[ { "image_filename": "designv11_32_0001082_bf00047358-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001082_bf00047358-Figure1-1.png", "caption": "Fig. 1. Assembly of the electrode system. In A, a vertical cut of the electrode shows the platinum electrode (1), the plastic body of the electrode (2) and the silver electrode (3), with their electrical connections. In B is an exploded view of the system, showing, over the electrodes, the 75/~m teflon disk (5), the polyacrylamide gel (4) and the black plastic cap (8). In C the complete assembly is represented in a vertical cut. The space for the sample (6) is created by the teflon disk (5). The window (7) for light is also represented.", "texts": [ " However, the method is subject to much error (Lavorel 1976) and sometimes leads to confusing results (Bader et al. 1983). In this report we wish to ameliorate the performance of bare platinum electrodes. We based this study on the electrical and electrochemical phenomenons occuring in the system. The application of the new standards suggested here will raise the sensitivity, the frequency response and the reliability of the bare platinum electrode system for further research in the field of photosynthesis. Schemes of the electrode used for the demonstrations are shown in Fig. 1. The platinum electrode (1) consisted of a 6.5 mm diameter (33 mm 2) polycrystalline platinum disk. The disk was surrounded by plastic (2), exposing 273 only one side of the electrode. A silver ring (3) encircled the plastic and the platinum electrode. The silver electrode had an inner diameter of 13.0 mm and an outer diameter of 20.3mm for a total area of 190mm 2. The electrodes (1, 3) and the plastic (2) were then polished to yield a fiat surface. Contact between the electrodes was made by a 30% polyacrylamide gel (4) prepared with a 0", " The decay time constant of this curve has a value of 42 ms. This shows that only a 1000 fZ resistance in the polarization circuit is sufficient to slow the response time of the electrode by a factor of two. Whether the electrical resistance in the system is contained in the polarization circuit or elsewhere does not matter, as the effect is the same. To show this, the thickness of the electrolyte layer between the electrodes was reduced. In our system, the electrolyte (sodium chloride) is contained in the polyacrylamide gel (see Fig. 1). The gel (2 mm thickness) was measured to contain 1.6 kg m -2 of sea water, equivalent to a 1.6 mm layer of conducting electrolyte. The conductivity of sea water is approximately 3.2fZ -~m-l ; therefore the calculated resistance of the gel between the electrodes is 21 Q. A dialysis membrane is sometimes used to contain the electrolyte (Chandler and Vidaver 1971, Swenson et al. 1986). We used a dialysis membrane which could retain approximately 0.013 kg m-2 of seawater. This is equivalent to a 13pm layer of seawater between the electrodes" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002858_cdc.2007.4434390-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002858_cdc.2007.4434390-Figure1-1.png", "caption": "Fig. 1. Euler Angles of the Falling Rolling Disc", "texts": [ " Leaving this term off for now, using the transpositional relations (3), and integrating by parts yields: \u03b4I = \u222b b a {( \u2202C \u2202\u03b8i + \u2202C \u2202uI \u03b3I siu s + \u00b5\u03c3\u03b3\u03c3 siu s ) \u03b4\u03b8i \u2212 d dt \u2202C \u2202uI \u03b4\u03b8I \u2212 \u00b5\u0307\u03c3\u03b4\u03b8\u03c3 } dt We thus have the following Boltzmann-Hamel equations for the kinematic optimal control problem: d dt \u2202C \u2202uI \u2212 \u2202C \u2202\u03b8I \u2212 \u2202C \u2202uJ \u03b3J SIu S = \u00b5\u03c4\u03b3\u03c4 SIu S (9) \u2212 \u2202C \u2202\u03b8\u03c3 \u2212 \u2202C \u2202uJ \u03b3J S\u03c3uS = \u2212\u00b5\u0307\u03c3 + \u00b5\u03c4\u03b3\u03c4 S\u03c3uS(10) q\u0307i = \u03a6i SuS (11) These represent a minimal set of 2n first order differential equations: the n \u2212 m equations (9) for the unconstrained uI \u2019s, the m equations (10) for the multipliers \u00b5\u03c3\u2019s, and n kinematic relations (11) for the q i\u2019s. The falling rolling disc can be described by the contact point (x, y) and Classical Euler angles (\u03c6, \u03b8, \u03c8), as shown in Figure 1. We will take the coordinate ordering (\u03c6, \u03b8, \u03c8, x, y). Suppose we have direct control over the body-axis angular velocities: w1 = \u03c9d = \u03c6\u0307 sin \u03b8 w2 = \u03b8\u0307 w3 = \u2126 = \u03c6\u0307 cos \u03b8 + \u03c8\u0307 and the system is subject to the nonholonomic constraints x\u0307 + r\u03c8\u0307 cos\u03c6 = 0 and y\u0307 + r\u03c8\u0307 sin \u03c6 = 0 We wish to steer the disc between two points while minimizing the cost functional: I[\u03b3] = 1 2 \u222b b a ( w2 1 + w2 2 + w2 3 ) dt We will choose as quasi-velocities: u1 = \u03c6\u0307 sin \u03b8 u2 = \u03b8\u0307 u3 = \u03c6\u0307 cos \u03b8 + \u03c8\u0307 u4 = x\u0307 + r\u03c8\u0307 cos\u03c6 u5 = y\u0307 + r\u03c8\u0307 sin \u03c6 The quasi-velocities (u1, u2, u3) = (\u03c9d, \u03b8\u0307, \u2126) represent the angular velocity expressed in the body-fixed frame, and are coincident with the kinematic controls" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003745_tpwrd.2010.2068567-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003745_tpwrd.2010.2068567-Figure4-1.png", "caption": "Fig. 4. Mult-body calculation model of the V-shape insulator strings. (a) Composite insulator. (b) Porcelain insulator (XP1-300).", "texts": [ " In addition, two types of porcelain insulators (XP1-300 and XWP2-300) with a minimum mechanical failing load of 300 kN can be applied to the lines. The two types of porcelain have the same shape dimension: a structure height of 195 mm and a plate diameter of 400 mm. Differently, the weight of porcelain insulator of type XWP2-300 (15.4 kg) is heavier than that of type XP1-300 (13.5 kg). The calculation model of the V-shape insulator string applied to the 750-kV compact transmission line is shown in Fig. 4. It is set up with the ABAQUS software system. The distance of connection ends in the link plate is 300 mm. As shown in Fig. 4(b), the number of porcelain insulators (XP1-300) in the string is 38. The calculation for the mechanical performance of the V-string is based on the 750-kV overhead transmission project. The typical tower of the single and double circuit is illustrated in Fig. 5. The conductors selected in the project are steel-cored aluminum strands (LGJ-400/35) for 8-bundle and arranged as inverse triangle in the tower window. The conductors suspended by the V-shape insulator strings will be bearing the load generated by wind" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000240_s0263574701004027-Figure11-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000240_s0263574701004027-Figure11-1.png", "caption": "Fig. 11. A modified accurate vector chain for leg i.", "texts": [ " By referring to Figures 6, 7 and 8, xM , yM and zM are the partial position deviations which are measured by the laser beam along the x, y and z axis respectively. There are two methods by Patel17 and Wang etc.7 available to develop a model of a Stewart Platform based machine tool that provides the framework to include the complete errors of the geometrical features for specifying the position and orientation deviation. By shifting the co-ordinates of the leg joints from Bi and Ai to Ci and Di respectively in Figure 11, two joint location errors described by vectors ci and di are introduced to the Stewart Platform. On the other hand, Li is a length error in the leg. Let Ai = Aui( ci )+ di , keeping roll-pitch-yaw angle constant will combine ci and di of Figure 11 to form a constant Ai. Based on the error model developed by Patil,14 computation of the position and orientation deviations of a Stewart Platform at a pose ={x, y, z, x, y, z} is given below: x y z x y z = a11 a66 L1 L6 IT 1x 0 0 IT 1y 0 0 IT 1z 0 0 0 0 0 IT 6x 0 IT 6y 0 IT 6z A1x A6x A1y A6y A1z A6z (1) The computation of the position and orientation deviations in equation (1) involves three sections; the first one is the analysis of inverse Jacobian matrix, J 1, the second one is the leg length errors, , and the third one N A is the positional errors of the joints in the Stewart Platform as shown by the equation (2): =J 1( N A), (2) The complete errors of the geometrical features in equation (2), which are identified as leg length and co-ordinate errors for the position of the joints, have to be identified in order to improve the positioning deviations of the moving platform" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003434_6.2008-4505-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003434_6.2008-4505-Figure7-1.png", "caption": "Figure 7 4.37\" diameter seal with L/R=0.35", "texts": [], "surrounding_texts": [ "Six different configurations of proof of concept foil face seals were fabricated in order to assess the impact of flow path radial length, axial preload and surface velocity on leakage. The six test articles are shown in Figure 5 through Figure 10. Two 9-inch OD thrust foil bearings, two 4.37-inch OD and two 3.82-inch OD configurations were fabricated providing different L/Ro ratios, angular gaps between pads and different flow paths. For each test seal, the outer periphery of the compliantly supported foil pads was open to atmosphere, thereby presenting a leakage path along the radius as opposed to the closed ends shown in Figure 3. Figure 11 and Figure 12 schematically show the tested configurations with the open ends and the primary flow paths. The importance of the open ends for these initial tests was to determine the baseline resistance to flow due to the total axial gap (htotal) in the angular segments between pads, the gap beneath the bump foils (hb) and the gap between the top smooth foil and the disc (hfilm), all without the end flanges and secondary seal elements to restrict flow. This would allow for an assessment of critical design parameters for the fundamental seal shape, such as an assessment of the importance of L/Ro ratio. Additionally, tests of the candidate seals with this arrangement and conducted under rotating conditions would, when compared to static/non-rotating tests, verify that the hydrodynamic pressures were generated and reduce total leakage. As shown in Figure 2 and Figure 3, both the angular gap and open ends will be eliminated in the final configuration, thereby only allowing leakage flow to pass through the minimum film height (hfilm). By eliminating the larger gaps associated with the pad angular spacing and the region beneath the compliant bumps in the face seal configuration, the leakage will be substantially reduced from the measured baseline configuration. It should be noted that during testing the total gap height was on the order of 0.031 inch, whereas hfilm was either zero when static tests were conducted or on the order of 0.001 inch when dynamic testing was conducted at speeds from 24,000 to 60,000 rpm. While hfilm initially increases during dynamic testing (see Figure 11), the generated hydrodynamic film pressure resists the radial inflow/outflow of high pressure air. Thus, the air is forced to flow behind the top smooth foil and through the passages formed by the bumps (approximately 0.021 inch high) as well as the gaps between individual pads. It should also be noted that with the high pressure at the OD, the inward directed pressure driven flow will also be restricted by the inherent outward self pumping action of the disc. Finally, while the gap between pads is approximately 0.031 inches high and between 6\u00b0 and 10\u00b0, flow in this gap is turbulent, even for differential pressures as low as 2 psig. Thus, when the end flanges are introduced at the OD and the pads overlap one another, the primary leakage path will be through the very narrow hydrodynamic film region, which, at about 0.001 inch, will result in leakage rates well below any present technology." ] }, { "image_filename": "designv11_32_0003856_1.3610033-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003856_1.3610033-Figure2-1.png", "caption": "Fig. 2 Hyperbola representing degenerate case of circle-point curve", "texts": [ " The fixed pivots Oa and Os which lie on the centerpoint curve may be determined by the Euler-Savary equation in the form Ai = Ai = 0 as seen from equation (18). The cubic then reduces to A,y2 + Atx2 + Aixy - AiV = 0 where ai = sin i(cos 0i \u2014 l ) bi = \u2014cos i(cos i \u2014 1) follow from equation (31), and A, = ^ + 6, + (cos - 1) = - ^ (cos i - 1)* ^ - - ; < \u00ab . * - I , . As = ai = sin i(cos i \u2014 1) Hence equation (32) becomes the rectangular hyperbola 2 sin i x2 \u2014 y2 -I xy - y = 0 COS i = 60 deg is represented. (31) (32) (33) (34) (35) Journal of Engineering for Industry M A Y 1 9 6 7 / 233 Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jmsefk/27510/ on 03/10/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use References 1 M. Krause, Analysis der ebenen Bewegung, Walter de Gruyther and Company, Berlin and Leipzig, 1920. 2 O. Bottema, \"Some Remarks on Theoretical Kinematics,\" Proceedings of the International Conference on Mechanisms, Yale University, 1961, pp" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003281_s0022112006004009-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003281_s0022112006004009-Figure1-1.png", "caption": "Figure 1. Illustration of the mechanism of the self-assembly of optical fibre by using a solder drop positioned on a rectangular horizontal wettable pad attached to a substrate. The fibre is submerged in the solder and initially misoriented at an angle \u03d50 relative to the pad long centreline. At the end of the self-assembly process, the fibre should be aligned with the pad centreline, while the solder wets the entire pad and part of the fibre (the wettable area). (a) Top view, and (b) side view. The wettable pad dimensions are w \u00d7 2a, and the fibre cross-sectional radius is R0.", "texts": [ " Numerical results for the three-dimensional model are presented and discussed in \u00a7 7, whereas those for the two-dimensional model are given in the Appendix. The predictions are compared with the experimental data in \u00a7 8. The conclusions are formulated in \u00a7 9. A short piece of optical fibre coated with a wettable layer was submerged in a drop of solder while the solder was being heated to its melting point. The fibre was withdrawn and a smaller solder drop was withdrawn on it and solidified. The optical fibre with the solidified solder drop on it was positioned on a horizontal rectangular wettable pad mounted on a substrate (figure 1). The fibre was initially misoriented by an angle \u03d50 relative to the long centreline of the pad. Then the substrate was heated. When the substrate had reached the temperature required to melt the solder, the solder drop started spreading over the pad and the entire wettable layer on the fibre. This was followed by fibre reorientation toward the pad centreline. The experiments were observed by an optical microscope (Olympus BX51) and a CCD camera (MotionScope PCI 8000S) at 250 f.p.s. Substrates were made of silicon chips with various pad dimensions deposited on them", " Then conditions (49) will be conserved for all the subsequent drop evolution, and the fibre will not rotate around its own axis. The fibre motion is described by only the x-projection of the moment-of-momentum balance, namely (38). We can rewrite this equation as d\u03c9\u03d5 dt = 3\u03b2Mx, (50) where \u03b2 = \u00b52a4 0 m\u03c3l20 (51) is the dimensionless parameter including the physical properties of the liquid and the main geometrical scales of the drop and fibre. Another important geometrical parameter involved is the half-length of the pad a rendered dimensionless by a0 (see figure 1). The initial angle between the fibre and the pad centrelines in the calculations was \u03d50 = 0.3 (about 17.2\u25e6). The evolution of the free surface of the liquid was found numerically for the different values of a/a0 and \u03b2 . An example for a/a0 = 1.3 is shown in figure 6. The time dependences of the angle between the fibre and the pad centrelines \u03d5(t) for the different values of \u03b2 are shown in figure 7. From this figure, it can be seen clearly that the angle \u03d5 tends to zero as t \u2192 \u221e in all the cases" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000222_tmag.2002.802291-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000222_tmag.2002.802291-Figure2-1.png", "caption": "Fig. 2. Schematic diagram of the system for measuring the efficiency characteristics of the LOA (f = 37:1 Hz).", "texts": [ " Fig. 1 shows the basic structure of the moving-magnet type linear oscillatory actuator. The LOA is symmetrical structure to a shaft. The LOA is composed of yokes, permanent magnets, coils, and brackets. The yokes of the LOA are made of laminated magnetic steel sheets. The LOA has the Nd\u2013Fe\u2013B magnets as the moving part. The two coils are connected in parallel, and each coil has 680 turns. The shaft is supported by linear ball bearings. The basic specifications of the LOA are listed in Table I. Fig. 2 shows the schematic diagram of the system for measuring the efficiency characteristics of the LOA under simulated compressor. The LOA and the load linear motor are connected to each other with the force sensor. The load is measured Manuscript received February 14, 2002; revised May 24, 2002. M. Utsuno, M. Takai, and T. Mizuno are with the Faculty of Engineering, Shinshu University, Nagano 380-8553, Japan (e-mail: utsuno@gipwc.shinshuu.ac.jp; t01a234@mail.shinshu-u.ac.jp; mizunot@gipwc.shinshu-u" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003807_j.wear.2009.02.016-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003807_j.wear.2009.02.016-Figure2-1.png", "caption": "Fig. 2. Schematic diagra", "texts": [ " It will depend on many factors, including the complexity of the problem, the number of data points in the training set, the number of weights and biases in the network, and the error goal. We shall therefore use each of the algorithms described in this section to train our network and based on their comparative performance decide on the best training algorithm for our problem. 3. Experimental details A number of experiments were carried out for training and testing the proposed neural network model. The tests were performed on a Ducom TR-20 pin-on-disc machine. A schematic diagram of the experimental set-up is shown in Fig. 2. The pin was made of ZnS having a hemispherical dome shape of 9.5 mm diameter and a central thickness of 5 mm. One hundred sixty millimeter diameter disc of 8 mm thickness were used and the materials of the disc were chosen as mild steel, copper, brass and polymethyl methacrylate (PMMA). The properties of pin and the disc material are given in Table 1. The experimental procedure consists of pressing the disc on a rotating plate and fixing the pin to the load arm. The pin stays on the disc with two degrees of freedom: one vertical, which allows its direct contact with the surface of the disc, and another horizontal which causes contact friction, activating the load cell with a strain which is a function of the friction torque" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002558_978-3-540-71364-7_29-Figure28.8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002558_978-3-540-71364-7_29-Figure28.8-1.png", "caption": "Fig. 28.8. Slave side: a) objects for haptic exploration b) screw and screwdriver", "texts": [ " Such a setup provides the operator with a realistic visual information about the location of the objects, the environment, and the telemanipulator. Here, the anthropomorphic construction of the telemanipulator plays an important role: the operator can drive it as if it were his/ her own arm. The visual information is useful not only for motion generation but also for handling the contact and minimizing effects of the impact. The experiment consists of three tasks: \u2022 tracking of free space motion \u2022 haptic exploration of different materials (soft and stiff), see Fig. 28.8a \u2022 driving a screw with an aluminium tool, see Fig. 28.8b. This last experiment consists of three phases: contact with extreme stiff materials, a classic peg-in-hole operation and manipulation in a constrained environment. Fig. 28.9 and Fig. 28.10 show the position and force tracking performance during haptic exploration of different materials (see Fig. 28.8a). The shaded areas indicate the several contact phases. One can see that during free space motion, the position tracking of the slave arm works very well while in the contact situation, as a consequence of the implemented impedance controller, the slave position differs from the master position. Please note that, as the force tracking is very good, this position displacement influences the displayed and felt environmental impedance in such that hard objects are perceived softer then they are. As the master controller is of admittance type, which reacts on the human force input, non zero forces (forces depend on the minimal master dynamics) are necessary during free space motion to change the actual end-effector position" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000263_ias.1995.530578-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000263_ias.1995.530578-Figure6-1.png", "caption": "Fig. 6: Locis of complex line current harmonics jho depending on control angle a, exact dc ripple model (R) as well as parameter reactance sum xx = 0.21 8 (A), 0.4 (m) and 1 (v ) assumed;", "texts": [ " Introducing the reactance sum effective for dc smoothing x z = X d + 2 X N , compare [9, lo], analytical calculations by switching functions result in the description of the complex line current harmonics 25 COSCL -- 90 c o s a - O O5 cosa ~ * 84 c o s a ~ xz x2 x 2 xz 31 3 48 3 -1--sinct -l+-sina 1 - E s s l n a 1 - 3 6 s s l n c t x2 xz xz XI: with the imaginary and real part, ah and bh , respectively, as listed in Table I ; the derivation of these formulas are outlined in the Appendix. The amplitudes and phase angles, as r.m.s. value and radians, respectively, are determined by 0.78 I ( I h ) R = dm; (16) h ( ' P h o ) R = arc tan ( ah / b h 1. (17) The corresponding behaviour in the complex plane is presented in Fig 6, describing the harmonics l h o ~ = ( I h o ) ~ / (I h )rr, = i hR exp( j cp ho ) depending on the control angle a with the reactance sum x z as parameter. Thereby, the usual operating range of ac/dc converter ist considered, i.e. control angles between 15\" and 165\" only. Due to the cosa-dependency of the imaginary parts a h , all locis are symmetrically with respect to the real axis. This modeling describes the influence of a rippled dc current on the behaviour of the complex line currents, if the commutation angles are negligibly small", "34 UN) of the dc shuntwound motor considered, whereby a resistive dc volt- age regulation of d, = D, / (2.34 UN) = 0.05 is taken into account. The locis demonstrate the effect of different smoothing reactance xd, constant network reactance XN = &Id / UN = 15% assumed. The behaviour of both negative sequences is and ill = f (ea) can be described by damped spirals, whereas the locis of the positive sequence i7 = f (ed) show additionally a cycloid for low dc reactances only. Generally, the occurance of cycloids corresponds to a significant change of the angle 'p7 for higher dc ripple, compare Fig. 6a) and [13]. The fundamental influence of decreased dc current smoothing is 21 71 obvious: essential higher 5th magnitude i5 in contrast to a strong reduction of i7, whereas i l l is damped only by the commutation effect according to Fig. 5. With the knowledge of thephase nngles, total harmonic generation of several converters can be estimated by geometric addition of the individual line current harmonics. Thereby, the reduction of harmonics by phase multiplication can be considered as a special case, e" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001232_tasc.2003.813042-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001232_tasc.2003.813042-Figure1-1.png", "caption": "Fig. 1. Photograph of the bulk superconducting rotor.", "texts": [ "2003.813042 teristics are measured by experiment to see the characteristics during overload operation and locked rotor tests are performed to know the effect of the heat to the torque characteristics. FEM analysis is also performed to know the dependence of the torque on slip frequency when the effect of the heat is ignored. Experimental apparatus of the motor consists of the bulk superconducting rotor and a stator that has 3-phase 4-pole copper windings. The photograph of the rotor is shown in Fig. 1. These specifications are shown in Table I. Three pieces of ring-shaped bulk superconductors were set to the shaft that was made of FRP. The rotor length is 45 mm and its outer diameter is 46 mm and inner diameter is 16 mm. A stator is the conventional one that has copper windings and laminated iron core. A hall sensor was set inside of the stator to measure flux density in the gap. Another bulk superconductor is used as a magnetic bearing at the bottom of the shaft. During the experiment, bulk superconducting rotor and the stator are cooled by the liquid nitrogen" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001068_bf02487718-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001068_bf02487718-Figure5-1.png", "caption": "Fig. 5 Three-segment manipulator", "texts": [ " and B 0 as a cut joint, the reduced tree system is an open chain (see Fig. 4). For a low-pair single chain, Eqs. (23), (38), (39) are simplified as follows: i 0 i = - - ~ i ~ (~--~(J~i)r0 i (i = 1 . . . . n) (40) j = l ~, ^ (j,,+ 1) r- ~c (A----~ i ) q~ -- 1 = 0 _ (41) j = 1 V .?4 uilgi3. + ~_Qil - ~'~) - D i t j - KFI j + C i - ~u:-+ 1,i# ~ = 0 (j = 1, n) (42) . ' , ~ # j ~ t - . . i= j J where ~u~) is the #j-th subrow of ~u0 . VII. EXAMPLE MANIPULATOR Consider a three-segment manipulator illustrated in Fig. 5 as an example [sl. When the end of Vol. 4, No. s Liu Yanzhu: Screw-Matrix Method 173 working arm is gripping the object with a spherical joint 04 which is moving along a smooth guide, the manipulator becomes a closed chain. Let 04. be the cut joint, then the reduced tree of the system will be an open chain when the arm is divorced from the ground. The parameters of the system are shown in the following table: J aj bj ~j vj ~j bi 0 --0 6 0 b2 n/2 0 6 :! f 0 0 n/2 1 3 q.~ Pj~ 01 0 n/2-o2 o ~ i z3 0 1 Pj2 P J3 --Pl --172 --P3 x , = x , (r x , = x2(r x3 = x3(r where ~ is the curve coordinate of O4 along the guide" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002323_bf00382472-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002323_bf00382472-Figure4-1.png", "caption": "Fig. 4. Unfolded situation of tke skoulder (rel. fig. 3).", "texts": [ " (1) The coordinates of the apex of the front cone are Xo ---- e cos ~ -- r; Yo ~-- -- e tan fl; Zo = e sin ~ + h. (2) where e represents the length of the line MT'. The line TP lies on the cone. I ts l eng th , / , is determined by /2 = (xo - x)~ + (y0 - y )2 + (zo - z)2, (3) or, using (1) and (2), by / 2 = e c o s ~ - - r + r c o s + - - e t a n f i - - r s i n + + (e sin \u00ab + h -- $(u)) 2 (4) Now the tube (lower part in Fig. 5.) is cut open along the line SS' and subsequent ly both pat ts (shoulder and tube) are f la t tened (see Fig. 4). Since TP is part of the cone, i t will remain straight in Fig. 4 as well. I ts length can also be obtained from /2 = (e t an f l + u ) 2 + (h - - e - - ~ ( u ) ) 2 (5) From (4) and (5), by el iminat ing/2, it is found tha t \u00a2(u) = h - - (6) e(1 + s i n ~) J I t can be seen from (6) tha t the boundary condition ~b(O) = h (7) has already been satisfied. The length of e will now be chosen so tha t @(nr) = 0. I t appears tha t e - ( 8 ) h(1 + sin ~) -- n r tan/~ -- 2r cos F rom the geometrical si tuation of the shoulder it follows tha t only solutions for whieh [x0l < r a r e admissible" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000433_s1474-6670(17)39653-2-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000433_s1474-6670(17)39653-2-Figure1-1.png", "caption": "Fig. 1. The excessive scheme of the MGC and a envelope of its angular momentum.", "texts": [ " Theo retical aspects of the SC spatial attitude con trol and precise stabilization were represented in a number of research works (Raushenbakh and Tokar , 1974; Zubov , 1982; Smirnov , 1981 ; Branets and Shmyglevsky, 1992; Crenshaw, 1973; Junkins and Turner , 1986; Hoelscher and Vadali , 1994) Well-known results on gyromoment control were * This work was supported by the RAS , the RFBR, Grant 97-01-00741, and by the Russian Space Agency (RSA). based on methods of optimization and Lyapunov functions , whereas the exact feedback linearization (EFL) technique was also applied to this problem (Singh and Bossart, 1993) . In this paper, our new results on such nonlinear problems, obtained by vector Lyapunov functions (VLF) , are presented. Model of manoeuvring SC takes into account: spatial angular motion of the SC body; movements of the MGC at the minimum-excessive scheme \"2-SPEED\"-type (Crenshaw, 1973), Fig. 1, and flexible solar array panels and antennas by 2-DOF gear stepwise drives; external torques . Model of each GD describes: nonlinear dynamics of control laws (CLs) for current loops in the gyrorotor (GR) 5-DOF electromagnetic suspension (EMS); flexi bility of the gyroshell (GS) preloaded ball bear ings; flexibility, dead band and kinematic defects in the gear; nonlinear dynamics of stepwise motor and electromagnetic damper (EMD) on the GD precession axis taking into account the dry friction torque" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001463_bf00046604-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001463_bf00046604-Figure2-1.png", "caption": "Fig. 2. The 'egg' position adopted on the inrun.", "texts": [ " Notation A D drag area A L lift area D aerodynamic drag F frictional resistance between skis and snow g acceleration due to gravity h equivalent jump height at end of inrun L lift 1 jump length EVALUATION OF THE FLIGHT MECHANICS AND TRAJECTORY OF A SKI-JUMPER R reaction between ski-jumper and ski slope s distance along inrun t time u horizontal component of velocity V T tangential velocity component at end of inrun v vertical component of velocity x horizontal coordinate x z horizontal length of jump y vertical coordinate, positive downwards 0t incidence angle of ski-jumper fl slope angle of inrun measured relative to horizontal coefficient of friction p air density 0 angle of trajectory relative to horizontal Subscript pertaining to the inrun 303 For the purposes of modelling the jump, it is first necessary to establish the equations of motion of the ski-jumper during the inrun and free flight phases. The forces acting on the ski-jumper in this phase are shown in Figure 2. Resolving the forces along the direction of the inrun, the equation of motion is dV m - - = m g sin fl - F - D, (1) dt where the drag D is given by O = ~p V2AD (2) and the frictional force F is given by F =/~R. (3) The reaction R is given by mV 2 R = m# cos fl + - - - L, (4) r where mV2/r is the centrifugal force on the jumper due to the change of curvature of the surface slope along the inrun, and L is the aerodynamic lift. In practice L is negligible on the inrun, and m VZ/r only becomes significant during the latter stages of the descent down the inrun" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002145_s0065-2911(08)60046-6-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002145_s0065-2911(08)60046-6-Figure7-1.png", "caption": "FIG. 7 . Wave shape of envelope used to model metachronal waves (a). Figs (b) and (c) represent paths traced by a n element of the envelope; (b) predominantly longitudinal motion, ( c ) predominantly transverse motion.", "texts": [ " This type of motion