u00ff in general. In Eq. (4)2, note that s` h\u00ffs ` h\u00ff for s 1, and s` h\u00ffs \u00ff` h for s \u00ff1; a similar interpretation holds for s` h s: Further, 0 Z 0, s` Z s` Y s` h\u00ffs , for s` 2Nnf0g, 5 s` YM\u00ff 0 h\u00ffs Xs `\u00ff1 i 0 i H 0 h s Xs `\u00ff1 i s i H, for s` 2Nnf0g, 6 where s` Y designates the distance from the material reference centroidal surface of layer (0) to the interface between layer s `\u00ff 1 and layer s`); see Fig. 3. Remark 2.1. It is clear that when we write ` 2N, the index ` designates both the upper and the lower layers; in cases like these when there is no confusion, we thus omit the use of the sign s. Thus, layer ` with ` 2N can also be designated as layer s` with s` sign ` j`j 2N, where sign is the signum function, and j j the absolute value operator. In other words, in the notation s`), ` always takes on positive values. Remark 2.2. In view of Remark 2.1, the summation in Eq. (6)1 is to be interpreted as follows: In the upper summation limit s `\u00ff 1 , we have `\u00ff 1 r0, and thus the sum in Eq",
            "e., for s \u00ff1 and ` > 0), \u00ff `\u00ff1 j\u00ff represents the deformation map of the bottom surface of layer \u00ff `\u00ff 1 (i.e., the layer just above layer \u00ff`)). Next, the construction of the expression (19) for s `\u00ff1 j s begins with the deformation map 0 j of the reference layer (0), and followed by the addition of the transverse \u00aeber vectors (e.g., i H i t of all layers between layer (0) and layer s`). For example, from Eqs. (18) and (19), the deformation map for layer (s ) (i.e., layer (+1) or layer (\u00ff1 ) (see Fig. 3) is described by s j 0 j s s s h \u00ffs s t, 20 0 j s 0 j s 0 h s 0 t: 21 Take another example; consider layer (+3). Combining the expressions Eqs. (18) and (19), we obtain 3 j \" 0 j 0 h 0 t X2 i 1 i H i t # 3 h\u00ff 3 t, 22 where we had used relation (4). Next, we describe the director rotation map ` L: S 24S 2 that maps the material basis vector E3 to the director ` t of layer `). To describe where ` L belongs to, we de\u00aene S 2 EM L 2 SO 3 jLC C, 8C 2 R3 and C E3 0 , 23 L. Vu-Quoc, I.K. Ebciog\u00c6lu / International Journal of Solids and Structures 37 (2000) 6705\u00b167376712 where SO(3) is the special group of proper orthogonal transformations in R3: Thus, L 2 S 2 E rotates E3 about axes of rotation perpendicular to E3, and thus induces no rotations about the E3 vector itself"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002492_iros.1996.571073-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002492_iros.1996.571073-Figure3-1.png",
        "caption": "Fig. 3 The Motion State of aRectangle",
        "texts": [
            " $ ( 6 ) h=O (7) and it shows that ifthe motion of the object is translational, its motion will be translation forever until rest. (b). Pure Rotation Motion ( v = 0 ) In this case, we can get that the net fiction and fiction torque are and T = -pg.Gjr-dm (9) respectively. Ifthe object is central symmetric, (10) + = 0 (1 1) that is so that if the object is central symmetry and at a time t the motion is purerotation, it will rotate foreveruntil rest while the position of COM is holding unchanged. Assume that the motion state of a rectangle is as shown in Fig. 3. Coordinate system oxy is a fixed global h e , c 6 7 is a h e fixed to COM and cx\u2019y\u2019 is a translational system also fixed to COM. Obviously, the relationship between OXY and c E 7 is v5 = v, -cos0 + vy -sin8 vq = -v, -sin 8 + vy cos0 (12) in c E 7 h m e , we get where, s is the whole area, p is the mass density in unit area of the object, respectively. Therefore, in oxy fiame we have the motion equations as follow: F, =FE-cose-F,,.sine=m.x (16) Fy =Fg.sin8+F,.cose=m.y (17) T = 1 . 0 (18) theoretically, by solving Eqs",
            " It is worth noting that ifv=O ( i.e., v,=O and v,=O), then F,=F,=O and it means that the rectangle rotates while COM remains at rest, and if w=O, then T=O, the motion is a pure translation, our conclusion in section 3 is verified. 4.2. Results of Simulation We made simulations to find the motion characteristics of rectangle. The simulation parameters are: a=O.lm, b=0.2m, p=9,8N/m2, the initial position ofCOM is (XO, yo, 6 o ) = (0, 0,O ). All ofsimulations we took areassumedthe initial velocity in y direction (see Fig.3 ) is zero. The simulation results are shown in Fig. 4, Fig. 5 and Fig. 6. v. m/s \\ 0.2 0.4 0.6 0.8 o radls 15 t sec 0.2 0.4 0.6 0.8 I , v t sec 0.2 0.4 0.6 0.8 e rad Fig.4.c The Composite Motion (v,=2m/s, oo= 20 rads), The Displacement xf = 0.914m, The Angles 8,=9.242 rad, The Motion Time t, = 0.925 sec. 0 .t sec x m Fig .5 The Displacement in y Direction is very small, but its variation is complicated. In Space (x, y 6 )the trajectory is acomplex curve. 0 0. Fig.6 The Relationship between Displacement(x,, yf), Angles (e,) and Initial Velocities (v,: 0 - 4 m/s, o o : O - 40 rad/$ Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002976_tec.2003.821833-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002976_tec.2003.821833-Figure2-1.png",
        "caption": "Fig. 2. Schematic structure of the test machine.",
        "texts": [
            " An increase in the rotor temperature has the equivalent effect on the input impedance as a reduction of the slip . This fact gives the presented method the name compensation method and it is used in the following 0885-8969/04$20.00 \u00a9 2004 IEEE manner: by having two impedance circle diagrams with additional information about the slip, the rotor temperature difference between points of identical slip can be determined. The first impedance circle diagram is called the reference diagram (ref) and the other the measurement diagram (meas). Fig. 2 shows the schematic structure of the test machine. Machine nameplate data are summarized in Table I. The principle of the compensation method is given in Fig. 3: There are the measured impedance circle diagrams of two starts of the test machine presented. The impedance phasor moves clockwise during the starting operation. The points of the measurement diagram and of the reference diagram have identical slip but not identical phasors. Because the rotor temperature during the measurement start was about hotter than during the reference start, the point corresponds to point of the reference"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001417_robot.1991.131637-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001417_robot.1991.131637-Figure2-1.png",
        "caption": "Figure 2. A two-disc robot navigating amidst discs.",
        "texts": [
            " In general, one would require \u201cclassification algorithm\u201d for general manifolds which surpasses the capabilities of present day mathematics. Is it possible t o make simplifying assump tions concerning the shapes of the obstacles that would keep the rigid-body problem realistic but afford straightforward recognition of the topological class of T ? Consider the following simple situation: The robot is a planar shape consisting of the union of two discs, all the obstacles are discs, and there is an outer circle bounding a disc-shaped \u201croom\u201d (see Figure 2). Assume that the obstacles are disjoint and do not intersect the outer boundary. However, there can be any finite number of obstacles, and they can be arbitrarily arranged. I t turns out that this problem is tractable. This is made possible by the general fact that union propagates. Namely, if the robot consists of the union of several shapes, then for each real-world obstacle the resulting C-space obstacle is the union of the C-space obstacles arising from intersection of the robot\u2019s subparts with the obstacle [7]",
            " The solid doughnuts can intersect each other in arbitrary manner, resulting in what seems to be a dense subset of the configuration spaces arising from arbitrary planar shape navigating amidst arbitrary planar obstacles. In particular, doughnut worlds are not necessarily path-connected. Is there a simplifying assumption about the relative size of the robot and the obstacles that guarantees a connected free space but retains the non-trivial aspects of the problem? Consider the following simplified situation: The size of each of the discs comprising the robot (but not necessarily that of their union) is smaller than the minimal gap between the obstacles (see Figure 2). It can be shown that this assumption guarantees that whenever two solid doughnuts in C S intersect each other, they meet exactly twice, and their boundaries meet along topological circles (or two points in the degenerate case). This, in turn, affords a complete characterization of the free configuration space: F is path-connected and, roughly speaking, is obtained by puncturing a solid doughnut (corresponding to the outer boundary in the real world) by smaller disjoint solid doughnuts (corresponding to the internal obstacles)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001286_zamm.19940740117-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001286_zamm.19940740117-Figure1-1.png",
        "caption": "Fig. 1. Solid disk geometry and possible cases for internal border radius z",
        "texts": [
            " However, as has been pointed out by GAMER, for material exhibiting linear strain hardening, meaningful results can be derived [5--71. As shown in [5], the plastic core of the elastic-plastic disk consists of two parts with different forms of the Tresca's yield condition. Of course, the same holds true for the fully plastic disk [6]. The above analyses consider the thickness of the solid disk as uniform. An attempt has here been made to investigate the fully plastic rotating solid disk of variable thickness. In the problem under consideration, the thickness h is assumed up to a definite radius a as constant (Fig. 1.) and outside this circular region vary according to a hyperbolic law in the form where h, is the thickness at b and n is the thickness parameter. On this assumption the problem can be solved in closed form. The analysis is based on the Tresca's yield condition, its associated flow rule and linear strain hardening. It is furthermore assumed that the disk is thin and that the variation of thickness is slowly and symmetric with reference to the mid-plane. In the present analysis, the location of the internal border radius z is considered for two cases: (1) in the part with variable thickness (Fig. l.a), (2) in the part with constant thickness (Fig. 1.b). In the following sections firstly we shall consider the case of the solid disk where the second plastic region starts at the variable thickness part. 2. Inner plastic region The plastic deformation of the solid disk is governed by the yield condition CT, = a. = gy . (2.1) If the work hardening law is taken to be o y = \"o(1 + v e q ) where a. is the initial tensile yield stress, q is the hardening parameter and E , ~ is an equivalent plastic strain. For slowly varying angular velocity, the equation of motion d - (hra,) - hoe = -h",
            "b), the stresses, radial displacement and strains in the uniform solid disk (z 5 r 5 a), setting n = 0 in the equations (3.6)- (3.9) are obtained as follows: 0 = - c ' r - ( l + w I + C k r - \" - W ' - 1 (1 + B ) p 2 r Z + oo (3.10) (3.1 1) g,, =. WC;r-(\"\"') + WCkr-('-'\"' - &oZr2 + 0, - -[1 1 + (1 - 3 ~ ) B l ~ o ' r ~ + (1 - v)oor 9 (3.12) 1 9 - - (1 + 3v - 8B) Qo2r2 where B = (1 + 3v) H/9 + 8H. These expressions agree with eqs. (14)- (18) in [6]. 4. Condit ions and results (3.13) The above general expressions in the first case (Fig. 1.a) contain the unknowns constants C,, C,, C,, C3 and C,. An additional unknown is the radius z separating the outer from the inner plastic region. For the determination of these six unknowns there are six conditions available. The most convenient ones are: continuity of radial stress and circumferential stress at r = z, continuity of radial stress and radial displacement at r = a, the condition of vanishing radial plastic strain at r = z and the condition of vanishing radial stress at the free boundary, r = 6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003996_tase.2005.846289-Figure14-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003996_tase.2005.846289-Figure14-1.png",
        "caption": "Fig. 14. Orthogonal slicing.",
        "texts": [
            " The computation of FIV and RFV is quite complicated, while in the proposed orthogonal LM system there is no staircase interaction by nature or the FIV is degenerated into the interface plane. Shown in Fig. 13 is the result of volume decomposition for the part in Fig. 9, the interface between the flat volume and the rest of the part is a horizontal plane, hence the computation is significantly simplified in this condition. The processing techniques for slicing and path generation in the conventional LM process planning can also be applied in this method. The only difference is that the slicing will be in the horizontal direction for the flat volume. As shown in Fig. 14, the part was separated into two parts: the flat volume and the steep volume. The flat volume was sliced along the horizontal direction and the steep volume was sliced along the vertical direction. To minimize the slicing error inherent in the LM processes, especially staircase errors of relatively flat surfaces, a novel orthogonal LM system has been proposed and developed. The mathematical model for deriving the slicing error in LM processes is described in this paper. The flat surface feature is extracted from the STL model, and special process planning procedures are applied to these features based on the proposed orthogonal LM system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003350_rspa.2004.1429-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003350_rspa.2004.1429-Figure1-1.png",
        "caption": "Figure 1. Sketch of the system defining the notation.",
        "texts": [
            " We may, however, conjecture that the averaged behaviour (over many successive impacts) will be simply to give an \u2018effective\u2019 Coulomb friction parameter me somewhat less than the value of m that pertains during periods of continuous contact. Let us first recapitulate the essential notations and equations for the problem, as presented in part I. We consider the dynamics of a rigid axisymmetric body with Proc. R. Soc. A (2005) centre-of-volume O and surface S which moves on a horizontal table, making sliding and/or rolling contact at a point P (figure 1). We restrict attention in this paper to bodies that are \u2018flip-symmetric\u2019, i.e. symmetric about the plane Oxy perpendicular to the axis of symmetry Oz. (The effects of flip symmetry breaking will be deferred to a subsequent paper, part III in this series.) With Ox in the plane defined by Oz and the vertical OZ, we may use Oxyz as a rotating frame of reference. Alternatively, we may use OXYZ, where OX is horizontal and OY coincides with Oy. Let M be the mass of the body and b its radius of cross-section in the plane Oxy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000487_elan.1140080417-FigureI-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000487_elan.1140080417-FigureI-1.png",
        "caption": "Fig. I. The design of the electrode flow cell used in this flow cell; A) depth view; B) axial view and C) illustrates the flow path ol'the injected sample zone in the ISE compartment.",
        "texts": [],
        "surrounding_texts": [
            "Electroanalysis 1996, 8, No. 4 sensing membrane, and (2) the reference stream that contained a constant chloride activity for a Ag/AgCl reference wire electrode, that was prepared by anodizing a 0.5 mm in diameter silver wire [12]. A flow ratio of 1 : 1 was employed and the carrier and the reference streams used in the flow cell was 0.1 M NaCl. Manual injections were carried out using a Rheodyne 5020 Teflon injection valve fitted with a 100 pL sample loop, and the background solutions were pumped through the electrode flow cell at a flow rate of 1.5mL/min using a peristaltic pump (Ismatec Sa). The FIP peaks were measured by an Orion 701A meter and recorded by a Hitachi (QD 25) pen recorder. Steady-state measurements with the calcium ISE were performed with an Orion double junction reference electrode (Ag/AgCl I saturated KCI )I 10% KN03). The electrode potential was monitored by an Orion 701A meter and a Hitachi (QD 25) pen chart recorder was used to record the response profile of the ISE. The stability criterion used in this arrangement was f 0.2 mV for 2 minutes (Fig. 2)."
        ]
    },
    {
        "image_filename": "designv11_24_0003264_j.engfailanal.2006.02.006-Figure9-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003264_j.engfailanal.2006.02.006-Figure9-1.png",
        "caption": "Fig. 9. Correct (above) and incorrect alignment (below).",
        "texts": [
            " This may be due to a malfunction of the welding equipment, or poor positioning of the ring\u2013flange\u2013piston rod assembly. A malfunction of the welding equipment, with below-specification power, can be ruled out \u2013 the control and monitoring processes show no sign that this has happened. Therefore, the most probable cause, i.e. insufficient heat generation, is probably due to poor positioning of the parts to be welded. That is, poor alignment of the ring\u2013flange\u2013piston rod assembly must have been the cause of the defective weld. Fig. 9 shows a diagram of the possible failure, which would have produced a heat distribution pattern less concentrated on the piston rod axis (below) than specified by the design situation (above). Because of the poor alignment shown in the lower part of Fig. 9, the weld nugget is not centred on the axis, but rather is displaced, producing cavities and poor heat distribution. A more detailed inspection of the failed shock absorbers shows that the flange has become welded to the piston rod (Fig. 10), displacing part of the carbon rich material at the break. This weld should not exist, according to specifications (Fig. 9). As can be seen in Fig. 11, at greater enlargement, there has been a clear fusion of the low carbon flange steel and the carbon rich piston rod steel. This could only be due to the passage of a current of sufficiently high intensity through this area. As mentioned, according to the manufacturer\u2019s specifications, this area should not be fused, since it should not be in the path of the current. The defective welding has caused at least one large 2 mm diameter cavity, and weak joints caused by true welding on the periphery"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003512_inmic.2003.1416742-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003512_inmic.2003.1416742-Figure1-1.png",
        "caption": "Figure 1 : TRS Configuration",
        "texts": [
            " 1 INTRODUCTION TRS is developed at PIEAS for the purpose of studying the dynamics of nonlinear multi input multi output (MIMO) systems. Specifically. this is a two input two output nonlinear system. The plant consists of two rotors. a main rotor and a tail rotor, mounted at each end of a lever bar. These rotors can rotate the lever bar about a horizontal axis and a venical axis. The angular positions of the lever bar about the two axles are the two outputs of the plant. Mechanical configuration of the plant is shown in figure 1 I The task is to control the angular position of the lever bar. The plant has two degrees of freedom; the azimuth angle (position in horizontal plane about the vertical axis) @and the elevation angle (tilt in vertical plane about the horizontal axis) 0. There is a strong coupling between movements about both axes. as each of ' the rotors can rotate the lever bas about both the vertical and horizontal axes. connected at right angle. The bar 11, acts as the horizontal axis. Two rotors are mounted on the lever arm: a Main rotor RM and a Tail rotor RI, with the resultant aerodynamic forces giving rise to moments in the e and @ directions respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003861_msf.505-507.949-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003861_msf.505-507.949-Figure5-1.png",
        "caption": "Fig. 5. Modeling of internal and external bevel gear.",
        "texts": [
            " (16) Combining { } { }2M p , { } { }M p n , equation (6) and equation (15), the equation of internal gear can be expressed in internal rotatable coordinate system 2S as { } { } { } { } T nnn p np T zyxzyx )1,,,(MM)1,,,( 2 222 = , and the detailed equation is, 2 2 2 2 cot 2 2 2 2 2 2 2 [( cos ) ( )][sin( ) cos cos( ) sin sin ] [ cos( ) cos sin( )sin sin ] ( sin )sin cos [( cos ) ( )][ sin( )sin cos( ) n j j c c c c n n j j c c x r F l e r E y r F l \u03b8 \u03b2 \u03b1 \u03c1 \u03b8 \u03b8 \u03b2 \u03d5 \u03d5 \u03b8 \u03b8 \u03b2 \u03d5 \u03d5 \u03b4 \u03b8 \u03b8 \u03d5 \u03d5 \u03b8 \u03b8 \u03d5 \u03d5 \u03b4 \u03b1 \u03d5 \u03b4 \u03b1 \u03c1 \u03b8 \u03b8 \u03b2 \u03d5 \u03d5 \u03b8 \u03b8 \u03b2 \u03d5 \u22c5 = + + \u2212 \u2212\u2206 + \u2212 + \u2212 \u2206 + \u2212 + \u2212 \u2212 \u2206 \u2212 + \u2212\u2206 \u2212 + + = + + \u2212 \u2212 \u2212 \u2206 + \u2212 + \u2212 \u2206 + \u2212 2 2 cot 2 2 2 2 2 2 2 cot 2 2 cos sin ] [cos( )sin sin( ) cos sin ] ( sin )cos cos [( cos ) ( )]cos( ) cos sin( ) cos ( sin ) sin [ sin ( ) sin cos ]sin( c c n n j j c c n j j e r E z r F l e r E F l E \u03b8 \u03b2 \u03b8 \u03b2 \u03d5 \u03b4 \u03b8 \u03b8 \u03d5 \u03d5 \u03b8 \u03b8 \u03d5 \u03d5 \u03b4 \u03b1 \u03d5 \u03b4 \u03b1 \u03c1 \u03b8 \u03b8 \u03b2 \u03d5 \u03b4 \u03b8 \u03b8 \u03d5 \u03b4 \u03b1 \u03b4 \u03b1 \u03c1 \u03b1 \u03b1 \u03b8 \u03b8 \u22c5 \u22c5 + \u2212 \u2206 \u2212 + \u2212\u2206 \u2212 + + = \u2212 + + \u2212 \u2212\u2206 + \u2212 \u2212 \u2212 \u2206 \u2212 + + + \u2212 \u2212 \u2212\u2206 + cot) cos( ) sin 0c ce\u03b8 \u03b2\u03b2 \u03d5 \u03b8 \u03b8 \u03d5 \u03b1\u22c5            \u2212 + \u2212 \u2206 \u2212 = . (17) Modeling of the internal bevel gear with double circular arc profile The modeling of the internal gear is the basement for virtual assembly of nutation drive, interference verification, NC manufacturing and stress analysis. Based on the equation (17) of the tooth profile of the internal gear, the three dimensional modeling shown in Fig. 5 can be obtained by producing the tooth parameters \u03b1 , \u03b8 and rotating angle c\u03d5 . Similarly, the modeling of external bevel gear can also be obtained. This paper develops the equation for determining the transmission ratio between two nutation gears based on the principle of a rotating coin on a table. The tooth profile with double circular arc for helical bevel gears in nutation drive is proposed. Then, the meshing coordinate system is presented and the meshing equations and tooth profile equations are derived based on the proposed circular arc tooth profile"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002674_0379-6779(87)90562-5-Figure9-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002674_0379-6779(87)90562-5-Figure9-1.png",
        "caption": "Fig. 9. The influence of support ing e lec t ro lyte on the cyclic vo l t ammet ry of PPP film deposi ted on BPG electrode (0.20 cm 2) in acetonitr i le solutions. Support ing electrolytes (0.1 M): (a) NaC104; (b) TBAP; (c) TBAFB. Scan rate: 200 mV s -1. The PPP film (thickness: 0.1 pro) was prepared on BPG electrode by a constant -potent ia l electrolysis at 0.5 V v s . SSCE as in Fig. 4.",
        "texts": [
            " The anodic peak currents, /pa, for the oxidation of PPP film deposited on BPG electrode as a function of potential scan rate, v. Supporting electrolyte: 0.1 M NaCIO4/ acetonitrile. The PPP films were prepared on BPG electrodes by a constant-potential electrolysis at 0.9 V vs. SSCE as in Fig. 4. Film thicknesses: (o) 0.10; (A) 0.60; (0) 2.4 pro. The cyclic vo l t ammet r i c response of PPP fi lm on BPG e lec t rode in ace toni t r i le solut ions conta in ing various suppor t ing e lec t ro ly tes is shown in Fig. 9. A well-defined cyclic vo l t ammog ram was ob ta ined in each elect ro ly t ic solut ion. As is well k n o w n fo r r edox p o l y m e r films, including elect roact ive e l ec t ropo lymer i zed ones [ l l b ] , the ' e lec t rochemica l d o p in g - undop ing process ' , i .e . , the up t ake or release o f suppor t ing e lec t ro ly t ic ions in to or ou t o f p o l y m e r films, occurs dur ing the i r o x i d a t i o n - r e d u c t i o n react ions. In some cases, the significant e f fec t of suppor t ing e l ec t ro ly te on the r e dox response o f the films has been observed [13a, 19] "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002025_a:1017943816350-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002025_a:1017943816350-Figure1-1.png",
        "caption": "Figure 1. Energization secuence of a PM stepper motor.",
        "texts": [