cannot therefore be modelled satisfactorily by a sinusoidal oscillation SOME BIOPHYSICAL ASPECTS OF CILIARY AND FLAGELLAR MOTILITY 19 of a sheet, a problem which has been studied by a number of authors (e.g. Taylor, 1951; Reynolds, 1965; Tuck, 1968). The appropriate model requires a sheet which is assumed to vibrate transversely and longitudinally, so that the general path traced by an element of the sheet is a closed curve; if both the vibrations are simple harmonic, the curve will be an ellipse (Fig. 7) . The theoretical analysis pertaining to this model is developed by Blake ( 197 lb), but it will be sufficient here to note the main conclusions and compare them with the available experimental evidence. A major result to emerge is that, for a freely swimming organism when the excursion of an element of the sheet is predominantly transverse, the direction of movement of the organism is opposite to the propagation direction of the metachronal wave; when an element executes a longitudinal vibration, the directions of wave propagation and of propulsion are the same" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003297_j.rcim.2008.07.002-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003297_j.rcim.2008.07.002-Figure4-1.png", "caption": "Fig. 4. The distribution of teeth on the spherical pitch surface.", "texts": [ " (21) and (22), eliminating (a j), 4 9 \u00f0x1 cosa y1 sin a\u00de2 \u00fe \u00f0y1 cos a\u00fe x1 sin a\u00de2 \u00bc a2 4 (23) Let h \u00bc O1O0, the above equation can be written as 4 9 h2 sin2 a\u00fe \u00f0h cos a\u00fe u\u00de2 \u00bc a2 4 The point of the undercutting limit can be expressed as u uc \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2 4 \u00fe 4 9 h2 sin2 a r h cos a (24) Suppose the pitch radius of the spherical gear is R \u00bc 36 mm, the center distance is 72 mm and the module is m \u00bc 3 mm, the distribution of the teeth is shown in Fig. 4. There is one tooth at the center, six teeth uniformly distributed on the first parallel and 12 teeth are uniformly distributed on the second parallel. All the teeth are uniformly distributed on a pitch ball. On the first parallel y \u00bc y(1) \u00bc 151. On the second parallel y \u00bc y(2) \u00bc 301. The addendum radius of the concave gear Ral \u00bc 36.00 mm and the addendum radius of the concave gear Rf1 \u00bc 29.25 mm. The addendum radius of the convex gear Ra2 \u00bc 42.00 mm and the addendum radius of the convex gear Rf2 \u00bc 35" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003575_978-3-642-14515-5_77-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003575_978-3-642-14515-5_77-Figure3-1.png", "caption": "Fig. 3 The FE foot model (consisting of 29 bones, 85 ligaments, 12 muscle groups and foot plantar soft tissue)", "texts": [ " These ligaments were constructed by referring to the MRI images and the 3D human anatomy software: Interactive Foot and Ankle 2.0 (Primal Picture Ltd. U.K). Due to the complexity of the human foot musculoskeletal system, in previous foot FE studies, the muscle actions were either simplified as force vectors applied directly to the points on the bones or were totally neglected [8, 12, 16]. In this study, twelve major muscle groups around talocrural, subtalar and metatarsal-phanlangeal joints were constructed in the ABAQUS environment (see Fig.3(a)). The musculoskeletal geometries of these twelve muscle groups were determined according to the MRI images and the 3D human anatomy software (see Table 1 for detailed information). The muscles were constructed by considering the mechanical properties of the realistic muscles. This includes both contractibility (ability to contract) and extensibility (the ability to be stretched). The muscle forces can not only be transmitted via linear path, but can also be transferred through curved path in 3D", " The simulation was conducted using ABAQUS/Explicit module, segmental inertia properties, contact mechanics and frictional properties were all considered. A rigid fixed plate was used to simulate the ground support, and the footground interface was defined as contact surfaces with frictional coefficient of 0.6 [16, 19], while joints surfaces and the interface between bone and foot plantar were all defined frictionless contact. The bones and soft tissues were meshed using the tetrahedral elements and the ligaments were meshed using truss elements (see Fig.3(b)). The mesh were determined by a converging analysis. In order to save computation cost, femur and shank bones were defined as rigid part in the simulation. The material properties of all structures included in the model were assumed to be homogeneous, isotropic and linearly elastic, which were listed in table 2, taken from the literature as cited. To validate the FE model, a one-meter-long pressure plate (RSscan, Belgium) was also used to record the foot pressure distributions at 250Hz during waking of the same subject used in the modeling study" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000001_s0389-4304(01)00108-4-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000001_s0389-4304(01)00108-4-Figure3-1.png", "caption": "Fig. 3. Timing chain layout.", "texts": [ " (c) Camshaft friction Camshaft torque was measured with torque meter 2, with the timing chain removed and with the powderbrake replaced by a motor connected to the camshaft. (d) Overall timing chain friction Overall timing chain friction was determined by calculating (Result of (a)) @ (Result of (b)) @ (Result of (c) 2). The above measurement and calculation revealed that overall timing chain friction accounted for 16% of the overall engine torque, see Fig. 2. 3.1. Parts arrangement around timing chain Fig. 3 shows the arrangement around the timing chain. The timing chain is engaged with sprockets fixed to the camshaft and crankshaft and slides on guides R and L. Guide R is fixed at both ends to the engine block, and guide L is mounted on the engine block so that it can swing through a small angle. Guide L is stretched by 0389-4304/01/$20.00r 2001 Society of Automotive Engineers of Japan, Inc. and Elsevier Science B.V. All rights reserved. PII: S 0 3 8 9 - 4 3 0 4 ( 0 1 ) 0 0 1 0 8 - 4 JSAE20014352 a chain tensioner with a force proportional to the main oil hole pressure, to maintain a constant timing chain tension" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001603_robot.2004.1308759-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001603_robot.2004.1308759-Figure2-1.png", "caption": "Figure 2 Visualization of instantaneous center of rotation wnstraint", "texts": [ " The velocity of the i\u2019 robot with respect to frame (MO} is computed as: As the formation maneuvers, maintaining the rigidity of this v b l sbxcture, our motion planning strategy aligns the direction of forward travel (the X axis of each robot) with the induced helicoidal velocity vector field. This planning strategy for developing motion plans for each mobile robot can be visualized using the notion of the Instantaneous Center of Rotation (ICR). In frame (MO), the location of instant center of the osculating circle is given by (O,-(l/~(s))). Further, graphically, we see that the ICR of each robot is constrained to lie on the l i e passing through the axle of each robot (Figure 2). Thus, when multiple robots form part of a virtnai structure moving with its helicoidal~ field, the ICR of each robot must now correspond to the instant center of the virtual structure (and thus the motions along the underlying path). This is used to uniquely determine the orientation of each mobile base; The corresponding twists of the h m e s (M, 1 , as they move to align themselves with this motion plan have a simplified representation in robot fixed frame {U? 1 as: where vi = 11 uCrll and w, are the magnitudes of the linear and angular velocities" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure5.21-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure5.21-1.png", "caption": "Fig. 5.21. Motion coupling using screw thread", "texts": [ "20 shows the linear errors along the X-direction collected from five cycles of complete bi-directional travel of the X-carriage. The average value from the five cycles is computed to minimise the effects of any random influence arising. Linear errors may arise from various sources, including geometrical deficiencies along the guideway and measurement offsets/errors. For the XY table under study, the largest error source is probably due to the nonlinearities in motion arising from the screw thread and associated backlash errors. Figure 5.21 shows the motion transfer mechanism from the screw thread to the moving carriage. The air gaps present in the mechanical interface can cause the actual displacement to vary rather significantly. This probably also explains the differences in linear error measurements in the forward and reverse directions. For the modelling of linear errors, m is chosen as m = 80 for the RBF. The terminating condition for the gradient weights tuning algorithm is defined as ems < 0.01, where ems is the mean squared error ems" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-FigureA.5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-FigureA.5-1.png", "caption": "Fig. A.5. Optics and accessories for straightness measurements", "texts": [ "7 which illustrate that the angular measurement is comprised of two linear measurements at a precisely known separation. Roll measurement is addressed separately in the next section as this measurement will typically require a level-sensitive device to be used. The objective of a straightness measurement is to determine whether the moving part is moving along a straight path. The main source for a straightness 5.3 Overview of Laser Calibration 137 error is the straightness profile of the guiding mechanisms which guide the motion of the moving part. The optics required for straightness measurement is given in Figure A.5. The straightness profile can be divided into two components: namely the horizontal and vertical straightness. The schematic of the set-up to carry out these measurements is given in Figure A.6. Figure 5.8 illustrates the two light paths of travel within the interferometer. The mirror axis serves as an optical straight edge to provide a reference for the straightness meaurements. Straightness and squareness measurements are usually done concurrently, since a squareness measurement consists of two straightness measurements carried out perpendicularly to each other" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003432_med.2007.4433822-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003432_med.2007.4433822-Figure3-1.png", "caption": "Figure 3. Principal axes system for the EFIGENIA EJ-2B HALE UAV", "texts": [ " The control station continuously maintains communication with the airborne platform and payload. This has been designed to operating under concept of \u201cvirtual Cockpit\u201d which allows to the operator the possibility of feeling the realism of flight operations, flight conditions and its performance. The vehicle have 6 DOF for controlling the EFIGENIA UAV attitude in flight using independent embedded fuzzy logic 16-bit DSP controller multiprocessor flight control computer in Roll, Pitch, and Yaw axis Figure 3. EFIGENIA UAV aircraft was modeled as a rigid body moving in space, using the variables (x, y, z) to represent the position of the UAV vehicle in body coordinates, and the variables \u03c8\u03b8\u03c6 ,, to represent the roll, pitch, and yaw angles of the EFIGENIA UAV with respect to the body coordinates. The combination of neural network and fuzzy logic system make possible to create an effective method for implementing the EFIGENIA autonomous navigation and flight control technique. In this way, the system allows a massive parallelism; learning ability, fault tolerance, etc" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002892_1.5061067-Figure12-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002892_1.5061067-Figure12-1.png", "caption": "Figure 12: CAD drawing of vane passage of an", "texts": [ " HIP temperature, pressure and time parameters were industry standards for the Ti-6Al-4V alloy and are generally conducted at a conservative margin below the beta transus temperature. The geometry of the airfoil, including a sharp interface with the saddle surface and the outer diameter of the capsule, makes this part difficult to consolidate. Several changes to the capsule interfaces to remove these stress concentrations were required to promote high pressure HIP consolidation. Laser consolidation of Ti-6Al-4V alloy to build tooling for net-shape HIP was investigated to manufacture segments of an impeller for demonstration. Figure 12 shows a CAD drawing of vane passages of an impeller. Because of the complex geometry of the component, as per PWR\u2019s suggestion, one 1/6 section (highlighted in red) of the impeller was selected as sub-scale feature to be built using laser consolidation of Ti-6Al-4V alloy. Based on the capability of the laser consolidation process, a CAD drawing of the vane passage segment was created (Figure 13a). The green \u201cleg\u201d portions are supporting structures for the required vane passage (red portion) and will be removed by CNC machining after laser consolidation" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003394_peds.2007.4487699-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003394_peds.2007.4487699-Figure3-1.png", "caption": "Fig. 3. A 2D linearised cross-sectional view of one phase of a RFAPM machine with overlapping stator coils in relation to the pole positioning and relative flux distribution.", "texts": [ " RFAPM machine with overlapping coils A three-dimensional view of the typical coil configuration of a RFAPM machine with overlapping stator coils are shown in Fig. 2. A two-dimensional linearised cross-sectional view along the nominal stator radius of only one phase of the overlapping stator coil configuration, with a sinusoidal radial flux density, a coil pitch, Oq, equal to the pole pitch, Op= 2p, a coil position a with respect to the flux density wave and a coil side with of 2A can be represented as shown in Fig. 3. For the analysis we assume that the stator thickness is much smaller than the nominal stator radius, i.e. h < rN allowing us to consider all the turns to be situated on the nominal stator radius. To begin the analysis, we start by looking at a single turn, say 1 and 1' of Fig. 3, as shown in Fig. 4. The flux-linkage for this turn at position d inside the coil, can be calculated as A1= j j Bp sin (Of) rdOdz = 4 Bp cos (ap) cos (6p) rft (1) The total flux-linkage for N number of turns, can be calculated by integrating with respect to d across the entire coil side-width (i.e. between -A and A), dividing by the coil sidewidth (i.e. 2A) to get the average flux-linkage and multiplying the result by N. The total flux-linkage for a typical coil with a wide coil side-width can thus be calculated as follows, AN = 4B cos (aP) cos (0) rLfd6 = pBpIN cos (a 2rnfkA with kA, the flux-linkage factor given by sin (AsP2) k,A=P (2) (3) The maximum coil side-width will be equal to T mechan-~Q ical degrees, i" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003624_978-3-642-03737-5_20-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003624_978-3-642-03737-5_20-Figure3-1.png", "caption": "Fig. 3. General model of an obstacle avoidance scenario \u2013 the geometrical and kinematical indices used by the algorithm for obstacle avoidance", "texts": [ " Both mathematical tools enable robot fast learning, building algorithms for environment understanding as well as decision making capabilities. To build intelligent control algorithms for avoidance of mobile and immobile environmental obstacles corresponding geometry model of the obstacle avoidance scenario should to be developed. For that purpose, the following geometrical as well as kinematical scenario models of obstacle avoidance as well as collision avoidance are developed. They are presented in Figs. 3 and 4. The point P in the model presented in Fig. 3 denotes the actual relative position of biped robot (i.e. the projection of its mass center to the ground support) with respect to the XOY inertial coordinate system. 0P is the starting point. Ro- bot moves towards the preview point. In general case, the preview point can be situated on some landmark object or part of object (e.g. edge, corner, etc.). Due to the presence of obstacles, biped robot has to change its course of motion to avoid collision and to continue motion towards the preview point", " The arrangement of the objects within the range bounded by the circle k causes the direction 2\u03b4 of escaping obstacles. If possible the robot should go forward or in lateral directions. Only in the case of a dead-lock, the robots have to go backward to continue the trip. Direction 3\u03b4 determines the course orthogonal to the 0\u03b4 . Robot is obliged to moves along the direction 3\u03b4 only in the case when the proximity sensors indicate that the robot can strike some objects (defined by the points 7T and 8T ) by the swinging leg as presented in Fig. 3. The proximity range is bounded by the ellipse e . A fuzzy block determines, according to the ac- tual situation in every sampling time, the direction 1\u03b4 , 2\u03b4 or 3\u03b4 in which the bi- ped robot has to move in order to escape the obstacles. Humans also reason in a similar way trying to optimize their trajectories moving towards the preview points in their environment. In a similar way, humans try to solve the problem of motion in the presence of mobile obstacles as presented by the model in Fig. 4" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001428_j.cam.2003.06.009-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001428_j.cam.2003.06.009-Figure1-1.png", "caption": "Fig. 1. Model of an inductor with a source of electromotive force emf ; i.", "texts": [ " Note that, here again, (3c) carries a part of (3b), through (1b). These homogeneous conditions are commonly encountered in electromagnetic problems either for physical (conditions at in&nity or associated with idealized materials) or symmetry reasons (for normal or tangential &elds). Their extension to nonhomogeneous ones can be done without diEculty. In addition to local conditions (3a\u2013c), global conditions on voltages or currents in inductors are considered, through functionals on local &elds (circulations and 0 and y\u03b22 > 0 respectively. Then, the distances of the shifts of x direction by each iteration are given by xB(y\u03b21) and xB(y\u03b22) from (44). Therefore, the condition such that the point Q must satisfy is as follows:{ xB(y\u03b21) \u2212 xB(y\u03b22) = xd y\u03b21 + y\u03b22 = yd ", " (48) Combining two equations of (48) leads to xB(y\u03b21) \u2212 xB(yd \u2212 y\u03b21) = xd, (49) where the range of y\u03b21 is 0 < y\u03b21 < yd in the case yd < y\u0304 or 0 < y\u03b21 < y\u0304 in the case yd \u2265 y\u0304 since y\u03b21 < yd from y\u03b22 = yd \u2212 y\u03b21 > 0 and y\u03b21 < y\u0304. Since (49) is a only one variable nonlinear function about y\u03b21 and can be easily solved on this range as mentinoned in Remark 3 later, we can get the coordinate of Q from (44) and (47). By shifting to Q, the target point is involved in \u2126 at second iteration. (2)-(ii) The target point is involved in \u21262 \u03b3: In this case as in the right hand of Fig. 10, to shift to the point R along the boundary (B) of \u2126 at first iteration. The first and second distances of the shifts of y direction are defined by y\u03b31 > 0 and y\u03b32 < 0 respectively. By the similar way, we get the following equation: xB(y\u03b31) + xB(yd \u2212 y\u03b31) = xd, (50) where the range of y\u03b31 is yd < y\u03b31 \u2264 y\u0304 since yd < y\u03b31 from y\u03b32 = yd \u2212 y\u03b31 < 0 and y\u03b31 \u2264 y\u0304. Therefore, the coordinate of R is obtained. By shifting to the obtained point R, the target point is involved in \u2126 at second iteration. Remark 3: In the above algorithm, it is necessary to solve (49), (50) and (47) by a numerical calculation" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000457_978-3-642-55848-1-Figure8.19-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000457_978-3-642-55848-1-Figure8.19-1.png", "caption": "Fig. 8.19. Model of the permanent magnet DC motor", "texts": [ " Information on the arm's angular velocity and position are measured at its shaft and fed out of the Frame. The position sensor is represented by a simple constant gain function component named Kfb. The reference signal of the position servo is generated by the IN component. The variables that are of interest for observing system behaviour, such as the reference input, the arm angular velocity, and the position and current drawn by the motor, are fed to an x-y display component. We next develop models of the main servo components, starting with the mo tor. The model of the DC Motor (Fig. 8.19) corresponds to the model of a perma nent magnet DC motor usually found in the literature [5, 6]. To show this we have added variables to the bond graph (normally stored in the ports). Gyrator GY describes the basic electromechanical conversion in the motor re lating the back emf eem! and the armature current ia at the electrical side to the torque acting on the rotor T m and its angular velocity 0) Tm =kt \u00b7ia } eemf = kt .0) (8.14) The coupling coefficient kt is known as the torque constant. The coupling coeffi cient in the second equation, usually denoted ka and called the back emf constant, is, in fact, the same coefficient. This is a consequence of the cross-coupling be tween variables in the electromechanical conversion and the conservation of power in the conversion. 8.4 Permanent Magnet DC Servo System 321 The electrical process in the armature winding is commonly described in terms of the armature resistance Ra and the self-inductance La. In the bond graph model of Fig. 8.19 it is represented on the electrical side by resistive and inertial ele ments, respectively, joined at a common effort (current) junction. Thus, the rela tion between the armature voltage e a across the electrical motor terminals and the armature current ia through it reads: L dia R\u00b7 e a = a Tt+ ala +eemf (8.15) Similarly, the process at the mechanical side is described by a resistive element that represents linear friction with coefficient Bm, and an inertial element that de scribes the rotation of the rotor of mass moment of inertia Jm\u2022 They are joined at the effort (angular velocity) junction" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003762_09544054jem1913-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003762_09544054jem1913-Figure1-1.png", "caption": "Fig. 1 Schematic diagram of the adaptive layer thickness computation", "texts": [ " The adaptive slicing method is suitable to satisfy this objective function [18]. The most popular and effective method suggested by Dolenc and Makela [12] for adaptive slicing is the method in which the maximum cusp height is considered as the criterion for surface finish of the part. Here, the layer thickness is computed based on maximum cusp height and local slope of the surface of the part in that layer. In the method presented in the current paper, Dolenc\u2019s method is employed for slicing the part adaptively. In a similar way to what can be seen in Fig. 1, in a given layer, all of the triangles which have intersections with the slicing plane are determined. For each of the triangles, the angle of \u03b8 (the angle between facet normal and the vertical normal to the horizontal plane) is obtained. The layer thickness can be calculated according to t = Ra cos (\u03b8min) (1) Parameter t represents thickness of layer, Ra is the maximum allowable surface roughness, and \u03b8min = min{\u03b8i} where \u03b8i represents the angle between facet and working plane of the RP machine" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002933_978-3-540-79982-5_24-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002933_978-3-540-79982-5_24-Figure1-1.png", "caption": "Fig. 1. Mechanism of switching between rigid and flexible modes. (a) When there is no vacuum, the links and bellows tube can take any shape. (b) When the pump creates a vacuum, the links move down and mesh with the ditch of the tube, locking the shape of the sheath.", "texts": [ " The outer sheath design consists of flexible toothed links and a bellows tube. In the flexible mode, because the inside pressure and atmospheric pressure balance out, the sealed cover does not shrink, and the toothed links disengage from the bellows tube. In the rigid mode, the sealed space is evacuated by discharging the internal air, and the atmospheric pressure presses the toothed links into the bellows tube, locking the shape of the outer sheath by pushing the tooth of the link into the chase of the bellows tube (Fig. 1). The bellows tube and toothed link mechanism can be locked as well as relaxed easily, providing a smooth transition between the flexible and rigid modes. We built a prototype of the outer sheath device and tested it in our laboratory. The prototype has an outer diameter of 20 mm, inner diameter of 8 mm, length of 300 mm, and can achieve a radius of curvature of 8.5 cm. The outer sheath consists of three long flexible toothed links, three nylon wires, a bellows tube, and a polyethylene cover (Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002514_ias.2006.256617-Figure13-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002514_ias.2006.256617-Figure13-1.png", "caption": "Fig. 13: Surfaces involved in the heat transfer coefficient estimation (the values are referred to the MA160 prototype).", "texts": [ " \u2212=+ =\u2212\u2212 \u2212\u2212 0nMFEWMFEW MFIAIAEW R 1 R 11RR (3) The forced convection thermal resistances are reported in the last row of Table II, Table V and Table VIII, respectively for the three prototypes. From Fig. 10 up to Fig. 12, the equivalent thermal resistances between the endwindings and the motor frame (REW-MF) together the forced convection contributions (REW-IA plus RIAMF) versus the rotor speed are shown. Starting from the thermal resistances and the involved surfaces the heat transfer coefficients can be determined by (2). The selection of the involved surface values is not a simple task. In this study the surfaces shown in Fig. 13 have been taken into account. The endwindings surface has been evaluated by its perimeter and the average diameter (Table I). Because this surface is not smooth (because the windings are typically constituted by wire), a corrective coefficient of \u03c0/2 has been adopted. It is important to underline that, by the thermal resistance point of view, the two end space regions have to be considered in parallel. As a consequence, the surfaces reported in Fig. 13 are the surfaces of the two endwindings and the inner surface of the two end caps. Assuming that the heat transfer coefficients between the endwindings and the inner air and between the inner air and the end caps are equal, the following equations can be defined: += \u2212 ECEWMFEW Equivalent S 1 S 1 R 1h (4) + + = \u2212\u2212 ECEWMFIAIAEW onvectionC Forced S 1 S 1 RR 1h (5) The hEquivalent heat transfer coefficient takes into account all the heat exchange phenomena that occur in the end space regions (natural convection, radiation and forced convection)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002158_ias.2005.1518846-FigureA-1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002158_ias.2005.1518846-FigureA-1-1.png", "caption": "Fig. A-1: Motor # 2", "texts": [ " 2002. 15. Magsoft Corp., http://www.magsoft-flux.com/, Troy, NY, USA. 16. N.S. Gameiro, and A.J. Marques Cardoso, \u201cAnalysis of SRM drives behaviour under the occurrence of power converter faults\u201d, 2003 IEEE Intern. Symp. on Industrial Electronics, ISIE '03., Vol. 2 , pp. 821-825, June 2003. Three motors were used for the analysis and the tests: Motor # 1: 4 phase; 8/6; rated torque: 2.0 Nm; base speed: 2,500 rpm; 42V. Motor # 2: 3 phase; 12/8; rated torque: 1.0 Nm; base speed: 3,000 rpm; 42 V (Fig. A-1). Motor # 3: 4 phase; 8/6; rated torque: 0.8 Nm; base speed: 2,500 rpm; 12V; 8 turns per pole (Fig. A-2). IAS 2005 2740 0-7803-9208-6/05/$20.00 \u00a9 2005 IEEE" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003762_09544054jem1913-Figure12-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003762_09544054jem1913-Figure12-1.png", "caption": "Fig. 12 The CAD and STL model of the mouse body", "texts": [ " In addition, ESTIMATOR has suitable accuracy to be used for optimization problems where build times are applied as objective functions. The solution time to calculate the build time is compared between EXACT and ESTIMATOR (STLbased methods) in Table 1. The results show that JEM1913 Proc. IMechE Vol. 224 Part B: J. Engineering Manufacture at YORK UNIV on November 7, 2012pib.sagepub.comDownloaded from ESTIMATOR has reduced the average solution time by about 28 per cent for the case study investigated. The next case study is a mouse body (100 \u00d7 60 \u00d7 25 mm) with more features, as well as free form surfaces. Figure 12 depicts the CAD and STL model of the mouse body. The input parameters are selected as for the former case. Figure 13 compares the contouring lengths in ESTIMATOR and VISCAM for the mouse body in six selected directions. This comparison confirms the accuracy of ESTIMATOR in applying exact algorithm to calculate total contouring travel length. The hatching lengths in EXACT, VISCAM, and ESTIMATOR algorithms are shown in Fig. 14. The results for total build time required to make the mouse are seen in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000952_21.105084-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000952_21.105084-Figure3-1.png", "caption": "Fig. 3. Position constraint in the first method.", "texts": [ " These seven variables should satisfy the following constraints: T(r - I)max* xb = x, -k WR:Xb (18) W ~ h = R : R ~ (19) and where hXb is the position of the mainbody coordinates expressed in the end-effector coordinates and bRh is orientation of the end-effector with respect to the mainbody coordinates which are functions of q l , q2,* . ., qn, and X , is the desired position of the force application. Equation (18) describes the position constraint of the end-effector that must coincide with the desired position of the force application (Fig. 3), and (19) represents the orientation constraints of the mainbody and end-effector. It is clear that (18) and (19) contain only six scalar equations with seven variables. Thus one has an underdetermined case. To solve for the position and orientation of the mainbody as well as ql, a simple method is to pick an arbitrary value for q l , then using (18) and (19) to solve for the rest variables. Alternatively, one may use the nonlinear programming technique to solve for an optimal position and orientation for the mainbody in terms of the energy consumption" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure2.10-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure2.10-1.png", "caption": "Fig. 2.10. Unrolling a rotary motor", "texts": [ " The increasingly widespread industrial applications of PMLM in various semiconductor processes, precision metrology and miniature system assembly are self-evident testimonies of the effectiveness of PMLM in addressing the high requirements associated with these application areas. The main benefits of a PMLM include the high force density achievable, low thermal losses and, most importantly, the high precision and accuracy associated with the simplicity in mechanical structure. PMLM is designed by 2.2 Permanent Magnet Linear Motors (PMLM) 25 cutting and unrolling their rotary counterparts, literally similar to the imaginary process of cutting a conventional motor rotary armature and rotary stator along a radial plane and unroll to lay it out flat, as shown in Figure 2.10. The result is a flat linear motor that produces linear force, as opposed to torque, because the axis of rotation no longer exists. The same forces of electromagnetism that produce torque in a rotary motor are used to produce direct linear force in linear motors. Compared to asynchronous linear induction motors, PMLM incorporates rare earth permanent magnets with very high flux density and are able to develop much higher flux without heating Unlike rotary machines, linear motors require no indirect coupling mechanisms as in gear boxes, chains and screws coupling" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000457_978-3-642-55848-1-Figure9.57-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000457_978-3-642-55848-1-Figure9.57-1.png", "caption": "Fig. 9.57. The robot geometry", "texts": [ " The only exception is the Link 3 component, because there is no torque at the tool tip, only a force. Hence the upper moment line is removed from the component, and all contained components; e.g. the ROTATION component of Fig. 9.44. The mass moments of inertia of the link components are set according to the values in Table 9.12. The coordinates of the end points of the links with respect to the mass centre of the link in the LinRot components (Fig. 9.40) are set in accor dance with the data of Fig. 9.57 and Table 9.12. The joint components are created as copies of the 3D joint component of Sect. 9.5.4 (Figs. 9.48 - 9.51). But there are some differences from joint to joint. The general structure is the same as given in Fig. 9.48, but the Joint rotation compo nents differ because the rotation matrices of the body (link) frames change from joint to joint. For every joint a specific transformer component is used. We show this for Joint 2, which rotates the frame of Link 2 with respect to the frame of Link1", " The wall restricts movement of the tool only in the base x -direction. The inter action with the wall is represented by a Contact component (see Sec. 6.4.1 and Figs. 6.53 and 6.54). The SF component defines the wall as being fixed, i.e. its ve locity is zero. There is no force on the robot arm when the tool is off the wall. The wall is modelled as a spring-damper system of relatively high stiffness constant and low damping as described in Sec. 6.4.1. The initial tool tip and wall positions are defined in Fig. 9.57 and Table 9.12. The tool tip can move freely over the wall y-z plane. The friction in that plane is represented by two SE components and is assumed to be zero The integrators shown in the figure are used for evaluating the position of the tool tip and are used only for monitoring its motion. The robot control is based on joints' variables, in addition to the signal of the interaction force taken from the Contact component. Initial values of the integrators are set according to the initial configuration of the manipulator arm in Fig. 9.57, i.e. x = 0.4 m, y = 0 and z = -0.3 m. All four signals are packed into a 4D signal bond (see Figs. 9.63, 9.62, 9.61 and 9.58). 392 9 Multibody Dynamics Now we come to the controller that has to ensure proper regulation of the robot. The model of the controller that we use is shown in Fig. 9.65. It uses hybrid force/position control with velocity feedback of the robot in the base (operational space) frame. The control law is based on the operational space control scheme of [9]. This uses transposed Jacobian control", " The parameters are defined as TO = 2 S, T1 = 3 S, T2 = 15 s, T3 = 16 s, RET = 0.5 s, and Fw = 50 N. The yend and zend are the values of the respective coordinates at t = T3. 396 9 Multibody Dynamics x = t < TO?Oo4 + 0.05 * t : (t < T3?0.5 : 004 + 0.1 * exp(-(t - T3)/RET)) Y = t < T1?0 : (t < T3? Ay * sin(2 * PI * (t - T1 )/PER) : yend * exp(-(t - T3)/RET)) z = t < TO? - 0.3 + 0.15 * t : (t < T1?0 : (t < T3? Az * sin(2 * PI * (t - T1 )/PER): zend * exp(-(t - T3)/RET))) F = t < T1?0 : (t < T2?Fw : 0) (9.146) Hence, starting from the initial configuration in Fig. 9.57, the manipulator joints are rotated in such way that the tip moves with a linear velocity of 0.05 m/s in the direction of the wall and with a velocity of 0.15 m/s in the z-direction. After 2 s, the tool tip reaches the centre of the wall; after 3 S the controller is switched to the force control. The tool tip is then moved over the surface of the wall, press ing into it with a force of 50 N. After 15 s, the force reference value is lowered to zero and, after 16 s the arm is removed from the wall by applying a simple expo nential time decaying trajectory with a decaying time constant of 0" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000271_robot.1994.351376-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000271_robot.1994.351376-Figure2-1.png", "caption": "Figure 2: Case Study 1: two different manipulation system holding an object", "texts": [ " Usually, solution to (7)-(8) is given as t = - G # w + N s (9) r = -JT(G#w+N%) (10) where G# is a generalised inverse (usually the pseudoinverse G+) of G, N is a base matrlx of U G), the null satisfy some optimisation criterion, see for example [2]. Some problems may be encountered using this a p proach for a general multi-manipulator aystem. In fact, due both to lack of mobility of the manipulators and to contact constraints the system may not be able to apply (and control some of the external wrenches. Analogously, it may i appen that the system cannot apply some of the possible contact forces, limiting the chances of exploiting techniques for grasp opthis* tion. For example, consider the simple manipulation system shown in fig.2.a. It is evident that only some of the internal forces can be controlled. In particular, it is not possible to control the force along the line joining the two contacts on the right, and any combination of contact torques. If the same object ie grasped (in the same grasping configuration with the mecha- both concerning the internal forces and the external wrenches. Note that in both the examples there are external wrenches, for example forces along 2, which cannot be applied by the system, but which can be a p plied on it without affecting joint torques. Typically, these force systems are balanced by friction constraints or by the same mechanical structure. An alternative approach to (9)-(lo), which gives an insight to the structure of the force systems acting in the manipulation device, is presented in the following. By introducing the matrix H, we rewrite (7) and (8) space of G, and s is a free vector, gener ah y chosen to nism shown in fig.2.b, a larger capa b S t y is expected, a8 w = eoi=-ez, (11) r = j T m i = j T f , (12) where 2 = Ht, and, in matrix form, aa Let us now define the matrix F such that its range s ace spans the h-dimensional null space of P, i.e. f ( F ) = U(P Analogous y to the velocity case, matrix F may be decomposed as F = IFT FT FTIT, where submatrices F1, Fa, Fs (with dunensions 6 x h, h x h, r x h, r e spectively are base matrices of the subspaces of exter- satisfy the constraints given by the interactions, the contact models, and manipulators kinematics", " In this case, the term in R(F24) has to be exploited to obtain a suitable force at contact 1 to compensate for the external wrench. In any case forces along the y direction at contacts 2 and 3 must be negative or null. Note that U(G) # R(F24), i.e. not all the forces in the null space of the grasp matrix may be actively applied by the manipulator. describes the possible preload situations. For examp%, the first column indicates that a negative z force at contact 2 and a positive z force at contact 3 may exist without affectmg external wrenches and joint torque. If the same object is grasped with the 4 dof finger shown in fig.2.bl matrix F as the structure reported in (14) where [0, 0.33, 0, 0, 0.33, 0, 0, 0.33, 0, 0, 0, 0lT, Sug- Block F 0 0 0 1 I -.:e5 :: 0 0 0 -.41I 5 Case Studies Case 1. Consider, ae 6rst simple example, the system of Fig. 2 .a The object is grasped with a one degreeof-freedom manipulator, and three contact points are present, located at c1 = [0,0,2]*, c2 = [0,2,1IT, and cg = [0,2,3IT respectively. The corresponding unit normal vectors are nl = [O , l ,OJT , n2 = [0, -&/2, -1/2]*, and n3 = [O, -&/2,1 2IT. Asauming sofe6nger contacts, matrix h in (14) re- 0 0 0 - .5 0 0 -.15 .15 -.I5 0 0 0 .5 -.is .a5 .a5 o 1 0 0 0 0 .15 -.16 0 -.15 -.75 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 .I 0 0 0 0 0 0 0 1 -:15 0 0 0 0 0 0 0 0 0 o -1 -" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002716_0041-2678(72)90033-4-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002716_0041-2678(72)90033-4-Figure1-1.png", "caption": "Fig 1 General principles of the machine and measuring systems", "texts": [ " Traction can thus only be measured if the plane is fxed, permitting only pure sliding Film thicknesses are less than 2 #m. This introduces severe constraints on the precision in both dimensions and relative positioning of each machine element *Maitre-assistant, tProfesseur, Laboratoire de M~canique des Contacts, Institut National des Sciences Appliqu~es, 20 avenue Albert Einstein, 69 Villeurbanne, France Isothermal conditions can be approached either by imposing small sliding speeds or by adequate cooling of the contact. Thus an apparatus (Fig 1) was built in which spherical or ellipsoidal specimens could be mounted and run at different TRIBOLOGY June 1972 111 speeds against a fixed transparent plate and in which either a constant or a variable load could be applied. Film shape was measured by interferometry, traction and load by strain gauge dynamometers. The electrodynamic, mechanical and optical parts of the apparatus will now be described. The electrodynamic system Among the many methods which can provide both constant and and variable loads an electrodynamic system was chosen in which the load application point can vary slightly with no modification in load" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003937_6.2009-5988-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003937_6.2009-5988-Figure1-1.png", "caption": "Figure 1. Regions for Example I.1", "texts": [ " Such sets S(\") will be referred to as generalized stability sets, and thus represent the set of all matrices which are stable relative to \", i.e. which have all their eigenvalues in \". Definition I.1. Let $ map Rn\"n into C. We say that $ guards S(\") if for all A \" S(\"), the following equivalence holds: $(A) = 0$ A \" %S(\") (2) Here S denotes closure of the set S and %S its boundary. The map is said to be polynomic if it is a polynomial function of the entries of its argument. Example I.1. Some guardian maps are introduced for classic regions (Fig. 1). \u2022 Hurwitz Stability: the open left half-plane, Co # is guarded by $H(A) = det(A% I) det(A) (3) where % denotes the bialternate product18 (see Appendix A). \u2022 Stability margin: the open &-shifted left half-plane region (i.e. Re(z) < &) is guarded by $m(A) = det (A% I & &I % I) det (A& &I) (4) \u2022 Let the conic sector with inner angle 2'. If we denote # = cos ' the corresponding limiting damping ratio, a guardian map corresponding to this conic damping ratio region is given by $d(A) = det ! A2 % I + (1& 2#2)A%A \" det (A) (5) \u2022 Let ( (> 0) the maximum desired pulsation of the eigenvalues" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003806_icelmach.2010.5608274-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003806_icelmach.2010.5608274-Figure5-1.png", "caption": "Fig. 5. The finite element mesh consists of 10734 elements", "texts": [ " The flux density distribution in machine core is calculated using the timestepping FEM coupled with the circuit equations of the supply circuit and the end windings. The Opera-2d/RM, a transient eddy current solver, extended to include the effects of rigid body (rotating) motion and also provides for the use of external circuits was chosen. The mesh was refined to minimize the solution errors. The mesh density is a compromise between accuracy and calculation time. Finally mesh consists of 10734 elements. The mesh is shown in Fig.5. The application of the field-circuit method to the modelling of the magnetic field distribution in an induction motor, taking into account the movement of the rotor, required the introduction of a special element to the model, which properly joins the unmoving and moving parts. In the applied module RM of the software packet Opera 2D, this element took the form of a gap-element. The gap region (Fig. 6) is divided quite uniformly on 264 elements along the circumference of the gap. It gives time of displacement of one element equal to about 3 10-5 s at synchronous speed, comparable with the average time step of computation" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002939_s11071-007-9215-4-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002939_s11071-007-9215-4-Figure1-1.png", "caption": "Fig. 1 Analytical model of the manipulator", "texts": [ " Thus, the balance between the effect of the excitation and that of gravity consequently determines the relative angle of the free link with respect to the active link; not only the high-frequency excitation but also gravity is required for the control method. Motivations of the study on the underactuated manipulators are, for example, to construct back-up strategies in case of actuator failure in extreme missions such as space robots and to realize cost reduction by employing fewer actuators. In this paper, we consider a two-link underactuated manipulator mounted on a base rotated at a constant angular velocity as shown in Fig. 1, which corresponds to the situation of the motion of a simple satellite spinning at a uniform spinning rate without nutation [13, 14]. By applying the earliermentioned control method based on high-frequency excitation, we carry out changing the trajectory of the tip of the rotated manipulator without state feedback of the free link. In zero-gravity environment, centrifugal force produced by the spin plays a substitutional role of gravity required for the control method. We seek the averaged equation of the motion of the free link by introducing multiple time scales", " Then, bifurcation analysis is carried out to recognize how the stable equilibrium states of the relative angle of the second link with respect to the first link vary. The tip can describe a circle with desired radius from the rotation center of the base. We theoretically clarify the reachable area of the tip of the manipulator. Finally, the validity of the theoretically proposed control method is confirmed by performing some experiments. 2.1 Analytical model of a two-link underactuated manipulator We consider an analytical model of a two-link underactuated manipulator mounted on a base as shown in Fig. 1. It is assumed that the links and the base can be rotated on a horizontal plane. The first joint of the manipulator has an actuator giving torque \u03c4 for the first link, which we call the active link. The second joint has neither actuator nor sensor and is called the free joint, and also the second link is called the free link. The physical parameters are as follows: m0: mass of the base (15.2 kg) m1: mass of the first link (1.234 \u00d7 10\u22121 kg) m2: mass of the second link (3.92 \u00d7 10\u22122 kg) l0: distance between the center of rotation of the base and the first joint (1" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001677_3527607692.ch6-Figure6.4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001677_3527607692.ch6-Figure6.4-1.png", "caption": "Fig. 6.4 Multilayer of ferrocenyl-tethered GOx built by cross-linking of GOx and 13 in the presence of glutaraldehyde on the surface of a gold electrode.", "texts": [ " Coupling of ferrocenyl groups was performed by reaction of 6 and EDAC in the presence of 2 M urea, and the resulting enzyme was shown to retain 90% of enzymatic activity as compared with native GOx [22]. 6.2.1.3 Electrical Wiring Immobilization of a redox enzyme in a conductive polymer network is another means of enabling electrical communication between the enzyme and the electrode (see Fig. 6.1, configuration C). A non-organized multilayer of ferrocene-tethered GOx was constructed on the surface of a gold electrode by cross-linking of GOx and 2-aminoethyl ferrocene 13 with glutaraldehyde (Fig. 6.4). The molar ratio between ferrocene and GOx in the film was found around 10 and the sensitivity of glucose response was proportional to the amount of GOx [23]. 1280vch06.pmd 15.09.2005, 17:41188 189 A multilayered network of GOx was assembled by a stepwise synthesis onto a gold electrode initially covered with a SAM of cystamine. Ferrocene groups were introduced into this network by reaction of 9 in the presence of EDAC, NHS and 1 M urea. The average number of Fc units per GOx molecule in the film was found around 8" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003167_gt2008-50257-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003167_gt2008-50257-Figure4-1.png", "caption": "FIG. 4 TOTAL PRESSURE PROBE (TOP LEFT) AND STATIC PRESSURE PROBE (TOP RIGHT); METERING POINTS IN SEALING CHAMBERS 1 AND 2 (BOTTOM)", "texts": [ " The measurement of swirl in the prechamber of the rig is a challenge because of the restricted available space. A comprehensive technique of 3D laser Doppler anemometry successfully applied to the swirl measurement in seals (e.g. [12]) was not considered due to the inaccessibility of the inlet of the current test bed. Also, available Pitot tubes or five-hole pressure probes were found to be too large. They would noticeably block the cross section of the sealing channel. Here, the preswirl velocity is calculated from static and total pressures, which are measured with two individual tubes (Fig. 4, top). The static pressure reading is taken slightly offset from the total pressure reading in circumferential direction. Small cylindrical probes with a diameter of 1.5 mm are used which are compact enough compared to the radial seal chamber height of 6 mm and distance between the sealing edges of 14 mm. The pressure taps of the two probes \u2013 side hole for total pressure, bottom hole for static pressure \u2013 are located in the center of each chamber. It is assumed that the pressure taps are thus positioned at the center of a vortex, so that axial and radial components of the flow are almost zero", " 6 and next section. The tap of the total pressure tube is therefore facing the tangential or rotational direction. The velocity component cu or swirl velocity is then calculated from these pressures in the following way, using the equations for compressible flows: ( ) 1\u03ba 1pp2 Ma \u03ba 1\u03ba st \u2212 \u2212\u22c5 = \u2212 (1) TRMacu \u22c5\u22c5\u03ba\u22c5= (2) Copyright \u00a9 2008 by ASME Terms of Use: http://www.asme.org/about-asme/terms-of-use The temperature is also measured in each chamber and is nearly equal to the ambient temperature (see Fig. 4, top). In the prechamber, only one set of static and total pressure probes is used for the determination of the swirl. In the subsequent chambers 1 and 2 (see Fig. 2) the determination of swirl is repeated at four locations over the circumference as shown in the bottom sketch of Fig. 4. The results of these individual measurements are averaged to obtain the mean swirl in the two chambers, cu1 and cu2. The swirl downstream of the last sealing tooth was not measured. An overview of further metering points in both sealing chambers is shown in Fig. 4. The circumferential pressure distribution at the casing wall of chamber 1 and 2 is measured by ten static bores, plus an additional two wall taps in the 4 Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 01/06/2018 prechamber and at the outlet. In this paper, the static wall pressures were used to check the feasibility of the static pressure readings for the swirl analysis. In each chamber the average temperature can be calculated from the reading of two k-type thermocouples" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003760_(asce)0893-1321(2009)22:4(331)-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003760_(asce)0893-1321(2009)22:4(331)-Figure2-1.png", "caption": "Fig. 2. Coordinate systems and forces", "texts": [ " Also, sampling intervals could vary except that notations would become more complicated. A performance index J q , q\u0307 should be chosen to satisfy some physical requirements such as the shortest path, the minimal energy, and the least time. To this end, the trajectory planning problem of this paper is mathematically formulated as the following optimization problem: min J q,q\u0307 s.t. q t0 = q0 q tf = q f M q,q\u0307 = 0 x \u2212 xi 2 + y \u2212 yi 2 + h \u2212 hi 2 r0 + ri 2, i = 1, . . . ,n 1 The investigation in this paper focuses upon a fixed wing flying vehicle as shown in Fig. 2 Vinh 1993 . Here force T is the thrust from the engine along the flying vehicle fuselage. The angle is the angle of attack. Force L is the aerodynamic lift which is normal to the direction of velocity v and in the symmetric plane lift-drag plane of the flying vehicle fuselage. Force D is the aerodynamic drag against the direction of velocity v. The relationship of the forces is shown in the coordinate systems in Fig. 3. Point mass M is the origin of two coordinate systems: the local-horizon system x \u2212y \u2212z and the wind-axis system x1\u2212y1 \u2212z1" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002168_3-540-29461-9_104-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002168_3-540-29461-9_104-Figure4-1.png", "caption": "Fig. 4. An artistic impression and a photographic view of sky cleaner 2", "texts": [ " This project was based on the collaboration with the Centre for Intelligent Design, Automation & Manufacturing at the City University of Hong Kong. Sky cleaner 2 is designed to be compact and easy to transport from place to place. The robot is featured with 16 suction pads which can carry a payload of approximately 45 kg including its body weight. Because of the special layout of the vacuum suckers, the robot can walk in all directions freely without attention to the seals. A pair of pneumatic cylinders provides both vertical and horizontal motion. A specially designed waist joint, located at the centre of the robot (as shown in Fig. 4), gives a turning motion to the robot. For a turning action, the position pin cylinder is aired to release the locking pin so that turning motions can be actuated by the waist-turning cylinder. The waist joint is used for the correction of inclination during the robot\u2019s movement. A relatively small degree of rotation (1.6\u25e6) per step is turned in the present stage. Only an on-board PLC executes a sequence of solenoid valves on/off actions to perform commands that are sent by the operator through the PC console" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000388_872115-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000388_872115-Figure8-1.png", "caption": "Figure 8: Arrangement of the Test Piece in the Intake Pipe", "texts": [], "surrounding_texts": [ "872115 5\nThere are basically no differences observed in tile formation of deposits if the injectors are tilted by 19\u00b0 toward the flow direction. In the case of air forced injectors, an additional air stream is mixted with the fuel at the injector. This air stream assures a -better dissipation as well as better centering of the fuel spray along the longitudinal nozzle axis. Thus, larger quantities of liquid fuel are concentrated on the valve tulip and the deposit formation is reduced when compared to the standard injection.\nIn the case of enriching the A/F mixture under stationary idling conditions using standard injection, a smaller mass of deposits is produced due to the greater washing effect (Figure 6).\nThe carburetor was used for the formation of the mixture to eliminate the washing effect at low A/F ratios. In addition, the engine was operated under steady state conditions. The formation of the deposits is increased considerably with extremely rich mixtures (Figure 6). The additional deposits primarily consist of cindery particles as indicated by morphological studies under the SEM as well as by results obtained from energy-dispersive X-ray analysis. The particles reach the valve disk by the internal exhaust-gas recirculation. This type of deposit has a porous structure within lubricant and fuel can be stored and remain at the valve for a long time.\nSHORT-TIME SIMULATION FOR INVESTIGATIONS ON THE DEPOSIT FORMATION ON INLET VALVES\n- St3ndard Injection, Instationa,y\nTest, 40 hours - Carburetor, Stationary Test,\n20 hours\nSCREENING TESTS CONCERNING deposit formation of lubricants and fuels mainly examine the thermal effects /4, 7, 9, 10/ whereas other influences such as internal EGR or the washing effect as they occur in production engines are not considered. By investigating the influence of the engine, a test arrangement with a heated test piece mounted in the intake pipe of an IC engine close to the inlet valve (Figure 7, 8), requires minimal test time and effort.", "6 872115\nThe cylindrical test piece can be mounted on a heatable cartridge which is screwed into the intake port of the engine. The lubricant reaches the test piece through a capillary tube. The formation of the mixture is assured either by a carburetor or by an injection. The intake pipe can be heated to different desired temperatures to get different vaporous fuel fractions. The recirculated exhaust gas mass can be varied by means of the valve timing. The repeatability of the deposits was found to be to +/- 5 - 20 % depending on the boundary conditions. There was no valve overlap during the gas exchange so that the internal exhaust recircling was nearly O. Table 2 shows the test conditions:\n0.5 ml/h 300\u00b0C 900 rpm 40\u00b0C Lubricant volume flow Test piece temperature Engine speed Intake pipe temperature\nTable 2: Engine Test Conditions for the Short-Time Test Method\n8\nmg\nIII III o ::aIII o 0 Ql o 4\nSample\n6\n5\n2 \u2022 '-=- \u2022 =F=_:P\"''''~\nf-------'!\\o--'\\;I-------+---- Test Eng ine without internal EGR--.\n3.0\n9 Production Engine\nValve \u2022\n.-'.III 2.2III 0 ~ 1.8-III 0 0- 1.4Ql 0\n1.0 Test Engine with\n0.6 internal EGR\n0.2 '---'1r---...L-----I------l..------' 1 0.5 0.7 0.8 0.9 1.0\nAir Fuel Ratio\nFigure 9: Oeposits as a Function of the A/F Ratio", "872115 7\n......-\"- }Standard Deviation\n......,;~\"'\" lM.ao Valu, with without\nIntake Maniflold Heating\nc: .2..., u Cl... LL Ql ::i5 ;:, o (J) 8 4 12\n16\nDeposit Mass Soluble Fraktion\n4\n6\n2\n1O....---------,;r--...,20 mg %\n8\nUl o a. Ql o\nUl Ul Cl\n:::E\nFigure 10: Deposits with and without Intake Pipe Heating (Internal Exhaust Gas RecirculatIon)\nTo assure that a sufficient quantity of exhaust gas is in the intake pipe, the camshaft was advanced by 30\u00b0 CA. The exhaust gas ir tile cylinder is compressed after the exhaust valve closes and then is introduced into the intake pipe.\nVariations in the A/F ratio prove that the internal exhaust gas recirculation has an influence on the deposit formation in the test arrangement which was used. Figure 9 shows that the deposits quantity remains constant when changing the A/F ratio if engine is run without exhaust gas recirculation. If exhaust gas reaches the intake pipe, the deposit formation is greatly increased at rich A/F ratios. Therefore, the test engine with exhaust gas recirculation exhibits the same behavior as the production engine with carburetor and EGR.\nThe vaporizing conditions for the fuel deteriorate when the temperature of the intake pipe is reduced by 30 degree (from 40 to 10\u00b0C). When the A/F ratio equals A= 0.66, the resulting higher liquid fuel fractions produce lower deposits even at a high EGR rate (Figure 10).\nThe washing effect apparantly compensates for a potential increased formation of deposits due to particles. When the deposits are washed in polar solvents, it is found out that the soluble fraction in the deposits are considerably higher when the engine is operated at a reduced temperature of the intake pipe (Figure 10). The lower intake pipe temperature leads to a higher liquid fuel fraction at the test piece. Therefore, more soluble fractions remain on the test piece. The results show that this test method correctly reproduces the tendency of lubricants and fuels to form deposits. Table 3 presents the test data for both methods, the \"40 h-driving cycle test\" and the It short-time test ll :" ] }, { "image_filename": "designv11_32_0000240_s0263574701004027-Figure12-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000240_s0263574701004027-Figure12-1.png", "caption": "Fig. 12. Initial setup of the Stewart platform using calibration tool.", "texts": [ " Since we are only interested in the errors in the leg length based on equation (2), a new equation to formulate the simulated deviation in terms of the errors in the leg lengths and encoder is simplified to an equation =J 1( ). The simplified equation is shown below: xs ys zs xs ys zs = a11 a66 L1e L6e (3) Where ={ xs, ys, zs, xs, ys, zs}, and = { L1e . . . L6e}. Patel14 assumed that the values of are constant for all the poses, , within the work area of a Stewart platform. At the setup position as shown in Figure 12, a calibration tool is attached to both ends of a leg to calibrate the leg to the initial setup length that is specified by the manufacturer. As a result, an error in the calibration tool will produce a constant error, C, in the leg lengths. On the other hand, each leg contains a leg-measuring device (encoder) so that is a measurable quantity with a perfect value of 1. However, a measuring error in the encoder produces an error in the lengths of the leg. This paper makes the assumptions that the value of is the error produced in either the calibration tool or the encoder", " Due to the length measuring error , in the encoder, we assume that the length with the error is now equal to 1+ . It is suggested earlier that the errors in the Stewart platform are symmetrical and identical; this suggests that the errors in encoders, , are the same for all the legs. As a result, the encoder error and change of leg length Li from the datum length (Li ) are the functions to each variable Lie of equation (2). The leg length error in leg i is Lie =( Li ) in which is a constant for i=1 . . . 6 (3) The initial setup of the Stewart platform for the simulation 1 is shown in Figure 12: (i) We simulate a situation when the datum height of the Stewart platform is set to z=734.5 using a calibration tool, which has calibrated all the legs to the initial length of 619.995 mm. (ii) The moving platform of the Stewart platform is then moved to a height of Z=800 in the simulation. The moving platform of the Stewart platform is then traversed along X and Y-axes with a measuring error of in the encoder so that the leg length error Lie =( Li ), i=1 . . . 