            " (55) Consequently, the states x, \u03b7, e are locally ultimately bounded and will converge to the ball given by B(x, \u03b7, e) = {(x, \u03b7, e): Vco(x, \u03b7, e) d/\u00b5co}. The basic PM stepper motor consists of a rotor and a stator. The rotor features two axially slotted cylinders displaced by half a slot or \u201ctooth\u201d; one of the cylinders or \u201cgears\u201d is a permanent north magnet. The stator, has a different number of teeth than the rotor gears, so that the rotor will never be aligned with the stator teeth. Each slot in the stator is an electromagnet which can be alternatively made north or south. Figure 1 shows the energization sequence of a PM stepper motor. Figure 1(a) illustrates the initial position with windings A and C energized and windings B and D de-energized. To make the rotor move a step clockwise, windings B and D are energized in an N\u2013S orientation as it is shown in Figure 1(b). The mathematical model for a PM stepper motor is given by the following equations (see [16] for details) dia dt = va \u2212 Ria +Km\u03c9 sin(Nr\u03b8) L , dib dt = vb \u2212 Rib \u2212Km\u03c9 cos(Nr\u03b8) L , (56) d\u03c9 dt = \u2212Kmia sin(Nr\u03b8)+Kmib cos(Nr\u03b8)\u2212 B\u03c9 \u2212Kd sin(4Nr\u03b8) J \u2212 \u03c4l J , d\u03b8 dt = \u03c9 where ia , ib, and va , vb are the currents and voltages in phases A and B, respectively, w is the rotor (angular) speed and \u03b8 is the rotor (angular) position. L and R are the selfinductance and resistance of each phase winding, Km is the motor torque constant, Nr is the number of rotor teeth, J is the rotor inertia, B is the viscous friction constant and \u03c4l is the load torque"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002683_j.actamat.2004.07.039-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002683_j.actamat.2004.07.039-Figure4-1.png",
        "caption": "Fig. 4. Schematic explanation for the quenching behavior of the droplet with 217 K initial undercooling shown in Fig. 3 (c).",
        "texts": [
            " At the final stage of quenching for both droplets (a) and (b), the solidification front reached the edge and then remaining melt solidified from edge to center reversely (last four frames). This was observed through the first solidified layer which had already cooled below TM. For the large initial undercooling droplet (c), three different contrasts were found at t = 0.4 ms after the typical initial impact behavior (t = 0.2 ms). The schematic explanation for this quenching behavior is shown in Fig. 4. The droplet had large initial undercooling more than 200 K. Once the solid was formed at the impact, the dendrite growth occurred quasi-adiabatically into the undercooled melt. The low, medium and high contrasts observed were due to undercooled melt, heated melt by latent heat and solid, respectively. For typical metallic materials (eS = eL = const.), the melt heated by latent heat reaches TM and its brightness is same as that of solid at TM. For Si, however, larger e of solid resulted in the brightness difference for solid and liquid at TM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001967_910017-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001967_910017-Figure4-1.png",
        "caption": "Fig. 4(b)",
        "texts": [
            " - - r - one S-S crank for one rigid guiding body (spindle assembly). First, we have one equation from equation (3) for the S-S crank: i J 1 ~lx(~~Z-~oz) + 4Z(~1x-~ox) ( H ~ ~ - T ~ ) H ~ ~ + ( H ~ ~ - T ~ ) H ~ ~ ~ ( H ~ ~ - T ~ ) ~ ~ ~ = ~ = 2 IX (A lz -A oz ) + Alz(~;x-~ox) We then have two equations from equation (4) for each R-S crank: ( ~ l p - ~ o x ~ ~ l ~ + ( ~ l y - ~ ~ y ~ ~ l y ~ ( ~ l z - ~ o z ~ ~ l z = ~ DOUBLE-WISHBONE SUSPENSION u;Bxl + tfyByl t u>BZ1 = 0 A Double-Wishbone suspension is shown in Fig. 4 with the equivalent RSSR-SS mechanism ( c ~ ~ - c ~ ~ ~ ~ ~ ~ + ( c ~ ~ - c ~ ~ ~ ~ ~ ~ + ( c ~ ~ - c ~ ~ ) ~ ~ ~ ~ o and all the joint coordinates. From the coordinates of points p and Q we can calculate u;tlx + u'C t uitlz = 0 the direction cosine U(u;,Ji ,ui) of the line Y lY that passes through the PolXts P and Q,and Finally we have a direction cosine equation: the coordinates of point Co, which the line u 2 t u 2 + u z 2 = 1 and C T intersect with perpendicularity. x 0 1 Y Fig. &(a) A Double Wishbone Suspension The Equivalent USSR-SS Mechanism Using the velocity matr+x 05 Instant Pttch (2) we replace each of B ,B "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003917_0278364905058242-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003917_0278364905058242-Figure5-1.png",
        "caption": "Fig. 5. (a) Three cubes in contact c-space, (b) their mutual partition into subcubes along the separating planes, and (c) the induced subcube graph.",
        "texts": [
            " Hence we can associate with each maximal cube an orientation vector, which is aligned with the si-axis of the limb that cannot be lifted from the three-limb postures parametrized by the cube. The orientation vectors play an important role in the graph construction described below. In the second stage, the algorithm partitions the maximal cubes as follows. The algorithm constructs an arrangement of all separating planes of the maximal cubes, where each separating plane contains one of the faces of the cubes. Using this arrangement, the algorithm partitions the cubes as illustrated in Figure 5. The figure shows three cubes and their mutual partition along the separating planes into subcubes. During the partition process, each subcube inherits the orientation vector of its parent cube. The resulting subcubes have disjoint interiors and satisfy the following projection property. Any two subcubes either have the same projection on one of the coordinate planes, or their projection on all three coordinate planes have disjoint interiors. If two subcubes share a projection they are called compatible, and the si-axis aligned with the direction of projection is called the direction of compatibility",
            " Every edge represents lifting and repositioning of a particular limb. The lifting of a limb must leave the robot in a stable two-limb posture. The orientation vector of a subcube describes which limb may not be lifted from the three-limb postures parametrized by the subcube. Hence all edges emanating from a node must be orthogonal to the orientation vector of the subcube associated with the node. Moreover, all edges of the subcube graph are straight lines parallel to the si-axes in contact c-space (Figure 5c). For example, when an edge is parallel to the s1-axis, motion along this edge means that only limb 1 is moving, while the footholds of limbs 2 and 3 remain fixed. According to Lemma A1 in Appendix A, the motion of a limb between any two subcubes connected by an edge can be executed such that reachability is maintained throughout the limb\u2019s motion. Finally, the start and target three-limb postures, denoted S and T , are added as special nodes to the subcube graph. The construction of edges from S and T to the other nodes of the graph is described below"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003589_b978-0-12-093480-5.50006-4-Figure2.4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003589_b978-0-12-093480-5.50006-4-Figure2.4-1.png",
        "caption": "FIG. 2.4 Form of the set (24)",
        "texts": [
            " We have x* = \u03bb* = 0 and Assumption (S) is satisfied. We have Lc(x,\u00c0) = -xp 4- \u03bb\u03c7 + ic |x | 2 , VxLc(x,A) = -pxp~l + \u03bb + ex, V2 xLc(x,A)= -p(p - 1)XP-2 + c. A straightforward calculation shows that V2 xLc(xU) > 0<=>|x| < Lc/p(p - l ) ] 1 / (*-2 ) , VxLc(x,/l) = 0<>\u03bb = x(pxp~2 - c). 112 MULTIPLIER METHODS Using these relations it can be verified that Lc( \u00b7, A) has a unique local minimum x(A, c) with V^x Lc[x{X, c), A] > 0 for all (A, c) in the set (24, {(\u039b,\u03bf\u0390\u03bc, < ^ [ - ^ ] ' \" ' - V - - \u00bb . , > \u201e}, shown in Fig. 2.4. The order of growth on the allowable distance of A from A* is (p \u2014 \\)/(p \u2014 2) and tends to unity as p increases. Thus, we cannot demonstrate, in general, a better than linear order of growth of the allowable distance of A from A* as c increases. Proposition 2.4 can yield both a convergence and a rate-of-convergence result for the multiplier iteration K+i = K + ckKxk)- It shows that if the generated sequence {Ak} is bounded [this can be enforced if necessary by leaving Afc unchanged if Ak + ckh(xk) does not belong to a prespecified bounded open set known to contain A*], the penalty parameter ck is sufficiently large after a certain index, and after that index minimization of LCk(\u00b7, Ak) yields the local minimum xk = x{Xk,ck) closest to x*, then we obtain xk^>x*, \u00c0k-*\u00c0*"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003971_ijvd.2005.008472-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003971_ijvd.2005.008472-Figure1-1.png",
        "caption": "Figure 1 Typical decoupler/isolator assembly consisting of a one-way clutch and a torsional spring separating the accessory pulley from the shaft",
        "texts": [
            " The magnitude of tension drop across an accessory depends on the accessory load as well as its rotary inertia. As the engine speed increases, the frequency of crankshaft pulses increases, causing an increase in tension drop which, in turn, increases the likelihood of belt slip on the pulley. The alternator with its very large moment of inertia is most susceptible to dynamic tension fluctuations hence there is a need to find ways to reduce the steady-state peak tension drop across it. One-way clutches (Figure 1) have been used in a variety of dynamic systems for many years for power transmission, as mechanical diodes to rectify oscillations into rotary motion (Mockensturm and Balaji, 2005). One other interesting use of one-way clutches has been to decouple large-inertia elements to reduce loads in oscillating systems (Mockensturm and Balaji, 2005). In this paper, the clutch is introduced in the FEAD to allow a high inertia element (e.g. alternator) to overrun the system when the pulley is decelerating",
            " The piece-wise non-linear system obtained is linearised about the equilibrium configuration in both engaged and disengaged states to obtain analytical solutions using a method described by Mockensturm and Balaji (2005). The effect of non-linear terms is considered by the numerical integration of the equations of motion using the fourth order Runge-Kutta method, and good agreement is obtained between the two sets of results for small oscillations about the equilibrium. The basic model of a one-way rigid clutch between two rotary elements undergoing relative rotation, as illustrated in Figure 1, is described below. The outer ring is under some arbitrary external harmonic moment excitation Text t . The accessory shaft is subjected to a constant moment loading Tf. In the engaged state, the rigid clutch forces the outer ring with inertia I1 and the accessory shaft with inertia I2 to move as one, I1 1E t Text t \u00ffM t 1 I2 1E t M t \u00ff Tf; 2 where M t is the moment transferred through the clutch and 1 is the motion of the outer ring (and accessory shaft). For clarity, a subscript E is used to denote a variable in the engaged state"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000150_1.2834596-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000150_1.2834596-Figure2-1.png",
        "caption": "Fig. 2 One-dimensional contact geometries for (a) journal bearing (peri( 2 3 ) odic contact), and (b) inclined plane slider bearings (open ended wedge contact)",
        "texts": [
            " - ^ = 0 , -Kij = r , j + p6ij (5) The total stress tensor is TTJ,, which is composed of the extra stress plus the isotropic pressure p, where Sij is the Kroneker delta. In most flows of Newtonian fluids, the total normal stress (defined with Bird's convention) approximately equals the pres sure. We now write out these equations in component form assum ing two-dimensional flow with v,ixu X2, t) and tJ2(JCi, x^, t), see Fig. 1. We obtain the continuity equation: -p-oiyov] - -\u0302oTciw - X-oo7(i)\u21227(i)mj)- (1) dxi 8x2 (6) Nomenclature a = { \u2014 ) slope parameter = (7?i\u201eiet \u2014 //,,u)/Wi\u201eie\u201eEq. (23),Fig. 2 De = ( \u2014) Deborah number = \\oU/ L, H, Ho = (m) film thichness, reference value. Fig. 1 ka< kt = (-) integration constants, Eq. (11) L = (m) contact length parameter. Fig. 1 p. Pa \u2014 (Pa) pressure, ambient pres sure, R \u2014 (m) journal bearing radius. Fig. 2 t = (s) time, U = (m/s) sliding velocity. Fig. 1 Ui, V2 = (m/s) velocity components (filmwise, crosswise). Fig. 1 X = ( \u2014 ) filmwise dimensionless coordinate. Fig. 1, Eq. (21) Xi, A;2 = (m) spatial coordinate com ponents (filmwise, cross wise). Fig. 1 79. 7(1)0 = (1/s) rate-of-strain compo nents 6ij = (\u2014) Kronecker delta \u20ac = ( - ) eccentricity ratio, Fig. 2, Eq. (23) 9 \u2014 ( \u2014 ) journal bearing filmwise coordinate. Fig. 2, Eq. (23) ^0, ^00 = (s) fluid relaxation, retarda tion time parameters /Xo = (Pa \u2014 s) viscosity I'll, Til, = (Pa) total, extra stress com ponents, Txt. T\u201e, = ( - ) total, extra stress compo nents (dimensionless), Eq. (21) w = (1/s) journal bearing rota tional speed. Fig. 2, Eq. (23) Superscripts [A ]\u0302 = denotes the Newtonian (lubrication) theory solution [D] = denotes the Deborah number (viscoelastic) correction solution Journal of Tribology JULY 1998, Vol. 120 / 623 Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use the continuity equation ( 6 ) , integrating the result with respect to X2, and applying the Vi boundary conditions of (10) gives: j,dH 2 Ho 4 - 4 l ' k\u201e = \u0302 (12) These velocity field results are exactly the same as would be obtained for the Newtonian fluid",
            " The best alternative would seem to be that the flow directed normal stress TTU must balance the ambient pressure at the film ends, which would be the situation in the case of a stationary free surface with negligible surface tension. However, TTH varies across the gap, so the best we can do is. 7rii(jCi) = Mix,) 7r\u201e(0) = 7tn(L) . X2)dX2 TT,l(Xi,. Jo 1 / M ] = 7r22(x,) + 2/ioXot/' - 5 4 + 2fc\u201e - 7 + - fc? li \\ ti 3 (21) For demonstrative purposes, we analyze two specific film shapes, the journal bearing and the simple wedge contact (plane slider), respectively: h = \\ + e cos e, 6 = 2TTX; h = I - ax, (24) see Fig. 2. For the journal bearing case, HQ is the radial clearance and the sliding speed U = uiR. For the wedge case. Ho is the inlet film thickness. For the journal bearing, performing the integrations of Eq. (15) and nondimensionalizing, we have: T^\u201em = 7rv,(0) + 6IT(0; e) + hlf{0; e) De ( l+\u00a3)^ A V ^ H ( 1 + 6 ) ' h' 1 (1 +eY (25) Vl ~e^ arccos e + cos h K IT: - arccos e -I- cos 27r 700 ^ 1 ( - \u00a3 sin g ^ o\u0302\u201e (1 - e ^ ) TOO ' 3 2 ( 1 - \u00a3 ^ ) \u2022 e sin 0 + IT + 3/\u00b0\u00b0 - If (26) ''^aix) = TTyyix) -I- 2 D e 1 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001531_robot.1995.525721-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001531_robot.1995.525721-Figure1-1.png",
        "caption": "Fig. 1 Definition of constants and variables",
        "texts": [
            " 2 S t a t e m e n t of problem In this paper, for the manipulator with N-th degrees of freedom in A4-dimensional (A4 = 2 or 3) work space with K obstacles, it is considered to plan the trajectory which has the more shortened travelling time and makes the manipulator reach the goal. The initial configuration of the manipulator, the goal position of the endeffector and the obstacles spaces are given beforehand. The obstacle is considered to be the ball ( the circle in the case of 2-dimensional work space) and its center and radius are given. The link and the joint of the manipulator are given the number 1 N N as shown in Fig. 1 and variables are defined as follows. P, : the joint positon vector, n = 1 , 2 , - . - , N + 1 It expresses the position of the endeffector for IZ = N + 1. G : the goal position vector of the endeffector L, : the length of the link, IZ = 1,2 , . .. , N 0, : the joint variable, n = 1,2 , . + I , N Ok : the position vector of the center of the obstacle k, k = I 1 2 , - * - , K - 3069 - IEEE lnternatlonal C o n f e r e n c e on Robolics a n d Automation 0-7803-1965-6/95 $4.0001995 IEEE R k : the radius of the obstacle k, k = 1 , 2 , ' "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002175_1.1515333-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002175_1.1515333-Figure5-1.png",
        "caption": "Fig. 5 Discrete model of a rotating tine",
        "texts": [
            " Therefore a numerical approach is preferred. The idea of splitting the cantilever beam up into discrete elements connected using torsion springs has been well documented @4,10#. By way of a brief review, the tines are split into n rigid elements of mass and length: m5 rAL n l5 L n (4) And by equating strain energy expressions for the tine and torsion spring, the spring constant k for any one of the n torsion springs may be shown to be: k5 EIn L (5) Applying this technique to the tines within a rotating brush Fig. 5 may be drawn. Taking any random element i within the tine, the governing equations for the tine deflection may be derived. Resolving the vertical and horizontal forces and taking moments about the mid point; Transactions of the ASME 7 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F mRiv 21lx~ i11 !2lxi50 (6) ly~ i11 !2lyi50 (7) Ti2T ~ i11 !2~lxi1lx~ i11 !! l 2 sin u i2~lyi1ly~ i11 !! l 2 cos u i50 (8) where Ti5k~u i2u i21! (9) The free end of the tine, element n, experiences no reaction at the tine end, Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002383_robot.1996.506891-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002383_robot.1996.506891-Figure2-1.png",
        "caption": "Figure 2: \u2018\u2018Surf\u201d contact with a five joints kinematic model.",
        "texts": [
            " This means that the contact point belongs to the Y-2 plane (Fig. 1). Fig. 6 shows the identified uncertainty parameters of the three point contact. Due to friction disturbancies on the forces measurements, only the kinetic energy error term of (4) is minimized. In the top figure the identified alignment error (full line) is compared with the specification (dashed line). When the alignment error is small, the insertion can start. The rotation angle about the peg axis (bottom figure) is small. This means that the surfcontact belongs to the Y-2 plane (Fig. 2). 4.3 Monitoring The detection of the transitions between the different contact situations is based on the total energy error function of the expected model. Jumps in Ea are detected with the Page-Hinckley test. Fig. 7 shows the total energy error for the successive contact situations. The insertion starts in free space. After 16 seconds a jump in the energy error is detected which means that the transition to the curve-face contact takes place. From now on, the model of the curve-face contact is valid"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001545_j.2161-4296.2000.tb00219.x-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001545_j.2161-4296.2000.tb00219.x-Figure2-1.png",
        "caption": "Fig. 2 Kinematic Model of a Tractor",
        "texts": [
            "errors from roll measurement noise 1 of more than 0.4 deg will exceed those from DGPS measurement noise 14 . Therefore, to utilize the centimeter-level accuracy of DGPS, roll measurement noise must be less than 0.4 deg. Pitch motion of the vehicle creates longitudinal positioning errors. However, in the steering control of the farm tractor, there is no ability to control motion in the longitudinal direction. Because only lateral tracking is being controlled, pitch motion was ignored in this work. Figure 2 shows a schematic of an off-road vehicle, including its CP. The equations of motion that describe the off-road vehicle shown in Figure 2 can be divided into the forward and lateral dynamics \u017d . \u017d .shown in equations 2 and 3 : \u02d9\u017d . \u017d . \u017d .n V cos p sin 2\u02d9 x 2 \u02d9\u017d . \u017d .e V sin p cos \u02d9 x 2 \u00a8 \u02d9 \u017d . p p V tan 3 4 x \u017d .3 \u00a8 \u02d9 p p u5 5 where u is control input; e is east position; n is north position; V is forward velocity; is heading;x \u02d9 \u02d9 is yaw rate; is steer angle; is steering slew rate; g yaw is yaw gyro bias; and p , p , p , pbias 2 3 4 5 are model-based parameters of the tractor, found in 15 . \u017d .The dynamics in equation 2 can be linearized about the operating point at each time step by \u017d "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000727_j.2168-9830.1999.tb00427.x-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000727_j.2168-9830.1999.tb00427.x-Figure4-1.png",
        "caption": "Figure 4. The first group\u2019s design",
        "texts": [
            "5 YC = Total cost of the project Lecture topics included, among others, non-contact sensors, gear systems, and design constraints. Several handouts were distributed from time to time. Project grades were based on quality of presentation, feasibility, and, in particular, creativity of the design. Students had to specify the challenges that they faced during the design and construction stages and how they overcame the challenges. In particular, the strategies they adopted to overcome challenges had to be described. Figure 4 shows one of the students groups\u2019 designs. In this design, once the block was placed on a designated space, a push sensor activated the system. To reduce the rpm of the motor a worm gear box was used (figure 5). The security system area (figure 6) was equipped with several optical sensors. To indicate the height of the block, different roller LEDs were used (figure 7). To adjust the timing of the height indicator, the students used a timing circuit (figure 8). The challenging part of this project was the design of the security area"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003764_095440605x32084-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003764_095440605x32084-Figure2-1.png",
        "caption": "Fig. 2 Geometry and forces for a truncated sphere impacting with a rough rigid surface",
        "texts": [
            " The felt on the outside of the ball has very low stiffness and allows the centre of mass of a tennis ball to move 2 mm, without appreciable stiffness. The rubber in the shell then begins to compress with a relatively high stiffness of 80 kN/m prior to buckling at 0.2 ms [15]. This causes a spike in the spring force in Fig. 1(c) up to 0.2 ms and prior to the lower effective stiffness of the buckled ball. The experimentally determined values of the constants were found to be ko \u00bc 21 kN/m, A \u00bc 16 106 N/m2, a \u00bc 1.65, B \u00bc 3.5 kNs/m [3, 15]. Figure 2 shows diagrammatically how a momentum\u2013flux force contributed to the model. Mass elements from the curved part of the sphere are instantaneously brought to rest in the deformed part of the ball. The mass per unit diameter of an undeformed ball is given by mB/2r, where r is the radius of the undeformed ball. Thus, the mass of the flat deformed and curved undeformed parts, md and mc, can be approximated by [11] md \u00bc yB r mB 2 , mc \u00bc 2r \u00fe yB r mB 2 (4) The momentum\u2013flux force, Ri, is approximated by Ri \u00bc m yd y yB (5) It is assumed that the momentum\u2013flux force only acts in the impact phase and switches off in the rebound phase, as with previous authors [11, 13]",
            "comDownloaded from on a piezo-electric force platform at 26 ms. It can be seen that the force due to the spring is maximum during the middle phase of the impact when the deformation is greatest, whereas the momentum\u2013 flux force is greatest at the beginning of impact where the velocity is greatest. The damping force reverses direction during rebound when the velocity of the centre of mass reverses direction. It can be seen that the model compares well with the experimentally determined forces throughout the impact. Figure 2 indicates a sphere impacting from the left with an initial impact velocity ni, at an angle, ui below the horizontal and with angular rotation vi. During impact, there are reactions Rkc due to the spring and damper of the viscoelastic model and reactions due to the momentum\u2013flux force at both the front and rear of the ball. Owing to the oblique impact and the rotation that is set up in the sphere during impact, these reactions are not equal. From Fig. 2, it can be seen that the absolute velocity of a mass element at the front of the sphere will be faster than a mass element at the rear of the ball due to topspin created during impact. The momentum\u2013flux forces would only be the same if there was no spin on the sphere. The horizontal and vertical velocities of mass elements at the front and rear are given by Front: vx \u00bc v cos u vr cosb vy \u00bc v sin u\u00fe vr sinb Rear: vx \u00bc v cos u vr cosb vy \u00bc v sin u vr sinb (6) where all terms are at time t during impact and v is the angular velocity at that instant",