6. (iii) The leg length error produces simulated positional deviations at seven points in Figure 6" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002621_j.jmatprotec.2007.12.030-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002621_j.jmatprotec.2007.12.030-Figure2-1.png", "caption": "Fig. 2 \u2013 The annotated photograph of the set-up for a Nd:YAG laser surface hardening.", "texts": [ " The same pulse setings were used for both alloys. The oval beam, after being efocused, had a minor axis of 8 mm and a major axis of 2 mm. The area of the oval beam was 0.75 cm2, giving a peak rradiance of the beam of 4.0 kW/cm2. Top gas shielding was rovided by a 25 l/min flow of nitrogen in a trailing jet con- figuration delivered by an 8.0 mm diameter tube oriented at 15\u25e6 from the surface and 45\u25e6 from the horizontal and 1 cm from the beam spot. The annotated photograph of the set-up of the Nd:YAG laser surface hardening is shown in Fig. 2. An infrared surface treatment monitor was utilized to monitor the process of surface hardening. The monitor is integrated at b Fig. 3 \u2013 Monitor signal of surface hardening of gray cast iron output 500 mV (pointed by the dark arrow). hardware and software with a PC computer. The data collection rate used was 2500\u20135000 Hz. The monitor system noise (standard deviation) when not surface treating was 0.20 mV. The values of Rockwell C hardness along the treated tracks were measured using a portable hardness tester" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003214_1.2839011-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003214_1.2839011-Figure1-1.png", "caption": "Fig. 1 Kinematic model of the parallel manipulator", "texts": [ " In this paper, an assistant homing strategy is proposed for a redundantly actuated PKM. Based on the redundant limb length which can be read from the absolute encoder, the condition for performing the assistant homing is determined. After the assistant homing, the redundant limb is controlled by force mode with force command value being zero, and other limbs start to return to their zero positions. The homing strategy is incorporated into the numerical control system of the redundantly actuated PKM. 2.1 Structure Description. As shown in Fig. 1, a 3 degree of freedom DOF parallel manipulator is composed of a gantry frame, a moving platform, two constant length links, and two extendible links. Sliders E1D1 and E2D2 drive links A1D1 and A2D2 when they slide along the vertical guide ways. Links E1B1 and E2B2, which are driven by two actuators, are extendible struts with one end fixed to sliders E1D1 and E2D2 and the other connected to the moving platform A2B2. Limb E1B1 is a redundant limb with an active actuator. Combining the 3-DOF parallel manipulator with a feed worktable, a redundantly actuated PKM with 4-DOF is created. 2.2 Inverse Kinematics. In practical application, the parallel manipulator is a subpart of the machine tool. In kinematic modeling, the base coordinate system O-XY shown in Fig. 1 is identical with the real machine coordinate system of the machine tool such that the kinematic model can be applied directly into the control system. A moving coordinate system ON-XNYN is fixed on joint point A1 with the YN axis along the vector from point A1 to B1. Let the position vector of point A1 be rON = xy T in the base coordinate system. The position vector of point Bi i=1,2 can be expressed as rBi = rON + RrBi N , i = 1,2 1 where R is the rotation matrix from the coordinate system ON-XNYN to O-XY and R = cos sin \u2212 sin cos is the rotation angle of the moving platform; rBi N is the position vector of point Bi in ON-XNYN, and rBi N = 0l5 T; l5 is the length of the moving platform. According to Fig. 1, the following equations can be obtained rBi \u2212 rEi = linEi, i = 1,2 2 rON \u2212 rDi = lnDi, i = 1,2 3 where rEi and rDi are the position vectors of points Ei and Di; nEi and nDi are the unit vectors of links EiBi and AiDi; li and l are the length of extendible link EiBi and the constant length link, respectively. Based on Eqs. 2 and 3 , the inverse kinematic solutions of the manipulator can be written as APRIL 2008, Vol. 130 / 044501-108 by ASME 7 Terms of Use: http://www.asme.org/about-asme/terms-of-use w s r 3 i c t a Y a w d P o c 0 Downloaded Fr q1 = y l2 \u2212 x + d/2 2 4a q2 = y l2 \u2212 x \u2212 d/2 2 4b l2 = x \u2212 l5 sin \u2212 d 2 2 + y + l5 cos \u2212 q2 \u2212 l6 2 4d here d is the width between two columns, l6 the height of the lider, and q1 and q2 the Y coordinate values of points D1 and D2, espectively" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003008_j.mechmachtheory.2007.05.001-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003008_j.mechmachtheory.2007.05.001-Figure3-1.png", "caption": "Fig. 3. Robot hand as a case study.", "texts": [ " If (31) for a candidate does not have solution, then the candidate cannot equilibrate wk\u0302. If rmin;k\u0302 for a candidate is not less than Q\u0302, neither is Q\u00f0G\u00de. Thus such candidates can be removed without computing their Q\u00f0G\u00de. Step 5. Search for a candidate whose Q\u00f0G\u00de is less than Q\u0302 in the remaining. Remove those encountered in the searching process, for which Q\u00f0G\u00de < 0 or Q\u00f0G\u00deP Q\u0302. If no such remainders exist, then bG is the globally optimal grasp; otherwise, update k\u0302; Q\u0302, and bG, and return to Step 4. Fig. 3 sketches a hand, whose palm is fixed at the end of an axle and fingers are equally hinged around the axle and driven by a single actuator not shown. It looks somewhat humanoid, but all the balls are fixed joints except that the three balls attached to the axle are hinges. Thus the hand has only 1 DOF. Contacts with an object are made by only the fingertips, namely the hemispheres at the ends of fingers. Each one is of radius r = 5 mm. Let piH, i \u00bc 1; 2; 3 be the position vectors of the ends of fingers relative to frame FH , which are expressed by p1H \u00f0b1\u00de \u00bc \u00bd L sin b1 \u00fe R 0 L cos b1 T p2H \u00f0b2\u00de \u00bc \u00bd \u00f0L sin b2 \u00fe R\u00de cos\u00f02p=3\u00de \u00f0L sin b2 \u00fe R\u00de sin\u00f02p=3\u00de L cos b2 T p3H \u00f0b3\u00de \u00bc \u00bd \u00f0L sin b3 \u00fe R\u00de cos\u00f04p=3\u00de \u00f0L sin b3 \u00fe R\u00de sin\u00f04p=3\u00de L cos b3 T where L = 60 mm, R = 10 mm, and b1; b2; b3 are the rotation angles of the fingers, as indicated in Fig. 3. Let diH, i \u00bc 1; 2; 3 be the vectors giving the directions of fingertips, which relative to frame FH are d1H \u00f0b1\u00de \u00bc \u00bd sin\u00f0b1 a\u00de 0 cos\u00f0b1 a\u00de T d2H \u00f0b2\u00de \u00bc \u00bd sin\u00f0b2 a\u00de cos\u00f02p=3\u00de sin\u00f0b2 a\u00de sin\u00f02p=3\u00de cos\u00f0b2 a\u00de T d3H \u00f0b3\u00de \u00bc \u00bd sin\u00f0b3 a\u00de cos\u00f02p=3\u00de sin\u00f0b3 a\u00de sin\u00f02p=3\u00de cos\u00f0b3 a\u00de T where a \u00bc p=3. To grasp an object, first, let the palm contact the object such that the z-axis of frame FH is parallel to the inward normal at contact. Denote the contact position by rp. Then pOH and ROH can be adopted as pOH \u00f0/;w\u00de \u00bc rp\u00f0/;w\u00de hnp\u00f0/;w\u00de ROH \u00f0/;w; h\u00de \u00bc \u00bd op tp np R\u00f0h\u00de where / and w are the parameters of the object surface, h = 30 mm, and R\u00f0h\u00de 2 R3 3 gives a rotation of the hand about np: R\u00f0h\u00de \u00bc cos h sin h 0 sin h cos h 0 0 0 1 264 375 where h 2 \u00bd0; 2p=3\u00de" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure1.3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure1.3-1.png", "caption": "Fig. 1.3. Solder bump deposition", "texts": [ " A flip chip is a chip mounted on the substrate with various interconnect materials and methods, such as tape-automated bonding, flux-less solder bumps, wire interconnects, isotropic and anisotropic conductive adhesives, metal bumps, compliant bumps and pressure contacts, as long as the chip surface (active area or I/O side) is facing the substrate. One of the earliest flip chip technologies was solder-bumped flip chip technology, as a possible replacement for the expensive, unreliable, low productivity, and manually operated face-up wire-bonding technology. Bumps are formed by injecting molten solder into etched cavities in a glass mold plate across a wafer. The mold plate is heated to just below melting point of the solder. The injector includes a slightly pressurized reservoir of molten solder of any composition. Figure 1.3 illustrates the process of solder bump deposition. The use of flip chip technologies in the manufacture of IC devices has increased tremendously in recent years. As the size of devices gets smaller, the precision required to align the solder bumps on the chip to the pads on the substrate becomes more crucial. Besides flip chip assembly, high-precision robots are also used to assemble micro-electronic and mechanical components. Biotechnology is the technology to manipulate the structure and function of biological systems, especially when used in food science, agriculture, and medicine" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003564_978-1-4020-8600-7_38-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003564_978-1-4020-8600-7_38-Figure1-1.png", "caption": "Fig. 1 Notation.", "texts": [ ", 1996; Lin and Burdick, 2000; Eberharter and Ravani, 2004; Zhang and Ting, 2005); (ii) the attempt to approximate the displacement in the c-space with a spherical or hyperspherical displacement, and, then, to use a distance metric of the spherical, SO(3), or hyper-spherical, SO(N), space (McCarthy, 1983; Larochelle and McCarthy, 1995; Etzel and McCarthy, 1996; Larochelle, 1999; Tse and Larochelle, 2000; Belta and Kumar, 2002; Angeles, 2005; Larochelle et al., 2007). Jadran Lenarc\u030cic\u030c and Philippe Wenger (eds.), Advances in Robot Kinematics: Analysis and Design, 361\u2013369. \u00a9 Springer Science+Business Media B.V. 2008 R. Di Gregorio In this literature, a metric is said to be bi-invariant if it depends neither on the choice of the reference system fixed to the rigid body (body frame), nor on the choice of the reference system fixed to the observer (inertial frame) (Figure 1). Moreover, a metric is said left-invariant (right-invariant), if it does not depend on the choice of the body frame (the inertial frame). With reference to the above-reported definitions, the following results have been demonstrated: (1) no bi-invariant Riemannian metric can be defined in the special Euclidean group, SE(3) (Park, 1995); (2) the size of the rigid-body must be considered for defining meaningful distance metrics (Kazerounian and Rastegar, 1992; Rico-Martinez and Duffy, 1995); (3) bi-invariance is not necessary to define meaningful distance metrics (Lin and Burdick, 2000)", " Nevertheless, only some subgroups have distance metrics that are easy to use and with a straightforward geometric interpretation. The subgroup of the spatial translations, T (3), and the subgroup of the spherical motions, S(3), are among these subgroups. Since any displacement can be obtained by composing one spatial translation with one spherical motion, T (3) and S(3) will be used to decompose spatial displacements. When a rigid body is constrained to translate, its pose (\u2261 position) is uniquely identified by the coordinates of the origin,O (Figure 1), of the body frame measured in the inertial frame. The following distance metric is commonly adopted in T (3) \u03b4T (O1,O2) = |O2 \u2212O1|, (1) where O1 and O2 are two position vectors, measured in the inertial frame, that locate the position of the origin of the body frame in the two poses, and |(\u00b7)| denotes the magnitude of the vector (\u00b7). The distance metric \u03b4T (O1,O2) is bi-invariant in T (3). Moreover, a limitation on \u03b4T (O1,O2) (e.g. \u03b4T (O1,O2) < c) has a clear geometric meaning. In fact, it means that O2 must be located inside a sphere with center O1 and radius given by the imposed condition (Figure 2). 364 A Novel Point of View to Define the Distance between Two Rigid-Body Poses When a rigid body is constrained to perform spherical motions with the same center, hereafter assumed coincident with the origin of the body frame, its pose (\u2261 orientation) is uniquely identified by the rotation matrix, R(\u03b8), whose column are the three unit vectors of the body-frame axes projected onto the inertial frame (Figure 1). Such a matrix can be written as an explicit function of three independent parameters, which, in the notation adopted here, are collected in the 3-tuple vec\u03b8 . The set that collects all the rotation matrices is named SO(3), and the above considerations state an isomorphism between S(3) and SO(3). In the literature, a number of distance metrics have been proposed for SO(3) (e.g., Ravani and Roth, 1983; Park, 1995; Larochelle et al., 2007). The following distance metric is among the proposed ones: \u03b4s(\u03b81, \u03b82) = cos\u22121 ( tr(R(\u03b81)) TR(\u03b82))\u2212 1 2 ) , (2) where R(\u03b81) and R(\u03b82) are the two rotation matrices that locate the two rigid-body orientations with respect to the inertial frame (Figure 3), the image of cos\u22121(\u00b7) is restricted to the range [0, \u03c0], and tr(\u00b7) denotes the trace of the matrix (\u00b7)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000243_095441002321029035-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000243_095441002321029035-Figure6-1.png", "caption": "Fig. 6 Hertzian cylinder\u00b1cylinder contact", "texts": [], "surrounding_texts": [ "The forms used are those given by the Hertzian theory for a contact between two cylinders on a length supposed to be in\u00aenite (see F ig. 6). The maximum stress in compression (also called Hertzian pressure) is sC \u02c6 pHertz \u02c6 2 p p KD CE r MPa \u20261\u2020 where KD \u02c6 equivalent diameter (mm) CE \u02c6 inverse of the equivalent module (MPa\u00a11) p \u02c6 applied pressure for unitary width (N= mm) with KD \u02c6 2r1r2 r1 \u2021 r2 \u20262\u2020 CE \u02c6 1 \u00a1 n2 1 E1 \u2021 1 \u00a1 n2 2 E2 \u20263\u2020 p \u02c6 F=L \u20264\u2020 where, for i \u02c6 1, 2, ri \u02c6 pitch radius of cylinder i (mm) Ei \u02c6 elasticity module (MPa) ni \u02c6 Poisson coefficient F \u02c6 applied load (N) L \u02c6 contact length (mm)" ] }, { "image_filename": "designv11_32_0003919_s10846-010-9488-6-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003919_s10846-010-9488-6-Figure1-1.png", "caption": "Fig. 1 Small flying robot TDL30 (upper side of OAV)", "texts": [], "surrounding_texts": [ "Recently, several ducted-fan type OAVs (Organic Aerial Vehicle) have been developed in many countries [1]. Most of those systems have been developed for military service use. The OAV is found in the FCS (Future Combat Systems) of the U.S. Army [2]. It is being developed as a platoon-level OAV. The OAV is a singlepropeller propulsion system. The merits of those systems have simpler structures than helicopter types and smaller-size than quad-rotor types. It is important that the duct makes the operator safe from the blade rotation. Rotor crafts have abilities of vertical take-off and landing. In addition, hovering at a point is very useful to survey a target closely. The efficiency of propulsion with duct grows up to approximately 41% in theory [3]. Taking that into consideration, a ducted single propeller propulsion rotor craft has some obvious practical applications, if the noise of sound due to the blade rotation will be reduced. In this paper, we show a developed platform, a ducted-fan type flying robot, for indoor flight surveying which was designed small and light weight. We focused on development of attitude stabilization and a hovering control algorithm. In the design attitude controller, we applied a PD control method and assumed that the attitude feedback closed-loop system as a massdamper-spring second order system. The P gain is a spring constant and the D gain is a damping coefficient. In the hovering control, the attitude closed-loop dynamics was implemented with a lateral-longitudinal transition model. The simple transition model of the flying robot makes it possible to approach the model based control in mathematically. An ultrasonic positioning system was used as the 3D space local position reference which was developed in the previous study. The position reference system has 2 cm RMS of precision and 20 Hz of output frequency. The results of control experiments show the proposed methods are useful to the design controller." ] }, { "image_filename": "designv11_32_0000263_ias.1995.530578-Figure10-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000263_ias.1995.530578-Figure10-1.png", "caption": "Fig. 10: Locis of line current harmonics i depending on emf ed for dc drive with current-limit acceleration (example); 5th harmonic (a), 7th harmonic (b) and 11th harmonic (c), parameter: dc reactance xd = 0.05 (T), 0.2 (A), 0.5 (r) and 10 (e).", "texts": [ " 8a) lines out, that the considered parameter set is in the neighbourhood of the accuracy 21 70 limit of the idealized law. Choosing the higher degree of approximation, according to Fig. 7a) the dc ripple model (R), the error is reduced to ( A ~ J ~ ) ~ = + 0.2\". In general, this example points out the recommendation to check the possibility of selecting a higher approximation degree, determined by the ranges of validity in Fig 7 for h = 5 and 7 only. The second example refers to the behaviour of the complex line current harmonics of a dc drive with current-limit acceleration. Fig. 10 presents the pointer tips of the current vectors& = &, / = ih exp (i oh) depending on the normalized emf ed = Ed / (2.34 UN) of the dc shuntwound motor considered, whereby a resistive dc volt- age regulation of d, = D, / (2.34 UN) = 0.05 is taken into account. The locis demonstrate the effect of different smoothing reactance xd, constant network reactance XN = &Id / UN = 15% assumed. The behaviour of both negative sequences is and ill = f (ea) can be described by damped spirals, whereas the locis of the positive sequence i7 = f (ed) show additionally a cycloid for low dc reactances only" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003249_1.2821385-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003249_1.2821385-Figure2-1.png", "caption": "Fig. 2 Instantaneous centers and critical points. \u201ea\u2026 Center from two positions and \u201eb\u2026 center from three centroids.", "texts": [ " This is the same as the condition of singularity for the point undergoing a two-parameter motion; that is, the tangent vector with respect to the first parameter and that with respect to the second parameter are mutually dependent for the points on the envelope. The mutual dependence of the tangent vectors can occur also in the interior of the workspace or swept area; then, they are referred to as the internal singularities. In the case of motion of a rigid body in a plane, any given finite displacement can be produced by a pure rotation in the plane Poinsot\u2019s central axis theorem ; the center of this rotation can be determined through the identification of the homologous points on the object Fig. 2 a . The sequence of curves in the generative representation defined above can be idealized as discrete instances of a rigid body, provided that the difference in the shape of the successive curves is negligible. Thus, we can identify a sequence of Poinsot centers of rotation, referred to here as the instantaneous centers of sweep, for the given sequence of curves. Each curve can be generated by the motion of a point, and the tangent vector at a point on the curve defines the instantaneous direction of motion of the point on the curve" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000696_pvp2002-1093-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000696_pvp2002-1093-Figure1-1.png", "caption": "Figure 1 Analytical model of the joint", "texts": [ " Rfi,Rro = resistance of the flange inner and outer sections (\u00b0C/W) R~ = resistance of the hub (\u00b0C/W) R~c = external film resistance of the hub (\u00b0C/W) e~ = internal wall film resistance of the flange thickness (\u00b0C/W) Rso = external film resistance of the shell (\u00b0C/W) R p = resistance of cover plate (\u00b0C/W) R pf = resistance of the of the cover plate portion between ri + th and ri - th (\u00b0C/W) Rpfo = external resistance of the of the cover plate portion between r~+ th and ri - th (\u00b0C/W) R pi, R oo = internal and external film thermal resistance of cover plate (\u00b0C/W) R s = resistance of shell (\u00b0C/W) R h i = internal film resistance of shell and hub (\u00b0C/W) R~ o = external film resistance of shell (\u00b0C/W) t = equivalent thickness of upper and lower flange (m) t r = thickness of flange (m) t h = equivalent thickness of hub (m) t~ = thickness of shell (m) Tf,TI, = flange and hub temperatures (\u00b0C) Ta = flange wall inside surface temperature (\u00b0C) Tea = flange temperature at hub outer radius (\u00b0C) T i , T O = inside fluid and outside fluid temperatures (\u00b0C) Tp ,T = cover plate and shell temperatures (\u00b0C) Tp~ ,Too = cover plate center location wall inside and outside surface temperatures (\u00b0C) Ts~ , To = shell inside and outside surface temperatures (\u00b0C) us, u f, u h = radial expansion of shell, flange, hub at radius r (m) 2 Copyright \u00a9 2002 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/03/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use THEORETICAL ANALYSIS In order to determine the steady state temperature distribution in the individual joint components due to an internal hot fluid, the joint is broken into separate components namely the shell, the hub, the flange ring, the bolt, the gasket and the blind ~ver plate. As shown in Fig. 1, the vessel is treated as a thick cylinder connected to the flange through the hub. Heat flow through the hollow section of the hub is assumed to take place from the shell to the flange ring because the latter has a smaller thermal resistance and acts as a cooling fin. The flange and the adjacent part of the cover plate are replaced by an equivalent ring which is separated into two sections. The inner section is treated as a thick cylinder with a thickness equal to that of the hub with no heat dissipation to the outer boundary. The outer section, which is considered as a cooling fin, is treated as a finite cylinder with heat loss from all outer faces to the outer boundary. The blind cover plate is separated into three sections as shown in Fig. 1. The inner section is a plate with a radius equal to that of the flange ring inner radius and the heat flow is assumed to take place in the plate axial direction. The middle and outer sections are considered to be a thick cylinder and a finite cylinder respectively with radial dimensions equal to that of the adjacent inner and outer sections of the mating flange. The temperature at the inside radius of the inner section of the cover plate is considered to be at the same temperature to that of the inner section of the flange ring at the inside radius" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003120_ijmtm.2008.017497-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003120_ijmtm.2008.017497-Figure5-1.png", "caption": "Figure 5 Specimen used for the experiment", "texts": [ " This results in a dense structure, which requires a longer build time. This is the rate that the FDM head moves in thousandths of meter per second. It can be varied (Stratasys\u00ae Incorporated, 1999). Conversely, medium speed will give the better surface quality for the prototypes. In order to properly define accuracy, a standard sample needs to be designed to represent some common dimensional, geometric features and surface roughness for FDM part quality evaluation. The designed part is depicted in Figure 5. Minimum deviation between fabricated part dimension and CAD model dimension was selected as one of the part accuracy criteria. To measure the deviation, each axis (X, Y and Z) was studied separately. For finding deviation of each axis, length (X), width (Y) and height (Z) values of the fabricated parts were measured using the Mitutoyo BH303 CMM. Then, deviations from CAD model dimension were calculated as the error percentage. For example, deviation in the Z-axis was calculated through equation (1)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003784_1.3184692-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003784_1.3184692-Figure1-1.png", "caption": "Fig. 1 Vibration model", "texts": [ "org/about-asme/terms-of-use 2 t r d c p d u e t t G i s F e w M a l p fl o i p s t fi a i w a t f t b a 1 Downloaded Fr Vibration Excitation The vibration of a gear pair comes from two kinds of excitaions: parametric excitation and displacement excitation. Parametic excitation is attributed to the variation in meshing stiffness uring meshing. On the other hand, displacement excitation omes from a geometrical error of the gear tooth shape such as a rofile error, lead error, or pressure angle error. To simplify the considerations, a simple single degree of freeom vibration model, as used by many investigators 15\u201318 , is sed, as shown in Fig. 1. Gear blanks and gear shafts are considred rigid components that have the moment of inertia J and have he base radius rb. The meshing part is modeled as a spring with he stiffness K and a damper having the damping coefficient C. ear errors can be modeled as displacement error e in the meshng part. T is the applied torque and is the rotation angle. Subcripts 1 and 2 refer to the driving and driven gears, respectively. rom this model, the equation of motion for the gear pair can be xpressed along the line of action as Mx\u0308 + Cx\u0307 + K t x \u2212 e t = W 1 here M = J1J2 J1rb2 2 + J2rb1 2 , x = rb1 \u00b7 1 \u2212 rb2 \u00b7 2, W = T1 rb1 = T2 rb2 is the equivalent inertia mass of the gear pair along the line of ction, x is the relative displacement between two gears along the ine of action, and W is the static normal transmitting load" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003789_13506501jet718-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003789_13506501jet718-Figure3-1.png", "caption": "Fig. 3 Local reference frame and fixed reference frame", "texts": [ " O1 and O2 are the centres of the upper and lower pads respectively, O and O\u2032 are the geometric centres of the bearing and the journal. Also, OO1 = OO2 = D = Cd\u0304 (D and d\u0304 are named Fig. 2 Sketch of elliptical bearing ellipticity and ellipticity ratio, respectively) as shown in Fig. 2. In order to use the results of equations (5) and (6), a fixed frame OXY with its origin in the centre of the bearing and two local reference frames O1X1Y1 and O2X2Y2 with their origins in the centres of arch pads are assumed, as shown in Fig. 3. By means of equations (5) and (2a), the fluid film pressure distribution and the film thickness in each local reference frame can be expressed as hi = C \u2212 Xi cos \u03b8 \u2212 Yi sin \u03b8 (7a) pi = 3\u03bc h3 i ( Z 2 \u2212 L2 4 ) [(\u03c9Xi \u2212 2Yi) sin \u03b8 \u2212 (\u03c9Yi + 2Xi) cos \u03b8 ] (7b) where i = 1, 2, and 1 denotes the upper pad and 2 denotes the lower pad. (Xi, Yi) and (X\u0307i, Y\u0307i) are the displacement and velocity components of the journal centre O\u2032 in the local reference frames. (X , Y ) are the coordinates of the journal centre O\u2032, and (X\u0307 , Y\u0307 ) are the components of the velocity of the journal centre O\u2032 in the fixed reference frame OXY . The relation of every local reference frame to the fixed reference frame is clearly shown in Fig. 3. Therefore, the relations between (X1, Y1, X\u03071, Y\u03071) and (X , Y , X\u0307 , Y\u0307 ) are X1 = X , Y1 = Y + D = Y + Cd\u0304, X\u03071 = X\u0307 , Y\u03071 = Y\u0307 Similarly, X2 = X , Y2 = Y \u2212 D = Y \u2212 Cd\u0304, X\u03072 = X\u0307 , Y\u03072 = Y\u0307 With these relations, from equation (7) each pad\u2019s fluid film pressure distribution and the film thickness in the fixed reference frame can be written as\u23a7\u23aa\u23a8 \u23aa\u23a9 h1 = C(1 \u2212 x\u0304 cos \u03b8 \u2212 ( y\u0304 + d\u0304) sin \u03b8) p1 = 3L3\u03bc\u03c9 C 2 ( z\u03042 \u2212 1 4 ) p\u03041 (8) JET718 Proc. IMechE Vol. 224 Part J: J. Engineering Tribology and\u23a7\u23aa\u23a8 \u23aa\u23a9 h2 = C(1 \u2212 x\u0304 cos \u03b8 \u2212 ( y\u0304 \u2212 d\u0304) sin \u03b8) p2 = 3L3\u03bc\u03c9 C 2 ( z\u03042 \u2212 1 4 ) p\u03042 (9) where\u23a7\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23a9 p\u03041 = (x\u0304 \u2212 2y\u0304 \u2032) sin \u03b8 \u2212 ( y\u0304 + d\u0304 + 2x\u0304\u2032) cos \u03b8 [1 \u2212 x\u0304 cos \u03b8 \u2212 ( y\u0304 + d\u0304) sin \u03b8 ]3 p\u03042 = (x\u0304 \u2212 2y\u0304 \u2032) sin \u03b8 \u2212 ( y\u0304 \u2212 d\u0304 + 2x\u0304\u2032) cos \u03b8 [1 \u2212 x\u0304 cos \u03b8 \u2212 ( y\u0304 \u2212 d\u0304) sin \u03b8 ]3 (10) 3.1 Fluid film force of the upper pad Let \u03b21 (see Fig. 3(a)) be the arc angle of the upper pad. Since the pressure must be non-negative, the fluid film region of the upper pad is [\u03d511, \u03d512] \u00d7 [ \u2212L 2 , L 2 ] where [\u03d511, \u03d512] = [ \u03c0 \u2212 \u03b21 2 , \u03c0 + \u03b21 2 ] \u2229 [\u03b31, \u03b31 + \u03c0] in which \u03b31 = \u2212sign( y\u0304 + d\u0304 + 2x\u0304\u2032) arccos ( \u2212 x\u0304 \u2212 2y\u0304 \u2032 A1 ) , A1 = \u221a ( y\u0304 + d\u0304 + 2x\u0304\u2032)2 + (x\u0304 \u2212 2y\u0304 \u2032)2 Physically, in order to guarantee that the fluid film is ruptured on the boundary of the fluid film region [\u03d511, \u03d512] \u00d7 [\u2212 L 2 , L 2 ] , the fluid film pressure at \u03d511 and \u03d512 should be zero", " Using the interpolation method, the modified pressure function is obtained as p\u2032 1 = 3L3\u03bc\u03c9 C 2 ( z\u03042 \u2212 1 4 ) ( p\u03041(\u03d512) \u2212 p\u03041(\u03d511) \u03d512 \u2212 \u03d511 \u03b8 + p\u03041(\u03d512) \u2212 p\u03041(\u03d512) \u2212 p\u03041(\u03d511) \u03d512 \u2212 \u03d511 \u03d512 ) (11) Also, the fluid film pressure of the upper pad is approximately modified to pu = p1 \u2212 p\u2032 1 (12) Consequently, the fluid film force components of the upper pad can be obtained through the integration of the dynamic pressure pu { fux(\u03d511, \u03d512) fuy(\u03d511, \u03d512) } = \u222b 1/2 \u22121/2 Ldz\u0304 \u222b \u03d512 \u03d511 \u2212pu { cos \u03b8 sin \u03b8 } Rd\u03b8 = \u222b 1/2 \u22121/2 Ldz\u0304 \u222b \u03d512 \u03d511 \u2212p1 { cos \u03b8 sin \u03b8 } Rd\u03b8 + \u222b 1/2 \u22121/2 Ldz\u0304 \u222b \u03d512 \u03d511 p\u2032 1 { cos \u03b8 sin \u03b8 } Rd\u03b8 (13) where \u222b 1/2 \u22121/2 Ldz\u0304 \u222b \u03d512 \u03d511 \u2212p1 { cos \u03b8 sin \u03b8 } Rd\u03b8 = \u03bc L3\u03c9R 4C 2 \u222b \u03d512 \u03d511 2p\u03041 { cos \u03b8 sin \u03b8 } d\u03b8 (14) \u222b 1/2 \u22121/2 Ldz\u0304 \u222b \u03d512 \u03d511 p\u2032 1 { cos \u03b8 sin \u03b8 } Rd\u03b8 = \u03bc L3\u03c9R 4C 2 { f\u0304 \u2032 x(\u03d511, \u03d512) f\u0304 \u2032 y (\u03d511, \u03d512) } (15) Proc. IMechE Vol. 224 Part J: J. Engineering Tribology JET718 in which { f\u0304 \u2032 x(\u03d511, \u03d512) f\u0304 \u2032 y (\u03d511, \u03d512) } = \u22122 \u23a7\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 p\u03041(\u03d512) sin \u03d512 \u2212 p\u03041(\u03d511) sin \u03d511 + p\u03041(\u03d512) \u2212 p\u03041(\u03d511) \u03d512 \u2212 \u03d511 (cos \u03d512 \u2212 cos \u03d511) p\u03041(\u03d511) cos \u03d511 \u2212 p\u03041(\u03d512) cos \u03d512 + p\u03041(\u03d512) \u2212 p\u03041(\u03d511) \u03d512 \u2212 \u03d511 (sin \u03d512 \u2212 sin \u03d511) \u23ab\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23ac \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23ad 3.2 Fluid film force of the lower pad Let \u03b22 (see Fig. 3(b)) be the arc angle of the lower pad. Since the pressure must be non-negative, the fluid film region of the lower pad is [\u03d521, \u03d522] \u00d7 [ \u2212L 2 , L 2 ] for \u03b32 \u2208 (0, \u03c0) [\u03d521, \u03d522] = [ 3\u03c0 \u2212 \u03b22 2 , 3\u03c0 + \u03b22 2 ] \u2229 [\u03b32, \u03b32 + \u03c0] for \u03b32 \u2208 (\u2212\u03c0, 0) [\u03d521, \u03d522] = [ \u03b32 + 2\u03c0, 3\u03c0 + \u03b22 2 ] where \u03b32 = \u2212sign( y\u0304 \u2212 d\u0304 + 2x\u0304\u2032) arccos ( \u2212 x\u0304 \u2212 2y\u0304 \u2032 A2 ) , A2 = \u221a ( y\u0304 \u2212 d\u0304 + 2x\u0304\u2032)2 + (x\u0304 \u2212 2y\u0304 \u2032)2 For the similar reason described in section 3.1, the modified pressure function of the lower pad is introduced p\u2032 2 = 3L3\u03bc\u03c9 C 2 ( z\u03042 \u2212 1 4 ) ( p\u03042(\u03d522) \u2212 p\u03042(\u03d521) \u03d522 \u2212 \u03d521 \u03b8 + p\u03042(\u03d522) \u2212 p\u03042(\u03d522) \u2212 p\u03042(\u03d521) \u03d522 \u2212 \u03d521 \u03d522 ) (16) The fluid film pressure of the lower pad is modified approximately as pl = p2 \u2212 p\u2032 2 (17) Integrating the dynamic pressure pl , the fluid film force components of the lower pad can be obtained as{ flx(\u03d521, \u03d522) fly(\u03d521, \u03d522) } = \u222b 1/2 \u22121/2 Ldz\u0304 \u222b \u03d512 \u03d511 \u2212pl { cos \u03b8 sin \u03b8 } Rd\u03b8 = \u222b 1/2 \u22121/2 Ldz\u0304 \u222b \u03d522 \u03d521 \u2212p2 { cos \u03b8 sin \u03b8 } Rd\u03b8 + \u222b 1/2 \u22121/2 Ldz\u0304 \u222b \u03d522 \u03d521 p\u2032 2 { cos \u03b8 sin \u03b8 } Rd\u03b8 (18) where \u222b 1/2 \u22121/2 Ldz\u0304 \u222b \u03d522 \u03d521 \u2212p2 { cos \u03b8 sin \u03b8 } Rd\u03b8 = \u03bc L3\u03c9R 4C 2 \u222b \u03d522 \u03d521 2p\u03042 { cos \u03b8 sin \u03b8 } d\u03b8 , (19) \u222b 1/2 \u22121/2 Ldz\u0304 \u222b \u03d522 \u03d521 p\u2032 2 { cos \u03b8 sin \u03b8 } Rd\u03b8 = \u03bc L3\u03c9R 4C 2 { f\u0304 \u2032 x(\u03d521, \u03d522) f\u0304 \u2032 y (\u03d521, \u03d522) } (20) in which{ f\u0304 \u2032 x(\u03d521, \u03d522) f\u0304 \u2032 y (\u03d521, \u03d522) } = \u22122 \u23a7\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 p\u03042(\u03d522) sin \u03d522 \u2212 p\u03042(\u03d521) sin \u03d521 + p\u03042(\u03d522) \u2212 p\u03042(\u03d521) \u03d522 \u2212 \u03d521 (cos \u03d522 \u2212 cos \u03d521) p\u03042(\u03d521) cos \u03d521 \u2212 p\u03042(\u03d522) cos \u03d522 + p\u03042(\u03d522) \u2212 p\u03042(\u03d521) \u03d522 \u2212 \u03d521 (sin \u03d522 \u2212 sin \u03d521) \u23ab\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23ac \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23ad 3" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000364_robot.1988.12028-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000364_robot.1988.12028-Figure8-1.png", "caption": "Figure 8: Three-Point Initial Grasp.", "texts": [ "3 Translat ional Lift-off The first goal of grasping is to break all contact with the support. With this in mind, it makes most sense to use the translation region in planning the initial grasp. However, with only two finger contacts, T is a set of distinct points, and impossible to contact (practically speaking). However, we will show that using a three-point initial grasp enables the translation region, T, to gain finite length, thus becoming usable. One way to achieve a third finger contact is by laying the first finger against an edge (see f5 in Figure 8). Next, the equilibrium equation (1) must be satisfied. The particular solution of equation (1) in which we are interested is the one for which the third and fourth contacts break, which can be stated as Removing the third and fourth columns from W and noting that the first and fifth contact angles are equal, we can solve equation (1). Substituting the result into inequality (12) yields sin(w1 - w2) > 0 (13) t5 > o (14) tg sin(yr1 - y~ 2) + t5 COS(Y2) te s i n ( ~ 1 - ~ 2 ) < o . cos(w1) C O d V 1) < t2 < cos(yr1) ( 1 3 These inequalities define the translation, T, region in which squeezing with the second finger causes the object to translate along the first finger breaking both support contacts" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002429_fuzzy.2006.1682005-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002429_fuzzy.2006.1682005-Figure1-1.png", "caption": "Fig. 1. Pendubot\u2019s schematic.", "texts": [ " However they can be transformed into linear matrix inequalities. This can be done by pre-multiplying and post-multiplying them by . The resulting expressions (28) and (29) are linear matrix inequalities that can be treated by numerical methods widely known as LMI techniques. The new unknowns are now and . The rest of the proof follows similar to theorem 2 In this section we apply the latter result to an under-actuated nonlinear system named pendubot. The schematic of the pendubot (Pendulum Robot) is shown in Figure 1. Basically, it can be described as an electromechanical system composed by two rigid links. The first link (Link 1) is directly under the influence of a dc motor, which is the only actuator within the system. The second link (Link 2) stills under-actuated, therefore its behavior is similar to that of the inverted pendulum on a car. So, the interesting problem is to control the link 2. To do this, the system has two outputs given by two encoders placed in each one of the joints. In that way, the dynamics of the resulting system are much more richer than those given by the inverted pendulum" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002091_aim.2003.1225147-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002091_aim.2003.1225147-Figure6-1.png", "caption": "Figure 6 Orthogonal Relation Between Internal Force and Driving Force", "texts": [], "surrounding_texts": [ "DINATES THE WIRE LENGTH COOR- In this chapter, basing on the principle of orthogonalization, I analyze the motion convergence of feedback control in the wire length coordinates. The feedback control in the wire length coordinates is a widely used method for the parallel-wire system, since wire length can be easily obtained by calculation of Euclidean norm between endpoints ofthe wire, under an assumption that an endpoint of wire in each actuator is fixed. However, the redundant actuation obstructs to prove the motion convergence directly. Kawamura et al. proved that the motion of the parallel-wire driven robot converges to the desired wire length basing on both Lyapunov stability and Vector Closure conditions[3]. Unfortunately Kawamura's proof can be applied to only the n+ 1 wires case, it is inapplicable to more than n+l wires case. Actually, the C.R. type which utilize more than n + 1 wires for the n D.0.F motion is widely developed, since we can easily obtain is larger work space than the robot using n + 1 wires[5]. Therefore it is important for the parallelwire robot with more than n + 1 wires to guarantee the stability and the motion convergence as well. Here, the principle of orthogonalization plays a very important role to guarantee the motion convergence in the case with more than n+ 1 wires. A Lyapunov function using a projection matrix obtained from the principle is introduced in this chapter. 51 2 Dynamics In stability analysis of control in t.he wire length coordinates, I assume that the mass of wire and viscosity coming from air can be ignored, because they are extremely smaller than those of other mechanical parts. Moreover, I suppose that this system with m (m > n) wires satisfies the conditions of Vector closure for any time, Under such assumptions, the actuators dynamics is represented by A$+ BQ+at = 7 (12) where, q E 32\": wire length vector, A E W\"\": actuator inertia matrix, B E Rmxm: actuator viscous friction coefficient matrix; at E 8\": wire tension vector, r E 32\": motor torque vector. The matrices A and B include the inertia and the v i s cosity of gears. On the other hand, the end-effector dynamics is expressed by x + g o = f , (13) Control in Wire Length Coordinates Here, I employ a PD feedback control law in the wire length coordinates. Like usual parallel-link mechanism, inverse kinematics of parallel-wire mechanism is easily calculated. As the result, a desired wire length vector qd which corresponds to a desired position-orientation of the task oriented coordinates CO is obtained. By using the desired vector q d , the input 7 is given by ~ = - K ~ A q - K v A 4 + v ; ~ + v ~ (17) where Aq = q - q d , Kp E Rmxm and K, E P\"\"' denote feedback gain matrices. The term vi, E RRm means internal force vector which satisfies wvi, = 0. (18) The final term v, E I\" is added in order to compensate gravitational force. The vector v, must satisfy w v , = vg. (19) FromEquations (5), (12), (13), (15), (16), (17), (18) and (19), the closed loop equation is expressed by - Mq + (B+W+Mo*++W+ ( B . -Ma+So ) W+T 1 q +KpAq + KvAq - v;, + v = 0. (20) where, (21) - M = ( A + W'MoW\"). And then substituting the projection relation described by Equations (10) and (11) into Equation (20) yields - M(Q4 + Qii) + { B + W + M o W + + W + ( i&fo + S o ) W+') Qq +KpAq + KvAq - ~ t n + v = 0. (22) where MO E 8\"'\": inertia matrix, SO(Z, k) E Rnx\": skew-symmetric matrix, I E 32% position-orientation of the center of gravity, go E 32\": gravitational vector, f E R\": force-moment vector. As seen Figure 3, the Wire tension at generates motion of.the end-effector. Hence, the force-moment vector f is given by Equation (2) and the inverse relation is given vector Q and the vector x, it is given by the following equations[3], Q = W x, (14) j. = W + T Q . (15) V is given by In the next section, it is investigated whether the wire length vector q converges to the desired one qd or not. Motion Convergence Now, We are at the position to prove stability of parallelwire drive robots. Consider a candidate of Lyapunov function which includes the projection matrix Q follows: by Equation (5). As for velocity relation between the V = 1 . , q T Q ~ Q Q + ~ A q T K p A q , (23) where the matrix Q means Q(v - v;,,). The candidate function is'positive. The time derivation of the function T . (24) T V = qTQm(QQ + Qq) + Aq KpAq From Equation (15), we obtain (16) +~qTQ[S$(W+)M~W+T]QqT. (25) d dt % = - ( W + T ) q + w'q. 51 3 By substituting Equation (22), We obtain [5] H.Kino, H.Miyazono, C.Wou, S.Kawamura : \u201cRealization of Large Work Space using Prallel Wire Drive Robots? ,end Asian-Control conference, vol. 3, pp. 591-594, 1997. V = -qTQBQq - g T Q K V Q g . (26) [6] N. Yanai, bf. Yamamoto and A. Mohri, \u201cAnti-Sway Control for Wiresuspended Mechanism Based on Dynamics Compensation\u201d, PTOC. of IEEE International Conference on Robotics and Automation, WPII-12-4, 2002. The time derivation of the function V is negative, so the candidate function V becomes a Lyapunov function. At last, We know that the motion converges to a maximum invariant set which satisfies V = 0. In this case, since V = 0 means Qq = 0, I conclude 171 A. B. and S. K. Agrawal, \u201cCable Suspended Robots: Design, Planning and Control\u201d, PTOC. of IEEE International Conference on Robotics and Automation, WPII-12-2, 2002. [81 V,D,Nguyen: ~cConstructiug Force-closure Grasp in 3D\u201d, Proc. of the 1987 IEEE Int. Conf. on Robotics and Automation, pp. 240-245, 1987. (91 S.Arimoto, \u201cControl Theory of Non-linear Mechanical Systems: A Passivity-based and Circuittheoretic Approach\u201d, Ozford Univ. Press, 1996 q = q = o (27) 9 = Qd (28) as time t tends to infinity as long as the motion is within Vector Closure space. Moreover, from Eq.(20) We know T = Vi\u201d i vg, (29) v = Vi\u201d, (30) as time tends to infinity. CONCLUSION In this paper, I have investigated the principle of orthogonalization for completely restrained parallel-wire driven system. A Lyapunov function using the principle of orthogonalization has been introduced to prove the motion convergence of wire length feedback scheme for general parallel-wire robots with more than n+ 1 wires, even though it was not guaranteed to converge at the desired wire length in previous research. The principle of orthogonalization plays very important role for com~ pletely restrained parallel-wire driven system. Therefore, this concept might be useful for analysis of other control methods for the parallel-wire driven system. References [l] T.Higuchi, A.Ming: \u201cStudy on Multiple Degree-of- Freedom Positive Mechanism Using Wires\u201d, Prceedmg of Asian Conference on robotics and its a p plication, pp. 101-106, 1991 [Z] H.Osumi,Y.Shen,T.Arai,\u201dThe Manipulability of Wire Suspension System\u201dTrans. Robotics Soci- \u2018ety of Japan,Vol.l2,No.7 pp.1049-1055(1094)(in Japanese). 131 S.Kawamnra, H.Kino and W.Choe, \u201cHigh speed manipulation by using parallel wire driven robots\u201d, ROBOTICA, Cambridge University Press, vo1.18, part 1, January/February, pp.13-21, 2000. 141 S.Kawamura and K.Ito: \u201cA New Type of Master Robot for Teleoperaiton Using A Radial Wire Drive System\u201d,Proc. of the 1993 IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, vol. 1, pp. 55-60, 1993. 51 4" ] }, { "image_filename": "designv11_32_0003449_09596518jsce656-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003449_09596518jsce656-Figure5-1.png", "caption": "Fig. 5 The definition of the geometry features of weld pool: (a) topside weld pool; (b) backside weld pool", "texts": [ " 4, in which the top left is the back topside image, the top right is the front topside image, and the bottom is the backside image. The back topside image of the pool can be divided into the following parts: nozzle, deposited area of metal heap, weld pool brim, base metal, arc and its shadow, weld wire, and so on. In the front topside image, the gap, groove, weld pool, and weld wire are clear. The weld pool contains abundant information about the welding process. The geometry parameters of the weld pool are important character for weld quality. As shown in Fig. 5, the topside length Lt, maximum width Wt, and half-length ratio Rhl can be used as the characteristic parameters to describe the shape and size of the topside weld pool, the halflength ratio Rhl was defined by the following formula: Rhl~ Ltt LthzLtt |100%. The backside pool is specified by the maximum width Wb. A real-time image processed algorithm has been developed to extract these parameters [17]. As shown in Fig. 6 and Fig. 7, the process of image processing include scalemultiplication-based edge detection, noise removing, calibration, and piecewise curve fitting" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000604_auv.1996.532407-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000604_auv.1996.532407-Figure7-1.png", "caption": "Figure 7: Phase 3 Arrangement", "texts": [], "surrounding_texts": [ "Costello, David and Kendall L. Carder, \u201cUsing Ilnmanned Vehicle Systems for Ground-Truthing Oceanographic Satellite Data\u201d ,447-454. NOAA Proposal. from USF: SFS.5 \u201cUtilization of Bottom Classification/ Albedo Package for Bottom MapFling and Feature Classification, and for Quantification of the Components of Upwelling Radiance in Coastal Waters\u201d p41-46. White, Keven, and Smith Samuel, \u201cFuzzy Behvioral Controllers Using Criteria Based Decision Making for E3ottom Following Missions in AUVs.\u201d 9th Annual IJUST 1995 New Hampshire, pp. 337-342. White, K. A., \u201cDesign and Implementation of an Altitude Flight Controller for the FAU Ocean Voyager 11\u201d. Masters Thesis, Ocean Engineering Department, Florida Atlantic University, Boca Raton Florida, 1995. Langenback, R.M., and Rae, G.J.S. \u201cFuzzy Logic Docking Control for an Autonomous Underwater Vehicle.\u201d 9th Annual UUST 1995 New Hampshire, pp.253-261. G.J.S. Rae and S.M. Smith, \u201cA Fuzzy Rule Based Docking Procedure for Autonomous Underwater Vehicles,\u201d Proceedings IEEE-Oceans \u201992, Newport RI, pp. 539- 546, October 1992. G.J.S. Rae, S.M. Smith, D.T. Anderson, andA.M. Shein, \u201cA Fuzzy Logic Docking Algorithm for Two Moving Underwater Vehicles,\u201d American Control Conference, San Francisco, June 1993, in press. [8] S.M. Smith, G.J.S. Rae, D.T. Anderson, andA.M. Shein, \u201cFuzzy Logic Control of .Autonomous Underwater Vehicle,\u201d Control Engineering Practice, Voi 2. No. 2, pp. 321-331, 1994 (invited)." ] }, { "image_filename": "designv11_32_0003443_6.2007-6784-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003443_6.2007-6784-Figure1-1.png", "caption": "Figure 1. Flat earth reference coordinate system", "texts": [ " However, at low airspeeds, namely, under Mach 1, the airframe input-output interaction increases greatly and the projectile dynamic becomes too slow to guide and control effectively the munition onto a designated target. II. Reference Coordinate Systems The development of guided spinning projectiles requires a careful selection of the reference coordinate systems for stability and guidance and control analysis/synthesis and also for onboard computation and mechanization19. Three reference coordinate systems were used in this analysis: Flat earth Body frame Body frame non-spinning The origin of the flat earth reference frame is set at the gun muzzle as shown in Fig. 1, since this is the starting point of the 6DOF simulations. The positive x-axis is in the longitudinal plane of the gun and points ahead. The positive y-axis points to the right when looking forward from the gun. The positive z-axis, normal to the x-y plane, is pointing down. The body frame is fixed to the projectile with its origin at the projectile center of mass. Thus, it follows exactly the projectile attitude. The body frame non-spinning is similar to the body frame, but it does not spin with the airframe" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000935_0094-114x(87)90079-6-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000935_0094-114x(87)90079-6-Figure1-1.png", "caption": "Fig. 1. Scheme of a conventional 6R robot.", "texts": [ "0, and 1, [when (m + n) = 6], which can be obtained by solving the 6 constraint equations. Generally, the solution of the Second Kind of Kinematical Problem for a n R - m P robot with (m + n) = 6, is obtained by use of iterative method. However, under certain special conditions, for example, in cases of conventional 6R robots, conventional 3R-3P robots, etc., closed-form solution can be derived through the application of the algebra of rotations. Conventional 6R robot In a conventional 6R robot, as shown schematically in Fig. 1, we have m = 0, n ffi 6, and \u00a2a~ ffi i, m : = k , \u00a2.03 --~ \u00a2.04 ~-03~ m j , \u00a2otffik, Rb~- lbi, aloffi 13o 1, a2o = 0, a3o ' j = a,o ' j = 0, aso----0. In this case, using equations (2) and (6), we can reduce equations (16), (17) and (20) into the following two equations. (06,tO6j) \u00ae R ~- (06k) \u00ae {[(05 + 0, + 03)j] \u00ae {(0:k) \u00ae [(0,i) \u00ae R]}), (21) s6 = (06X) \u00ae {[(0s + 0, + 03)j] \u00ae {(02k) \u00ae [(1~o +/b)i]}} + (06k) \u00ae {l(05 + 0,)i] \u00ae ,,3o \"4- (06k) \u00ae [(05j) \u00ae a40]}. (22) In the First Kind of Problem, 0j, 02, 03, 04, 05, 06 are given, and we can calculate the values of 06~ and mt~ directly from equation (21) by repeated use of equations (4) and (5), and the corresponding values of s~ from equation (22) straight-forwardly" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000301_tra.2002.999655-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000301_tra.2002.999655-Figure5-1.png", "caption": "Fig. 5. (a) Module used to build the VGT and initial position of it and (b) successive positions.", "texts": [ " It remains only to calculate the Jacobian matrix, the form of which is 0 0 0 0 0 @2VF @xj@xj @2VF @xj@yj @2VF @xj@zj 0 0 @2VF @yj@xj @2VF @yj@yj @2VF @yj@zj 0 0 @2VF @zj@xj @2VF @zj@yj @2VF @zj@zj 0 0 0 0 0 = 0 0 0 0 0 @F x j @xj @F x j @yj @F x j @zj 0 0 @F y j @xj @F y j @yj @F y j @zj 0 0 @F z j @xj @F z j @yj @F z j @zj 0 0 0 0 0 : (18) The components of this matrix appears in the following equation: @F x j @xj =KR n i=1 KSi (N + 1)(xj xoi) 2 + d2ij dN+3ij @F y j @yj =KR n i=1 KSi (N + 1)(yj yoi) 2 + d2ij dN+3ij @F z j @zj =KR n i=1 KSi (N + 1)(zj zoi) 2 + d2ij dN+3ij @F y j @xj = @F x j @yj KR n i=1 KSi (N + 1)(yj yoi)(xj xoi) dN+3ij @F z j @xj = @F x j @zj = KR n i=1 KSi (N + 1)(zj zoi)(xj xoi) dN+3ij @F z j @yj = @F y j @zj = KR n i=1 KSi (N + 1)(zj zoi)(yj zoi) dN+3ij : (19) The potential function defined in (16), the first derivative (17), and the second derivative (18) are substituted into (4), (9), and (11), respectively, so that (7) can be solved for each iteration. Here we look at the result of the analysis of the performance of a spatial VGT in an environment with obstacles. The starting point is as in Fig. 5(a). The VGT has thirty modules, ninety actuators, and 183 rigid rods. Each parallelepiped forming part of an obstacle is discretized into 6 6 2 points. Also, the modular composition of the VGT is described. Fig. 5(b) shows the successive positions of the VGT. This paper has looked at a new and general approach to the inverse position problem for hyper-redundant multibody systems in environments with obstacles. The method proposed is used to minimize a potential function that unifies on the one hand obstacle avoidance and on the other optimization of the redundancy. The method has been tested for a great variety of variable geometry trusses with various redundancy levels, with several environments containing obstacles, and with paths of every kind" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001258_60.50821-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001258_60.50821-Figure4-1.png", "caption": "Figure 4 -- Temperature contours at (0) 5 sec and (b) 15 sec.", "texts": [ " The rotor iron has the Stal ni\"sc Steel Tu\ufffde Steel Laminations \\ Capper Bar ir-l - -- -- - -' ---.--\ufffd-:=- 1 \ufffdI 3 9130 .1 [ __ ,L t\ufffd\ufffd __ =- \ufffd ___ __ __ J-o:J::i FI \ufffdLJre 1 -- Geometry of a saOJre bar e,bedded In the rotor laminations Of on Induction motor. 0.1'\" AI rgop rotor, the eddy currents in the rotor iron are neglected. A convection boundary was placed at the top surface of the stainless steel rotor can with an h value of 7.32 W/m2\u00b7C. Figures 2 and 3 show the flux and loss contours obtained from the eddy current analysis. Figure 4 shows the heat diffusion by the temperature contours at 5.0 and 15.0 seconds . Figure 5 shows the rise in temperature at the center of the bar in 12 seconds. This rise in bar tem pera ture is compared with the full scale test results. The test was cond ucted for 8 seconds only. The maximum difference is found to be within engineering accuracy. Figure 2 - - Real component of the flux contours, -c\ufffd\ufffd -====\ufffd\ufffd=-\ufffd\ufffd-\ufffd+\ufffdJ\ufffd --.-.. ---.. . ----.- -_ ... __ ... .... _ ... -_J J ... __ _ figure 3-- LOSS contours in the tor" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002398_s0022-0728(75)80358-5-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002398_s0022-0728(75)80358-5-Figure3-1.png", "caption": "Fig. 3. Concentration dependence of the height of the second anodic peak of cysteine (resting \u2022 electrode, other experimental conditions as in Fig. 1). Base electrolyte: (1) phosphate buffer pH=7.0, (2) low molecular weight fraction of HBS, (3) high molecular weight fraction of HBS, (4) HBS.", "texts": [ " Only cysteine gives a current which increases with the stirring in both phosphate buffer and HBS. Cysteine added to the solutions of electrochemically active species in phosphhte buffer solution (all concentrations equal to the average value in HBS) gives an anodic current which is practically the same in the presence and absence of these substances. The electrochemical oxidation of cysteine at the Pt-electrode is only slightly inhibited in the low molecular weight fraction whereas the inhibition in the high molecular weight fraction is much larger (see Fig. 3). The influence of albumin on the electrochemical behaviour of cysteine With the aim of ascertaining the role of proteins in the inhibition of cysteine oxidation by the high molecular weight fraction of HBS the model experiments were carried out with the inhibition of this reaction by human serum albumin which represents about 60~o of all serum proteins. The influence of albumin on the I-E curve of cysteine in phosphate buffer solution is shown in Fig. 4. First it was necessary to decide whether cysteine and albumin compete when they are adsorbed on the surface of the electrode" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003062_s1560354708050067-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003062_s1560354708050067-Figure5-1.png", "caption": "Fig. 5.", "texts": [ ", the equation of motion and domains \u03a9 and \u03a90 are unchanged (this substitution converts the orientation of the OZ axis). Therefore one can restrict oneself with an analysis of the case p\u03c6 0, p\u03c8 0. Consider some subcases. 1. For p\u03c6 = p\u03c8 = 0 one has \u03c4 = 0 and the right hand side in (3.5) does not depend on c0. The comparison of inequalities (2.8) and (3.5) shows that \u03a90 \u2282 \u03a9. In equation (3.2) it holds vx = const, therefore the system is dynamically equivalent to the inverted pendulum. Its phase portrait is shown on Fig. 5a. 2. For p\u03c6 = p\u03c8 = 0 system (3.2) can have two or none equilibrium positions depending on a value of c0. Typical phase portraits are shown on Figs. 5b and 5c. Note that equilibrium positions are necessarily in \u03a90, but not necessarily in \u03a9. In this situation there is a non-uniqueness of the motion, i.e., both equilibrium (corresponding to a stationary motion of the body) and detachment of the disc from the support are possible. 3. For p\u03c6 = p\u03c8 all phase trajectories of the system (3.2) are bounded; the corresponding model phase portraits are shown on Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000964_j.1471-4159.1984.tb06095.x-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000964_j.1471-4159.1984.tb06095.x-Figure3-1.png", "caption": "FIG. 3. Competitive inhibition of the [14C]phenylethylamine oxidation (type 6 MA0 activity) by NAP-5-HT. The assay procedures fol lowed that described in Fig. 1. The ['4C]phenylethylamine concentrations ranged from 1.5 to 10 pM. The NAP-5-HT concentrations were 0 (o), 0.1 (o), and 0.3 p M (A). K , determination is shown in the inset. The line of best fit was determined by linear regression analysis.", "texts": [ " Inhibition of MA0 activities by NAP-5-HT Figure 1 shows that NAP-5-HT inhibits both types of M A 0 activities in rat brain cortex with similar potency. A 50% inhibition of type A and type B activities was obtained with 0.40 F M and 0.28 FM NAP-5-HT, respectively. Kinetic studies revealed that NAP-5-HT inhibited each type of M A 0 activities by competing with the substrate (Figs. 2 and 3). The K i value for NAP-5-HT inhibition of serotonin deamination was determined to be 0.19 F M (Fig. 2) and 0.21 p M for inhibition of phenylethylamine deamination (Fig. 3). These latter results indicate again that NAP-5-HT has similar binding affiiliry to both types of MAO. The K , values for serotonin and P-phenylethylamine were determined to be 70 F M and 9 F M , respectively, which are similar to that reported for rat liver J . Neuroc'rem., Vol. 43, N o . 6 . 1984 1682 S. CHEN ET A L . MAOs, 71 F M for serotonin and 1.7 p M for phenylethylamine (Tipton and Mantle, 1981). Photodependent effect of NAP-5-HT on MA0 NAP-5-HT has a typical nitroazidophenyl derivative spectrum with absorption maxima at 258 nm and 470 nm (Fig", " The specificity of the photodependent incorporation of NAP-5-HT to type B M A 0 was indicated by a protection experiment utilizing phenylethylamine, the substrate for type B MAO. As shown in Fig. 7 inclusion of phenylethylamine during photolysis of the enzyme and NAP-5-HT mixture prevented the photoinactivation of type B enzyme. A 100% protection was achieved at 100 pM of phenylethylamine. The high concentration of phenylethylamine required for complete protection may be due to the higher binding affinity of NAP-5-HT (Ki = 0.21 pA4) than phenylethylamine (K! a = 9 pA4) (see Fig. 3 ) . Also NAP-5-HT irreversibfy binds to the enzyme upon irradiation (see following section), whereas the substrate phenylethylamine is deaminated and released from the active site of the enzyme during these treatments. Photodependent irreversible labeling of type B MA0 by NAP-5-HT Evidence for a photoinduced covalent labeling of NAP-5-HT to type B MA0 is provided by the following experiments. A set of four samples was prepared: (1) a control containing only cortex homogenate, (2) a sample containing cortex homogenate and 5 pM NAP-SHT, but not photolyzed (dark control), ( 3 ) a sample containing cortex homogenate and NAP-5-HT and subjected to photoirradiation, and (4) a final sample containing cortex homogenate together with previously photolyzed NAP-5-HT", " However the type B MA0 activity in the photolyzed sample was inhibited 74% and the inhibition remained after two washings (Table 1) . Furthermore a 70% inhibition of enzymatic activity was still observed by assaying the 10 times-diluted, washed, photolyzed sample (data not shown). This experiment indicates a clear photoinduced irreversible binding of NAP-5-HT to type B MAO. This notion was further supported by the ki- J . Neurochem., Vol. 43, No. 6. 1984 netic analysis in which a noncompetitive inhibition was obtained after photoirradiation (Fig. 8) , whereas a competitive inhibition was seen in the dark (Fig. 3). Two possible explanations can be given to this result: ( 1 ) the photolytic derivative(s) of NAP-5-HT binds to a site different from the active site of MA0 (i.e., a typical noncompetitive inhibitor), or (2) NAP-5-HT incorporates irreversibly into the active site of MA0 upon photolysis (i.e., an irreversible inhibitor). Since we have shown that the photodependent inhibition of type B MA0 by NAP-5-HT can be reduced by including phenylethylamine in the irradiation mixture, i.e., there is a competition between photoactivated NAP-5-HT and phenylethylamine for binding to MAOs, we therefore think that the changes in kinetic profile for NAP-5-HT inhibition that results after the photoirradiation indicates an irreversible binding of NAP-5-HT to the active site of type B MA0 following photolysis", "21 pA4 for types A and B MAO, respectively; Figs. 2 and 3). Since we have recently found that 4-,.