            " The initial spin was found to lie between +80 rad/s with a measurement accuracy of approximately +20 rad/s. The rebound spin was measured in the same manner. Figure 4 shows typical images for a ball entering from the left with a velocity of 33.9 m/s at 23.28 to the horizontal with topspin of 20 rad/s and impacting with a rough surface (m \u00bc 0.62). The ball rebounds to the right at 19.8 m/s at 34.88 and with topspin of 667 rad/s. Figure 5(a) shows the displacement of the centre of the ball in Fig. 4 assuming it is a truncated sphere (point 0 in Fig. 2) with respect to the initial contact point. Similar coordinates are shown for the smooth surface (m \u00bc 0.51). It can be seen that the vertical displacement of the centre of the ball was approximately the same for both the rough and smooth surfaces and reached a maximum of approximately 20 mm. The ball travelled 97 mm in the horizontal direction on the smooth surface compared to 87 mm on the rough Proc. IMechE Vol. 219 Part C: J. Mechanical Engineering Science C02704 # IMechE 2005 at BRIGHAM YOUNG UNIV on May 18, 2015pic"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003358_j.fss.2005.05.003-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003358_j.fss.2005.05.003-Figure4-1.png",
        "caption": "Fig. 4. Flexible-joint robot arm system.",
        "texts": [
            " First, we represent the system as a T\u2013S fuzzy system, modelling our system with rules having linear subsystems as consequents.We then discuss a systematic way on how to find a Levi decomposition of the Lie algebraLA generated by the Amatrices of the linear subsystems of this model. In this decomposition, the matrices in the semisimple part should form a stabilizable pair with the Bl matrices of the system. Finally, we design the controller so that the system is stable. The flexible-joint robot arm system used in this paper is shown in Fig. 4. The system is described by the following equations [6]: I1\u03081 +mgl sin( 1)+ k( 1 \u2212 2) = 0, I2\u03082 + k( 2 \u2212 1) = u. (40) In the equations, u is the torque input, I1 the link inertia, I2 the motor inertia, m the mass, g the gravity constant, l the link length, k the stiffness, 1 joint1 angular position, and 2 joint2 angular position. The state equations of the system are: x\u03071 = x2, x\u03072 = \u2212mgl I1 sin(x1)+ k I1 (x3 \u2212 x1), x\u03073 = x4, x\u03074 = k I2 (x1 \u2212 x3)+ u I2 , (41) where x1 = 1, x2 = \u03071, x3 = 2 and x4 = \u03072"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003258_detc2005-84712-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003258_detc2005-84712-Figure3-1.png",
        "caption": "Figure 3. Pathological spherical 4-bar mechanism.",
        "texts": [
            " The first and second order cone is K1 q0 V ( IK ) = { (u, v \u2212 2u \u2212 w, u \u2212 2v, v, w) ; u, v, w \u2208 R } K2 q0 V ( IK ) = { x \u2208 R5| ( x2 )2 + ( x3 )2 + x5 ( x4\u2212x3 ) = 0 } II. I-tangent cone to V : It holds Cq0 V ( IK ) \u223d Cq0 V ( I ) . III. Tangent cone to V : It holds Cq0 V = Cq0 V ( IK ) . IV. Discussion: In q0 the kinematic tangent space is a three-dimensional vector space and the kinematic tangent cone is a two-dimensional irreducible cone in R5. Due to \u03b4diff (q0) = dimTq0 V ( IK ) = 3 and \u03b4loc (q0) = dimCq0 V = 2 the point q0 is a singularity with deg (q0) = 1. The particular construction of the spherical 4-bar mechanism in figure 3 is immobile, by inspection. Shown is the 9 nloaded From: https://proceedings.asmedigitalcollection.asme.org on 01/04/2019 Terms of U (only possible) reference configuration q0 = 0. I. Kinematic tangent cone to V : The filtration in q0 terminates with D(2)(q0) , so (3) after \u03ba = 2 steps. It holds Cq0 V ( IK ) = K2 q0 V ( IK ) , where K1 q0 V ( IK ) = {( u + \u221a 2v,\u2212 \u221a 2u \u2212 v, u, v ) ; u, v \u2208 R } K2 q0 V ( IK ) = { 0 \u2208 R4 } . II. I-Tangent cone to V : It holds Cq0 V ( IK ) \u223d Cq0 V ( I ) . III. Tangent cone to V : It holds Cq0 V = Cq0 V ( IK ) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000909_039139889201500110-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000909_039139889201500110-Figure2-1.png",
        "caption": "Fig. 2 - Construction of hollow fiber used in the in vivo experiments in diabetic patients (membrane length 15 mm, outer diameter 0.8 mm).",
        "texts": [
            " Tests were started immediately after insertion of the hollow fiber. Subcutaneous glucose concentrations were followed continuously with the glucose sensor. The flow rate of the enzyme solution in the microdialysis system was 60 microliters/minute. The sensitivity factor was calculated from the data obtained from t=40 to t=70 and from t=150 to t=180, when the glucose sensor signal was stable. To eliminate the risk of enzyme leakage in case of damage, a new type of hollow fiber was developed consisting of two different types of membranes (Fig. 2). The new fiber was used in the glucose clamp studies in type I diabetic patients. Positioned inside the polyethylene tubes is a cellulose hollow fiber (Spectra/Por, Spectrum Medical In., Los Angeles, USA; MWCO 9000 Dalton) with a polysulfone hollow fiber (Amicon Diaflo, MWCO 10,000 Dalton, Danvers, MA USA) around it to prevent enzyme leakage. If the cellulose membrane is damaged, the leaking enzyme will be trapped by the surrounding polysulfone membrane but the re sulting flow disturbance can be detected, making it possible to remove the fiber in time"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002308_0094-114x(88)90020-1-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002308_0094-114x(88)90020-1-Figure2-1.png",
        "caption": "Fig. 2. RRCRC mechanism.",
        "texts": [
            " The solution can be obtained from equations ( I- 7). rn~'=450g, ms=1650g, m*=1088g , m]=1968g, m~=2OOg, m ,=250g , nh~=375g, 7 \" = 8 . 7 c m , 75=9cm, 7 \" = 5 c m , 13=12cm, 7/ t=8cm, L = l , = l O c m , J;,~: = 11000 gcm 2, Js: = 356900 gcm 2, Jl3: = 16500 gcm 2, J~: = 168920 gcm\". 3. COMPLETE BALANCING OF RRCRC MECHANISMS Here is a complicated example of the complete balancing of shaking force and shaking moment in the RRCRC 5-bar mechanism with force transmission irregularity. The RRCRC mechanism is shown as the solid lines in Fig. 2. The dotted lines express additional links. The principle and method of the complete balancing of this mechanism is similar to that stated above. It should be noted that only the additional links, 3 dyads and a triad, are used here to realize both shaking force and shaking moment balancing except only one counterweight. It shows that additional links is effective not only to shaking force balancing, but also to shaking moment balancing. Now, the complete balancing equations can be obtained as follows"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003970_0021-9797(79)90240-6-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003970_0021-9797(79)90240-6-Figure1-1.png",
        "caption": "FIG. 1. Main geometrical characteristics of a heterogeneous, cylindrical particle; symbols are explained in the text.",
        "texts": [
            " The liquid/fluid interface is initially planar and the particle is assumed to approach it with the cylinder's axis parallel to it. The surface of the cylindrical particle consists of strips of two kinds of materials, which exhibit different equilibrium contact angles with respect to a given system of fluids. The 293 Journal of Colloid and Interface Science, Vol. 71, No. 2, September 1979 0021-9797/79/110293 -08502.00/0 Copyright \u00a9 1979 by Academic Press, Inc. All rights of reproduction in any form reserved. strips are parallel to the axis of the cylinder and successively located on the cylindrical surface (see Fig. 1). The number of strips is a parameter of the problem. We may expect that under certain conditions the interfacial influence can keep the particle floating, in an equilibrium position, at the interfacial region. Naturally, if this floating particle was forced to move completely into region 2, it would pass through the interface and sink in this region. The particle will sink into the lower fluid, if the criteria for floating, as they result from the analysis, are not satisfied. Neumann and Good (6) have developed the thermodynamic model (Free Energy Analysis) of a system comprised of a solid vertical fiat plate with a smooth homogeneous surface, fixed in position, in contact with an L/V interface",
            " A minimization of AF then would represent a variational problem which would lead to a rederivation of the Laplace equation (the Euler equation of the variational problem) and Young equation (the transversality condition). It has been shown (2, 3) that for a homogeneous cylinder at a fluid interface AF~ = -2q5 cos 0e [6a] o r Journal of Colloid and Interface Science, Vol. 71, No. 2, September 1979 d - - AF~ = - 2 cos 0e [6b] d6 in a differential form. The surface of the cylindrical shell in our case is supposed to consist of strips of equal circular length, each covering a sector having an angle ~bst = 2~r/m (see Fig. 1). Thus the equilibrium contact angle 0e around the cylinder is a given periodic function (a piecewise constant) of the angle ~b. By an integration of Eq. [6b], AF; can be expressed readily as a function AF~ = f(ch,Oel,0e2,m ). [71 For any fixed values of 0el, 0e2, and m, f is a known continuous, piecewise linear function of 6. Work is done on the system to alter interfacial area 23 as the system goes from the reference state to some other configuration. The change in free energy AF2 associated with this work may be divided into two parts , AF21 and AF22 , AF2 = AF21 + AF22 [8a] where AF21 represents the free energy change associated with the change of the area of the interface due to the capillary rise only and not to the particular shape of the shell, as if a planar shell was formed by the three-phase line and the axis z, and AF22 represents the free energy change associated with the change of the area due to the particular shape of the shell"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001568_2.2731-Figure12-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001568_2.2731-Figure12-1.png",
        "caption": "Fig. 12 In-plane ow conditions of 45-deg delta wing at \u00be = 30 deg and \u00c1 = 50 deg.",
        "texts": [
            " One would expect the rollrate-induced camber to have a similar effect on part-span leadingedge vortices, i.e., to work toward or against reestablishing the full vortex-induced lift, similarly to the effect of the pitch-rate-induced camber.19 Thus, the roll-rate-induced camber should generate roll damping for a sharp-edged 45-deg delta wing, and the measured wing rock around \u00c1 \u00bc 50 deg at \u00be D 25 and 30 deg (Fig. 9) must have been caused by the rounded leading edge. For \u00be D 30 deg and \u00c1 D 50 deg Eq. (2) gives 3 D 21 deg for the windward wing half. That produces the situation illustrated in Fig. 12. Thus, oneneeds to analyze the ow over a moderatelyswept wing leadingedge.The effectiveangleof attack for the leading-edge cross section in Fig. 12 is determined as follows9: \u00aeeff D tan\u00a11.tan \u00be cos \u00c1/ (3) For \u00be D 30 deg and \u00c1 D 50 deg Eq. (3) gives \u00aeeff \u00bc 24 deg. As the AR for the right wing half is 4.00 in Fig. 1 and 4.85 in Fig. 12, \u00aeeff is close to the angle for maximum lift \u00ae D 25 deg in Fig. 2. Thus, during wing rock the right wing half in Fig. 12 would be describing roll oscillations that produce a plunging motion of the rounded leading edge at an angle of attack close to that for maximum lift. When this motion is taking place in the near-stall region, as in the presentcase, undamping-in-plunge has been measured for airfoils20 (Fig. 13). The negative damping-in-plunge has been shown to be generated by the moving wall effect on the initial boundary-layer formation near the forward ow stagnation line,21 as illustrated in Fig. 14. The experimental data trend toward reestablishing damping for \u00ae > 15 deg in Fig",
            " During the downstroke, the movingwall effect promotes ow separation, also generating undampingin-plunge. At higher angles of attack, certainly beyond \u00ae \u00bc 20 deg in Fig. 13, the ow has become totally separated on the leeward side, and only the attached ow on the windward side of the airfoil reacts to the plunging motion, generating damping. For nite-AR wings the undamping will start at a much higher angle of attack than in the two-dimensional case (\u00ae \u00bc 10 deg in Fig. 13).22 The wing stall at \u00ae \u00bc 24deg (Fig.2) for thewing in Fig. 12 corresponds to 10 deg < \u00ae < 15 deg for the airfoils in Fig. 13. Consequently, one expects the maximum undamping-in-plunge, correspondingto \u00ae \u00bc 15 deg in Fig. 13, to occurat \u00ae \u00bc 30 deg for the wing in Fig. 12 and last until \u00ae > 34 deg, correspondingto \u00ae > 17 deg in Fig. 13. This explains why the oscillations around the trim point at \u00c1 D 0 at \u00be D 35 deg (Fig. 15) and \u00be D 45 deg (Fig. 16) are damped. The important lesson to be learned from the low-speed results for the thick 45-deg delta wing with a large leading-edge radius1 is that, because of the large leading-edge radius needed for heat protection, aerospace vehicles with delta-wing planforms of moderate leading-edge sweep will experience nonslender wing rock of the type described in Ref"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000273_0167-8442(94)00004-2-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000273_0167-8442(94)00004-2-Figure1-1.png",
        "caption": "Fig. 1. Schematic of gear tooth and engaged gears.",
        "texts": [],
        "surrounding_texts": [
            "The weight function method based on the crack opening displacement is used to derive the stress intensity and shape factor for a cracked gear tooth. An isolated force is applied at points of engagement with the mating gear. The analysis applies to narrow gears such that the two-dimensional stress state prevails. Analytical and experimental results are compared for an edge crack located at the root of the gear.\n1. Introduction\nFailure analysis of gears is complex because the formulation must include the combined effects of load, geometry and material. Based on the concept of fracture mechanics, a pre-existing crack is assumed to be present at a critical location such that attention could be focused locally near the crack tip where failure would presumably initiate. The stress intensity factor provides information not only for the load transmitted to the crack tip but also the influence of geometry which will be accounted for by the shape factor.\nThis work is concerned with determining the Mode I stress intensity factor for a cracked gear tooth by invoking a number of simplifying assumptions. This is accomplished by application of a weight function derived from the crack opening\n* Corresponding author.\ndisplacement. The results are compared with those obtained experimentally.\n2. Analytical treatment\nConsider a gear tooth loaded by an isolated force F at B in Fig. l(a). The location of B is at the engagement point that changes position as the gear engages and disengages with its mating part. Note that t h e line of action in Fig. l(b) rotates with the gear motion. An edge crack [2] of length a is assumed to prevail at the root of the gear tooth as shown in Fig. 2(a) where the tooth width is S. The isolated force F may be replaced by an equivalent force and moment system. This is illustrated in Fig. 2(b).\nThe analysis will be limited to narrow gears [1] such that the stress state can be approximated as two-dimensional. Analyzed will be the effect of bending and forces on the cracked portion of the gear tooth.\n0167-8442/94/$07.00 \u00a9 1994 Elsevier Science B.V. All rights reserved SSDI 0 1 6 7 - 8 4 4 2 ( 9 4 ) 0 0 0 0 4 - K",
            "2.1. Weight function\nFor two-dimensional crack problems, the stress intensity factor expression can be written as [3]:\nK= J;o'(x)m(a, x) dx (1)\nwhere m(a, x) is known as the weight function. It can be calculated from a reference solution to be taken as the compact test specimen in this work. The tractions on the crack are ~(x) such that the crack is along the x-axis, Fig. 2(a). A form of m(a, x) is\nE 3Vr(a , X) m(a, x) - gr 3a (2)\nfor plane stress. For plane strain, the Young's modulus in Eq. (2) can be replaced by E/(1 - u 2) with u being the Poisson's ratio. The crack opening displacement is G(a, x). The subscript r refers to the reference problem. Since or(x) can be negated by another problem of the same geometry without a crack, this gives the solution for a free surface crack. Such a procedure is wellknown and needs no further elaboration.\nReferring Eq. (1) to the reference state and making use of Eq. (2), the result is [4]:\nfo\" aG( a, x) [K~(a)]2=E \u00b0r(X) i)a dx (3)",
            "The crack opening displacement is given by [5]\nVr(a , X ) = 4\u00a2a-~/'a-x Yt(a )\n(a -x)3/2G(a) + (4)\nin which a =a/S. The width of the compact tension specimen is taken to be the same as that of the gear tooth width S. Yt(a) is referred to as the shape factor and G(a) is given by\nG(a) = - - [ I i ( a ) - 4~/-dlE(a)Yt(a)] (5) I3(a)\nThe quantities Ij ( j = 1, 2, 3) stand for\nf[[vt( l l (a) = \"tr~/2-O'o a)12a da\n12(a) = trr(x a - x dx,\nI3(a) = f;O'r(X)(a - x ) 3/2 dx (6)\nIn Eq. (4) and the first of Eqs. (6), cr 0 refers to the nominal stress in the problem.\nSubstituting Eq. (4) into Eq. (2) and performing the differentiation with reference to the normalized crack length variable a, the result is\n[ a-x m(a,x) ~/'rr(a---x) l+ml ( \" - -~ )\n+ m 2 ( - ~ ) 2] (7)\nsuch that mj (j = 1, 2) are given by\n1 m, = yt(a ) [2aYt'(a) + 3G(a)] + 1\n1 m 2 - - [2aG'(a) -G(a)] (8)\n4Yt(a)\nThe prime denotes differentiation with respect to 0~.\n2.2. Crack surface tractions\nReturning to Fig. 2(a), the stresses induced by the forces and moment can be computed. Assume that Fy introduces a uniform stress\nFy (9) %0 = b--S\non the x-axis where the edge crack prevails. The gear thickness is b. The moment caused by F x and Fy is\nM r =FxL -FyC (10)\nThis is balanced by a linearly distributed stress field with the neutral axis at x = S/2 such that\n6M r / 2x O'm(X ) = -~-T [1 - --~- ) (11)\nThe combined stress %(x) can thus be obtained:\nO'y(X) = &re(X) --O'y 0 (12)\nEquations (9) and (11) can be put into Eq. (12) to yield\nory(x)=~---~[6(LFx-CFy)(l- 2-~--~)-Fy]\n(13)\nThe shear stress ~'xy on the crack plane is ex rxY = b'--'S (14)\nwhich pertains to a Mode II loading. This effect is small for this problem and can be neglected.\n2.3. Stress intensity and shape factor\nLet %(x) in Eq. (13) be the stress or(x) in Eq. (1) while m(a, x) is given by Eq. (7), an expression for K can be obtained from Eq. (1):\nK=O'8v~f;{6FL(c\u00b0s\u00a2~-Csin\u00a2~)(1-2--~--~)\ndx \u00d7 (15)\n~a(a - x )"
        ]
    },
    {
        "image_filename": "designv11_24_0003768_j.mechmachtheory.2005.10.010-Figure19-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003768_j.mechmachtheory.2005.10.010-Figure19-1.png",
        "caption": "Fig. 19. Contact stress analysis between the planet worm-gear and the sun-worm.",
        "texts": [
            " The approach for application of finite element analysis has the following advantages: the development of solid finite analysis model is completed by using the equations of the tooth profile; the load distribution is performed as the drive running in actual working process and do not require an assumption; the stress analysis is completed by automatically choosing different points at contact curve in the drive running process. Based on the above discussion, the finite element analysis for different shapes of meshing rollers is implemented. Fig. 19 gives the contact stress analysis between the planet worm-gear and the sun-worm meshing via spherical rollers. The selected parameters in the numerical calculation are chosen as follows: i21 \u00bc 1 8 , the transmission ratio between the sun-worm and a planet worm-gear, q = 8 mm, the radius of meshing spherical rollers, a0 = 119 mm, the centre distance between the sun-worm and a planet worm-gear, r2 = 62.5 mm, the radius of reference circle of a planet worm-gear, P = 10 kW, the transmission power of the toroidal drive, n = 1500 rpm, the angular velocity of the sun-worm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000062_3.26486-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000062_3.26486-Figure1-1.png",
        "caption": "Fig. 1 Wrap-around fin model geometry.",
        "texts": [
            "5 This paper presents the initial results for establishing the capability of predicting the roll moment coefficient for a projectile with wrap-around fins through viscous computations with a threedimensional, full Navier-Stokes code. The experimental data used for comparison were obtained from Refs. 1,6, and 7. The reports document a comprehensive effort to experimentally determine how changes in geometry affect the aerodynamic forces generated by wrap-around fins. A standard wrap-around fin projectile determined by the Technical Cooperation Program (TTCP), as seen in Fig. 1, was used as the basic configuration. A number of geometric variations to the basic configuration were made. The aerodynamic forces of each configuration were measured and documented. The configuration for the wrap-around fin projectile modeled in the computation was derived from the standard set by the TTCP.1'6 Although the body retains the dimensions of the standard TTCP configuration, the fins differ slightly. The standard TTCP configuration had fins with symmetric leading and trailing edge bevels"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000334_1.555334-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000334_1.555334-Figure2-1.png",
        "caption": "Fig. 2 Schematic drawing of the test rig",
        "texts": [
            " Experiments were performed with the aim of improving a wet clutch engagement with respect to engagement smoothness and surface temperatures. The purpose was to show how this optimization can be achieved in an test apparatus which can control both drive torque and normal force. This knowledge can be used in automatic transmissions to increase the smoothness of gear shifts and the life of the clutches. The experiments were performed in a wet clutch test rig, and the apparatus and test procedure are fully described in Holgerson (1997). An overview of the test rig is presented in Fig. 2. The apparatus is driven by a hydraulic motor (1) which can apply a drive torque during the entire engagement. Inertia plates (4) can be mounted on a gear wheel (2). The wet clutch plate is mounted on a meshing gear wheel (3) with a gear ratio of 1:1. A hydraulic cylinder (5) applies the normal force to the clutch plate (12). The separator plate (11) is mounted on a non-rotating backing holder (6). The brake torque and normal force are measured with two piezoelectric load cells (7, 8). The force cell has a capacity of 200 kN and the torque cell 200 Nm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003625_1-84628-269-1_7-Figure7.8-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003625_1-84628-269-1_7-Figure7.8-1.png",
        "caption": "Figure 7.8. Sensor locations selected for the experimental ranking evaluation",
        "texts": [
            "3, the five candidate sensor locations are ranked as follows: (1) node group 2071/2076, within the bearing static load zone, (2) node group 1995/2074, located within the recess on top of the bearing, 900 counterclockwise from the load zone, (3) node 1431, along the bottom edge of the housing plate, (4) node 612, top edge of the housing plate, and (5) node group 2132/2139, within the recess opposite the bearing load zone. The EfI method provides a structural effect-based numerical approach to comparatively selecting candidate sensor locations. To evaluate the validity of such an approach, an experimental study was conducted in which accelerometers were placed at four sensor candidate locations selected as above, marked as through in Figure 7.8. For comparison with locations not recommended by the EfI method, accelerometers were also placed at locations and . The test bearing, containing a 0.1 mm hole as a seeded defect in the outer raceway, was set to rotate at 900 rpm, under a preload of Ps = 1,833 N, applied opposite to the X-direction. The characteristic frequency related to the outer raceway defect (BPFO) was calculated to be 79 Hz, based on bearing geometry and rotational speed. The sensor outputs at the six selected locations were evaluated with a waveletbased enveloping technique, as described in Section 7",
            " With the harmonic wavelet packet transform, the signal is decomposed into a number of sub-frequency bands. From the time\u2013frequency domain distribution of the energy content of the signal, information on the working condition of the machine component being monitored can be obtained. To evaluate the effectiveness of the various signal processing techniques introduced above, two case studies were conducted where bearing vibration signals measured from experiments were analyzed comparatively. In the first case study, sensor output at location as specified in Figure 7.8 was analyzed using the traditional power spectrum, bandpass filtering-based signal enveloping, and wavelet transform-based enveloping. As shown in Figure 7.15, the power spectrum technique was not able to detect the existence of the BPFO component, as it was submerged in the spectrum of other components. The wavelet-based enveloping spectrum is significantly more effective in displaying the BPFO component than the traditional enveloping technique, showing a ratio of 2.6 between BPFO and the next strongest component in the spectrum, as compared to a ratio of 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000205_bf00205979-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000205_bf00205979-Figure2-1.png",
        "caption": "Fig. 2. Causes of mechanical behaviour [fl(t)]: a effects of present forcing functions [F(t)] and past states; b the theoretical influence of future states; e the theory of circular causality including newtonian and anticipatory (1 and 2) causal links (see text for details)",
        "texts": [
            " Joint angular patterns across walking speeds (normalized to 100% of stride) exhibit only magnitude changes with fixed timing. The present work assumes that such stereotypic patterns are not completely aborted when environmental constraints force only a momentary modulation in the locomotor pattern. Instead, anticipated future states are simply used to reorganize these stereotypic profiles towards the required changes. The employment of a projected future state in conjunction with present and past causal factors in order to modify the on-going movement dynamics will be referred to as 'circular causality'. In Fig. 2a, the common newtonian perspective of causality is shown with the present behaviourial state, 1 fl(t), leading to the next state in time, fl(t + ~), in conjunction with both present forcing functions [F(t)] and influences from past states (B'). In Fig. 2b, information about the future behaviourial state is also used to modify the present state. However, this latter case is physically impossible. Therefore, a representation of the future state (the result of some form of internal model) is required. The estimated future state is shown by fl(t + z) in Fig. 2c. In this final configuration, the present system state is now the effect of the estimated future state, as well as past and present forcing functions. Just how the estimated future state becomes causal is shown below. Figure 3 presents a conceptual view of the model where the controller is divided into a higher level to generate the desired movement goal (the level of the internal models) and a level of feedforward control which provides the forcing functions necessary to drive the system. In the general system terminology of Klir (1985), these sections are referred to as the goal-generating and goal-seeking elements, respectively",
            " The ratio used in the present model depends on the relationship between the height of the obstruction and a predicted, instantaneous, vertical position of the toe, y(t + z), at the same point in space as shown below. rc = obstacle height/y(t + T) (1) Figure 4 provides the details of the goal-generating section of the simulation where static environmental characteristics are compared with the predicted body endpoint movement. For normal gait, the toe and the heel are the logical body endpoints which are at higher risk of colliding with the environment. This part of the model is represented by links 1 and 2, and by/~(t + z) in Fig. 2c. In the present simulation, the physical constraint offered by the obstruction is given meaning with respect If this pi-number indicates the potential occurrence of a collision, a criterion for clearance - a safety margin - can be set as a multiplicand to the pi number, providing an adjusted ratio (n' in Fig. 4) related to desired clearance. The parameter re' represents an expression of safe obstacle clearance and is used in conjunction with an internal model of the lower limbs to calculate new static joint angles and their differences from the stereotypic data at this future point in time",
            " Finally, a ratio of the new static joint angles to the stereotypic, unobstructed angles at the same point in projected time is calculated for each joint. This creates a gain for angular change shown as 30 at the - - ~ ( t + x); FUTURE UNCORRECTED POSITION . . . . . . FUTURE STATIC ADJUSTEMENT output of the internal model of the lower limbs shown in Fig. 4. The challenge to the system is to use the future, desired static clearance state to modify the present stereotypic locomotor pattern; that is, to model link 1 in Fig. 2c. The modifications toward the desired static state required to clear the obstacle at the future point are incorporated into the dynamic patterns by the introduction of a set of functions [~oj(t) in Fig. 4\"1 which, beginning in late stance, weight the stereotypic patterns as a percent of deviation at each lower limb joint where 0% maintains the stereotypic pattern and 100% results in full deviation as dictated by the static prediction of angle change (i.e. represented as the ratio fO of adjusted angle to nonadjusted angle) at mid-swing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001396_robot.1991.131590-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001396_robot.1991.131590-Figure2-1.png",
        "caption": "Figure 2: Compliance, accommodation and mobility centers are superimposed.",
        "texts": [
            " Consequently, the dynamic behavior of the grasp will not be identical on all degrees of freedom. Hence, the Admittance Center does not exist at that origin. In this case, the Compliance, Accommodation and the Mobility Centers do exist at 0 but are disoriented. It implies that such a grasp will have a directionally coupled (nonlinear) behavior. On the other hand, if the three frames were coincident and if all degrees of freedom had identical dynamic behavior then, the Admittance Center is said to exist in that common frame (Figure 2) and the frame would then be called the Admittance Frame. Such a grasp, as pointed out earlier, will have a directionally decoupled (linear) behavior. To demonstrate the importance of this concept, the three consequential advantages are discussed in the following three sections and are demonstrated via illustrative examples. 3 Ease of Specifying the Behavior ii'hen controlling a grasp to achieve an Admittance Center, the desired location of the admittance center and the desired dynamic behavior must be specified"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002608_an9851001381-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002608_an9851001381-Figure1-1.png",
        "caption": "Fig. 1. of the ion-selective electrode (a ) Manifold design; (b) microconduit; and (c) sectional view",
        "texts": [
            " This study is important in view of the possibility of the potentiometric monitoring of lithium during therapeutic treatment of manic psychosis. In this respect, a wide range of materials has been used in the development of lithium electrodes,5-15 but their selectivities are frequently unsuitable for the clinicial assay of lithium in blood serum. Experimental Apparatus and Materials Microconduits made from PVC blocks were used as a sample cell and incorporated into a microconduit FIA assembly of the type previously described by RGiiEka and Hansenl6 (Fig. 1). The indicator electrode contained sensor membranes as described below and the reference electrode consisted of a silver wire coated with silver chloride in contact with 0.14 M sodium chloride solution [Fig. l(b)]. For preparing the silver - silver chloride electrode, silver wire is treated with a solution of sodium chloride (0.3 g) and disodium hydrogen phosphate (0.3 g) in 5 cm3 of bleach solution (Formula 77 Bleach from Robert McBride Group, Manchester, was used but other ordinary household bleach solutions are also suitable)",
            "1 M barium chloride solution through the microconduit for 6 h, and then allowing the electrode to remain in contact with the solution for a further 12 h. With the lithium polypropoxylate membrane electrode, 0.1 M lithium chloride solution was used. For some of the barium polypropoxylate membranes, potassium tetra-p-chlorophenylborate was incorporated in the ratio of 1 part of KTpClPB to 2 parts of Ba(PPG 1025)0.69. (TPB)2. The indicator electrodes were assembled into the manifold and microconduit FIA system as depicted in Fig. 1. When not in use, the barium polypropoxylate electrode was kept in contact with 0.1 M barium chloride solution and the lithium polypropoxylate electrode was kept in 0.1 M lithium chloride solution. Selectivity Coefficients (kfEt B) The selectivity coefficients were determined by a variation of the matched potential technique.18719 Thus, a series of lithium standards (0.1-10 mM) made up in sodium chloride solution (0.14 M) were injected into the carrier FIA stream of sodium chloride solution (0.14 M)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002689_j.mechmachtheory.2004.12.016-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002689_j.mechmachtheory.2004.12.016-Figure5-1.png",
        "caption": "Fig. 5. All possible configuration of Assur 5-link in Example 1.",
        "texts": [
            " The equation of this coupler point curve is a tricircular and can be derived as \u00f0x2 \u00fe y2\u00de3 \u00fe \u00f0 190:76x 79:69y \u00fe 1327:09\u00de\u00f0x2 \u00fe y2\u00de2 \u00fe \u00f09072x2 \u00fe 8001xy 14633x \u00fe 47890y \u00fe 2261960\u00de\u00f0x2 \u00fe y2\u00de \u00fe \u00f0 7196024x2 5600615xy 2645437y2 \u00fe 11040445x 23215529y \u00fe 119323289\u00de \u00bc 0 On the other hand, the equation of the circle is \u00f0x 70\u00de2 \u00fe \u00f0y 30\u00de2 \u00bc 602 The four-bar AoABBo with coupler link ABC, coupler curve, and the circle are all plotted in Fig. 4. Six intersection points, i.e. C1, C2, . . . and C6, between the coupler curve and the circle are also marked. The coordinate of these intersection points can be solved numerically, e.g. by using MATLAB, as [18.61, 60.96], [11.92, 45.06], [11.30, 42.42], [26.91, 11.75], [30.55, 15.21], and [60.45, 29.23]. All possible configurations of this Assur 5-link are shown in Fig. 5 as well. A special case when both ternary links are similar [8] is analyzed in this paragraph. All three revolute joints of the fixed ternary link now become the singular foci of the coupler curve in the real plane [12]. A singular foci is the intersection point of the asymptote lines at infinity, e.g. y = \u00b1 ix + h. Let the coordinate of a singular focus be [a,b], both asymptotes can be expressed as y = \u00b1 ix + b ai. By substituting y = \u00b1 ix + b ai into the coupler curve equation as in Eq. (1), this tricircular sextic equation becomes a function of x and is of order 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003258_detc2005-84712-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003258_detc2005-84712-Figure6-1.png",
        "caption": "Figure 6. Two-dimensional mode of Wunderlich\u2019s mechanism.",
        "texts": [
            " Discussion: The kinematic tangent space is a threedimensional vector space. The kinematic tangent cone is the union of a two-dimensional vector space C\u2032 q0 V ( IK ) and a one-dimensional vector space C\u2032\u2032 q0 V ( IK ) . These are the tangent spaces to respectively two- and one-dimensional manifolds (modi). I.e. the mechanism can enter modi with different dimensions. Figure 5 shows a configura- 10 wnloaded From: https://proceedings.asmedigitalcollection.asme.org on 01/04/2019 Terms of Us tion in a mode with \u03b4loc= 1 and figure 6 shows one in a mode with \u03b4loc = 2. Due to \u03b4diff (q0) = 3 and \u03b4loc (q0) = dimCq0 V ( IK ) \u2261 max(dimC\u2032 q0 V ( IK ) , C\u2032\u2032 q0 V ( IK ) ) = 2 the point q0 is singular with deg q0 = 1. The mechanism is kinematotropic. The planar 8-bar mechanism in figure 7 is a combination of a planar 4- and 5-bar mechanism. Shown is the reference configuration q0 = 0. I. Kinematic tangent cone to V : The kinematic tangent space is identical to the kinematic tangent cone, i.e. Cq0 V ( IK ) = Tq0 V ( IK ) , where Tq0 V ( IK ) = {(\u2212r, 0, r, s + 2t,\u22122s\u2212 3t, s, t, 0) ; r, s, t \u2208 R}"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001738_12.377044-Figure13-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001738_12.377044-Figure13-1.png",
        "caption": "Fig. 13 Shear strength of overlap joints of sheet metal with 1,25 mm thickness",
        "texts": [
            " In the case of precipitation hardening alloys, it is possible to partially compensate the loss in strength by a following heat treatment which possibly can be combined with the heat treatment for car body lacquer. After 10 hours at 1 70\u00b0C or half an hour for 2 10\u00b0C, for instance, 80 to 90 % of the value of the precipitation hardened base material are achieved in the case of originally cold hardened material, see figure 12. In the precipitation hardened condition an increase in strength to values near to those of the base metal are possible, too. However, a decrease in ductility has to be taken into account. With A1MgSi alloys strain at failure values of 3 to 5 % are reached, only. Figure 13 illustrates the situation observed in overlap joints of sheet material4. The shear strength depends on the seams width in the joint plane. As long as the seam width is narrower than the thickness of the thinner one of the joint sheet metals, the joint cross section is the weakest point and a shear fracture is observed there. The strength increases with increasing seam width, then. As soon as the seam width surpasses the sheet thickness the direction of the fracture changes to perpendicular to the joint plane"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003135_1.2389233-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003135_1.2389233-Figure2-1.png",
        "caption": "Fig. 2 Metal pushing V-belt structure",
        "texts": [],
        "surrounding_texts": [
            "1 i s s d s m t t i t o I o r a u d t\nm b c\nJ 2 A\n8\nDownloaded Fr\nNilabh Srivastava e-mail: snilabh@clemson.edu\nImtiaz Haque e-mail: imtiaz.haque@ces.clemson.edu\n106 EIB, Flour Daniel Building, Department of Mechanical Engineering,\nClemson University, Clemson, SC 29634\nTransient Dynamics of the Metal V-Belt CVT: Effects of Pulley Flexibility and Friction Characteristic A continuously variable transmission (CVT) offers a continuum of gear ratios between desired limits. The present research focuses on developing a continuous one-dimensional model of the metal V-belt CVT in order to understand the influence of pulley flexibility and friction characteristics on its dynamic performance. A metal V-belt CVT falls under the category of friction-limited drives as its performance and torque capacity rely significantly on the friction characteristic of the contact patch between the belt element and the pulley. Since the friction characteristic of the contact patch may vary in accordance with the loading and design configurations, it is important to study the influence of the friction characteristic on the performance of a CVT. Friction between the belt and the pulley sheaves is modeled using different mathematical models which account for varying loading scenarios. Simple trigonometric functions are introduced to capture the effects of pulley deformation on the thrust ratio and slip behavior of the CVT. Moreover, since a number of models mentioned in the literature neglect the inertial coupling between the belt and the pulley, a considerable amount of effort in this paper is dedicated towards modeling the inertial coupling between the belt and the pulley and studying its influence on the dynamic performance of a CVT. The results discuss the influence of friction characteristics and pulley flexibility on the dynamic performance, the axial force requirements, and the torque transmitting capacity of a metal V-belt CVT drive. DOI: 10.1115/1.2389233\nKeywords: CVT, metal V-belt, friction characteristic, pulley flexibility, inertial effects, belt-pulley inertial coupling\nIntroduction\nOver the last few decades, environmental concerns have made t imperative for the government of most of the nations to impose tringent regulations on the fuel consumption and exhaust emisions of the vehicles CAFE standards in the U.S., ACEA stanards in Europe, etc. . Lately, continuously variable transmissions CVT have aroused a great deal of interest in the automotive ector due to the potential of lower emissions and better perforance. CVT is an emerging automotive transmission technology hat offers a continuum of gear ratios between high and low exremes with fewer moving parts. CVTs are aggressively competng with automatic transmissions, and today several car manufacurers, such as Honda, Toyota, Ford, Nissan, etc., are already keen n exploiting the various advantages of a CVT in a production car. n spite of the several advantages proposed by a CVT, the targets f higher fuel economy and better performance have not been ealized significantly in a real production vehicle. In order to chieve lower emissions and better performance, it is necessary to nderstand the dynamic interactions occurring in a CVT system in etail, so that efficient controllers could be designed to overcome he existing losses and enhance vehicle fuel economy.\nThis paper outlines a detailed one-dimensional continuous odel of a metal pushing V-belt CVT considering the effects of\nelt-pulley inertial interactions, pulley flexibility, and friction haracteristic of the contact zone. The model gives a profound\nContributed by the Design Engineering Division of ASME for publication in the OURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 17, 006; final manuscript received September 28, 2006. Review conducted by Ahmed\n. Shabana.\n6 / Vol. 2, JANUARY 2007 Copyright \u00a9 20\nom: http://computationalnonlinear.asmedigitalcollection.asme.org/ on 01/\ninsight into the dynamics of a CVT system, which could be exploited further to design efficient controllers and reduce associated losses.\nThe basic configuration of a CVT comprises the two variable diameter pulleys kept at a fixed distance apart and connected by a power-transmitting device like a belt or chain. One of the sheaves on each pulley is movable. The belt can undergo both radial and tangential motions, depending on the loading conditions and the axial forces applied to the pulleys. The pulley on the engine side is called the driver pulley and the one on the final drive side is called the driven pulley. Figures 1 and 2 1 depict the belt structure and the basic configuration of a metal V-belt CVT. Torque is transmitted from the driver to the driven pulley by the pushing action of the belt elements. Since there is friction between the bands and the elements, the bands, like flat belts, also aid in torque transmission. Hence, there is a combined push-pull action in the belt that enables torque transmission.\nA sundry of research has been conducted on different aspects of a CVT, e.g., performance, slip behavior, efficiency, configuration design, loss mechanisms, vibrations, operating regime, etc. Most existing models of belt CVTs, with a few exceptions, are steadystate models that are based on the principles of quasistatic equilibrium. Gerbert 2 performed some detailed analysis on the slip behavior of a rubber belt CVT. Slip was classified on the basis of creep, compliance, shear deflection, and flexural rigidity of the belt. Micklem et al. 1 incorporated the elastohydrodynamic lubrication theory to model friction between the metal belt and the pulley and also studied the transmission losses due to the wedging action of the belt. Sun 3 did a performance-based analysis of a metal V-belt drive and obtained a set of equations to describe the belt behavior based on quasistatic equilibrium. Friction between\n07 by ASME Transactions of the ASME\n28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use",
            "t a t u m e d\np r fi t d l f s e e V s a p t u t b f I o m p S c b m p a\nJ\nDownloaded Fr\nhe individual bands in a band pack was also taken into considertion in the model development. Kobayashi et al. 4 investigated he torque transmitting capacity of a metal pushing V-belt CVT nder no driven-load condition. Their research focused on the icroslip characteristic of the V-belt due to the redistribution of lemental gaps in the belt and reported a simulation procedure for etermining slip-limit torque based on steady-state assumptions.\nCarbone et al. 5 developed a theoretical model of a metal ushing V-belt to understand the CVT transient dynamics during apid speed ratio variations. Nondimensional equations were dened to encompass different loading scenarios; however, the inerial coupling between the belt and the pulley was not modeled in etail. Carbone et al. 6 used two friction models, namely a Couomb friction model and a viscoplastic friction model, to model riction between the belt and pulley and to accurately predict the hifting dynamics during slow and fast maneuvers. Later, Carbone t al. 7 extended their previous work 5 to investigate the influnce of pulley deformation on the shifting mechanism of a metal -belt CVT. The authors suggested that in steady state, the presure and tension distributions were unaffected by pulley bending nd depended only on the thrust ratio. However, pulley bending layed a significant role in determining the transient response of he variator. Sorge 8 analyzed the mechanics of metal V-belts nder the influence of pulley bending. The flexural rigidity has remendous influence on the seating and unseating behavior of the elt. Rapid variation of curvature may change the direction of rictional forces, thereby, affecting the torque capacity of the CVT. de and Tanaka 9 also experimentally investigated the influence f pulley bending on the contact force distribution between a etal V-belt and pulley sheave. They observed that asymmetrical ulley deformation led to nonuniform contact force distribution. attler 10 analyzed the mechanics of a metal chain and V-belt onsidering both longitudinal and transverse stiffness of chain/ elt, misalignment and deformation of pulley. The pulley deforation is modeled using a standard finite-element analysis. The ulley is assumed to deform in two ways, pure axial deformation nd a skew deformation. The model was also used to study effi-\nournal of Computational and Nonlinear Dynamics\nom: http://computationalnonlinear.asmedigitalcollection.asme.org/ on 01/\nciency aspects of belt and chain CVTs. Bullinger and Pfeiffer 11 developed an elastic model of a metal V-belt CVT to determine the power transmission characteristic at steady state. Pulley, shaft, and belt deformations were taken into account. The frictional constraints were modeled using the theory of unilateral constraints. The belt dynamics was specified by separate longitudinal and transverse approaches. The transversal dynamics was modeled using Ritz-approach based on B-splines. The longitudinal dynamics was described by using Lagrange coordinates.\nSrivastava et al. 12,13 developed a transient dynamic model of a metal pushing V-belt block-type CVT considering the inertial interactions between the belt and the pulley in significant detail. The authors used a continuous Coulomb friction approximation to model contact between the belt element and the pulley. The interaction between the band pack and the belt element which has been neglected in a lot of previous models was also taken into account during the course of model development. The authors observed that not only the configuration and loading conditions, but also the inertial forces, influence the dynamic performance of a CVT, especially its slip behavior and torque capacity. The authors suggested that CVT, being a highly nonlinear system, needs a specific set of operating conditions, which can be found using an efficient search mechanism, in order to successfully meet the load requirements. They used a genetic algorithm GA to capture this feasible set and also highlighted its efficiency in capturing this set by comparing it to the results generated by design of experiments DOE . The optimization objective function was suitably chosen to maximize torque transmission capacity of the CVT. Srivastava et al. 14 also developed a metal pushing V-belt CVT model in steady-state to study its microslip behavior and to investigate its steady-state operating regime. They discussed the influence of torques and axial forces on belt slip. Slip is based on redistribution of gap among belt elements and formation of inactive arcs, as proposed by Kobayashi et al. 4 . The model is able to predict the maximum transmittable torque before the belt undergoes gross slip. The authors observed that the CVT operates in definite regime of axial forces and torques. They predicted the minimum axial force necessary to initiate torque transmission and also the maximum axial force that the CVT can sustain based on slip behavior and not on stress/wear/fatigue effects .\nAlthough the friction characteristic of the contacting surface inevitably plays a crucial role in CVT\u2019s performance, literature pertaining to the influence of friction characteristic on CVT dynamics is scarce 2,6,15 . Almost all the models, except a few, mentioned in the literature use Coulomb friction theory to model friction between the contacting surfaces of a CVT. However, depending on different operating or loading conditions and design configurations, the friction characteristic of the contacting surface may vary. For instance, in case of a fully lubricated CVT, the friction characteristic of the contacting surface may bear a resemblance to Stribeck curve 16 rather than to a continuous Coulomb characteristic. Moreover, very high forces in the contact zone may further lead to the conditions of elasto-plastic-hydrodynamic lubrication, which may yield a different friction characteristic. It has also been briefly reported 15 in the literature that certain friction characteristics induce self-excited vibrations in the CVT system. However, it is not clear whether such phenomenon is an artifact of the friction model or the real behavior of the system. It is, thus, necessary to study the influence of different friction characteristics on the performance of a CVT. It is also important to note that although an exact knowledge of the friction characteristic in a CVT system can only be obtained by conducting experiments on a real production CVT, these mathematical models give profound insight into the probable behavior that a CVT system exhibits under different operating conditions, which may be further exploited to design more efficient controllers.\nThe research reported in this paper focuses on the development of a detailed transient dynamic model of a metal pushing V-belt CVT. The goal is to understand the transient behavior of a belt\nJANUARY 2007, Vol. 2 / 87\n28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use",