~oro-3-nitrophenyl azide is a potent competitive inhibitor for type B MA0 (Ki = 0.78 pM) (results to be published elsewhere), the 2-nitro4-azidophenyl group on NAP-5-HT may be responsible for its inhibition of type B MAO. Upon photolysis the inhibition of NAP-5-HT to type B MA0 was greatly enhanced. A 50% inhibition of the MA0 activity resulted with only 35 nM NAP-5-HT onesixth of the Ki value (Ki = 0.21 p M for type B MAO; Fig. 3). The photodependent covalent insertion of NAP-5-HT into the active site of type B MA0 is evident because the photoinduced inhibition by NAP-5-HT cannot be eliminated by extensive washing (Table 1) and NAP-5-HT becomes a noncompetitive inhibitor with respect to the substrate upon photoirradiation (Fig. 8). In addition the semilog plot of activity remaining versus time (inset, Fig. 6) shows a linear relationship up to 2 min of irradiation. However the photodependent inhibitory profile is complicated by the protective effect of earlier generated photolytic products of inhibitor when irradiation longer than 2 min is applied so that the log of activity remaining versus time is no longer linear with time after 2 min" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003447_iros.2007.4399022-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003447_iros.2007.4399022-Figure2-1.png", "caption": "Fig. 2. Example: grasp with two contact points", "texts": [ " 1 satisfy (20) and therefore the corresponding static friction forces are valid. On the other hand, the virtual slidings as shown in the right of Fig. 1 do not satisfy (20) and therefore the corresponding static friction forces are invalid. Omata and Nagata\u2019s formulation imposes a \u201cglobal\u201d constraint on friction forces; in other words, their constraint is on the combination of the friction forces. On the other hand, friction models such as Coulomb\u2019s law impose only \u201clocal\u201d constraints on each of the friction forces. Let us consider a two-fingered grasp as shown in Fig. 2(a). In this case, when an external force (e.g. gravity) is applied to the object vertically downward, static friction forces shown in Fig. 2(b) can be generated to prevent falling down of the object. Of course, they are valid in Omata and Nagata\u2019s formulation. Then, let us consider a similar grasp as shown in Fig. 3(a). This grasp has an additional contact between the object and the \u201cpalm\u201d (P3) in comparison to Fig. 2(a). In this case, when an external force is applied to the object vertically downward, static friction forces shown in Fig. 3(b) could also be generated. However, these friction forces are invalid in Omata and Nagata\u2019s formulation; the virtual object motion vertically downward does not satisfy (20), because such a motion will break the contact P3. Intuitively, when a contact point is added to a robotic grasp, the robustness of the grasp should be larger than or equal to the original grasp. However, in Omata and Nagata\u2019s formulation, the additional contact may invalidate some friction forces and make the grasp less robust\u2014this is paradoxical" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000457_978-3-642-55848-1-Figure9.52-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000457_978-3-642-55848-1-Figure9.52-1.png", "caption": "Fig. 9.52. Prismatic joint in space", "texts": [ "6, we meet some specific examples of such transformations. Revolute joints play an important role in the design of robotic manipulators. They offer the simplest way to change the orientation of robot links. The compo nent model introduced here gives the main functionality of such joints. They are used later for the building of manipulator models. This is illustrated in Sec. 9.6. Prismatic Joints Prismatic joints have already been described in Sec. 9.2.2. The basic difference here is that the axis of the joint can be anywhere in space (Fig. 9.52). To describe the effects of prismatic joints on bodies connected by such a joint, we define a body frame AxAYAZA attached to one body at point A. The z-axis is directed along the relative displacement of the joint (joint axis). There is also a second body B and a frame attached to it. The precise positions of the frames are not specified and can be defined as is the most convenient, e.g. by using Denavit-Hartenberg convention [9]. The frame Oxyz is the base frame. Let B be a point on the second body", "47, but of course its model will be different. The ports are assumed compounded such that the port variables are 6D flows and efforts at the connection of the joint to the bodies (the upper and lower in Fig. 9.47). The side port is used for actuation of the joint. We develop the governing equations first. They are generalizations of the corresponding equations for the planar case in Sec. 3.2.2, but are expressed with respect to the body frame, not the base frame, as we did for plane revolute joints. The position vector of point B (Fig. 9.52), the reference point of the body that can slide along the joint, is given by 382 9 Multibody Dynamics (9.120) where RA is the rotation matrix of frame A with respect to the base and r ABA is its relative position with respect to body frame A. By differentiation with respect to time, we get for its velocity (9.121) where A drts V AB =Tt (9.122) is the relative velocity of the junction. Substituting from Eq. (9.65) in Eq. (9.121) we get R A R A A VB =VA + AVAB + AWA xrAB (9.123) Multiplying from the left by the transposed rotation matrix R/, we find (9" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001027_bf00934324-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001027_bf00934324-Figure3-1.png", "caption": "Fig. 3.", "texts": [ " For V o - < Vlo, the optimal maneuver is a split S; for Vo--- V2o, the optimal maneuver is a half-loop; for Vlo < Vo < V2o, the optimal maneuver is a three-dimensional path, the final altitude increasing monotonically from the value at V~0 to that at V2o. This sequence is independent of the initial altitude. Also, computational results with T / W = 0 . 8 show that the sequence is independent of the thrust/weight ratio. The dashed curve in Fig. 2 corresponds to values of Vo for which the trajectories are essentially horizontal. Figure 3 shows the trajectories for Vo = 190, 200, 220, 240, 250 m/see and ho = 1 km; Figs. 4a-f the corresponding time histories of velocity, path inclination, angle of attack, bank angle, power setting, and load factor. It should be pointed out that, for all maneuvers in the vertical plane, ~(t) is nearly constant. The singularity in the differential equations for cos 3' = 0, which causes numerical problems for split-S and half-loop maneuvers, is circumvented by switching at Vo = Vlo and Vo = V2o to the two-dimensional equations of motion (~ = 0, ~ = 0)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002243_s00231-006-0204-9-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002243_s00231-006-0204-9-Figure2-1.png", "caption": "Fig. 2 Schematic of the cryogenic vacuum unit. 1 vacuum chamber, 2 thermal shield, 3 sample support, 4 optical window, 5 spring, 6 cold head, 7 samples, 8 ball bearing, 9 heating laser beam, 10 probing laser, 11 triple prism", "texts": [ " The sample support is installed on the second cold head of the two stage GM cryocooler (Gford-McMaban cycle cryocooler), at the same time, to eliminate the effect of thermal radiation on the temperature of the samples, the sample support is surrounded by a thermal shield which is connected to the second cold head of the GM cryocooler. The sample support is put in the vacuum chamber. Two optical windows are installed on the side of the vacuum chamber in order to make the heating laser beam and the probing laser beam get through. The test system consists of the cryogenic unit, the laser optical circuit unit, the measurement unit and the vacuum unit. Figure 2 shows the cryogenic vacuum unit. During testing, the vacuum pump was started firstly. When the vacuum level of the vacuum chamber reached 10\u20131 Pa, the GM cooler was turned on. The vacuum level of the vacuum chamber can reach and maintain 10\u20133 Pa. Test was performed under an average vacuum condition of 10\u20133 Pa. By varying the voltage of the heater, which was located in the sample support, the temperature of the sample was controlled in the range from 20 to 300 K. When the temperature of the sample was steady, the measurement was conducted at one temperature point" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001660_3-540-29344-2_43-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001660_3-540-29344-2_43-Figure2-1.png", "caption": "Fig. 2. The test environment used in the prototypical implementation.", "texts": [ " The diameter of the robot is only 55 mm and the height is 35 mm. Therefore, multi-robot experiments have low space requirements. The Khepera can be extended via modules that can be plugged onto it. For our scenario, we are using K-Team's radio turret to add communication capabilities. The turret can communicate with up to 32 robots within a range of 10 m at a maximum da ta rate of 9600 bits/sec and supports (acknowledged) unicast and broadcast messages. We have designed an eight-shape like environment to test the intersection management (cf. fig. 2). The road from south to north is the major road and the one from west to east the minor road. The intersection itself is divided into three zones, as proposed by the MLaP: the search zone^ the planning zone and the action zone. Depending on the zone the robot currently passes, it has to perform different actions. Therefore, the robot has to have a mean to detect the different zones. To avoid the use of a global position system, we are using specific landmarks in the environment for this purpose. Each robot starts at a fixed, pre-defined position (robot insertion point in fig. 2) and performs wall following. If it detects a hole in the wall, it turns 90 \u00b0 to the left and continues wall following. Wi th every turn, the robot updates its internal compass (the default after a reset is north) . After three turns, the search zone starts . The robot continues until it detects a pin at the left side. The pin marks the beginning of the planning zone. The planning zone has a pre-defined length. Hence, by measuring the distance with the wheel encoders, the robot knows when the action zone starts ", " 4 Collaboration algorithm The distributed algorithm tha t enables collaboration between mini robots is based on analyzing the pa th tha t each robot wants to drive through the intersection. By utilizing the zone approach, the necessary information from all other robots can be collected and analyzed. Each robot decides randomly in which direction it will drive after passing the intersection. As every robot knows (from its internal compass) the direction from which it will approach the intersection, each robot can construct the pa th tha t it will drive through the intersection. For this purpose, the intersection is divided into four sectors (cf. fig. 2). The intersection pa th is represented via a list tha t contains the numbers of the sectors in the order they are passed. For example, if the robot approaches the intersection from south and wants to continue to west afterwards, the intersection pa th is {4 ,2 ,1} . Please note tha t our robots drive on the right lane. The algorithm tha t each robot executes is outlined in fig. 3. In the search z o n e , each robot tries to discover all other robots tha t are also in the planning zone. This is done by periodically broadcasting the intended path through the intersection" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001215_ias.1997.643139-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001215_ias.1997.643139-Figure1-1.png", "caption": "Fig. 1 Doubly salient doubly excited VR machine.", "texts": [ " Whereas most high speed machines have self excitation capability, namely PM ,and Lundell generators, VR generators are inherently completely passive and have no internal excitation means. This study has investigated means by which excitation could be provided to self excite the VR generator thereby permitting easy stand-alone operation without the need for a 1,arge bulky exciting means. While VR generators have no self-excitation capability of their own, a separate stack and winding could be installed to provide its excitation riequirements during starting as shown in Fig. 1. The right hand side of this figure corresponds to the lamination stack of the main VR generator (viewed in a plane having one axis in the direction of rotor rotation). The left hand side of the figure shows a separate stator lamination stack into which is fitteld a small field winding. The armature windings of the VR annature are extended so that they also enclose the poles of the second lamination stack. Hence, field current applied to the field winding will induce voltages in the main armature windings which, in turn, can be rectified" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002807_iros.2007.4399285-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002807_iros.2007.4399285-Figure2-1.png", "caption": "Fig. 2. WL-16RIV (Waseda Leg \u2013 No.16 Refined IV) Fig. 3. Definition of coordinate systems and vectors", "texts": [ " In this research, we aim to develop a new stabilization control under unknown external disturbance caused by passenger\u2019s active dynamic motion. This disturbance compensation control consists of the following five key points: \u2022 Disturbance input discrimination \u2022 Waist trajectory computation \u2022 ZMP variation computation \u2022 Landing point variation computation \u2022 Foot trajectory computation A. Disturbance Input Discrimination To measure forces and moments caused by a passenger\u2019s active motion, we use a 6-axis force torque sensor placed between the passenger\u2019s seat and the pelvis (Fig. 2). However, when a robot carries a load or a human, the sensor also detects the inertia forces and the moments caused by them. These are not external forces, and a robot should not compensate for them. This is because inertia forces and moments caused by a load or a human are taken into account when generating a walking pattern. So, external forces are discriminated by subtracting the calculated inertia forces from the measured data. B. Waist Trajectory Computation When unknown external force acts on a walking robot, first the robot accelerates the waist so that a measured ZMP is equal to a reference ZMP", " Furthermore, we can see that time width is in inverse proportion to force strength roughly. Fig. 6 shows the recoverable region in changing the walking cycle, while the waist particle weight is constant. The shorter the walking cycle is, the bigger force strength the robot can adapt to in the same time width. Through the simulation, the effectiveness of the developed disturbance compensation control was confirmed. As an evaluation experiment, some walking experiments were conducted by using WL-16RIV (Fig. 2) under unknown external force. Firstly, to confirm the simulation result, we did fundamental experiments that a human pulled the robot carrying no loads forward and sideways while WL-16RIV stepped and walked forward. Then, the walking cycle was 0.78 s/step, and the peak force strength was about 70 N. In this experiment, the external force was not rectangular but a triangular, because a human pulled the robot and it was impossible to exert an impulse force. WL-16RIV realized a stable walk under such an external force" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003109_j.ijmecsci.2007.11.006-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003109_j.ijmecsci.2007.11.006-Figure2-1.png", "caption": "Fig. 2. Impulse \u2018free-body\u2019 diagram for a cue ball with forward \u2018English\u2019 spin striking a object ball initially at rest.", "texts": [ " Here, it is considered the case in which the cue sphere is launched with a forward spin, so that the vertical impulse acts downwards on the sphere 2, and upwards to the sphere 1. Accordingly, the sphere 1 jumps off the horizontal surface. As far as this effect does not affect significantly the horizontal components of velocity, the separation of the sphere 1 from the pool will be ignored in the following. In this scheme, the sphere 2 is submitted to impulsive forces resulting from its interaction with the horizontal surface. As schematized in Fig. 2, these forces can be described in terms of a main normal reaction impulse, N, and a frictional impulse, Ff , subsequently decomposed into its components in the x and y directions, Ffx, Ffy. Here N can be taken as equal to F tv, a condition that ensures that the vertical component of the centre of mass velocity of the sphere 2 is strictly equal to zero after the impact. Assuming that F tva0, so that the linear and angular velocities of the sphere 2 immediately after the impact will be given by m2v2x \u00bc v2 cos d2 \u00bc F n \u00fe Ffx, (9) m2v2y \u00bc v2 sin d2 \u00bc F ty Ffy, (10) m2Ro2x \u00bc \u00f05=2\u00deFfy, (11) m2Ro2y \u00bc \u00f05=2\u00de\u00f0F tv F fx\u00de" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000857_a:1016334307899-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000857_a:1016334307899-Figure1-1.png", "caption": "Fig. 1. Electrochemical cell overview and detail of electrodes and thermocouple in the alumina crucible.", "texts": [ " In summary, we will examine the electrochemical behaviour of sodium carbonate\u2013sulfate melts under conditions similar to those of kraft smelts as a first step towards a conceptual electrochemical causticizing process. The goal is to test the feasibility of electrochemically converting the bulk of the Na2CO3 and Na2SO4 to Na2O and Na2S. Dissolving a sodium oxide-containing melt in water will then yield the desired sodium hydroxide. Conversion of sodium sulfate to sodium sulfide will benefit the kraft process since sodium sulfate is an inactive deadload in kraft pulping. 2. Experimental details 2.1. Apparatus 2.1.1. Electrochemical cell A flanged Inconel reactor (20 cm i.d., 76 cm height) (\u2018a\u2019 in Figure 1) was inserted into a top loading furnace (model 56822, Lindberg, Watertown, WI) (\u2018b\u2019). The temperature of the bulk molten salts in an alumina crucible was controlled to 5 C as monitored by a K-type thermocouple (Omega Engineering, Stamford, CT) in a one-fourth inch round-bottom alumina well (Omega Engineering) (\u2018c\u2019). Multiple ports on top of the reactor were equipped with polypropylene compression fittings (Swagelok, Solon, OH) (\u2018d\u2019) to allow height adjustment of the electrodes, the purge port (Omega Engineering) (\u2018e\u2019) and the thermocouple well" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000372_oceans.1999.799732-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000372_oceans.1999.799732-Figure2-1.png", "caption": "Fig. 2 Schematic diagram for Twin Burger 2", "texts": [ " In this research, off-line training is used to avoid divergence in evaluation function and reach to a reasonable degree of convergence. K. Ishii, T. Fujii, T. Ura, and T. Suto (6-151 developed various kind of neural network structures for identification and also control of various AUV systems. lshii did the most recent work on system identification and he developed an independent model for each single degree of freedom of Twin Burger 2, which can be called as SDFNNI. Figure 1 shows Twin Burger 2, originally constructed in 1994 as a brother vehicle of Twin Burger 1 constructed in 1992. Figure 2 shows this vehicle schematically. The main specifications of this AUV system are listed in Tab. 1. In this research, we extend Ishii's model for coupled mode and also derive a system identifier for multi input-multi output system, named CMNNI. each layer. The processing of the i -th neuron of the n - th layer is given by: Table 1 The main specifications of Twin Burger 2 - Overall length Overall Breadth Overall Depth Dry weight Actuators Sensors - - - Computer system - Construction 0.76 m 0.62 m Depth sensor CCD color imaging system 8 channel ultrasonic range finder 2 flow meters
10xT800 Transputers with 16M RAM 4x T425 Transputers with 4M RAM I x AD TRAM 1 x DA TRAM IX RSTRAM 1994 II" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001805_elan.200402888-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001805_elan.200402888-Figure1-1.png", "caption": "Fig. 1. Schematic representation of the assembly of the two half-cells. Exploded view (left) and cross-section view (right). indicates that the source solution flow is perpendicular to the plane of the sheet.", "texts": [ " Ce st ( st/ so)C0 so st [M]b so (5) This latter condition is the condition under which metal speciation measurements should be performed. Since F 1 only when so st, the condition also implies thatVst Vso. Considering that mL volumes are often used for test solutions, microliter volumes are required for Vst which is readily achievable only by microtechnological means. An other reason of using very smallVst values is to decrease the accumulation time in the strip solution [19]. The cell is shown in Figure 1. It consists of three main parts: Electroanalysis 2004, 16, No. 10 \u00b9 2004 WILEY-VCH Verlag GmbH& Co. KGaA, Weinheim \u00b1 the strip half-cell (Figure 2) with the working microelectrodes WE (3 5 Ir-based Hg-plated square array), an auxiliary electrode of micro-size MAE (0.25 mm2 of iridium), part of the strip channel, a containment ring made of UV patterning Epon SU-8 that surrounds WE and MAE (dimensions: 2.8 0.5 0.28 mm) and a microfabricated structure also made of Epon SU-8 all around the chip to reach a good sealing and good mechanical stability", " 10 \u00b9 2004 WILEY-VCH Verlag GmbH& Co. KGaA, Weinheim PLMcarrier or solvent adsorb on these particles while metal complexes do not. This modified version of GIME is called adsorbing gel integrated microelectrode (AGIME). Both the WE and MAE are covered with the adsorbing gel which fills the containment ring. The small width of this containment ring insures a good mechanical stability of the gel. After 24 h conditioning of the gel in NaNO3 (10 1 M), the different parts of the minicell are assembled as shown in Figure 1. Complete assembly of the minicell takes less than 3 min, which minimizes the solvent evaporation. The source and strip channels are perpendicular to each other and the distance hst between the microelectrodes and the PLM is 480 20 m (Figure 1b). The effective receiving volume of the strip solution is estimated to be 0.8 L. The nature and properties of the PLM used here have been explained elsewhere. The carrier is a crown ether (1,10 didecyl-1,10-diaza-18-crown-6 (Kriptofix 22DD)) with laurate, LA, as lipophilic co-anion. Both 10 1 M 22DD and 10 1 M LA are dissolved in toluene/phenylhexane (1 :1). The source solution consists of 10 2 M MES (morpholinoethane-sulfonic acid) at pH 6.00 with varying concentration of Pb (II) and Cd(II). This buffer solution is non complexing for Pb and Cd [24], so that so 1" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001487_j.mechmachtheory.2004.05.004-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001487_j.mechmachtheory.2004.05.004-Figure5-1.png", "caption": "Fig. 5. The distance between two point-lines.", "texts": [ " (47) shows that the relationship between the endpoint offsets hA, hB, and hC is generally not the same linear combination as that of the point-lines. In planar cases (i.e. s \u00bc 0), the linear combinations of two given unparallel point-lines result in a pencil of point-lines 4 containing the two given point-lines. It can be observed from Eq. (47) that the pencil of point-lines has an invariant endpoint offset if hA \u00bc hB. The point-line operator may be used to evaluate the distance between two point-lines. Let A\u0302 and B\u0302 (Fig. 5) be two point-lines. Without losing generality, their reference points are assumed to be at the origin O of the reference frame. To calculate the displacement operator, the reference point should be changed from the origin O to a new point on the common normal s _ . Let M be the new reference point, whose position vector can be obtained by calculating the intersection point of two unit line vectors a _ and s _ (see Appendix A for detail). Then, the coordinates of point-lines A\u0302 and B\u0302 with respect to reference point M can be calculated by using Eq", " More specifically, h\u0302 states the dual distance between the two associated oriented lines, and Dh states the amplitude of the translation of the point-line along itself. Let the positions of a point-line be given by the direction cosines and the position vectors of the endpoint. This example shows how the point-line representations, point-line operator, the common-normal axis, the dual angle, and the amplitude of translation are obtained. The calculation concerning the Clifford algebra was accomplished by using CLIFFORD [1]. For the two positions A\u0302 and B\u0302 of the point-line shown in Fig. 5, the direction-cosine vectors a and b of the directed line and the position vectors E and F of the endpoints E and F are respectively as follows: a \u00bc 0:6287i\u00fe 0:7544j\u00fe 0:1886k; E \u00bc 1:0i 2:0j\u00fe 0:7k; b \u00bc 0:2403i\u00fe 0:9013j\u00fe 0:3605k; F \u00bc 2:0i\u00fe 0:6j\u00fe 1:5k: The unit line vectors corresponding to the initial and final positions, following Eq. (7), are a _ \u00bc a\u00fe ea0 \u00bc a\u00fe eE a \u00bc 0:6287i\u00fe 0:7544j\u00fe 0:1886k 0:9053ie \u00fe 0:2515je \u00fe 2:0118ke; b _ \u00bc b\u00fe eb0 \u00bc b\u00fe eF b \u00bc 0:2403i\u00fe 0:9013j\u00fe 0:3605k 1:1357ie \u00fe 0:3606je 1:6584ke: The endpoint offsets corresponding to the initial and final positions, with respect to the reference point at the origin O, are hA \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0E K\u00de \u00f0E K\u00de p \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0E a a0\u00de \u00f0E a a0\u00de p \u00bc 0:7481; hB \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0F L\u00de \u00f0F L\u00de p \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0F b b0\u00de \u00f0F b b0\u00de p \u00bc 1:5621: The point-line representations corresponding to the initial and final positions, following Eq" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003575_978-3-642-14515-5_77-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003575_978-3-642-14515-5_77-Figure1-1.png", "caption": "Fig. 1 Skeletal geometry of the human foot complex", "texts": [ " The objective of this study is to develop a novel 3D FE human foot model with more detailed subject-specific representation of all major musculoskeletal structures, which can be used to investigate the delicate interactions and responses inside of the foot musculoskeletal complex. IFMBE Proceedings Vol. 31 A. 3D FE Musculoskeletal Foot Modeling The skeletal geometry of the foot FE model was reconstructed from medical CT images (Lightspeed16, General Electric Company, Fairfield, U.S.A), which were obtained by scanning the right foot of a healthy male subject (age: 27 yrs, weight: 75kg; no history of lower limb injury or foot abnormalities) with a 1.5 mm slice interval. The images were segmented to obtain the boundaries of bones and soft tissue (see Fig.1(a)) by using Mimics 10.0 (Materialise, Leuven, Belgium). SolidWorks software (Dassault Syst\u00e8mes, SolidWorks Corp., U.S.A.) was used to process boundary surfaces to build solid models for each bone and the foot plantar soft tissue (see Fig.1(b)). To accurately locate the origins of some ankle plantiflexor muscles, femur and shank bones are also constructed (see Fig.1(c)). The solid bones were then imported and assembled in the FE software package ABAQUS (Simulia, Providence, U.S.A). Based on the foot skeletal model, a total number of 85 foot ligaments including plantar fascia were integrated into the model in the ABAQUS environment (see Fig.2). These ligaments were constructed by referring to the MRI images and the 3D human anatomy software: Interactive Foot and Ankle 2.0 (Primal Picture Ltd. U.K). Due to the complexity of the human foot musculoskeletal system, in previous foot FE studies, the muscle actions were either simplified as force vectors applied directly to the points on the bones or were totally neglected [8, 12, 16]" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001422_oxfordjournals.jbchem.a133832-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001422_oxfordjournals.jbchem.a133832-Figure1-1.png", "caption": "Fig. 1. Set-up for the preparation of microcapillanes. (1) Metal rod for holding the set-up. (2) Metal hollow needles (fixed to (1)). (3) Free end of the capillary. (4) Small gas burner. (5) Plastic \"sleeve,\" connecting the capillary and the piston rod. (6) Syringe cylinder. (7) Plastic sleeve fixed to (1) and serving as guide for (6). (8) Plastic ring, fixed to the cylinder and limiting its movement. (9) The syringe piston. (10) Sealed end of the syringe.", "texts": [ "com /jb/article-abstract/91/4/1435/787529 by G oteborgs U niversitet user on 17 January 2019 1436 R. TIROSH and A. OPLATKA sured in a pH-stat (Iff) and protein concentrations determined by the Biuret method. Preparation of Glass Mwrocapillaries\u2014Glass capillaries of 1 mm i.d. and about 4 cm length were heated at the center on a small gas flame and stretched so as to form a microcapillary path of 20-100 nm i.d. and 2 cm length. Better control of the stretching was achieved by the use of a syringe in the following way (Fig. 1): by pulling to the left the piston 9 of the syringe through the rod 5, a stretching force acting on the connected capillary is produced due to the sub-pressure inside the syringe. The capillary is \"guided\" by two syringe needles 2 and is manually held at its left end 3. The capillary is now heated in the region between the needles and upon softening will be stretched by a definite amount (usually 8 mm) which is determined by the initial pulling of the piston. The whole procedure is repeated for a second time with heating carefully performed at the narrowed part of the capillary up to the moment at which stretching starts" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003214_1.2839011-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003214_1.2839011-Figure2-1.png", "caption": "Fig. 2 Position workspace of the manipulator", "texts": [ " 130 / 044501-108 by ASME 7 Terms of Use: http://www.asme.org/about-asme/terms-of-use w s r 3 i c t a Y a w d P o c 0 Downloaded Fr q1 = y l2 \u2212 x + d/2 2 4a q2 = y l2 \u2212 x \u2212 d/2 2 4b l2 = x \u2212 l5 sin \u2212 d 2 2 + y + l5 cos \u2212 q2 \u2212 l6 2 4d here d is the width between two columns, l6 the height of the lider, and q1 and q2 the Y coordinate values of points D1 and D2, espectively. Workspace and Singularity The position workspace of the parallel manipulator 7,8 is the ntersection of two subworkspaces associated with two kinematic hains shown in Fig. 2. Each subspace is the region encircled by wo arcs with the radius of l. In Fig. 2, OiL and OiU are the lower nd upper limit positions of slider EiDi, and qiL and qiU denote the coordinates of OiL and OiU. The region Q1Q2Q3Q4 is the reachble workspace. Task workspace is one part of the reachable orkspace. In practical applications, the task workspace is usually efined as a rectangular area. As shown in Fig. 2, the rectangle 1P2P3P4 is the task workspace with width of 970 mm and height f 630 mm. The orientation workspace is \u221290 deg to 90 deg. Based on the method for investigating singularity 9 , it can be oncluded that when one of the limbs A1D1 and A2D2 is in a 44501-2 / Vol. 130, APRIL 2008 om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 08/27/201 horizontal position and/or when limbs A1D1 and A2D2 are collinear, the parallel manipulator reaches the singular configuration. In theory, there is no singularity in the task workspace" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003385_tmag.2007.916179-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003385_tmag.2007.916179-Figure6-1.png", "caption": "Fig. 6. PEEC mesh on the conductor.", "texts": [], "surrounding_texts": [ "We present in this paper a new formulation based on a PEEC-FEM coupling in order to model complex electromagnetic devices. This formulation is particularly well adapted for simulation of devices having a large number of conductors, typically for geometries where the PEEC method is very well suited. FEM allows taking into account ferromagnetic parts, without a great computational effort. Through a simple example, we have validated this new formulation and have shown some advantages with respect to a pure FEM method." ] }, { "image_filename": "designv11_32_0000039_bf02325718-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000039_bf02325718-Figure3-1.png", "caption": "Fig. 3--The compensated load cell", "texts": [ " The testing-machine load cell was therefore only used for machine control. A smaller load cell of 25-kN dynamic capacity was mounted beneath it. The compensation was applied to the 25-kN load cell. The machine load cell, which was stiffer than the 25-kN load cell by a factor of ten, was considered as part of the crosshead. A Bruel and Kjaer accelerometer, Type 4338, was mounted, axial with the loadstring, on the stud adaptor to the 25-kN load cell. The cable was led out through drillings in the stud, as shown in Fig. 3. Square steel plates, with steel blocks bolted to the edges, were attached to the lower flange of the load cell and to the end of the actuator rod, to simulate a pair of grips. The mass of each simulated grip was approximately 100 Kg. The reference specimen was mounted between these, as shown in Fig. 4. Two reference specimens were used, with stiffnesses of 1400 kN/mm and 550 kN/mm. A range of adaptors (studs and beams) was also used to reduce the stiffness of the second reference specimen, to a minimum of 4 kN/mm" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000364_robot.1988.12028-Figure17-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000364_robot.1988.12028-Figure17-1.png", "caption": "Figure 17: Translation Region after Lift-off.", "texts": [ " MANIPULATION PLANNING An object may be manipulated in an infinite number of ways to achieve a desired grasp. One way to begin is by choosing an initial grasp in the translation region. During the first instant of manipulation, i . e . lift-off, the second finger could be moved toward the object with the first finger held fixed. After lift-off, the translation window and the translation regions still exist and can be used for manipulation planning. The other liftabililty regions vanish with the third and fourth contact forces (see Figure 17). In a three-point frictionless grasp, stability is only maintained if the second contact is in the translation region. If the second finger's contact is kept within the translation region then as the fingers squeeze, the object will slide up the first finger, toward the palm. If two contacts are on a flat edge of a finger maintaining constant orientation, then the translation region does not change with respect to the object during translation. In this case the object may be pushed up the first finger by the second, simply by maintaining a constant orientation of the pushing link" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003008_j.mechmachtheory.2007.05.001-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003008_j.mechmachtheory.2007.05.001-Figure2-1.png", "caption": "Fig. 2. Illustrating the computation of the L2 distance.", "texts": [ " pconv A\u00f0z\u00de \u00bc pA\u00f0z\u00de, where conv\u00f0 \u00de denotes the convex hull of a set. 3. pA[B\u00f0z\u00de \u00bc maxfpA\u00f0z\u00de; pB\u00f0z\u00deg. 4. pR\u00f0A\u00de\u00f0z\u00de \u00bc pA\u00f0RTz\u00de, where R is a matrix denoting a linear mapping. 