            "e d t t t i c d\n2\ne i t i m d\np h e t t m\n8\nDownloaded Fr\nlement as it travels from the inlet to the exit on both driver and riven pulleys and also to evaluate the system performance under he influence of pulley flexibility and varying friction characterisics of the belt-pulley contact zone. The inertial coupling due to he radial and tangential motions of the belt over the pulley wraps s also taken into account. The modeling analysis and the results orresponding to the metal pushing V-belt model are discussed in etail in the subsequent sections.\nModeling of a Metal Pushing V-belt CVT The belt-CVT model presented in this paper is subjected to the xternal conditions of a constant driver angular speed, a constant nput torque applied to the driver pulley, and a constant load orque on the driven pulley. The model captures various dynamic nteractions between the belt and the pulleys as a belt element\noves from the entrance to the exit of the pulley. The model evelopment and analysis includes the following assumptions:\n\u2022 Elements and bands are treated as a continuous belt; \u2022 The center of mass of the element and that of the band pack\ncoincide; \u2022 Belt length is constant; \u2022 The belt is considered to be an inextensible strip with zero\nradial thickness and infinite axial stiffness; \u2022 Impending slip condition exists between the band pack and\nthe element; \u2022 Bending and torsional stiffness of the belt are neglected; \u2022 Line contact between the belt and the pulley is parallel to\nthe pulley axis.\nIt has been observed 7\u201311,17 that elastic deformations of the ulley sheaves significantly influence the thrust ratio and slip beavior of a belt CVT. However, instead of a detailed finitelement formulation of pulley sheaves, simple trigonometric funcions as outlined in 7,10,17 are used in this model to describe he varying pulley groove angle and the local elastic axial defor-\nations of the pulley sheaves. Figure 3 7 depicts the model for\nFig. 3 Pulley deformation model\nom: http://computationalnonlinear.asmedigitalcollection.asme.org/ on 01/\npulley deformation. The following equations describe the pulley deformation effects as introduced by the model in Fig. 3\n= 0 + 2 sin \u2212 + 2\nR tan = r tan 0 \u2212 tan \u2212 0 1\nIt is to be noted that although the amplitude of the variation in the pulley groove angle is small, it is not constant during shifting transients. Sferra et al. 17 proposed the following correlations for the variation and the center of the pulley wedge expansion, ,\nFig. 5 Free body diagram of driver band pack\nTransactions of the ASME\n28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use"
        ]
    },
    {
        "image_filename": "designv11_24_0001897_robot.1997.614281-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001897_robot.1997.614281-Figure2-1.png",
        "caption": "Figure 2: Representation of the robot with virtual legs",
        "texts": [
            " 1 b); walk when the legs on the same side move together (fig. IC); trot when diagonal legs move together (fig. Id) In order to simplify the dynamic model we use the virtual legs introduced by Raibert [9]: one virtual leg symbolizes two real legs with simultaneous motion (fig. le-f). The three gaits differ by the motion of the platform. In this paper, we study only the first gait, and limit the number of actuators to obtain the simplest model of the virtual quadruped with feet. This model is given in fig. 2. The situation of the platform is described by three components: the coordinates of the platform middle point x, z, and the orientation angle 8. The configuration of leg 1 is defined by q l , q2. The configuration of leg 2 is defined by q3 and q4, in a frame fixed to the platform. The vector of configuration of the robot is denoted x = (x, z, 8, q l , q2, q3, q4). The vector x allows to describe double support, single support and no support phases. 0-7803-361 2-7-4/97 $5.00 0 1997 IEEE 1094 T . D,(x) x = O (2) D,(x$ + B,(x,x) = 0 (3) where B, is a 3-dimensional vector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000553_s0003-2670(98)00512-1-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000553_s0003-2670(98)00512-1-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of the flow cell reactor. PTFE tube was packed with coimmobilized LeuDH/NAOD/POD beads and coiled spirally and set in front of a photomultiplier tube (PMT).",
        "texts": [
            " The time course of the immobilization process was monitored by a spectrophotometer (Jasco Uvidec100-VI) with a \u00afow cell at 280 nm. POD and NAOD activities in the solution were assayed by measuring with H2O2 and o-dianisidine as substrate [29] and the initial rate of oxygen consumption rate with a oxygen monitor (TOA DO-32A) with NADH as substrate [25], respectively. POD and NAOD were immobilized with 47% and 57% yields, respectively. The immobilized enzymes were washed with 0.1 M Tris-HCl buffer (pH 8.0) to saturate the free linking sites. The tube was coiled spirally and used as \u00afow cell as shown in Fig. 1. The FI system used in this work is outlined in Fig. 2. The luminol solution and the NAD solution were each pumped by Hitachi L-6000 LC pumps at a \u00afow rate of 0.3 ml min\u00ff1: the total \u00afow rate through the \u00afow cell was 0.6 ml min\u00ff1. Sample solutions were injected through a Sanuki SVM-6M six-way valve equipped with a 20 ml loop into the NAD solution. The chemiluminescence was measured at room temperature (20 28C), with a Soma S-3400 luminometer, connected to TOA FBR251A recorder. Plasma (10 ml) was diluted with water to 10 ml and \u00aeltered on an ultra\u00aeltration membrane (Advantec USY-1, nominal molecular weight cut-off 10 000)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001455_50006-1-Figure5.16-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001455_50006-1-Figure5.16-1.png",
        "caption": "FIGURE 5.16 Drive magnet and coil for an axial-field actuator.",
        "texts": [
            "187) This nonlinear first-order system is solved subject to the initial conditions x(O) = x o, v(O) = v o, and i(O) = i o. [2 Axial-field actuators are moving coil actuators. These actuators are well suited and widely used for applications that require controllable bidirectional rotation. For example, they are routinely used for positioning read/wri te heads in computer disk drives. These actuators consist of pie-shaped magnets that are positioned above (and/or below) a coil that is free to rotate as shown in Fig. 5.16. When the coil is energized, it experiences a torque and rotates either clockwise or counterclockwise depending on the direction of current. A mechanical component such as a spring is often used to provide a restoring torque, and to fix the unenergized position of the coil (Fig. 5.17). Axial-field actuators can be designed and optimized prior to fabrication using lumped-parameter analysis [9, 10]. We develop a model for performing such analysis in the following example. EXAMPLE 5.9.1 Determine the equations of motion for the axial-field actuator shown in Fig. 5.16. Assume that the coil has n turns. SOLUTION 5.9.1 This device is a moving coil actuator and is governed by Eqs. (5.102), di(t) dco(t) dt = -L VS(t) - i(t)(R + Rr + [(~ x r) x Bext \" oil l [ i ( t ) f c [rx(dlxBext)] l:-ffTmech(0)] dt Ym oil dO(t) dt = ~o(t). dl (5.188) 394 CHAPTER 5 Electromechanical Devices Here, L and Rcoil a r e the inductance and resistance of the coil, and y~ is its moment of inertia above the z-axis. We need to evaluate the induced voltage and torque integrals in Eq. (5.188). We use a cylindrical coordinate system at rest with respect to magnets as shown in Fig. 5.16. Before we begin, we state some simplifying assumptions. Assumpt ions: The first assumption is that the magnetic field due to the magnet is essentially uniform and constant across the coil, that is, {-BmagT. 0 ~ 0 ~ 0rn Bmag = BmagT. - 0 m ~ 0 ~ 0, (5.189) where - 0 m and + 0 m define the angular positions of the radial edges of the magnet. In reality, the field distribution above the magnet varies with height, and from point to point at a fixed height. However, an average value of Bmag that is adequate for this analysis can be obtained using three-dimensional FEA, closed-form analysis [11], or measured data if the fabricated magnet is available"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001306_rnc.692-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001306_rnc.692-Figure2-1.png",
        "caption": "Figure 2. Symmetric sector.",
        "texts": [
            " Robust Nonlinear Control 2002; 12:1209\u20131226 W > 0 \u00f036c\u00de Q > 0; V > 0; P > 0 all diagonal \u00f036d\u00de The constraints in this optimization program are defined so that l > lmax\u00f0G\u00de: Hence, the minimization of l reduces the value of the diagonal entries of G: The minimum value of l can be seen as the maximum generalized eigenvalue of the pencil \u00f0Q; V \u00de: problem (36) is a quasi-convex optimization program that can be solved to global optimality by interior point methods (see [16] for details). The following problem min trace\u00f0V \u00de; s:t: \u00f036b 36d\u00de \u00f037\u00de is a convex programming alternative to problem (36). The value of G \u00bc VQ 1 is reduced by minimizing the trace of the denominator V : The second sector configuration considered in this section is the one depicted in Figure 2. It is assumed that the angle between the lines f \u00bc x and dx is the same as the angle between f \u00bc x and gx: With respect to sector (9), the relation between the lowerbound parameter g and d should be g \u00bc d 1: Hence, the objective of maximizing the total angle of the sector may be accomplished by minimizing g: Assuming that all nonlinearities are of the same kind, this configuration implies GD \u00bc I: An optimization problem can be formulated with the help of the change of variables V :\u00bc 1 2 \u00f0G\u00fe G 1\u00deQ \u00f038\u00de The following convex optimization problem, obtained from (21) and (38), tries to reduce the value of G: min trace\u00f0Q V \u00de s:t: ATP \u00fe PA Q ATW \u00fe V WA\u00fe V Q \" # 50 W > 0 V > Q > 0; P > 0 all diagonal \u00f039\u00de Copyright # 2002 John Wiley & Sons, Ltd"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002332_1.1510593-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002332_1.1510593-Figure1-1.png",
        "caption": "FIG. 1. Configuration of the rotating conductive disk and electromagnet: ~a!",
        "texts": [
            " From the net eddy current, the induced magnetic flux density is calculated by using Ampere\u2019s law. In the fourth step, the net magnetic flux density is expressed by using an exponential function that is satisfied in the two extreme cases in which the net magnetic flux density equals to the applied magnetic flux and zero, when the angular velocity is zero and infinite, respectively.7 Finally, by using the Lorentz force law,11 the braking torque is numerically calculated and the results are compared with the experiment. Figure 1 shows a rotating conductive disk in which we analyze the eddy currents. a and b are the width and radial length of the rectangular pole of the electromagnet. rd , R, and d are the radius of the disk, distance to the pole center from the center of the disk, and thickness of the disk, respectively. A direct current is applied to the coil wound around the electromagnet to produce a constant magnetic flux density B through the pole projection area. The conductive disk rotates at a constant angular velocity v in the counterclockwise direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002950_iecon.2004.1433334-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002950_iecon.2004.1433334-Figure2-1.png",
        "caption": "Fig. 2 Generation of Imaginary time vector fiom flux error",
        "texts": [
            " The d q components of imaginary time vector are determined by the procedure as follows: Stator voltage equation can be written its: * * * - - dry, v, = Rsi, + - dt Under the condition of negligible stator resistance, it can be simplified as: A Fs = FsAt or A vSd +j A vsq = kd + j v , )At (5 ) Comparing real and imaginary parts of (5 ) gives: (7) where At is the sampling time T, . Therefore imaginary switching times in d-q stationary reference h e are calculated as follows: Ysq - v s q T, = A vsq r, =-T, = V, At(= T,) x V, vm and (9) and This is shown graphically in Fig.2 while the schematic of the proposed method is shown in Fig.3. Therefore a new concept of imaginary time vector is introduced given by equation (10) that i s directly responsible for calculating the actual switching instants of the inverter. In any case, magnitude of imaginary time vector can not be more than the sampling timeT,, . Components of imaginary time vector can be converted into three-phase using simply two-to-three phase transformation tbat gives imaginary switching times T', , Tsb & T,, "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000975_iros.1994.407615-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000975_iros.1994.407615-Figure6-1.png",
        "caption": "Figure 6: The same task as in the previous figure, but the robot is shown in the goal position. This time a human programmer produced the path by specifying three intermediate points to allow for obstacle avoidance.",
        "texts": [],
        "surrounding_texts": [
            "for i := 1 to (n - 1) U := ( ~ i + l - t i-1)/2 A := 1 while (COLLISION(zi-1, b )\nor COLLISION(b, zi+l))\nand 11 b - t i [ I > Emin b := zi - ( t i - 0)/2('-') X : = A + l\nendwhile if not COLLISION(zi-1, b )\nand not COLLISION(b, zi+l) := b\nendif endfor\nAlthough this algorithm converges in an obstacle-free space to a straight line, the converge is slow. Therefore, the retraction algorithm does not change the global location of a polygon very much, but it is suitable for a subsequent treatment of an optimized polygon. This requires a combination of the represented algorithms:\n4.4 Composition of Methods Each of the three algorithms shown here has its own advantages: only deleting vertices for example is well for shortening the polygon but cannot improve the smoothness, whereas the cutting off triangle corners is good for smoothing but not for a large changing of the global location of the polygon. This suggests a combination of these algorithm that makes use of the special advantages.\nIf, for example, one wants to compute the shortest path, one should iteratively make use of the deletion algorithm and the cutting algorithm (figure 4). The more often these algorithms are repeated the shorter the polygon becomes, though a very good result is computed already by two or three iterations.\nNevertheless, this is only a local optimum for two reasons: all algorithms shown here make only local changes that will not find a far away located better solution; secondly, all changes made here convert a convex polygon to a convex polygon; so if the optimum would be concave it cannot be reached. In addition to the control of the cutting algorithm the alternating use of the algorithms can be used to control the properties of the resulting polygon. A final deletion of vertices destroys the perfect smoothness but produces a very short polygon, while first using the deletion and afterwards the cutting algorithm produces a polygon that is short and smooth. If one primarily wants to get a very short path but smoothness is also desirable, one should first compute the shortest path and then smooth it by using the retraction algorithm.\n5 Experimental Results\nBecause of the relative simplicity of the algorithms we soon got a prototype running which is implemented in C on a Unix workstation. The results of the performed experiments with many different environments and tasks show that the polygonal optimizer is fast and efficient.\nWe tried simple scenes with primitive obstacles, tasks with holes for the robot to reach in (like the one in figures 5 to 8), and even very difficult environments with strong obstacle constraints and large bulky payloads (like the one in figure 9).\nThe results are best estimated through the figures themselves. Table 1 give additional information regarding path length and computation time.",
            "IV/ IIW I\nI I\nFigure 8: Leff: Another, different, automatically planned path. Right: The same path after optimization for smoothness. Note that here another local optimum than in figure 7 is obtained.\nFigure 9: A very difficult pick-and-place task. The large plate has to be moved from the shelf (visible on the left of the left picture) to the trestles (in front of the right picture). All six degrees of freedom must be taken into account because the payload is bulky and the environment is very tight. In both pictures the same optimized path is shown.",
            "6 Future Work and Further Issues Our future work will first be concentrated on the efficient parallelizing of the algorithms. Secondly we want to consider special features of robots, for example the fact that some areas of the configuration space can be reached only with great effort and thus should be avoided if possible; another problem to be dealt with is the mechanical and physical properties of the robot.\nFinally, we are looking for new fields of application. We reflect on autonomous mobile robots or computercontrolled milling machines. Possibly the algorithms are also suitable for the smoothing of discrete mathematical functions.\nReferences [l] Berchtold, S.: Optimierung von automatisch gener-\nierten Roboterbahnen. Institut fur Informatik, Technische Universitat Miinchen, Diploma Thesis, 1993\n[2] Bobrow, J.E.: Optimal Robot Path Planning Using the Minimum-Time Criterion. IEEE J. of Robots and Automation 4, 443-450 (1988)\n[3] Bobrow, J.E.; Dubowsky, S.; Gibson, J.S.: TimeOptimal Control of Robotic Manipulators Along Specified Paths. Int. J . of Robotics Research 4, No. 3,\n[4] Donald, B.R.; Xavier, P.G.: Time-Safety Trade-08s and a Bang-Bang Algorithm for Kinodynamic Planning. Proc. IEEE Int. Conf. on Robotics and Automation, Sacramento, California, 1991, pp. 552-557\n[5] Galicki, M.: Optimal Planning of Collision-free Trajectory of Redundant Manipulators. Int. J. of Robotics Research 11, No. 6, 549-559 (1992)\n[6] Glavina, B.: Solving Findpath by Combination of Goal-Directed and Randomized Search. Proc. IEEE Int. Conf. on Robotics and Automation, Cincinnati, Ohio, 1990, pp. 1718-1723\n[7] Glavina, B.: A Fast Motion Planner for 6-DOF Manipulators in PD Environments. Proc. Fifth Int. Conf. on Advanced Robotics, Pisa, Italy, 1991, pp. 1176-1181\n[8] Heinziger, G.; Jacobs, P.; Canny, J.; Paden, B.: Time-Optimal Trajectories for a Robot Manipulator: A Provably Good Approzimation Algorithm. Proc. IEEE Int. Conf. on Robotics and Automation, Cincinnati, Ohio, 1990, pp. 150-156\n[9] Hollerbach, J.M.: Dynamic scaling of manipulator trajectories. ASME J . of Dynamic Systems, Measurement, and Control 106, 102-106 (1984)\n3-17 (1985)\n[lo] Hwang, Y.K.; Ahuja, N.: Gross Motion Planning - A Sumey. ACM Computing Surveys 24, No. 3,219- 291 (1992)\n[ll] Latombe, J.-C.: Robot Motion Planning. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1991\n[12] Pfeiffer, F.; Johanni, R.: A concept for manipulator trajectory planning. IEEE J . of Robotics and Automation 3, No. 3, 115-123 (1987)\n[13] Shiller, 2.; Dubowsky, S.: Robot Path Planning with Obstacles, Actuator, Gripper, and Payload Constraints. Int. J . of Robotics Research 8, No. 6, 3-18 (1989)\n[14] Shiller, 2.; Lu, H.-H.: Robust Computation of Path Constrained Time Optimal Motions. Proc. IEEE Int. Conf. on Robotics and Automation, Cincinnati, Ohio, 1990, pp. 144-149\n[15] Shin, K.G.; McKay, N.D.: Minimum-time control of robotic manipulators with geometric path constraints. IEEE Trans. on Automatic Control 30, 531-541 (1985)\nI161 Shin, K.G.; McKay, N.D.: A dynamic programming approach to trajectory planning of robotic manipulators. IEEE Trans. on Automatic Control 31,491-500 (1986)\n[17] Singh, S A . ; Leu, M.C.: Optimal trajectory generation for robotic manipulators using dynamic programming. ASME J . of Dynamic Systems, Measurement and Control 109 (1987)\n[18] Wang, D.; Hamam, Y.: Optimal Trcjectoy Planning of Manipulators With Collision Detection and Avoidance. Int. J . of Robotics Research 11, No. 5,460-468 (1992)\n[19] Zhang, Y.; Munch, H.: Modellgestlitzte optimale Bewegungsplanung fir Industrieroboter. VDI Berichte Nr. 1094, Berlin, 1993\n[20] Zhu, W.H.; Leu, M.C.: Planning Optimal Robot Trajectories by Cell Mapping. Proc. IEEE Int. Conf. on Fbbotics and Automation, Cincinnati, Ohio, 1990, pp. 1730-1735"
        ]
    },
    {
        "image_filename": "designv11_24_0000809_1.2826964-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000809_1.2826964-Figure4-1.png",
        "caption": "Fig. 4 A typical primary link",
        "texts": [
            " The procedure for mechanisms with a non-pseudotriangular structure is similar, except that the balance equations need to be solved simultaneously for n levels of primary links if there are n mechanical transmission lines connected to a primary link. Once the joint forces associated with these n pri mary links are found, reaction forces associated with the second ary links can be solved recursively from the higher level vertices to the lower level vertices. Since there are only a few linear equations to be solved simultaneously, this link-by-link re cursive procedure can be computationally more efficient than the general purpose computer programs. Dynamics of Primary Links. Figure 4 shows the free body diagram of a typical primary link / with two revolute joints connecting it to primary links i - 1 and / + 1. Assume that primary link i carries j secondary links and is the last link of k mechanical transmission lines. The force and moment balance equations for hnk / can be written in the following recursive forms: 242 / Vol. 120, JUNE 1998 Transactions of t>ie ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002316_s0925-4005(03)00427-1-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002316_s0925-4005(03)00427-1-Figure2-1.png",
        "caption": "Fig. 2. Experimental set-up used for potentiometric measurements with the alliin biosensor (ammonia electrode).",
        "texts": [
            "25 ml/min. Samples were exchanged by a flow rate of 10 ml/min. In order to simplify sample treatment and to reduce the time for single analytical measurements in comparison to conventional methods, like chromatographic techniques (HPLC), a new method based on immobilised alliinase and an ammonia gas electrode as part of a flow-through apparatus should be developed. For this approach, the ammonia electrode was mounted on a specially designed flow-through cell with an adjustable inner volume of 85 l (Fig. 2). In a first set of experiments, alliinase was immobilised on ConA/agarose, which placed inside the flow-through cell in direct contact with the outer membrane of the electrode. The system was operated at a flow rate of 0.25 ml/min using buffer solutions at pH = 7.0 (20 mM). This buffer was selected, because the activity maximum of the alliinae is at pH = 7 [8]. To increase sensitivity of the electrode, the inner electrolyte was diluted 1:9 with water [2,12]. Temperature of the flow-through cell was stabilised at 36"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000991_bf02473422-Figure6-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000991_bf02473422-Figure6-1.png",