5. Suppose that A and B are subsets of Rn1 and Rn2 , respectively. Let z \u00bc \u00bdzT 1 zT 2 T 2 Rn1\u00fen2 , where z1 2 Rn1 and z2 2 Rn2 . Then pA B\u00f0z\u00de \u00bc pA\u00f0z1\u00de \u00fe pB\u00f0z2\u00de: Proof. The proof is straightforward. Detailed explanation of parts 1\u20134 can be found in [34]. h From Theorems 3 and 4(1), q\u00f0S1; S2\u00de can be computed by q\u00f0S1; S2\u00de \u00bc min zk k\u00bc1 fpS2 \u00f0z\u00de \u00fe pS1 \u00f0 z\u00deg \u00f013\u00de Eq. (13) is illustrated in Fig. 2. The functions pS1 \u00f0 z\u00de and pS2 \u00f0z\u00de together with the vector z determine a pair of parallel hyperplanes H 1 and H 2 that support S1 and S2, respectively, i.e., H 1 \u00bc fxj zTx \u00bc pS1 \u00f0 z\u00deg and H 2 \u00bc fxjzTx \u00bc pS2 \u00f0z\u00deg \u00f014\u00de The value of pS1 \u00f0 z) (resp. pS2 \u00f0z\u00de is the distance from 0 to H 1 (resp. H 2\u00de along z (resp. z). The value of pS\u00f0z\u00de is the distance from H 1 to H 2 along z. Thus q\u00f0S1; S2\u00de is the minimum value of the directional distances between all such pairs of supporting hyperplanes given by (14)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000361_amc.2002.1026960-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000361_amc.2002.1026960-Figure5-1.png", "caption": "Fig. 5 Simulation Result", "texts": [ " So when the A@ becomes zero, a center angle of a heel increases in proportion to a center angle of COM. The variables mentioned above are collected as Eq. ( 1 1 ) - (SCOMend 'COMstnrt ) T P = [ ~ c O M , r c O M ' r ~ , r - (el - e z ) , e G , ~ 4 ] ( 1 1 ) ' sCOM increases automatically according to falling forward, and other ,variables are controlled to each reference. The relationship between p and b is represented by 439 3. Simulation In the proposed method, a simulation of body posture control is conducted using a six-links model shown in Fig. 5. Each value, which is used in this simulation, is as fol lows. The desired paths and joint angles are obtained from following value. The controller becomes Fig. 4. The desired acceleration p2 is decided by a PID controller, the biped walking model with a free joint is able to track the desired body posture. Fig. 5 shows a stick graph of this simulation result. Each stick shows each link. At first, a support-leg of the six-links biped-walking model contacts at the origin. Then, this model shifis its position for the right side. The configuration is plotted until the swing-leg lands. Fig. 5 shows that the COM and the heel position of swing-leg track the desired circle path and the heel joints angles are controlled to the desired joints angles. 4. Experiment The 6-axis biped robot \"Ken\" has been developed as shown in Fig. 6 . This robot can use foot toe as a free joint and it has rotary encoders of the resolution 2500 440 (pulse/rev) at the toe to measure the angle between the foot sole and the floor. Dc servomotors with 1OO:l harmonic gears are used as the actuators of other joints, which have rotary encoders of the resolution 1000 (pulse/rev) on the motor shafts also" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001949_0003702041389300-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001949_0003702041389300-Figure1-1.png", "caption": "FIG. 1. Solid-phase disk holder configurations (A) without and (B) with N2 delivery.", "texts": [ "2 mm nylon membranes were obtained from SchleicherSchuell (Dassel, Germany). These membranes were dissected into 8 mm disks, and 3 mL of solution containing PABA in benzene were spotted. Depending on the specific experiment, 5 mL of heavy-atom solutions were deposited on the solid surface (with or without the previous addition of 5 mL of a-CD solution) and dried on a heating plate for 3 min at 30\u201340 8C before spotting the benzene analyte solution. The disk was then placed in a laboratory-constructed solid substrate holder (Fig. 1A), and the RTP spectrum was collected at 908. The holder is a metallic chamber covered with a low luminescence paint, with a hole where the disk is held in an optimized position with respect to the incident beam. In cases where N2 purging was applied, the configuration shown in Fig. 1B was used. This configuration is very easy to implement and consists of a usual quartz cell where an adequate support of expanded polystyrene was introduced. A gentle N2 flow was delivered from the top through a septum. A restraining pin was designed to hold the nylon in place. Solutions for calibration curves were obtained by convenient dilutions of the benzene standard solution and SS-RTP measurements were subsequently carried out by the procedure described above. AM1 Calculations. Geometry optimization was done with the AM1 program contained in the Hyperchem package, version 5", " Figure 5 shows a comparison between the spectra obtained from PABA spotted on a nylon disk, when treated with a-CD and iodide anion, and that corresponding to APPLIED SPECTROSCOPY 841 the background of a similarly treated nylon. As can be observed, the RTP intensity of PABA in the mentioned conditions is significantly stronger than the blank. Influence of Nitrogen Purging. Though SS-RTP signals are detected even in an aerated environment, a significant enhancement of the phosphorescence emission is observed when N2 is flushed into the sample compartment during about 2 minutes (see Fig. 1B). This result suggests that, although the solid matrix protects the triplet state of PABA, the elimination of oxygen favors the phosphorescence process.21,33 No significant improvement was found with a longer N2 treatment. Analytical Figures of Merit. The analytical figures of merit (AFOM) of PABA adsorbed on nylon under the different evaluated conditions were estimated. The obtained results are shown in Table I. The linear relationship between the amount of retained PABA and the phosphorescence intensity was corroborated applying the F test recommended by IUPAC" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000846_s10008-002-0267-6-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000846_s10008-002-0267-6-Figure1-1.png", "caption": "Fig. 1. Schematic representation of the apex of a cavity microelectrode", "texts": [ " PANi powderwas stored in a closedbottle in an air atmosphere. Theoverall formula, C24H20N4O4S, was identified from elemental analysis, which corresponds to the sulfate emeraldine salt: For the studies in hydrochloric acid, the sulfate ions were removed by passing a large amount of 1 mol L\u20131 HCl solution over the emeraldine powder. The resulting product was identified as C24H20Cl2N4. Electrochemical measurements Electrochemical measurements were carried out within a classical three-electrode cell. The working electrode was a CME schematized in Fig. 1. The diameters of the cavity of the electrodes used were 25 and 50 lm, the depth of which were 12 and 20 lm, respectively (for a detailed description of this electrode, see [26, 27, 28]). The cavity was filled with pure material grains (i.e. without any adjunction of additives such as graphite or carbon black) using the electrode as a pestle. As one of the redox states of PANi is a good electronic conductor [18, 19], no graphite or carbon has to be added to perform the electrochemical measurements" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003109_j.ijmecsci.2007.11.006-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003109_j.ijmecsci.2007.11.006-Figure1-1.png", "caption": "Fig. 1. Schematics for the impact between billiard balls.", "texts": [ " This formulation incorporates, following Marlow [22] and Alciatore [23], friction with the pool and extends prior studies on billiard-ball collisions [24], and ball rebounds on horizontal rough surfaces [25] where a discontinuous model based on the formulations of Brach, and Kane and Levinson was discussed. In agreement with literature [2\u201325], the coefficients of restitution and friction will be taken here as material-dependent, velocityindependent constants. Experimental data on steel, rubber, and regulation billiard balls are used in addition to some literature data for testing the proposed relationships. Let us consider the collision between two homogeneous spheres moving on a flat horizontal surface. As schematized in Fig. 1, a normal-tangential coordinate system is chosen such that the line through the sphere centres is the normal axis \u00f0x\u00de. The tangential axis \u00f0y\u00de is perpendicular to the normal axis and lies in a horizontal plane parallel to the supporting surface. The z-axis is defined by the outward direction normal from the supporting surface. It is assumed that the cue sphere 1 is projected with a linear velocity vo against the object sphere 2 which is initially at rest. We consider the case in which a forward horizontal spin, oo, with components oox, ooy, along the x, y, axes, and a vertical (or pivotment) spin, ooz, along the z-axis are imparted to the cue sphere", " Taking initial angular velocity components o2x\u00f00\u00de \u00bc 0, o2y\u00f00\u00de \u00bc 0, oox \u00bc oo sinc, ooy \u00bc oo cosc, the corresponding values after the impact will be, o2x \u00bc 0, o1x \u00bc oox \u00bc oo sinc, and RF tv \u00bc I1\u00f0o1y ooy\u00de \u00bc I2o2y, (3) RF th \u00bc I1\u00f0oz1 ozo\u00de \u00bc I2oz2. (4) Notice that this formulation can easily be applied to billiard-ball collisions taking M \u00bc 1, and to describe the rebound of a sphere against a rough, infinitely massive vertical plane taking M \u00bc 0. Introducing the angles of impact and scattering depicted in Fig. 1 and taking M \u00bc m1=m2, Eqs. (1) and (2) can be rewritten as M\u00f0vo cosc v1 cos d1\u00de \u00bc v2 cos d2, (5) M\u00f0vo sinc v1 sin d1\u00de \u00bc v2 sin d2. (6) The inelasticity of the impact can be described, as usually, in terms of the \u2018normal\u2019 coefficient of restitution, e, defined as the negative ratio between the normal components of the relative velocity of the points of contact after and before the impact. In the studied case this definition yields e \u00bc \u00f0v2 cos d2 v1 cos d1\u00de=vo cosc. (7) Accordingly, the normal impulse can be expressed as Fn \u00bc m1 1\u00fe e 1\u00feM vo cosc", " For the spin about vertical axis one can write m2Roz2 \u00bc m1\u00f0Roz1 Rozo\u00de \u00bc \u00f05=2\u00deFth. (13) As a result of the impact, the spheres are projected along the horizontal plane with a combination of translation and rotation motions. Then, friction with the horizontal surface determines, as described by Hopkins and Patterson [26], that the spheres describe curved paths until the pure rolling motion is finally established. This situation corresponds to rectilinear motions defining post-transition angles, W1, W2, as shown in Fig. 1. The law of angular momentum yields, for the centre of mass velocities when pure rolling motion is reached, vnjx \u00bc Ron jy, vnjy \u00bc Ron jx \u00f0j \u00bc 1; 2\u00de : Rmj\u00f0v n jx vjx\u00de \u00bc I j\u00f0on jy ojy\u00de and Rmj\u00f0v n jyx vjy\u00de \u00bc I j\u00f0on jx ojx\u00de, so that vnjx \u00bc \u00f05=7\u00devjx \u00fe \u00f02=7\u00deRojy, (14) vnjy \u00bc \u00f05=7\u00devjy \u00fe \u00f02=7\u00deRojx. (15) Combining the above equations, one can obtain velocityindependent equations for post-collision and post-transition angles in function of the angle of impact, the mass ratio, M, and the coefficients of restitution and friction (vide infra) providing that appropriate force laws are used", " Two-sphere collision experiments involving rolling without spin prior to impact were performed with steel bearings, billiard ball and rubber balls. Experimental data provided a satisfactory agreement with predictions from the previously described models, the best fit between theory and experiment being obtained for the values of the coefficients of restitution and friction listed in Table 1. Fig. 8 shows a typical photograph recorded on a billiard pool, providing an image comparable with the scheme depicted in Fig. 1. Fig. 9 compares experimental data values of tan d1 (a) and tan W1 (b) vs. tanc with theoretical predictions for the oblique impact of rubber superballs. ARTICLE IN PRESS Table 1 Values for the coefficients of restitution and friction for the studied materials determined from the best fit between theoretical equations (23), (24), (40) and (41) and experimental data Billiard balls Steel bearings Rubber balls Billiard balls (Ref. [23]) Ball\u2013ball coefficient of restitution 0:97 0:02 0:92 0:02 0:88 0:03 0:93 0:03 Ball\u2013ball coefficient of friction (dynamic) 0:07 0:02 0:14 0:02 0:60 0:03 0:06 0:04 Ball\u2013ball coefficient of friction (static) 0:18 0:03 Ball\u2013table coefficient of friction (dynamic) 0:15 0:02 0:15 0:02 0:55 0:03 0:10 0:05 Comparison from the values recently provided by Alciatore [23]" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002603_0022-4898(73)90138-9-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002603_0022-4898(73)90138-9-Figure5-1.png", "caption": "FIG. 5. Loaded plate analogy and wheel load.", "texts": [ " soil response behaviour) are suitably related and modified through some correlating function. Thus, if one can describe or evaluate the response function characteristics, and if the correlation functions are known, it becomes obvious that the surficial load parameters will be identified and accounted for. The simple analogy of a loaded plate (for simulation of wheel loading) of like contact area produces pressure-sinkage relationships not unlike those used in conventional bearing stability analyses. Figure 5 shows the required response from the Loaded plate Soil surface, /-\" i .. ..)//.__ J 0 and GI > 0 are the PI feedback gains. It should be pointed out that the integral term is not necessary but it improves the steady-state error. From (16), (24), and (25), one can obtain the error dynamics as (GF + 1)ef + Gref = 0: which is stable provided that the gains are positive definite, i.e. F(t ) + F,( t ) as t + 00. VII. SIMULATION RESULTS In this section, we describe the results obtained from simulation of a typical five-bar mechanism, as shown in Fig. 1. The closed-loop is cut in the right hand support, i.e. point A in Fig.1, and translation motion of point A is prohibited by imposing constraint equations. The constraint error is controlled by the NewtonRaphson method -where the error tolerance is E = Assuming that the gravity is the only applied force, the linkage falls from its initial condition at q o = [2.1 1.89 1.46 1.89IT and q o = 0. Given L = 1, the Jacobian matrix is singular at position q = [K 0 K 0IT. Trajectories of joint angles are shown in Fig. 2A. As expected, the mechanism goes through the singular configuration that is clearly evident from the spike in the graph of the condition number of the Jacobian matrix in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002642_13506501jet276-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002642_13506501jet276-Figure1-1.png", "caption": "Fig. 1 Experimental apparatus", "texts": [ " The current study presents the detailed comparison of experimental and numerical results obtained with a single dent located within an EHD point contact. Thin film colorimetric interferometry (TFCI) is used to obtain film thickness distribution from chromatic interferograms. Obtained results are compared with data provided by a numerical solver for the contact problem that was developed and tested. Experiments were carried out using an experimental apparatus consisting of a high-pressure ball on disc tribometer equipped with a microscope imagining system and a control unit [24]. In the tribometer (Fig. 1), a circular EHD contact is formed by loading and rotating a steel ball against a flat surface of chromium coated glass or sapphire disc. Both the ball and disc can be independently driven by servomotors to achieve different slide to roll ratios. The glass and sapphire discs have 150 and 110 mm in diameter, respectively. Their surfaces are optically smooth. Properties of contacting bodies and lubricants used in this study are given in Table 1. Experimental data for the comparison with numerical simulation were chosen from different series of experiments when various materials of the disc and types of lubricant were used for smooth and dented surface" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003261_amc.2008.4516095-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003261_amc.2008.4516095-Figure2-1.png", "caption": "Fig. 2. Robot with (a) zero turning radii, (b) actual turning radii, RT", "texts": [ " Let us also focus on achieving one goal and avoiding obstacles along the way. A robot has many sensors that contribute to the \u201coverview\u201d of an environment. Feedback needs to be assessed in real-time to adjust the course of the robot. Two things need to be considered for path alteration: turning radius and size of the dynamic window as described in [13]. The specific algorithms for real-time obstacle avoidance are beyond the scope of this paper. Therefore, only key points will be discussed for completeness of the O 3 techniques. As shown in Fig. 2(a), the easiest approach is to assume the robot is a point position and can change its course at any time. However, when implemented, this is not often the case as seen in [3]. As outlined in [1], a dynamic window is common among implicit algorithms for obstacle avoidance. The sensors available on the robot govern the exact dimension of this window. These can include laser range finders, sonar, machine vision, and magnetic/GPS positioning. An example of the window approach is seen in Fig. 3. Depending on the sensors used, only certain directions may need monitored (i" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002278_09544097jrrt75-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002278_09544097jrrt75-Figure8-1.png", "caption": "Fig. 8 Two-dimensional simulation model \u2013 kinematics and definitions", "texts": [ " This model is validated by comparing the results from laboratory tests, according to section 3. Further on, it should be possible to identify and simulate phenomena that are specific to the present test rig and to make approximate corrections in the test results for such phenomena. Finally, by comparing the results from simulations with those of laboratory tests, it should be possible to identify at least the order of magnitude of unknown parameters. A two-dimensional mechanical system is considered as shown in Fig. 8. The links and end bearings are assumed to be massless. Elastic deformations of the link as well as the loading mass assembly are considered. The actual position of the loading mass centre of gravity (c.o.g.) is described via a vector q. As the geometry of all the components in the system is known, vector q can be written as q \u00bc A1 \u00fe A2 B1 \u00fe B2 \u00fe C \u00fe D1 D2 E1 E2 \u00fe F\u00fe VflexC \u00fe VflexF (1) where the vectors A1, A2, E1, and E2 describe the geometry of the bearings, B1, B2, D1, and D2 the contact surfaces of the link, jCj the nominal length of the link, and F the position of the loading mass c", " force perpendicular to link Fcyl force in hydraulic cylinder Fj1, Fj2 tangential forces in contacts 1 and 2 g gravitational acceleration ( \u00bc 9.81 m/s2) G vector from lower nominal end bearing centre to connection point of hydraulic cylinder H hydraulic cylinder vector J moment of inertia of loading mass assembly k12 k3 tangential stiffnesses km lateral structural stiffness of loading mass assembly klink resulting lateral stiffness in links, end bearings, and contacts K secantial stiffness as defined in Fig. 19. m mass of vertical loading N1, N2 normal forces in contacts 1 and 2 Pij vector from points i to j (points 1\u20136 defined in Fig. 8) q vector from origin to centre of gravity of loading mass, including elastic deformation VflexC vector of elastic deformation in links, end bearings, and contacts VflexF vector defining elastic deformation in loading mass assembly ai angle of the position vectors, i \u00bc A12H wB2, wD2 angles m01, m02 friction coefficient, contacts 1 and 2 Definitions Stiffnesses are defined according to Fig. 19 Tangential stiffness ki \u00bc dF dx Sectioni i \u00bc 1, 2, 3 Secantial stiffness K \u00bc F0 x0 Proc. IMechE Vol. 220 Part F: J" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000364_robot.1988.12028-Figure10-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000364_robot.1988.12028-Figure10-1.png", "caption": "Figure 10: Translation Region for a Vertex.", "texts": [ " cos(w1) C O d V 1) < t2 < cos(yr1) ( 1 3 These inequalities define the translation, T, region in which squeezing with the second finger causes the object to translate along the first finger breaking both support contacts. In Figure 9, the translation region is indicated by the double bold line. An interesting property of translation regions is that the internal grasp force required to lift the object is constant throughout T for a given edge. The translation region for a vertex is determined by substi tuting equation (1 1) into inequalities (13). (14) and (15) (see Figure 10). 2.4 Graphical Construction A graphical method to determine the liftability regions of any planar curve with or without vertices for two- and three-point initial grasps has been developed based on the above analysis. It is best to illustrate the method with the following example. First, the perimeter of the object is partitioned into the regions I and I1 which are delimited by the points on the curve whose normals are vertical. The region, I, is the set of curve segments for which all normals have a component in the negative x-direction, excluding the curve segment between the supporting contacts" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001215_ias.1997.643139-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001215_ias.1997.643139-Figure2-1.png", "caption": "Fig. 2 Showing side view of excitation when employing permanent magnets.", "texts": [ " In general, the VR generator power is fed to a hard variable PWM converter and from there to a dc link capacitor. Hence, once the required excitation is supplied for a brief period, the dc link capacitor could be charged by extracting energy from the prime mover. After the field winding current is removed, both stacks could be used for electromechanical energy conversion in the usual manner. As an alternative to the use of a wound field winding, magnets can be placed on the core of the second lamination stack as shown in Fig. 2. Excitation of the machine takes place in much the same manner as before. However, in this case, the magnet cannot be \u201cturned off\u2019 and must remain in the armature winding circuit at all times. The magnets must now be sized to withstand the effects of armature reaction. While the magnets may become a problem at high speeds in which the emf they produce equals or exceeds the associated converter voltage capability, they could be sized so this situation would not occur. With proper sizing of the magnets, their magnetization of a portion of the machine could be used to produce additional useful permanent magnet torque", " 6 (a) shows the self inductance Ls of the variable reluctance machine when one of the rotor poles is aligned to the stator pole, and Fig. 6 (b) and (c) when the rotor pole is 20 and 45 degrees, respectively, away from the aligned position. The finite element analysis study was carried out also for the doubly salient permanent magnet machine to obtain (1) magnetic flux in the stator poles per unit core length and (2) the machine parameters, The doubly salient permanent magnet machine has the exactly same geometric dimensions as the variable reluctance generator. Two permanent magnets are placed in the stator yoke as shown in Fig. 2. The permanent magnet of Nd-F,-B with the remnant induction Br of 1.1 T was assumed for this analysis. Figure 7 shows the magnetic flux distribution when the machine is excited by the permanent magnet. The magnetic flux inside of one of the three phase stator poles of the machine per unit core length versus the rotor position i.s plotted in Fig. 8. Fig. Fig. 5 Finite element analysis result to show the magnetic flux distribution of the variable reluctance generator with the hase 2 excitation, where the rotor is rotated lf mechanical degrees from the aligned position" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000432_s1474-6670(17)37890-4-Figure9-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000432_s1474-6670(17)37890-4-Figure9-1.png", "caption": "Fig. 9. Front view", "texts": [], "surrounding_texts": [ "The control group at the Department of Automation and Control has quite a long tradition in real time experiments as well as in using and developing of the various teach ware. The first computer experiments were accomplished in 80s using the process control computer RPP-16 and the mini-computer Hewlett Packard 85 equipped with additional AID, DI A converters. In that time, Basic was the main programming language. Several electromechanical and thermal plant models have been controlled. Later, the SUN-Workstation period started. The simulation software changed to using of CC and Simnon tools and also own software - SimulC has been developed. Gradually, the top position among all other software gained Matlab/Simulink. The effort was oriented to the development of own toolboxes and support programmes. In this way, the new software was developed e.g. for the design of fuzzy controllers, which enables faster and more comfortable editing of fuzzy rules and membership functions. In the last period our attention was dedicated to the development of real time experiments under real time Matlab toolbox and workshop. The plant models are being made accessible to students and colleagues via Internet. The other very often used tool is Maple V, which enables symbolic calculation and analytical design of control algorithms. 2. EXPERIMENTS IN CONTROL EDUCATION The necessity of learner experimental work in laboratories represents one important aspect of engineering education. Students solve practical problems and gain experience and practice needed for their future career. At the Department of Automation and Control students start with subject System Theory in the 2nd school year. In this phase of study, they are working mainly with simulation models in the Matlab environment. In the previous years the subject was too theoretical and so students had difficulties to see its practical importance for their study. Introduction of real systems increased transparency of the solved examples. Similar situation exists also in the subsequent subject Theory of Automatic Control. In the 3rd year of study students have already possibility to start the work on their own projects and they can choose, except of other topics, e.g. the design of animated models and their control algorithms or the control of real plants. The real systems are used for illustration of various problems also in the subjects Nonlinear Control and Synthesis of Nonlinear Control. The main motivation for using of plants in the educational process is clear physical \"visibility\" of the controlled dynamics, and also the necessity to exercise all design steps starting with the plant identification and ending with the evaluation of the control results achieved with the particular model. Students like such control education. Unfortunately, the number of students is high in comparison with the number of available real plants. A possible solution of this problem is building of remote and virtual lab that gives learners access to laboratories via Internet (Fig. 1 ). Fig.l. Experiment control with the real plant through Internet The model development is running in two directions: 1. design of virtual devices 2. design of real physical plants In the first case, the effort is to develop virtual systems using animated models accessible also through Internet. So, students are not restricted to be present in the university laboratories. Another point is that students do not need to install simulation software at home, they can perform a part of their work through Internet by means of specially developed web pages (Fig.2) HTML document User Interface - theory (VI) enabling - examples of the computations user interacion Math model with <;rnl1h';nn simulation JAVA ..-J'..... f--..!U!J annlUllu.....et--l ay - results Visualization - animation animation - displaying variables interaction Fig.2. Schematic structure of developed pages In the second case, the use of real plants brings more complex contact with controlled systems. However, it is more cost and place demanding. The technical requirements and maintenance of such devices are also higher. For each particular design, the problems of the state reconstruction, measurement quantisation and control signal limitation will be taken into considerations. 3. ANIMATEDMODELS As it was already indicated before, the idea is to offer to students a simplified mathematical model of a system in graphical animated environment and to give them possibility to choose own system parameters and control constraints and to run own simulations. They are used as a preparation for real time experiments. By playing with animated model students can increase the theory understanding. In the following, examples of the animated models are presented. 3.1. Two tank system The two tank system belongs to the basic plants usually used in educational process. It is not very fast and enables to verify a wide spectrum of control algorithms. Fig.3. Two tank model The system model (Fig.3) can be described by equations where Si are the tank areas and Ui are flow factors . The plant parameters have been identified as follows S: = 2.025\u00b7 1O-'m2 , S2 =2.02S \u00b7 1O-'m\" a; = 2.08.10-5 m 2s-: ,a2 = i.63 .10-5 m:'s-: 3.2. Racket attitude control The simplified model of the \"attitude control problem of the racket\"' is sketched in the Fig. 4. Fig.4. Sketch description of the racket attitude model Parameter () is an angle denoting deviation of the racket from its vertical position (output variable), f3 is the trust angle (controlled variable) and a denotes the thrust vector. Parameter L determines the distance between the thrust and the racket center of gravity. The control aim is to achieve and to keep the vertical position of the racket. The rotation around the vertical axis will be neglected. In fact, one should consider a rotation around two horizontal axes. However, since the control problem is equivalent and autonomous for both axes, only one horizontal axis can be taken into account. The thrust angle f3 can be changed only by constant velocity \u00b1R according to W=Ru whereby the action value is u E { -1, 0, + I}. After denoting the moment of inertia of the racket as I, the racket attitude dynamics can be described as I (j = aL sin~ For small angles ~ it holds sin~ == ~. After a simple manipulation one gets ii = a.L WI I = (aLRI I)u For I=const., the whole dynamics of the system can be described by the tripple integrator. Controller (time optimal action (racket altitude) L-=-_~ value L-.