        "caption": "Fig. 6 Slab loaded with a",
        "texts": [
            " EFFECTS OF QUASI-CONCENTRATED LOADS IN N U MERICA L C O M P U T I N G As a second example of the relevance of the width of a quasi-concentrated load on the associate displacements, consider a common situation where displacements due to concentrated loads are obtained by numerical simulation. In all such computations, the displacement associated with a concentrated load is a function of the width of this concentrated load, which is related to the size and type of the finite element used to model the structure. Clearly, such results are non-objective because they are mesh dependent. To illustrate this effect and the way to proceed, consider the simple problem shown in Fig. 6, where relative displacements UAB are sought in a rectangular slab loaded with a concentrated force applied on node A. Generalized plane stress, v = 0.3, and unit thickness are considered. Computations were based on the program Cosmos/M ~. Six meshes, as shown in Fig. 6, with 10 x 10, 20 x 20 quasi-concentrated load. and 50 x 50 elements, were used with rectangular isoparametric elements with 4 or 8 nodes. Let us assume that the concentrated load applied in node A (Fig. 6) is distributed over an effective area of width a, dependent on the type and size of the finite element. Thus, according to Equation 11, the relative displacement UAB can be written as 2P I r l P ( t + v ) UAB ~ ~ C + In a - H(O) 7zE cos 2 0 (22) where It(O) is the additional compliance due to the finite dimensions of the slab. Point B is far from the loads applied on the contour of the slab. This result can be written as UAB=2~P'FK(O)+lnr-I=2P[K(O)+ln a J roE D (23) where D is the slab depth, and terms independent of r/a are gathered in K(O), i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001474_s0167-8922(08)70580-7-Figure6.2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001474_s0167-8922(08)70580-7-Figure6.2-1.png",
        "caption": "FIGURE 6.2 Typical geometries of non-flat hydrostatic bearings; a) footstep, b)",
        "texts": [
            "13) becomes: 21sq n2R4 h H, = Non-FZat Circular Hydrostatic Pad Bearings Flat hydrostatic bearings are only suitable for supporting a load normal to the plane of contact. In some mechanical systems it is, however, very convenient to support oblique loads while allowing rotation and non-flat circular pad bearings are suitable for this purpose. Examples of non-flat bearings used in mechanical equipment are bearings based on a conical or hemi-spherical shape. The typical geometries of these bearings are shown in Figure 6.2. Non-flat circular pad bearings can be analysed in the same manner as already discussed for flat circular pads. For example, the geometry of the conical bearing is shown in Figure 6.3 and the following analysis is applicable. 314 ENGINEERING TRIBOLOGY spherical, c) conical, d) hydrostatic screw thread. Over the flat part of the bearing surface, hydrostatic pressure is equal to the supply pressure while a nearly linear decrease in pressure prevails in the conical bearing region. The pressure profile is then very similar to the flat pad bearing pressure profile already discussed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000750_jp2:1992241-FigureI-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000750_jp2:1992241-FigureI-1.png",
        "caption": "Fig. I. PHAN pattem of splay-type b~ a nematic cell with opposite boundary conditions. A magnetic field H is applied normally to the cell plates. The tilt- and twist-angles b ~y, z and 45 ~y, z ) are periodic functions of the transverse in-plane coordinate y, with wavelength A. Both tilt- and twist-anchorings are supposed to be weak at the H-wall (z = 0) and strong at the P-wall (z = d).",
        "texts": [
            " Theory. PHAN PATTERN. Let us consider a nematic layer confined between two substrates, placed at z = 0 and z = d, where the easy directions are H- (along the z-axis) and P- (along the x-axis), respectively. The anchoring is supposed to be strong only at the planar wall. We are looking for the existence of the transverse periodicity, with the wave vector parallel to the y-axis : hence the tilt angle 0 and the twist angle 4i turn out to be depending on y and z, I-e-, 0 = 0~y, z) and 4i = 4i~y, z) (see Fig. I). In order to simplify the notation of spatial derivatives which is necessary to describe the director distortion, hereafter the subscript y (or z) means a partial derivative with respect to y (or z, respectively). By assuming, as usual, the Rapini-Papoular form for the anchoring energy density [17-19], and by taking into account the surface contribution due to the surface-like saddle-splay elastic constant K~~, the linearized surface reduced free energy density (which is the free energy density divided by K/2) is given by : gs = Li( 4~) Lil \u00b0) + 2(1 + K24/K) 1\u00b0o 4~j,o 4~o \u00b0j,ol (I) where L~~ = K/W~~ are de Gennes-Kldman extrapolation lengths (I = 4i, 0 at the homeotropic wall (z = 0, index o) [20, 21], W~~ being the relevant anchoring strengths"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002308_0094-114x(88)90020-1-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002308_0094-114x(88)90020-1-Figure1-1.png",
        "caption": "Fig. 1. RSPC mechanism.",
        "texts": [
            "[9], can be used to balance the shaking moment of the mechanism. Quite few numbers of additional links are needed to reach both the shaking force and shaking moment balancing of the mechanism. The RSPC and RRCRC mechanism are completely bal- anced as examples. Simple balancing equations are also given in this paper. 2. COMPLETE BALANCING OF RSPC MECHANISM In order to illustrate the balancing method of this paper clearly, a simple example of the complete balancing of RSPC mechanism is worked out firstly. The RSPC mechanism is shown as the solid lines in Fig. 1. Here, R, S, P and C express the revolute. spherical, prism and cylindrical pairs, respectively, n h is mass of link/. )T,()TIi) is the vector of mass center in coordinates O,. hi and Si are the lengths of link i in axis ~ and Z~, respectively. 0u, ~u are angles from ~, to ~i, and ~Tj to Z~, respectively. It can be seen that this mechanism is a mechanism with a irregular force transmission because link 3 is not having a no-sliding pair chain connection to the frame of the mechanism. The inertia force caused by m 3 can not transfer to the frame of the mechanism regularly, and so it can not be balanced by counterweights. Here, a triad is used to solve the problem of inertia force balancing of the link 3. This triad is a planar symmetrical slide mechanism, it is composed of two links, link 7 and 8, and two sliders, and is connected to the existing mechanism through a spherical pair. The structure of the triad is shown in Fig. 1 as the dotted lines on the right hand side. Because the lengths of link 7 and 8 are the same, the motions of these two links are converse, If m 7 is equal to m 3 +m~' +ms , then the inertia forces caused by m 3, mff and m8 can be balanced by m 7. In this case, the shaking force of the whole mechanism can be balanced by the triad and other counterweights. Owing to the opposite motions of links 7 and 8, the inertia moments caused by these two links cancel each other automatically. Therefore, no additional dynamic behavior acts to the existing mechanism. This is the advantage of the triad, and this method is very simple and can be easily applied to practical mechanisms. Now, the balancing of shaking force in the mechanism with force transmission irregularity is achieved, the general theory and method of Ref.[9] can be applied to the complete shaking force and shaking moment balancing of the mechanism. The connection between links 2 and 3 is a prism pair in Fig. 1, the relative motion of these two links is only a slide, but not a rotation. Then, they have the same rotation and produce the inertia moments in the same direction of axis Z'3. Therefore, only one dyad can balance the inertia moments caused by the rotations of links 2 and 3. The dyad is composed of two links, link 13 and 16, and a slider, it connects to the link 3 with a prism pair which can rotate with the link 3, but not slide along axis Zs. Because the length of link 16 is equal to that of link 13, the rotation of the two links in a plan are converse in respect to the frame of the mechanism, and so the inertia moment caused by link/6 can cancel that caused by the links 2, 3 and/3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002241_s0039-9140(03)00360-6-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002241_s0039-9140(03)00360-6-Figure3-1.png",
        "caption": "Fig. 3. (a) Cyclic voltammogram in aqueous 0.1 M phosphate buffer/0.1 M NaClO4 for a GC electrode modified with an electrodeposited film of 6,17-diferrocenyldibenzo[b ,i ]5,9,14,18- tetraaza[14]annulen]-nickel(II). (b) Upon addition of NO to a final concentration of 18.8 mM. Scan rate 10 mV s 1.",
        "texts": [
            " Thus, it can be used as a disposable biosensor only. We have also studied different strategies for the analytical determination of NO based on the use of chemically modified electrodes exhibiting potent and persistent electrocatalytic activity towards the oxidation of NO. These modified electrodes have been used as amperometric sensor for the determination of NO in solution. The sensors were prepared by electrochemical deposition of 6,17- diferrocenyldibenzo[b ,i ]5,9,14,18-tetraaza[14]annulen]-nickel(II) (see Fig. 3) or indium(III) hexacyanoferrate(III) onto GC electrodes. In the case of 6,17-diferrocenyldibenzo[b ,i ]5,9, 14,18-tetraaza[14]annulen]-nickel(II), the compound in acetonitrile solution adsorbed strongly on the electrode surface to form electroactive layers. Electrodeposition of films can be also achieved from acetonitrile solutions at constant potential of /0.7 V. If after the electrodeposition the electrode is removed from the solution, rinsed with acetone, and placed in an acetonitrile (0.10 M TBAP) solution containing no dissolved compound, the cyclic voltammetric response exhibits two redox couples at /0.51 and /0.83 V, respectively. Potentials that are quite similar to those observed for the compound in solution. We ascribed the first to the simultaneous one-electron oxidation of the two non-interacting ferrocene units and the second is assigned to the metallocalized NiII/III oxidation [17]. In aqueous solutions the films are also electroactive as can be seen in Fig. 3 a, which shows a cyclic voltammogram for a GC electrode modified with an electrodeposited film of 6,17-diferrocenyldibenzo[b ,i ]5,9,14,18- tetraaza[14]annulen]-nickel(II) in a phosphate buffer/NaClO4 (0.1/0.1 M) at pH 7.0. A well-defined reversible voltammetric wave ascribed to the ferrocene/ferrocinium couple is observed. This reversible voltammetric wave has a formal potential of /0.55 V and the symmetrical shape anticipated for a surface-confined redox species. The films adhered strongly to the electrode surface and were stable to rinsing with acetone or water",
            " However, the remaining electroactive material is quiet persistent. The electrocatalytic activity of electrodes modified as described above to the oxidation of NO in aqueous media was evaluated by comparing the voltammetric response of a modified electrode in a NO atmosphere with that obtained under atmosphere of nitrogen under otherwise identical conditions. In addition, the response for the modified electrode in the presence of NO was compared to that obtained for a bare GC electrode in a NO containing solution. Fig. 3b depicts the cyclic voltammetric response for a GC electrode modified with an electrodepos- ited film of 6,17-diferrocenyldibenzo[b ,i ]5,9,14,18- tetraaza[14]annulen]-nickel(II) in contact with pH 7.0 phosphate buffer solution (0.1 M) containing 0.1 M NaClO4 and 18.8 mM NO. As can be observed, in the presence of NO the cyclic voltammogram exhibits an enhancement in the anodic wave with a decrease in the cathodic peak current which is consistent with a strong electrocatalytic effect. Very similar results were obtained for electrodes modified with electrodeposited films of InHCF, as can be seen in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003463_cdc.2006.377242-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003463_cdc.2006.377242-Figure1-1.png",
        "caption": "Fig. 1. The ducted fan Micro Aerial Vehicle.",
        "texts": [
            " Notations For a bounded function s : IR \u2192 IRr we denote \u2016s\u2016\u221e = supt\u22650 \u2016s(t)\u2016 and \u2016s\u2016a = limt\u2192\u221e sup \u2016s(t)\u2016 in which \u2016 \u00b7\u2016 denotes the Euclidean norm. We use the compact notation Ca, Sa, Ta with a \u2208 IR to indicate respectively cos a, sin a and tan a. For a vector \u03c9 = (\u03c91, \u03c92, \u03c93) T, Skew(\u03c9) denoted the 3\u00d7 3 skew-symmetric matrix with the first, second and third row respectively given by [0,\u2212\u03c93, \u03c92], [\u03c93, 0,\u2212\u03c91] and [\u2212\u03c92, \u03c91, 0]. The architecture of ducted fan MAV considered in this paper is shown figure 1 and can be thought as divided into two different subsystems. The first one is given by a fixed pitch rotor driven by an engine. This subsystem generates the necessary thrust in order to actuate the overall system. The second subsystem consists of four controlled surfaces positioned below the main rotor deviating the air flow coming from the fan in order to compensate for engine torque and to generate the forces and torques necessary to control the system. 1-4244-0171-2/06/$20.00 \u00a92006 IEEE. 1539 A mathematical model for the system can be obtained from Newton-Euler equations of motion of a rigid body in the configuration space SE(3) = IR3 \u00d7SO(3)",
            " we could consider separately the effects of each control inputs in the overall dynamics. Since the centers of pressure of any two opposite surfaces are at distance dT , by means of control input c we obtain a resultant torque QF directed along z axis and given by QF = \u22122KFL dT w2 ec whereas inputs a and b are in charge of generating a couple of forces directed respectively along the body x and y axis and given by Fx = 2KFL w2 ea Fy = 2KFL w2 eb . Note that, since the center of pressure of the flaps placed at a distance d from the center of mass of the system, as clearly shown in figure 1, both forces Fx and Fy generate torques \u03c4F y = Fxd and \u03c4F x = \u2212Fyd respectively along y and x axis. These torques represents the desired control action to govern \u0398 dynamics. To complete analysis consider the effects of all drag forces F i D. Observe that the sum of the drag forces of each couple of opposite surfaces results both in a force directed in the same direction of Ve and in a torque perpendicular to the surfaces axis. Denoting with DF the overall resultant force of all four surfaces and with \u03c4D x , \u03c4D y respectively the torque along x and y axis we have DF = 2KFD w2 e ( 2c2 + a2 + b2 ) \u03c4D x = \u22122KFD dT w2 e (c \u00b7 a) \u03c4D y = 2KFD dT w2 e (c \u00b7 b) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002471_135065002760199943-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002471_135065002760199943-Figure3-1.png",
        "caption": "Fig. 3 The 12 eddy current gap sensors",
        "texts": [],
        "surrounding_texts": [
            "As the details of the theory have been previously published [20, 26], only the principles are given here."
        ]
    },
    {
        "image_filename": "designv11_24_0003162_iros.2005.1545603-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003162_iros.2005.1545603-Figure7-1.png",
        "caption": "Fig. 7. Pushing O around a vertex. (a) If \u03c3(s) = PRe(\u03c4(s)), its path is circular shaped of radius 2ro+rp. (b) The pusher path if \u03c3(s) = PRb(\u03c4(s)). (c) Calculating the radius of the pusher path of (b). It can easily be seen that",
        "texts": [
            " The complexity of both approaches is the same. B. Circular compliant segments When the object is pushed compliant around an outer vertex in a certain section i \u2208 I on the domain s \u2208 [is, ie], the section of O is circular shaped. If P is at the same relative position inside PR(\u03c4(s)) during the section, the path of the pusher is also circular. The radius of this pusher path depends on the exact position of P within PR(\u03c4(s)). If \u03c3(s) = PRe(\u03c4(s)) then the radius of the circular shaped path the pusher follows is 2ro + rp (Fig. 7a). If \u03c3(s) = PRb(\u03c4(s)), this radius is smaller. The smaller the radius of the path of the pusher, the smaller the combined sweep planes of O and P (because a larger part of the pusher moves inside the shadow region of the object which is collision free by definition). e = r2 p + 2rpro + 2r2 o . Using this observation, we use the following approach to create a pusher path. First, we try to determine the smallest s : PRb(\u03c4(s)) \u2208 RVPR(\u03c4(s), \u03c3(s)). If this s exists, we transit P to PRb(\u03c4(s)) and maintain that position for the rest of the section. This preserves completeness because this position for P maximizes the part of the path of P that is within the shadow region of O. As soon as PRb(\u03c4(s)) \u2208 RVPR(\u03c4(s), \u03c3(s)), the pusher can follow a path where \u03c3(s) = PRb(\u03c4(s)) for the rest of the section (provided that this path for P is collision free, else we report failure). If \u03c3(s) = PRb(\u03c4(s)) during a circular compliant section, then the radius of the path of P equals \u221a r2 p + 2rpro + 2r2 o (see Fig. 7b). Before the pusher can follow a path for which \u03c3(s) = PRb(\u03c4(s)) however, it first needs to reach PRb(\u03c4(s)). For this, we use the following approach, as illustrated in Fig. 8a..d. At the start of the section, we try to move P in a straight line perpendicular to the compliant edge. This will start pushing O around the vertex. If an obstacle is encountered, we follow the union boundary as long as P is moving toward the vertex of the compliant edge. In the meantime P pushes O along its desired path",
            " We can preprocess the scene in O(n2 log n) time such that a push plan for a straight line compliant section can be found in O(n log n) time. There are kc compliant sections, resulting in a total query time of all straight line compliant sections of O(kcn log n). B. Circular compliant sections As stated before, the preferred position of P during a circular compliant section i \u2208 I is PRb(\u03c4(s)). We try to find the smallest s : s \u2208 [is, ie] for which PRb(\u03c4(s)) \u2208 RVPR(\u03c4(s), \u03c3(s)). If this s exists, then \u03c3(s) = PRb(\u03c4(s)) and from then on the radius of the circular shaped path of P equals \u221a r2 p + 2rpro + 2r2 o (Fig. 7). The number of positions where a circular compliant section can occur, is 2n (at every vertex of the obstacles). We can preprocess the environment by finding all intersections of all possible circular shaped paths of P with the union boundary. For this we add circular arcs with radius \u221a r2 p + 2rpro + 2r2 o to the environment at every vertex. The total number of elements in this environment is O(n). We find intersections by using a plane sweep algorithm. The original version of this algorithm is described in [5] by Bentley and Ottmann"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003505_robot.2006.1642018-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003505_robot.2006.1642018-Figure4-1.png",
        "caption": "Fig. 4. The coordinates Oc.m.-XY Z is attached at the object which has two parallel surfaces in parallel with the Y Z-plane.",
        "texts": [
            " We are going to model dynamics of pinching under rolling contact constraints that may lead to actualization of the LeviCivita connection in a dynamic manner. OF 3-D OBJECT GRASPING As shown in Figs.2 to 4, denote the position of object mass center Oc.m. by x = (x, y, z)T on the basis of the cartesian coordinates O-xyz at the fixed coordinates. Define the Y Z-plane so that it is in parallel with two parallel surfaces of the parallelepiped rigid object and define the Xaxis so that it is orthogonal to the Y Z-plane (see Fig.4). It is well known that the overall motion of a rigid body can be expressed by the translational velocity vector of its mass center v(t) = (vx, vy, vz)T and the three unit vectors rX , rY , rZ corresponding to three mutually orthogonal axes X, Y, Z that can be recast into an orthogonal matrix R(t) = (rX , rY , rZ)T (1) Since R(t) belongs to SO (3), the 3 \u00d7 3 matrix \u03a9(t) defined as ( d dt R(t) ) R(t)\u22121 = \u03a9(t) (2) becomes skew-symmetric [16]. Hence, \u03a9(t) can be expressed as \u03a9(t) = \u239b \u239d 0 \u2212\u03c9Z \u03c9Y \u03c9Z 0 \u2212\u03c9X \u2212\u03c9Y \u03c9X 0 \u239e \u23a0 (3) and thereby the instantaneous axis of rotation of the object can be expressed by \u03c9 = (\u03c9X , \u03c9Y , \u03c9Z)T",
            " Since in this paper we assume that there does not arise any spinning motion around the X-axis, it is possible to assume \u03c9X = 0. Next, denote the centers of hemi-spherical finger ends by x0i = (x0i, y0i, z0i)T and the contact points between finger-ends and parallel surfaces of the object by xi = (xi, yi, zi)T for i = 1, 2. Then, it is obvious to see that xi = x0i \u2212 (\u22121)irirX . Since these two contact points can be expressed as ((\u22121)ili, Yi, Zi) from the local frame Oc.m. - XY Z attached to the object (see Fig.4), it follows that x = x0i \u2212 (\u22121)i(ri + li)rX \u2212 YirY \u2212 ZirZ (4) The two contact constraints between finger-ends and object surfaces can be expressed as Qi = \u2212(ri + li) \u2212 (\u22121)i(x \u2212 x0i)TrX = 0, i = 1, 2 (5) which is obtained by taking an inner product between (4) and rX . The rolling constraints between finger-ends and object surfaces can be expressed by equalities of two contact point velocities expressed by spherical coordinates of finger-ends relative to local coordinates of the object. In fact, the rolling constraints can be expressed as ri d\u03c6i dt = \u2212 d dt Yi, i = 1, 2 (6) ri d dt \u03b7i = \u2212 d dt (Zi cos\u03c6i), i = 1, 2 (7) where (\u03c6i, \u03b7i) denotes the contact points between finger-ends and object surfaces expressed in spherical coordinates (\u03c6, \u03b7) as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002473_s0020-7225(03)00241-6-Figure7-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002473_s0020-7225(03)00241-6-Figure7-1.png",
        "caption": "Fig. 7. Comparison of s12 for different values of n and rate constitutive equation for m \u00bc 0:25.",
        "texts": [
            " (45)\u2013(47) result in a system of differential equations which was first solved by Dienes [8] as: r11 \u00bc r22 \u00bc 2E \u00f01\u00fe m\u00de cos\u00f02b\u00de ln\u00f0cos\u00f0b\u00de\u00de \u00fe b sin\u00f02b\u00de sin\u00f0b\u00de2 \u00f048a\u00de r12 \u00bc E \u00f01\u00fe m\u00de cos\u00f02b\u00de 2b\u00f0 2 tan\u00f02b\u00de ln\u00f0cos\u00f0b\u00de\u00de tan\u00f0b\u00de\u00de \u00f048b\u00de r33 \u00bc 0 \u00f048c\u00de Contrary to Eq. (45), constitutive equation (6) gives rise to r33 for n 6\u00bc 0. The effect of using (6) for different values of n and the rate constitutive model (45) on true stress components are shown in Figs. 5\u20138 for m \u00bc 0:25. From Fig. 5 it is seen that r11 is symmetric relative to c, and for n \u00bc 1, r11 is bounded to E=\u00f01 2t\u00de\u00f01\u00fe t\u00de. For n < 0, r11 < 0 which is physically unacceptable. Also, from Fig. 6, for n \u00bc 1, r22 is bounded to E=\u00f01 2t\u00de\u00f01\u00fe t\u00de when c increases. In Fig. 7 s12 is anti-symmetric relative to c for all ns and coincide for n and n. For all the Cauchy stress components, there is very good agreement between Eq. (6) for n \u00bc 0, and Eq. (45). Finally, Fig. 8 reveals that r33 is symmetric relative to c while anti-symmetric relative to n. For n \u00bc 0 and the rate constitutive model, r33 is zero. The use of hypo-elastic constitutive equations for large strains in numerical applications usually require special considerations, as the strain does not tend to zero upon unloading in some elastic loading\u2013unloading closed cycles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002555_2005-01-2456-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002555_2005-01-2456-Figure1-1.png",
        "caption": "Figure 1 Problem Formulation. a) Schematic of a typical automotive torque converter and wet friction clutch (TCC). b) 3DOF semi-definite torsional model of an automotive driveline system.",
        "texts": [
            " In particular, the effect of the friction disc inertia is studied. Both analytical and numerical results show that this inertia significantly affects the system dynamics. Our predictions compare well with prior measurements on a passive vibration absorber experiment. Friction elements are commonly found in many mechanical and structural systems. For example, consider the automotive torque converter clutch (TCC) sub-system that consists of a fluid torque converter and in parallel a mechanical wet friction clutch as shown in Figure 1a. When the engine speed e \u2126 is low, the wet friction clutch is fully disengaged and only the fluid torque converter path is operational. The pump drives the turbine with a torque generated by a change in the momentum of the fluid. Torque amplification is allowed and a smooth shift or transition is allowed [1]. At a higher speed, the mechanical clutch is fully engaged and the fluid path is no longer in effect. Under this condition, the transmission is directly driven by the engine. The energy dissipated within the torque converter is minimized to enhance the fuel efficiency",
            " Although some state-of-the-art applications use the controlled slip technology, stick-slip phenomenon could still take place because of engine torque pulsations, friction characteristics and run outs in the contact surface etc. In fact, to the best of authors' knowledge, avoidance of stick-slip is still a technical challenge that might prevent more wide spread usage of control slip concepts. To study the dynamic effects of stick-slip within a driveline system with TCC, we will study the non-linear dynamic characteristics of a three-degree of freedom (3DOF) semidefinite torsional system with a friction-controlled path as shown in Figure 1b. The driveline system can be reasonably represented by a 3DOF semi-definite system with focus on the TCC subsystem. This is conceptually similar to the manual transmission formulation employed by Padmanabhan and Singh [6] to study gear rattle and to the automatic transmission model utilized by Yamada and Ando [7] to examine clutch judder. As shown in Figure 1b, I1 represents the combined torsional inertia of flywheel, front cover and impeller; I2 is the inertia of friction disc assembly (secondary inertia) and I3 is the reflected torsional inertia of the rest of the driveline system. The governing equations for this 3DOF semi-definite system with a non-linear friction path as given by f T are: )(),())(( 1131111 tTTCI ef =+\u2212+ \u03b4\u03b4\u03b8\u03b8\u03b8\u03b8 (1a) 0),()( 113222 =\u2212\u2212+ \u03b4\u03b4\u03b8\u03b8\u03b8 f TKI (1b) )()())(( 3231133 tTKCI D \u2212=\u2212\u2212\u2212\u2212 \u03b8\u03b8\u03b8\u03b8\u03b8\u03b8 (1c) Here, 21 ,\u03b8\u03b8 and 3 \u03b8 are absolute angular displacements, 1( )C \u03b8 is the engine speed-dependent viscous damping term which represents the fluid path, K is the linear torsional stiffness, )(tT e is the engine torque (including mean and dynamic terms) and )(tT D is the drag load as experienced by the driveline",
            " Therefore, the dynamic response is very sensitive to the judicious choice of \u03c3 . However, the best value of \u03c3 usually is not known a priori and it could depend on system parameters. Consequently, the discontinuous friction model should be used as benchmark if successfully implemented. Many researchers [9-13] have studied the conventional bilinear friction system (Figure 6) that assumes a massless link between the spring and the friction elements, i.e. 0 2 =I . Similar to the physical system of Figure 1b, equations for bi-linear friction system can be given on a state-by-state basis. First, for the positive slip state, the equation is: Desf T II I T II I TC II II 31 1 31 3 11 31 31 + + + =++ + \u03b4\u03b4 (10) Since no inertial body exists between the friction and spring elements, the torque acting on the torsional spring is constant ( sf T ). Consequently, the value of 2\u03b4 remains KT sf / and 2 \u03b4 is zero. Second, for the case of negative slip, the equation is rewritten by changing the sign of sfT in (10) Further, the equation for the pure stick state is given by: 1 3 3 2 2 2 1 3 1 3 ( )m p I I I C K T T t I I I I \u03b4 \u03b4 \u03b4+ + = + + + (11) The system of Figure 1b can now be compared with that of Figure 6. Both show the second order system behavior under the stick condition. However, under the positive or negative slip state condition, the bi-linear friction system exhibits a first order system behavior while the model with 2 I follows a second order system. For this reason, some key differences between these two systems are expected, as explored in the subsequent section. A comparison of equations (4) and (11) shows that the effect of the secondary inertia 2I could be negligible under the pure stick condition in the presence of a very small 2I ",
            " 2 2 1 2 1 2 1 ( ) ( ) 0 I I C I \u03b4 \u03b4 \u03b4 \u03b4+ + + = (21) Where the initial condition is defined as 1 2 20 0 ( ) t t V\u03b4 \u03b4 \u03b4 = = + = = . Finally, the approximate analytical solution of 1( )t\u03b4 is obtained. 31 2 1( ) cos( ) CC tt II nt V e e t\u03b4 \u03c9 \u2212\u2212  = \u2212     (22) Similar to 2 ( )t\u03b4 , a very high frequency oscillatory term is found in 1( )t\u03b4 along with an exponentially decaying term. Further, it is noted that the above analyses could be applied to the negative slip state in a similar manner. Figures 7 compare the results corresponding to 2 1/ 0I I \u2260 (system of Figure 1b) and 0 (the conventional bi-linear system of Figure 6) cases. As expected, the motion differences under the pure stick condition ( 0 1 =\u03b4 ) are minimal since 2 I is very small compared to 1 I as shown in Figures 7a. Under the slip condition ( 01 >\u03b4 ), the difference is however noticeable. As response makes a transition from stick to slip, 1\u03b4 of the bi-linear system (with 2 0I = ) shows a finite jump from zero to the value of 2\u03b4 at the end of previous stick state and then it goes back to zero (stick) gradually",
            " Unlike the bi-linear hysteresis case where the peak amplitude is constant ( KT sf / 2 =\u03b4 ), the amplitudes with non-zero 2 I exhibit \u201cresonance-like\u201d curves in Figure 9. Such resonances are dictated by a combination of 2 states: 2DOF and 3DOF system responses. A comparison of the rms maps in Figure 9b shows similar effects of 2 I . Next we compare our method with one benchmark example as available in the literature: Hartung et. al.\u2019s passive vibration absorber analyses [18]. Physical model of their study could be conceptually described by the subsets of Figure 1b since the friction is the only non-linear element in two degree of freedom systems. The governing equations for the system shown in Figure 10 are as follows using their nomenclature. 1 1 2 1 2(1 ) cos( )m c c k k t\u03be \u03be \u03be \u03be \u03be \u03c9+ \u2212 + + \u2212 = (23) 2 1 2 1 2 2( )sc c g\u03be \u03be \u03be \u03be \u03be \u03c1 \u03be\u2212 + \u2212 + = \u2212 (24) Aside from numerical simulation based on the discontinuous friction model, they also conducted an experimental study and investigated the effect of friction force amplitude s\u03c1 . Selected measured frequency response curves under three friction forces are extracted from [18] and illustrated in Figure 11"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002820_00207170500034071-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002820_00207170500034071-Figure2-1.png",
        "caption": "Figure 2. Diagram of hydraulic actuator with its driven link (shown in dotted line).",
        "texts": [
            " NI 0 NRN NI 2 6666664 3 7777775 \u00f019\u00de where PN i\u00bc1 i \u00bc 1 with i > 0. For manipulators that equally share the load, i is chosen as i \u00bc 1=N. As for V defined earlier, we adopt a solution, by which the manipulators share the load almost equally V \u00bc a1I 0 a1R1 a1I .. . .. . aNI 0 aNRN aNI 2 6666664 3 7777775 \u00f020\u00de where ai \u00bc 2\u00f0 1\u00dei N \u00f0 1\u00dei\u00f01 \u00f0 1\u00deN\u00de=2 , i \u00bc 1, . . . ,N \u00f021\u00de For example, given three cooperative manipulators, a1, a2 and a3 are 1/2, 1 and 1/2, respectively from (21). 2.2.2 Hydraulic actuators dynamics. With reference to figure 2, for the jth cylinder of the ith manipulator, the D ow nl oa de d by [ M cG ill U ni ve rs ity L ib ra ry ] at 0 5: 33 1 5 D ec em be r 20 12 following equations describe the non-linear valve flow characteristics (Nikseft and Sepehri 2000): For extension (X i sp, j 0) qiI , j \u00bc Cd \u00f0xisp, j\u00de ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Ps Pi I , j s \u00f022a\u00de qiO, j \u00bc Cd xisp, j ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Pi O, j Pe s : \u00f022b\u00de For retraction (Xi sp, j < 0) qiI , j \u00bc Cd xisp, j ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Pi I , j Pe s \u00f022c\u00de qiO, j \u00bc Cd xisp, j ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Ps Pi O, j s : \u00f022d\u00de where qiI , j and qiO, j represent fluid flows into and out of the valve, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000159_0165-0114(94)90214-3-Figure15-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000159_0165-0114(94)90214-3-Figure15-1.png",
        "caption": "Fig. 15. /~(~,, oJ-p lo t .",
        "texts": [
            " Because of the monotone function R(6~, oJle=\u00a2o.st, we obtain a higher maximum/~(es, ~)[max as before: /~(es, oes - AO'e~)max > / ~ ( ~ ' s , O'er)max \u2022 (11) We stop the searching procedure at n ( e , O'es ) i> 1 - 12 / (12) where o~e(0, 1) with condition (10). If this condition is not fulfilled we obtain a plateau and the whole domain of the FC is not appropriately utilized to cope with the given standard deviation o~. In this case one has to increase the scaling factor s~ until (10) is fulfilled. Figure 15 shows a typical /~(Es, crJ-plot and Figure 16 shows the corresponding block scheme. We choose the free parameter a~ such that for a linear FC characteristic between the upper and H. Hellendoorn, R. Palm / Fuzzy system technologies at Siemens R & D 257 and fuzzy inputs according to the complexity of the transfer function of the FC. In contrast to the SISO-case for crisp inputs, the transfer function for fuzzy inputs strongly depends on the width of the support and the shape of the input membership function"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002247_0094-114x(87)90067-x-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002247_0094-114x(87)90067-x-Figure1-1.png",
        "caption": "Fig. 1. A 4-loop chain.",
        "texts": [
            " The determinant polynomial or permanent of LoFM in symbolic notations yields the same set of combinations of terms which carry identical information. The permanent is used in this paper in preference to the commonly used determinant polynomial simply because none of its terms carries a negative sign. The information provided by the permanent of LoFM (VPF-LoF) helps to analyse all the chains of a family to enable selection of the optimum kinematic chain based on mobility properties for a specific purpose. For example, the VPF-LoF of the 2-F, 9-1ink, pin-connected kinematic chain shown in Fig. 1 is written as Per A4(KC, f, F)Lop =f, AAA + (F:,2Af. + F~3Af. + F~.AA 2 2 + &3f , f , + ~'.,f, A + F~f~A) + (2FI2F2,FI4f3 + 2FI3F23FI2f4 + 2r.F3.F,.A + 2,~2~F3.F2.f~) + [(2FI2F23F~Fl, + 2FI2F2,F~FI3 + 2F,3&3F2J,,) 2 2 2 2 2 2 + FI3F24 + F24F23)] (2) + (FI2 F~ The terms of the above permanent are arranged in five groupings in decreasing order of number of the DOF of the loops. The first grouping contains only one term representing a set of the DOF for five loops. The second grouping is absent because a loop cannot have connection with itself"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003427_1.2711223-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003427_1.2711223-Figure2-1.png",
        "caption": "Fig. 2 Segmentation of a fiber where 2b is the crimp spacing",
        "texts": [
            "org/ on 01/28/201 Fiber Mass Model Having formulated the rate theory, we are in a position to construct a specific model of a fiber mass. Figure 1 shows a scanning electron microscope SEM graph of a carded sliver of 50 m diameter PA6 fibers. In general one would have to treat each fiber as a particle in the sense of the previous section . When the fibers are slender and crooked, such a description would be very complex indeed. Instead we assume that the fiber is divisible into roughly straight segments, Fig. 2 , which can be treated as independent particles. The validity of such a description requires that the contact spacing along a fiber be smaller than the length scale on which the fiber can be considered straight the crimp spacing 2b in Fig. 2 , so that the stress due to the contact forces on the segment is much larger than that due to the load from the rest of the fiber. This may not seem to be the case judging from Fig. 1, but it should be appreciated that the material in the micrograph is only about 1% volume fraction. At 10% volume fraction the number of contacts between crimps is about eight. Several other objections can be raised against this proposition; perhaps most importantly it presumes independent rotation of segments belonging to the same fiber",
            " The transverse compliance is governed by torsion and bending of the test fiber s = r p = 16 3 ktea2 + 3 6 kbea4 49 where the geometric constant kt is unity for a simple torsion bar loaded by a couple ap at its midsection and fixed at its end sections. The axial compliance is governed by torsion and bending of the contacting fiber se = re pe = 16 3 kte a 2 + 3 6 kbe a 4 50 where the primed quantities refer to the contacting fiber. In all the three above equations, it is only the contact spacing, , that is not a contact variable or a constant. The magnitude of the elements of the position vector is assumed to be rn r a 51 and, assuming a random distribution of contacts along a fiber re xb 52 where b is half the crimp spacing Fig. 2 and x is a stochastic variable randomly distributed in the interval 0 x 1. In order to allow for a fiber size dependence the crimp spacing will be assumed to be directly proportional to the fiber size a b = a 53 where will be called the crimp ratio. Due to the random distribution of contacts, the distribution of the contact spacing is exponential f = 1 \u0304 e \u2212 \u0304 54 and the third moment of is 3 = \u0304\u22121 0 3e \u2212 \u0304d = 6\u03043 55 Now, the compliance related averages in Eq. 37 are rn 2 c sn c = 6 kb a2 c e\u22121a\u22124 3 c = kb a2 c e\u22121a\u22124\u03043 c 56 r 2 c s c = a2 c 16 kt \u22121 e\u22121a\u22122\u0304 c + 1 kb \u22121 e\u22121a\u22124\u03043 c 57 3 JULY 2007, Vol"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003996_tase.2005.846289-Figure12-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003996_tase.2005.846289-Figure12-1.png",
        "caption": "Fig. 12. FIV and refined feature.",
        "texts": [
            " 2) If no vertical interface exists, select one horizontal interface as the direction between the or axis along which the cube has a smaller range as the slicing direction of this flat volume. There are some advantages for the orthogonal LM system in terms of the processing of the interface since the deposition directions in this condition are orthogonal to each other. Otherwise, when the deposition directions are not perpendicular to each other, some special processing steps are needed to avoid the problem of staircase interaction: in Qian and Dutta\u2019s work [28], feature interaction volume (FIV) (shown in Fig. 12) was used to act as a bridge between different features, and the refined feature volumes (RFVs) are then obtained by subtracting the FIV from different feature volumes. The computation of FIV and RFV is quite complicated, while in the proposed orthogonal LM system there is no staircase interaction by nature or the FIV is degenerated into the interface plane. Shown in Fig. 13 is the result of volume decomposition for the part in Fig. 9, the interface between the flat volume and the rest of the part is a horizontal plane, hence the computation is significantly simplified in this condition"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002556_2005-01-1819-Figure4-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002556_2005-01-1819-Figure4-1.png",
        "caption": "Figure 4: 3D model of a five-speed manual transmission",
        "texts": [
            " was a traditional torsional model of a transmission) the model would predict no force transferred at the bearings. Therefore, the prediction would indicate that no vibrations from the transmission were being transmitted to the vehicle. The model can be excited by the fundamental harmonic an subsequent TE harmonics at the driving gear mesh, and at the final drive gear mesh to provide a prediction of the force at the bearings, in all directions. The following example illustrates a study where the above methods were applied to a five-speed manual transaxle (for model see figure 4), in order to reduce the gear whine. The model shown in figure 4 was analysed using RomaxDesigner . A static analysis was performed on the model in all gears and several load conditions. The proprietary software uses the rapid thin slice method to determine the magnitude and phase of the transmission error, at each of the meshing gears in the power flow. Including the driving gear mesh and the final drive gear mesh. Loaded transmission error measurements were obtained from the driving gears whilst \u201cin-situ\u201d. It was not possible to measure the final drive transmission error due to space constraints"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003767_sice.2006.314829-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003767_sice.2006.314829-Figure1-1.png",
        "caption": "Fig. 1. The starfish robot for the Q-Learning application",
        "texts": [
            " The total discounted return R(t) received by the learner beginning at time t is given by R(t) = rtl +yrt+2 + y2rt+3 ++n rt+n + (2) The action-value function implies the expected value of the total discounted return R(t) that the agent can obtain cumulatively on the reward rt determined by a certain action in each state. In this study, the reward rt is given in proportion to the advance distance. The optimal advance motion forms are obtained as the motion forms that obtain the maximized expected value of the total discounted return R(t) while the robot learns its motion by the Q-learning method. In order to inspect the motion forms, we employed a two-dimensional starfish robot with as shown in Fig. 1. It consists of four Al Motors, which were obtained from Megarobotics Co. Ltd., as an actuator. Each motor works with three patterns by changing its angle such as +52 deg, 0, and -52 deg. The motion patterns of the starfish robot joint are shown in Fig. 2. Each motor is controlled every 0.5 s by the computer through the RS-232C interface. In this study, this robot receives a reward in proportion to the distance that the robot actually travels from one state to next state. Thus, we used two PSD sensors to measure the distance when the robot moves from some state to the next state"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000335_3476.585138-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000335_3476.585138-Figure1-1.png",
        "caption": "Fig. 1. Intelligent sprinkler systems\u2014A mechatronic system: (a) an electromechanical device, (b) an electromechanical system, and (c) a mechatronic system.",
        "texts": [
            " A broad definition of Mechatronics, which incorporates all the above views is that: \u201cMechatronics is an engineering process that involves the design and manufacture of intelligent products or systems involving hybrid mechanical and electronic functions\u201d [8], [9]. The word \u201cintelligent\u201d in the above definition distinguishes Mechatronic systems from the commonly known electromechanical systems. For example, a solenoid is a widely used \u201celectromechanical device.\u201d The 1083\u20134400/97$10.00  1997 IEEE magnetized soft iron core moves linearly inside a coil of electrically conducting wires with passing electric current. As illustrated in Fig. 1, when this device is used in a sprinkler system, the linear motion of the core prompts the opening or closing of the valve which allows water to flow. The timing for water to flow through the valve during the designated periods can be simply controlled by installing a timer in the electric circuit that supplies current to the solenoid. The timer plus the solenoid and the mechanical valve thus constitute an \u201celectromechanical system.\u201d However, most sprinkler systems are expected to operate at desired periods which may vary with the days and the time of the year, together with preset amount of water flow (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002321_1.2930137-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002321_1.2930137-Figure2-1.png",
        "caption": "Fig. 2 Sectional view of the seal test rig",
        "texts": [
            " The experimental results presented by Benckert and Wachter (1980) and Leong and Brown (1982, 1984) were for long labyrinth seals with fins on the stator. The test seal, therefore, was designed relatively shorter with fins on the rotor in order to simulate the labyrinths in a shrouded turbine stage. Compressed air was used as the seal fluid in the experiments. The seal cavity pressure distribution was measured around the seal circumference and integrated over the rotor surface to get the tangential and radial seal forces. Description of the Seal Test Rig. A sectional view of the labyrinth seal test rig is shown in Fig. 2. The 187 mm (7.375 C = Cc -- Ce = Co -- e = er = / = Fr, Ft = h -- I = m = N = = seal radial clearance = orifice flow coefficient = energy recovery factor = nominal radial clearance = rotor eccentricity = eccentricity ratio (e/Co) = circumferential flow area = radial and tangential seal forces = seal fin height = cavity width = number of circumferential pressure taps = rotor rpm (also used to de note the unit for force, newton) n = P = q = R = Re = Rs = T = u = U0 = U = X = v = number of seal fins pressure (Po - seal inlet, Pe - seal exit) axial mass flow rate per unit circumferential length gas constant Reynolds number rotor radius gas temperature circumferential flow velocity inlet swirl velocity length of wetted surface friction coefficient at the walls kinematic viscosity <t> = P = T = e = O) = Subscript ( = J = r = s = reference angle shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002624_j.triboint.2005.08.002-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002624_j.triboint.2005.08.002-Figure1-1.png",
        "caption": "Fig. 1. Geometry of EHL of circular contacts under pure squeeze motion.",
        "texts": [
            " A numerical method for general applications is developed to investigate the pure squeeze action in an isothermal EHL spherical conjunction. The transient modified Reynolds equation as well as the elasticity equation are solved numerically. The effects of flow rheology of the lubricant as well as the elastic properties of solids on the performance of the squeeze film are proposed and discussed under constant load condition. Two spheres approaching one another can be expressed as the equivalent sphere approaching a plane. Consider the squeezing film mechanism as shown in Fig. 1, where an elastic sphere of radius R is approaching in an infinite plate with a velocity under constant load. The lubricant in the system is taken to be a non-Newtonian power-law lubricant. The equations of motion governing the axial symmetric flow of a compressible fluid under the assumptions of the lubrication theory, and neglecting the inertia terms, in one dimension, are given by dp dr \u00bc qt qz , (1) ARTICLE IN PRESS H.-M. Chu et al. / Tribology International 39 (2006) 897\u2013905 899 dp dz \u00bc 0. (2) Since the flow occurs under the pressure gradient only and the pressure is constant across the film"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0000033_jsvi.1999.2261-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000033_jsvi.1999.2261-Figure3-1.png",
        "caption": "Figure 3. Laminated cylindrical shells.",
        "texts": [
            " In the numerical analysis, it is found that the use of 4]4 mesh (16 shell elements) to model the plate gives the same fundamental frequency as the exact solution. On the basis of this result and previous experience on the analyses of composite shells [15], it was decided to use at least 96 elements (32 rows in circumferential direction and 3 rows in longitudinal direction) to model the laminated cylindrical shells having \u00b8/r ratio equal to 1. For cylindrical shells with large \u00b8/r ratios or with cutouts, more elements are employed to model the entire structures. In this section composite laminated cylindrical shells with three types of end conditions (Figure 3(a)) are considered, which are two ends \"xed (denoted by FF), one end simply supported and the other end \"xed (denoted by SF), and the two ends simply supported (denoted by SS). The radius of the shell, r, is equal to 10 cm and the length of the shell, \u00b8, varies from 10 cm to 40 cm. The laminate layups of the shells are [$h/90 2 /0] ns and the thickness of each ply is 0)125 mm. In order to study the e!ects of shell thickness on the results of optimization, n\"2 (20-ply thin shell) and 10 (100-ply thick shell) are selected for analysis",
            " Figure 6 shows the typical fundamental vibration modes for both thin and thick ([$h/90 /0] and [$h/90 /0] ) shells with two \"xed ends and under the 2 2s 2 10s optimal \"ber orientation. We can \"nd that when the shell length or the shell thickness increases, the vibration modes of these cylindrical shells have fewer waves in the circumferential direction. Similar results are also obtained for shells with other end conditions [25]. In this section, laminated cylindrical shells with r\"10 cm and \u00b8\"20 cm are analyzed. These shells contain central circular cutouts with diameter d varying between 0 cm and 12 cm (Figure 3(b)). As before, three types of end conditions and two laminate layups, [$h/90 2 /0] 2s and [$h/90 2 /0] 10s , are selected for analysis. Figure 7 shows the optimal \"ber angle h and the associated optimal fundamental frequency u with respect to the ratio d/r for thin ([$h/90 /0] ) laminated 2 2s cylindrical shells. From Figure 7(a) we can see that the optimal \"ber angle h of the cylindrical shells decreases with the increase of the cutout size. In addition, under the same d/r ratio, the shell with two simply supported ends has the largest value for the optimal \"ber angle",
            "e., vibration of entire shell). However, when the cutout sizes are large, the fundamental vibration modes are local (i.e., vibration of shell area near hole). Similar results are also obtained for laminated cylindrical shells with other end conditions [25]. WITH VARIOUS LENGTHS AND END CONDITIONS In this section, laminated cylindrical shells with r\"10 cm are analyzed. The length of the shell, \u00b8, varies between 20 cm and 40 cm. These shells contain central circular cutouts with diameter d\"8 cm (Figure 3(b)). As before, three types of end conditions and two laminate layups, [$h/90 2 /0] 2s and [$h/90 2 /0] 10s , are selected for analysis. Figures 10 and 11 show the optimal \"ber angle h and the associated optimal fundamental frequency u with respect to the \u00b8/r ratio for thin and thick ([$h/90 2 /0] 2s and [$h/90 2 /0] 10s ) laminated cylindrical shells with central circular cutouts. For thin shells, it seems that when \u00b8/r ratio is small (say \u00b8/r(3), the optimal \"ber angles increase with increase of shell length"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003122_acc.2003.1239789-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003122_acc.2003.1239789-Figure3-1.png",
        "caption": "Figure 3 A schematic of the experimental setup",
        "texts": [
            " The ,nwr PrnUdD\" FlgUre 1: A general layout of the air brakc system in trucks mechanical subsystem, illustrated in Figure 2, starts from the brake chamber and includes the push rod, the slack adjuster, the S-cam and the brake pads. Compressed air acts on the brake chamber diaphragm providing a mechanical force that is transmitted to the brake pads through the push rod and the S-cam. 3 The Experimental Setup The experimental test bench at Texas A&M University is essentially the front axle of a tractor. Compressed air is supplied by a compressor and a pressure regulator is used to modulate the pressure ofthe air being supplied to the treadle valve. Figure 3 shows a schematic of the experimental setup. The treadle valve used is the E-7 dual circuit valve mannfactured by Allied SignalslBendix (see Figure 4). The primary circuit is actuated by the pedal force and the secondary circuit acts essentially as a relay valve. A detailed description of the operation of the treadle valve can be found in [lo]: The compressed air from the treadle valve is supplied to the brake chamber through brake hoses. A pneumatic actuator is used to apply the treadle valve. The input pedal force and displacement are measured with a Proceedings ol the Ameli@\" Camrol Conteience Denver, Colorado June 4-6, 2003 1417 load cell and a linear potentiometer respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003767_sice.2006.314829-Figure2-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003767_sice.2006.314829-Figure2-1.png",
        "caption": "Fig. 2. Motion patterns of the starfish robot",
        "texts": [
            " The optimal advance motion forms are obtained as the motion forms that obtain the maximized expected value of the total discounted return R(t) while the robot learns its motion by the Q-learning method. In order to inspect the motion forms, we employed a two-dimensional starfish robot with as shown in Fig. 1. It consists of four Al Motors, which were obtained from Megarobotics Co. Ltd., as an actuator. Each motor works with three patterns by changing its angle such as +52 deg, 0, and -52 deg. The motion patterns of the starfish robot joint are shown in Fig. 2. Each motor is controlled every 0.5 s by the computer through the RS-232C interface. In this study, this robot receives a reward in proportion to the distance that the robot actually travels from one state to next state. Thus, we used two PSD sensors to measure the distance when the robot moves from some state to the next state. The position of the sensor is perceived by the external camera in the form of a voltage value. By converting the voltage data into distance, this system can provide the rewards for each state transition"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001455_50006-1-Figure5.23-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001455_50006-1-Figure5.23-1.png",
        "caption": "FIGURE 5.23 R e s o n a n t ac tua to r .",
        "texts": [
            " The response of the actuator is computed for the initial conditions i(O)= OA, 0(0)= 0 ~ and o~(0) = 0 rad/sec. The current profile i(t) is shown in Fig. 5.21. The rotation angle O(t) and angular velocity ~o(t) are shown in Fig. 5.22. Notice that the angular velocity ~o(t) passes through zero and turns negative as the angular position O(t) peaks at approximately 6.5 ms. C] Resonant actuators are used as drive mechanisms for scanning elements in optical scanning systems [12]. An example of such an actuator is shown in Fig. 5.23. In this actuator a wedge-shaped magnet provides an axial bias field, and a coil rotates above the magnet once it is energized. A torsional pivot mechanism provides the restoring torque. When power consumption is an issue, the torsional mechanism can be designed to render the actuator resonant at the scanning frequency. When this is the case, the actuator can be brought to a resonant oscillation with a sequence of low-energy pulse excitations, thus minimizing power consumption. We demonstrate this in the following example. EXAMPLE 5.10.1 Develop a model for the design of the axial-field resonant actuator shown in Fig. 5.23. SOLUTION 5.10.1 The behavior of this device is governed by the equations for an axial-field actuator as derived in Example 5.9.1. We repeat them here for 5.10 RESONANT ACTUATORS 403 convenience, di(t) dt 1 = ~ [V~(t) - i(t)(R + Rr - nBext(R 2 - R~)co(t)] dog(t)_ 1 [i(t)nBext(R 2 _ R21) + Tmech(O) ] dt Jm dO(t) dt = og(t). (5.204) Mechanical torque: The restoring torque is provided by a torsional pivot mechanism Tmech(0) -- -KpO. (5.205) Here, Kp is the spring constant of the pivot. This simple linear relation is typically only valid for limited rotations, for example, - 1 2 ~ <~ 0 <~ 12 ~ The 404 C H A P T E R 5 E l e c t r o m e c h a n i c a l Dev ices resonant frequency f for this mechanism is (5 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0002030_978-94-015-9514-8_25-Figure5-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0002030_978-94-015-9514-8_25-Figure5-1.png",
        "caption": "Figure 5. Leaves of deciduous trees with parallel secondary venation as compared to a miura-folding. (a) The miura-folding (Miura 1980), which was designed for astronautical applications (i .e. for zero gravity conditions where no deformation occurs) shows a marked non-linear increase of its projected area during unfolding. (b) A leaf with parallel corrugation at about 4SO from the midrib shows a more steady increase of its projected area. (c) Under load this cantilever structure tends to a shape of anticlastic curvature. The resulting warping creates a stiffening effect.",
        "texts": [
            " The lozenges of the pattern open without deformation when expanded in planar motion, as is the case in space under zero gravity conditions. It has been discovered that budding leaves with parallel venation such as those of beech or hornbeam can be modelled as a detail of the miura-ori (Kresling 1997b; Kobayashi et al. 1998). However, during deployment a stiffening mechanism is created by the warping of the corrugated lamina in between the secondary veins where the structure automatically takes a form with anticlastic curvature (Kresling & Vincent 1997) (Fig. 5). THE 3-DIMENSIONAL GROWTH PATTERN OF THE PINE CONE The helical or spiral arrangement of scales occurs commonly in plants from various families, e.g. buds of inflorescences, or fructifications of flowering plants, decidu ous trees or conifers. Fibres of two types in the scales enable them to react to humi dity and dry air, respectively, and to make them bend separately. The seeds which are formed in the interstices of the scales thus are freed for dispersal (Dawson & Vincent, in Robinson 1998). The folding pattern of the modelled mechanism named \"pineapple-pattern\" is composed exclusively of triangles which ensures a coupling of the opening of all dihedral angles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0001639_analsci.16.1157-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0001639_analsci.16.1157-Figure1-1.png",
        "caption": "Fig. 1 SIA manifold used in the simultaneous determination of nitrite and nitrate in waters. S, sample; C, carrier; R, chromogenic reagent; B, automatic burette; V, valve; D, detector; Mc, microcomputer; Cf, confluence; Hc, holding coil; RC, copperized cadmium column; R1=160 cm; Rc, reaction coil (100 cm); W, waste.",
        "texts": [
            " The communication between microcomputer and burette was made by standard serial RS232C protocol, whereas digital TTL signals, using an Advantech Model 818 interface card was used for the connection with the valve. The same interface card was used for data acquisition. The quality of the results obtained by the SIA system was assessed by comparison with those obtained by the reference method. Therefore, the procedures suggested by the \u201cStandard Methods for the Examination of Water and Wastewater\u201d19 were applied. The simple manifold used for the simultaneous determination of nitrite and nitrate by SIA is depicted in Fig. 1. The respective working parameters have been studied. Once the optimal conditions of operation were established, the analytical features of the system have been determined and the quality of the results assessed. The analysis by the proposed system consists basically in the sequential aspiration of defined reagent and sample zones, which are adjacent to each other in a holding coil. After the valve has been moved to the detector position, the flow is reversed and the zones mutually disperse and merge in each other as they pass through a reaction coil towards the detector. For the simultaneous nitrite and nitrate determination with the developed system (Fig. 1), a measuring cycle comprised the following operations: in a first step, aspiration of carrier and introduction on the pathway to the detector, aspiration of sample and introduction in the reductor column, aspiration of reagent and introduction in R1. Sequentially, reagent from R1, sample from reductor column, reagent from R1 followed by carrier were introduced in the pathway to the detector. In a second step, aspiration of carrier, reagent, sample and reagent again to the holding coil and, by reversing the flow, introduction of this sequence in the pathway to the detector, followed by the carrier"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003801_iros.2006.282533-Figure1-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003801_iros.2006.282533-Figure1-1.png",
        "caption": "Fig. 1 Serial and Parallel 3T1R manipulators",
        "texts": [],
        "surrounding_texts": [
            "Proceedings of the 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems\nOctober 9 - 15, 2006, Beijing, China\nDynamic Modeling and Identification of Par4, A Very High Speed Parallel Manipulator\nVincent NABAT\nFatronik France (Fundacion Fatronik)\nMontpellier - France\nvnabatgfatronik.com Abstract- This paper introduces the dynamic modeling and the identification of Par4, a four-degree-of-freedom parallel manipulator producing Schonflies motions (three translations and one rotation about a fixed axis). First of all, this paper presents how this robot is developed with the goal of reaching very high speed. Indeed, it is an evolution of Delta, H4 and 14 robots architectures: it keeps their advantages while overcoming their drawbacks. Experimentations done with the prototype prove that the robot is able to reach very high accelerations (15 G) and to perform an Adept cycle in 0.25 s. In order to improve its dynamic accuracy, a dynamic control could be necessary. Thus, this paper presents the dynamic modeling of the manipulator using a simplified Newton-Euler approach. The originality of this computation is to model the traveling as two separated parts and to determine the dynamic effects applied on each of them. Finally, since a dynamic control requires a good evaluation of dynamic parameters, an experimental dynamic identification is presented.\nIndex Terms - Dynamic Modeling, Dynamic Identification, Schoenflies Motion, PKM, Articulated traveling plate\nI. INTRODUCTION\nA new trend in the researches on parallel robotics is the development of lower mobility manipulators. Indeed, a lot of applications do not need six degrees of freedom (do]). A classification proposed by Brogardh [1] gives the necessary number of dof for different industrial applications. He shows that applications such as pick-and-place, assembly, cutting, measurement, etc. just need from three up to five dof: This paper focuses on 4 dof manipulators and particularly on 3T1R (3 translations- 1 rotation) architectures.\nSCARA robots (see Fig. la) were the first manipulators developed to produce these movements, also named Schoenflies motion [2]. These robots can reach good performances, but their serial architecture limits their velocities and accelerations. Indeed, this type of mechanism involves high moving masses which are not suitable for high dynamics. This problem can be overcome using parallel architectures first introduced by Gough [3] and Stewart [4]. The most famous 3T1R parallel mechanism was developed by Clavel [5] (see Fig. lb): the Delta is composed of three closed kinematic chains linking the traveling plate to the frame. Each chain is composed by an arm and a spatial parallelogram (the forearm).\nOlivier COMPANY, Frangois PIERROT, and Philippe POIGNET\nLIRMM UMR 5506 CNRS - University ofMontpellier\nMontpellier - France <company, pierrot, poignet> glirmm.fr\nHowever, this architecture is able to produce three translations and the rotational motion is obtained using a central \"telescopic\" leg built with universal and prismatic joints. Other architecture close to Delta, but using linear actuators is the Orthoglide [6]. Its particularity is to be isotropic at the center of its workspace.\nOther lower mobility mechanisms were developed in order to produce Schonflies motions. For example, the machine tool HITA STT has been proposed for reaching high tilting angle [7]. The particularity of this architecture is to use additional parts in the traveling plate in order to amplify the rotational motion. Schonflies motion generators have also been proposed by Angeles, such as Gross Manipulator [8] and SMG [9]. We can also mention Kanuk and Manta robots [10]. The first one is a fully parallel robot, but has a short rotational motion; whereas the second one is a hybrid architecture having unlimited rotation. Finally, H4 [11] and 14 [12] are 3T1R parallel manipulators using the concept of articulated traveling plate. The rotational movement is obtained using an internal mobility on the traveling plate, and an amplification or transforming device gives the desired range of rotational motion.\nThis paper presents a new architecture based on H4 and 14 architecture. This manipulator, named Par4, is an evolution of these mechanisms, and has been developed with the wish of reaching high speeds and accelerations. The paper presents experimental results showing that Par4 is able to reach an acceleration of 15 G. These performances have been obtained using a simple PI controller, but in order to go further, a dynamic control is planed to be implemented. The first step of the integration of such a control is to compute the inverse dynamic modeling of the robot. That is why this paper is focused on the dynamic modeling and the experimental dynamic identification.\n1-4244-0259-X/06/$20.00 C)2006 IEEE",
            "Par4 is a parallel manipulator composed of four closed kinematic chains and an articulated traveling plate. The kinematic chains are similar to the Delta, H4 and 14 ones. They are composed of an arm and a spatial parallelogram (forearm) linked with spherical joints. The traveling plate is composed of four parts: two main parts (1,2) linked by two bars (3,4) with revolute joints (see Fig. 2). Thus, its shape is a planar parallelogram and the internal mobility of this traveling plate is a circular translation produced by a PI joint [13] (a four-bar system producing a circular translation).\nThe prototype is built using arms and forearms made of carbon fiber (obtained from ABB Robotics, as spare parts of the commercial FlexPicker robot). The traveling plate is made of aluminum in order to decrease the moving masses.\nIn addition, the \"natural\" range of the rotational operational motion is [;T-/4; T/4] . That is why an amplification system has to be added on the traveling plate in order to make a complete turn: [-z; z]. Several options are available for this amplification such as gears or belt/pulleys. The prototype has been built using belt/pulleys system, with the first pulley fixed on one half traveling plate, and the second one is linked with a revolute joint to the second half traveling plate (see Fig. 2b).\nFrom a kinematic and geometric point of view, the modeling of Par4 can be assimilated to H4. These models are presented in [11].\nThis robot has been developed with the goal of taking advantages of the existing architectures, such as Delta, H4 and 14, and using the feedback of these developments to build a manipulator having the best possible performances.\nB. Evolution ofPar4 compared to Delta, H4 and 14\nThe key point of the study was to develop a robot able to reach very high dynamics, and having a homogenous behavior\nin the whole workspace. All these characteristics cannot be achieved at the same time neither by Delta, nor H4, nor 14.\n1) Delta robot The main weak point of Delta robot is the central telescopic leg providing the rotational motion. This RUPUR (R: revolute, U: universal, P: prismatic joints) chain suffers from a short service life, and involves a bad stiffness of the rotation motion.\nIn order to avoid the central telescopic leg, the concept of articulated traveling plate has been introduced with H4 and 14.\n2) H4 robot The traveling plate of H4 is realized with three parts linked by revolute joints (see Fig. 3a). A complete study of singularities of this robot including the notion of \"internal singularities\" has been developed in [11] and demonstrates that placing actuators in a symmetrical way, i.e. at 90\u00b0 one relatively to each other involves singular postures. Thus, the robot has to be built using a particular arrangement of motors, whose axes are presented in Fig. 3a with arrows. This non symmetrical arrangement entails a non homogenous behavior in the workspace and a limited stiffness [14] of the robot.\n3) 14 robot The internal mobility of 14 is obtained with a prismatic joint (Fig. 3b). The advantage of this architecture is to authorize a symmetrical arrangement of the actuators. As demonstrated in [12], it is possible to place the actuators at 90\u00b0 one relatively to each other. However, this architecture is more adapted to machine-tool application than to high speed pick-and-place. Indeed, commercial prismatic joints are not suitable for high speed and high accelerations, and have a short service life under such conditions. This inconvenient is due to the high pressure exerted on the balls of these elements at high acceleration conditions.\n4) Par4 robot Due to its traveling plate having the shape of a planar parallelogram, Par4 has all the advantages of the previous robots, without their drawbacks. Indeed, as presented in part ILA, the traveling plate of this robot is articulated, and is exclusively realized with revolute joints. In addition, a complete study of singularities presented in [15] demonstrates that it is possible to have the same arrangements of the actuators as 14. Thus, this robot is well suited to reach high dynamics and, at the same time, to have a good stiffness and a homogenous behavior in the workspace."
        ]
    },
    {
        "image_filename": "designv11_24_0000857_s0045-7825(99)00448-x-Figure3-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0000857_s0045-7825(99)00448-x-Figure3-1.png",
        "caption": "Fig. 3. Deformation under end tensile displacement.",
        "texts": [
            " The same block is now under an end tensile displacement, rather than force. The dimension ratio of the three sides is chosen to be 5:1:1 and the applied relative displacement (i.e. the ratio of the speci\u00aeed end displacement to the unit length) is 0.5. The same boundary conditions and collocation points as those in the \u00aerst case were applied. Constant k was set to 5 in the trial functions (7). The resultant relative displacements of points 1; . . . ; 25 at section x 4:375 in the x-direction are given in Table 2. The initial and deformed geometry are shown in Fig. 3(a), (b) and (c), respectively. Case 3. In the third case study we apply an end shear deformation to the same object with the same boundary conditions. The relative end displacement is chosen to be 0.6 and constant k to be 9 used in the trial function. The computed relative displacements in the x-direction at points 1; . . . ; 25 for section x 4:375 are listed in Table 3. The initial and deformed \u00aegures are shown in Fig. 4(a)\u00b1(c). From the case studies, it is clear that the proposed model o ers satisfying accuracy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_24_0003300_6.2004-6529-Figure9-1.png",
        "original_path": "designv11-24/openalex_figure/designv11_24_0003300_6.2004-6529-Figure9-1.png",
        "caption": "Figure 9. Path modification against the pop-up threat",
        "texts": [
            " Then, this replanning has two cases according to the current condition of each UCAV; the first one is initial path is affected by pop-up threat, and the other case is not affected case. First, the case of, the pop-up threat affecting the initial path, is considered. The potential field which was computed already cannot represent the presence of pop-up threat. Thus, the some strategies in the following is proposed to find some new candidate paths. 1. Modification of the current path This approach is to modify only the section which enters the dangerous area of the pop-up threat in current path, as it is illustrated in Fig. 9. This modification is to employ chain of masses system which suffers the virtual forces from threats 2. The initial path is divided into n sections of all the same size, and each nodes is treated as a mass. These masses are connected in a single line. And between masses, spring and damper system exist. Then we call this system chained masses systems. Each mass is suffering not only forces by spring and damper but virtual repulsive forces by threats. These virtual forces arise from the threats in their own dangerous American Institute of Aeronautics and Astronautics 7 modified path area where the masses exit"
        ],
        "surrounding_texts": []
    }
]