-----,--' angle of the thrust an!!le velocity Fig.S. Control structure for the racket attitude model For the state vector x = (0 , e,ii) the model is modified to 1 o o ~l [:: 1 + [ ~ 1 u, I u I ~ 1 o X3 aLRI I Up to now, the bang-bang time optimal control algorithm has been applied as the pre-programmed solution (Fig.5). Nowadays, we are developing the modified pole assignment control algorithms respecting the given amplitude and rate constraints. The described animated model is accessible through Internet. There is possible to change the setting of some parameters, as the moment of inertia I , the thrust a and the velocity of the change of the thrust angle R. During the simulation students can follow the control signal and also all state variables. (Fig.6) Predefined parameters for simulations: Initial error of the racket attitude: ~o = 0.0649 rad Thrust: Velocity R: Length L: Moment of inertia: a = 2 500 000 kgms\u00b72 R = 3.491e-3 rads\u00b7l L=30m I = 30 000 000 kgm2 Fig.6.Web page presentation of the racket attitude control 4. REAL PLANTS One of the main streams in the development of the contemporary control theory is obviously represented by the nonlinear control. In order to be able to \"touch\" and evaluate the newest control techniques, several plant models with typically nonlinear behaviour have been built. The aim was to offer to students various types of systems regarding their physical nature and their dynamics. In following it is possible to find short description of the available systems. 4.1. Two tank system Short introduction as well as dynamics description of this model (Fig. 7) was already done in the chapter 3.1. Fig.7 . Two tank plant Technical parameters of the real plant: Liquid Pump APO 050-01 Pump motor Up = +1- 24 V; Imax = 2 A; Liquid position sensor: capacity principle measured range of the liquid level ~h = 0-320mm range o/the capacity change Cx =0-1150pF/~ =320mm output sensor voltage input Input voltage supply pump amplifier liquid position sensor Uc =0-10 V/~h = 320 mm Ux =+15V;Ix = 1 A; Urn = +/- 18 V; Im = 5 A; Ux = +15 V; Ix = 1 A; The system offers wide spectrum of tasks which can be solved by students. Manual control, is relatively easy practicable, but tedious. The analytical design methods require to start with identification of this stable nonlinear system (analytical identification combined with experimental identification of particular nonlinear terms by planning experiments curve fitting, step response analysis, noise analysis) . After, they can start to verify various methods of linear control (LQ control based on linearization around fixed operating point, pole assignment control, PID control) or nonlinear control (generalised exact linearization, constrained control, anti-windup PID control). Students can compare these analytical design methods with the fuzzy, neural or adaptive control algorithms. 4.2. Magnetic levitation system It is a unstable nonlinear dynamic system with one input (current flow which influences magnetic field intensity) and one output (position of the steel ball). (Fig.8) The plant model is provided by Humusoft company. The motion equation is based on the balance of all forces, i.e. gravity force Fg, electromagnetic force Fm and the acceleration force Fa Fa = Fm -Fg Fg =mg; i-coil current [A] kc - coil constant mk - ball mass [kg] x - ball position [m] Xo - coil offset [m] g - gravity constant [ms\u00b72] Students can again exercise the manual control or some non-analytical way of controlling, e.g. fuzzy control. Another possibility is to use linear control (PD and PID control based e.g. on the generalised method by Ziegler and Nichlols) or nonlinear control design (based e.g. on the generalised method by Ziegler and Nichlols, exact linearization method (Isidori, 1995), control of constrained systems). However, in this way, it is necessary to start with identification of an unstable nonlinear system (steady state plant characteristic - curve fitting, step response analysis requiring closed loop stabilisation of the starting position and elimination of the measurement noise by multiple measuring). Electromagnetic reel Inductive position sensor Fig.8: Sketch description of the magnetic levitation model. 4.3. Helicopter model The helicopter rack model is representing one of the popular non-linear educational control problems. The model presented here is of our own production. It consists of a body situated on a base support. The body (carrying two DC motors with propellers) has two degrees of freedom. The axes of the body rotation, as well as those of the motors are perpendicular each other. The rotating propellers which are driven by DC motors influence both body position angles, i.e. the azimuth angle in the horizontal and the elevation angle in vertical plane. Incremental rotary sensors (lRC) measure both angles of the helicopter. The range of body rotation is \u00b148 degrees in elevation and \u00b1175 degrees in azimuth. Rotation of propellers are also measured by incremental sensors which provide frequency signal about their angular speed. The propellers are driven by DC motors feld by power amplifiers, which are integrated on the interface board. Power amplifiers are activated by output analogue signals from the superior level (PC with proper acquisition card). Main motor (elevation motion) controlled by signal 0 .. + lOV rotates only in one direction. Side motor (azimuth motion) rotates bi-directional and is controlled by signal \u00b11O V. Interface board includes also current sensors of both motors. Measured currents are represented in analogue form (\u00b15V DC). The interface board requires supplying voltages \u00b112V DC, +5V DC (available directly from acquisition card of PC), and 24-30V DC for motor supplying. The approximating helicopter model can be described by following differential equations: dWR I ( . k ' .1 \\....,2 ) -- =-\\CuRlR - M~lg'/J\\WRJ-UR -cJIRWR dt JR dqJH --=WH dt dWH 1 . J \\,.2 1 . -- =-(-kF~lgr\"WR!-URdR +-CuS1S- dt iH 2 -c!liIwH +mc COSqJH(gt!r -dlr03 sinqJH)) dws 1 ( . k . J \\...,2 ) --=- \\CuSIS - MSS1gr\"WS!-US -CpSWS dt is dCfJv \"dt=w.; dw.; \"dt = iv +mcdl cos2 qJH . J \\,.,2d 1. (kFsslgr\"Ws!-Us S COSqJH -- Cu~R COSqJH + 2 +2mcdlw.;wH sinqJH cosqJH -c.uvw.;) y = (qJH'CfJv r Its parameters were identified as follows Rotor R CuR=O.02 NmA-1 C~R= I.4Se-6 Nms dR=O.3II m JR=2.ge-S kgm2 2 kMR=6.S4e-8 kgm 2 kFR=3.4e-6 Ns Rotor S Cus=O.066 NmA- 1 c~s=4.ISe-6 Nms ds=O.279 m Js=4.5Ie-S kgm2 Horizontal axe c~H=6.7Se-8 Nms JH=8.57e-2 kgm2 Vertical axe c~v=2.6Se-8 Nms Jv=3.92e-2 kgm2 kMs=7.2Ie-8 kgm2 kFs=1.2Ie-S Ns2 mG=O.87S kg g=9.8I ms-I At the controller design of this system, students usually start with manual control. They are usually not able to take the helicopter near to the desired position. Again, it is a good motivation for the choice of automatic control. By its highly nonlinear dynamics, the helicopter-rack model gives an unique possibility to demonstrate basic features and limits of different linear control (LQ control based on linearization around fixed operating point) and nonlinear control concepts. For this purpose at least two different approaches are usually applied. The 1st one is based on the traditional linearisation around the working point. Limitation of this method for a higher state deviation from the working point are shown. The 2nd verified method is based on the application of the Byrnes/lsidori normal form. Since the standard procedure is not directly applicable due to the unstable zero dynamics, a simplified version of the controller design (Zimmer, 1995) can only be treated. Fig.! O. Birds-eye view ds For each particular design, the problems of the state reconstruction, measurement quantisation and control signal limitation are taken into considerations. Except of this the identification of an unstable nonlinear system (analytical identification combined with experimental identification of particular nonlinear terms by planning experiments - curve fitting, step response analysis requiring closed loop stabilisation of the starting position, measurement & quantization noise analysis) has to be done. The use of some kind of fuzzy or neural control represents an alternative to the above analytical design methods. 4.4. Mining Lift The mining lift (Fig. 1 I ) represents an own development. It is a strongly non-linear system with variable parameters. The main task of the lift control is to ensure fast and also smooth movement of the lift carriage without any oscillations. The total length of the elastic lift cable is variable in wide range. Also tension in the cable is changing during the transition, what causes non-uniform take up (with respect to the length). That strongly changes dynamic and static properties of the system. Pulling and releasing lift cable is realized by DC motor with take up reel. The motor is equipped with incremental position sensor and analogue speed sensor. Power amplifiers driving the DC motor are activated by output analogue signal (\u00b110V DC) from the superior level (PC with proper acquisition card). Fig.II Mining lift model Carriage of the lift moves vertically in linear frictionless bearing. Position of the carriage is measured by contactless photo sensor. Measured information can be provided to the interface board directly through fine spidery tape wires, which can cause increasing scrape friction. Better performance of carriage position transfer provides infra light transmitter (from the carriage) + receiver (on the base of the lift). Processing, encoding and decoding position signal is realized by micro controllers. Position information of the carriage and angular position of motor are provided in digital form (absolute or unitary code) to superior control unit. Analogue signals about actual speed and current of the motor are available as well (\u00b15V DC). The interface board requires supplying voltages \u00b112V DC, +5V DC (available directly from acquisition card of PC), and 24-30V DC for motor supplying. Electronics with infra-transmitter on the carriage are supplied from mini battery (2,7 .. 6V DC). The simplified model of the mining lift is sketched in the Fig.12. III m 1=10+11 Fig.I2: Sketch description of the mining lift. The system can be described by 2 differential equations d 2Z dl /-Io-R({J m-+b-+k =mg dt 2 dt I d 2({J d({J . I-Io-R({J J--+B-=Cul-kR-----=--- dt 2 dt whereby parameters were identified as follows Motor: Rm=3,2Q cu=O,13 Vs B=O,OOI Nms R=O,02 m Load: k=50 kgms\u00b72 10=2 m Lm=5,4 mH 1=2,9.10-4 kgm2 g= 9,81 ms\u00b7 2 b=O,8 kgs\u00b7 1 m=O,3 kg The system offers a wide spectrum of tasks. Except of manual control which is not easy practicable it is identification of a marginally stable nonlinear system (analytical identification combined with experimental identification of particular non linear terms by planning experiments - curve fitting, step response analysis, measurement & quantization noise analysis), linear control (LQ control based on linearization around fixed operating point), nonlinear control (generalised exact linearization, constrained control, anti-windup PID control) or fuzzy control with neural control." ] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure5.14-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure5.14-1.png", "caption": "Fig. 5.14. Cosine error", "texts": [ " When there is a variation in the air refractive index, a deadpath error may manifest in an apparent shift of the zero point, resulting in poor machine repeatability. Figure 5.13 shows an example of a deadpath error. To minimise this error, the interferometer optics <2> should be placed as close as possible to the retroreflector <5> without allowing them to touch. Cosine error arises when the laser and the desired measurement axis are not straightly aligned, so that the recorded measurement is shorter than the actual travel of the machine. The error increases with the travel distance and the misalignment. An exaggerated illustration is given in Figure 5.14 5.6 Factors Affecting Measurement Accuracy 143 The accuracy of an angular measurement can be affected even by a small change in the distance between the retroreflectors. The distance between the retroreflectors needs to be known precisely in order to convert the two linear measurements into an angular one. This change can occur due to variation in the temperature of the angular reflector housing. To minimise this error, excessive handling of the angular reflector, or contact with temperature varying medium should be avoided or minimised" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003707_kem.433.49-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003707_kem.433.49-Figure4-1.png", "caption": "Fig. 4 Titanium sheet metal heat shield assemblies containing SPF and SPF/DB components", "texts": [ " This geometry is used to provide more thermal protection for the structure above the engines but no longer allows a simple bent piece of sheet metal to act as the part. When heat shields were being developed for a twin aisle airplane, castings were the initial choice. However, the benefits from using sheet metal on the single aisle program convinced the designers to pursue a sheet metal design. Assemblies of sheet metals details are used to produce this structure. These assemblies contain single sheet SPF details as well as two-sheet SPF/DB components as shown in Fig. 4. A portion of these details are produced using a fine grain version of the 6Al-4V alloy which is described in more detail in the next section. SPF and SPF/DB of Fine Grain 6Al-4V Titanium [1,7]. Typically, 6Al-4V material, with a grain size of about 8 \u00b5m, is the alloy of choice for SPF and SPF/DB titanium components. A fine grain version of 6Al-4V, with a grain size of about 1 \u00b5m, has been jointly developed by Verknaya Salda Metallurgical Production Association, VSMPO, in Russia and Boeing. This alloy superplastically forms at approximately 775\u00b0C" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003422_med.2008.4602072-Figure9-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003422_med.2008.4602072-Figure9-1.png", "caption": "Fig. 9. The 100-gram Oscar II aerial robot controls its yaw turn visually by acting upon its two propellers differentially [17]. The two propulsion units are driven via the dual sensorless speed regulator described here, which acts as a speed governor for each propeller independently. The actual version of the robot is shown in the inset.", "texts": [ " Insensitivity to supply voltage variations Figure 8 shows another major benefit of the speed regulator, namely its ability to compensate for the drop in battery supply voltage.The ability of the speed regulator to reject large supply voltage variations, avoids the need for adding a bulky DC-DC power regulator on-board the MAV, while permitting the flight time to be extended under nominal conditions. To illustrate the beneficial effect of having a speed regulator on each propeller axis, we mounted the 1-gram dual speed regulator onboard the miniature Oscar II robot shown in figure 9. Oscar II is a 100-gram aerial robot developped in our laboratory to test various visuomotor control strategies inspired by animals\u2019 sensorimotor reflexes [17]. Each propeller of the Oscar II robot is driven by a 8-gram DC micromotor connected to the sensorless speed regulator described above. For the following tests, attitude control of the robot about the yaw axis was achieved by implementing two feedback-loops as described in figure 10: \u2022 an inner feedback-loop dealing with yaw angular speed. Yaw angular speed is measured with a micro rate-gyro (cf. figure 9). \u2022 an outer feedback-loop dealing with yaw angular position. Yaw angular position is measured with a miniature resolver onto which the robot is mounted (Fig. 9). Figure 11 shows the robot\u2019s response to a large angular step displacement (25 degrees). The parameters (Kp, Ks and Ki) of the yaw attitude controller were identical in both cases. The difference in the two responses shown in figure 11 illustrates the conspicuous damping effect brought about by having the rotor speed of each propeller regulated locally. In the absence of rotor speed regulation (governor turned OFF) the robot follows the step but the response is largely underdamped (figure 11 dotted line)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003397_tmag.2008.918920-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003397_tmag.2008.918920-Figure3-1.png", "caption": "Fig. 3. The PMs in the air-gap space. Regular PM shape.", "texts": [ " Such expression (2) is reciprocal to the conventional expression for , in the sense that the source of the magnetic interaction is the coil, whereas the collector geometry is the PM volume, as depicted in Fig. 2. Provided that the mentioned assumptions are met, (2) is useful because it simplifies analytical calculations for machines with regular stator coils and irregular PM shapes. In this section, an analytical expression is derived for the no-load flux linkage and electromotive force for the case of a PM machine with a simple stator winding, that is a slotless stator with an infinitely thin winding (Fig. 3). Although a simple stator winding is used, greater complexity is considered for the rotor. PMs with various block configurations are proposed [Fig. 4(b), (c), (d)]. A modification of the PM geometry will not change the analytical expression itself, but rather modify the integration boundaries, as will be discussed in Section III-C. Four PM shapes are proposed: a simple rectangular magnet [Fig. 4(a)], a pyramidal stack [Fig. 4(b)], a T-shape magnet [Fig. 4(c)], and a Halbach array [Fig. 4(d)] with two different magnet thicknesses for the tangential and the radial magnets. These shapes are more or less arbitrary. Other PM shapes could be analyzed with the same method. In the analysis, and are respectively the radius of the rotor and the stator. is the total thickness of the rotor magnets and is the mechanical air gap. With respect to the angles presented in Fig. 3, is the mechanical angle (in rad) with respect to the fixed stator winding (see Fig. 3). is the mechanical angle occupied by one pole. Upon rotation of the rotor, the latter will make an electrical angle with respect to the fixed stator (mechanical angle is ). The references for and are shown in Fig. 3. The stator coil is modeled as a surface current distribution laid out on the surface of the stator laminations with constant radius . The PMs are mounted on the surface of the rotor, which has a constant radius . In the derivation of the no-load flux linkage , the first step consists in expressing the magnetic field intensity created by the coil, as prescribed by (2). In cylindrical coordinates, the stator-created field has been derived in previous scientific literature [5] for an infinitely thin winding: (3) (4) where and are the radial and tangential components of the stator-created magnetic field intensity in cylindrical coordinates and is the number of pole pairs in the machine" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000561_robot.1995.525431-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000561_robot.1995.525431-Figure2-1.png", "caption": "Fig. 2: Basic action of the dynamic active antenna", "texts": [ " This approach was based on the Salisbury\u2019s original idea that the information obtained from a force/torque sensor made it possible to estimate the location of the contact point as well as the contact force. It was first pointed out by Salisbury [13] and was later extended to some more eneral and mathematical forms by Brock and Chiu [ll, Tsujimura and Yabuta [15], and Bicchi [16]. These approaches (121 - [15] can be categorized as passive sensing without utilizing any active motion. 3 Working principle The basic motion of the beam is exactly the same to that discussed in our former work. The beam is moved to search for an object until it hits the object as shown in Fig.2(a). The moment the beam hits the object, we send the stop signal to the actuator and then a free oscillation starts as shown in Fig.2(b). This free oscillation switches from contact to non-contact phases and vice versa. An experimental torque sensor signal at such oscillation mode is shown in Fig.3. It includes a lot of natural frequency components. The natural frequencies in the contact phase changes in accordance with the contact location. Under the following assump tions, we can compute those frequencies [l]. In Fig.$, we show the function curves of the fundamental(wl), second(wz) and third(q) order natural frequency in the contact state" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002666_elps.200700443-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002666_elps.200700443-Figure1-1.png", "caption": "Figure 1. Exploded cross-sectional schematic of the front block, spacer and middle block. (a) Running buffer flow enters front via 1/16 in. tubing and threaded fritted adaptor, (b) 5.7 cm long separation channel cut in front block, (c) dialysis membrane, (d) running buffer exits, (e) spacer with 6.7 cm long cut channel, (f) 5.7 cm long electrodes channel cut in back block, (g) 21 platinum wire electrodes (stretched between electrode pins), (h) coolant flow enters via barbed adaptor and (i) coolant exits.", "texts": [ " Next, Greenlee and Ivory [7] demonstrated an apparatus where the gradient was formed using a flat dialysis membrane sandwiched between two channels to gradually decrease the buffer conductivity in the separation channel. A similar principle has been demonstrated by Lee and coworkers [8] in which the separation channel comprises a hollow fibre membrane. These designs, however, give limited opportunities for \u2018shaping\u2019 the electric field during a run. A more recent design by Ivory included an array of electrodes, separated from the separation channel by a dialysis membrane, and under individual control, producing an electric field which could be shaped at will [9] (Fig. 1). Because of the capacity to change the electric field during a run, this version of the technique was dubbed dynamic field gradient focusing (DFGF). By dynamic control of the shape of the electric field, the point at which an analyte ion focuses could be moved up or down, such that analytes could in theory be eluted from the chamber, one at a time, as tightly focused bands. Unlike straightforward electrophoretic techniques (native PAGE, CE) where the field is constant and broadening increases with migration distance, FGF (/DFGF) is a focusing technique where ions can be focused tightly, offerCorrespondence: Dr" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002551_3-540-45118-8_47-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002551_3-540-45118-8_47-Figure1-1.png", "caption": "Figure 1. Conceptual illustration of an array of micro actuators that will operate in an aqueous solution. The wirebonding wires and electrical connections will be coated before aqueous operations.", "texts": [ " Hence, a new breed of micro-scale actuators is introduced to the MEMS community: actuators that can be actuated in an aqueous environment with large deflection, while consuming relatively low actuation voltage. In addition, laser-micromachining technique offers a relatively fast and inexpensive fabrication method, and will potentially give cheap and pseudo-batchfabricable ICPF micro actuators. We have initiated an effort to create micro-cellularmanipulators by using laser-micromachining to process a commercial perfluorosulfonic acid polymer (Nafion) [7]. Our goal is to eventually create an array of micro actuators capable of operating in biological fluids (see conceptually drawing in Figure 1). Details of the fabrication procedures and initial experimental results from our micro underwater actuators are presented in the following sections. The development of ionic polymer-metal composites actuators requires an interdisciplinary study in chemistry, materials science, controls, and robotics. For fabrication, the poor surface adhesion of any metal coating sandwiching the polymer was polymer surface will easily crack and peel off if there is no appropriate surface pretreatment. Bar-Cohen et al" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002610_0892705707082327-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002610_0892705707082327-Figure3-1.png", "caption": "Figure 3. Schematic graph of (a) one loop in knitted preform and (b) cross-section of the commingled yarn forming the loop.", "texts": [ " The melted matrix does not flow or penetrate transversely between the adjacent reinforcing fibers in the radial direction of the fiber in the hot pressing process. As the reinforcing fibers and matrix fibers are tightly blended together, the transverse penetration distance mentioned is very short and can be neglected. Therefore, hot pressing is taken to mean the process by which the matrix fibers in situ melt and integrate with the reinforcement. 3. The void content of the composites produced by hot pressing is 0. 4. The composites produced by hot pressing are board shaped and of even thickness. Figure 3(a) and (b) shows the schematic graphs of one loop in the knitted preform and the cross-section of the commingled yarn used for the preform, respectively. If Af (mm2) and Am (mm2) are the section area of the multi-ply reinforcing yarn and matrix yarn, respectively, nf and nm are the number of single-ply yarns in the multi-ply reinforcing yarn and matrix yarn, respectively, and lPre (mm) are the loop length of the knitted preform, respectively, then the volume of reinforcing fiber vf (mm3) and that of the matrix fiber vm (mm3) in one loop will be: vf \u00bc lPre nf Af: \u00f01\u00de vm \u00bc lPre nm Am: \u00f02\u00de If the loop density of the knitted preform is d1pre (loops/cm 2), the volume of reinforcing fiber vfpre (mm3) and that of matrix fiber vmPre (mm3) in 1 cm2 of preform will be vfPre \u00bc dlPre vf dlPre lPre nf Af: \u00f03\u00de vmPre \u00bc dlPre vm dlPre lPre nm Am: \u00f04\u00de According to Assumptions (1) and (2), the area of the composite is the same as that of the preform and the matrix fiber melted in situ and integrated with the reinforcement in situ, the volume of reinforcing fiber vfc (mm3) and that of the matrix vmc (mm3) in 1 cm2 of composite produced by hot pressing will be the same as the volume of reinforcing fiber and that of the matrix fiber in 1 cm2 of preform, i" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002768_s11664-007-0351-x-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002768_s11664-007-0351-x-Figure2-1.png", "caption": "Fig. 2. A schematic of the magnetic-field-assisted assembly process using feed tape1 (not to scale).", "texts": [ " The recesses are formed on the surface of the substrate in such a way that the shape and depth of the recesses matches the shape and thickness of the microcomponents. A highly coercive ferromagnetic material, such as cobalt or nickel, cobalt-palladium or a cobalt-platinum alloy, is deposited on the insulator substrate or wafer. The layer is patterned to form either simple or complex features at the bottom of the recesses, and is subsequently magnetized to act as a host for the microcomponents. Another approach to magnetic-field-assisted assembly using feed tape is illustrated in Fig. 2.1 A substrate is patterned with multiple recesses that are shaped to receive correspondingly matched microcomponents. The feed tape is used to attach the microcomponents temporarily. On completion of magnetic self-assembly of microcomponents, individual microcomponents are attached to the matching recesses on the substrate. The feed tape portions are guided by wheels, and a magnet moves adjacent and parallel to the substrate. Equivalently, the substrate moves continuously relative to guide wheels" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000227_s0142-1123(00)00049-9-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000227_s0142-1123(00)00049-9-Figure1-1.png", "caption": "Fig. 1. Spur gear profile and definition of outer point single engagement.", "texts": [ " An effective stress intensity factor which considers all the previous effects is defined as: DKeff,c5U\u00b7DKeff (3) and is used in the Paris and Colliepriest [21] fatigue propagation laws, with appropriate U values. The gear life predictions obtained with the different propagation laws were compared with experimental results obtained by loading gears used in automotive gearboxes: the results showed the importance of crack closure effects. An automotive spur reverse gear, used in a mediumsize automobile, was used for the tests. The gear geometry data can be found in Table 1 and the tooth profile, strongly corrected, is shown in Fig. 1, illustrating the condition of the outer point of single engagement. The nominal stress, snom, is calculated in the most stressed zone at the tooth root, defined by following ISO 6336: snom5 6Fth s2B (4) The fatigue tests were conducted by using special equipment able to load two teeth at the same time at the outermost point of single engagement, as shown in Fig. 2. Some electrical strain gauges were positioned on the sides of the teeth in order to verify the exact positioning of the gear and to ensure a uniform distribution of the load on the teeth", " The material of the gears is 18CrMo4 case-hardened. Table 2 contains the monotonic and cyclic, experimentally determined by Newaz [22], for both the core and the outer layer. All the gears are carburized and some of them were also shot-peened. The hardness profiles, produced by means of microhardness measurements, are shown in Fig. 3. The residual stress profiles experimentally measured by means of a diffractometer are shown in Fig. 4. The residual stresses were only measured along the width of the tooth (direction y in Fig. 1). Measurement in the other direction is not possible due to the great geometrical discontinuity. It is assumed [23] that the value in the other direction is equal to the one measured. The experimental tests were carried out on carburized gears. Different computational models characterized by different defect types and loading cases were created in order to study how crack propagation varies from one situation to another. The objective of this study is to assess the effect of crack closure on crack propagation and to obtain gear life predictions in agreement with experimental results" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001945_s0022-460x(77)80051-5-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001945_s0022-460x(77)80051-5-Figure1-1.png", "caption": "Figure 1. Definition of parameters.", "texts": [], "surrounding_texts": [ "one for the angular motion of the pendulum and one for the elastic motion of the bob. For small angles, an approximate solution for the spring motion is obtained independently of the pendulum motion. Then, the pendulum motion is described by a form of Ince's equation, which may be readily transformed into a Hill's equation. Periodic solutions of this equation are obtained by means of a procedure based on Hill's determinants and these solutions are used to plot stability diagrams in the parameter space. These diagrams can be regarded as three-dimensional Strutt diagrams and reduce to the ordinary Strutt diagram associated with Mathieu's equation when the spring stiffness becomes infinite. 2. EQUATIONS OF MOTION Consider the planar motion of a mass point m attached to a freely pivoting support by means of a massless linear spring of stiffness k. The so-called free length, 1, is the distance between the support and mass point when the spring is unstressed. The support motion, Y(t), is sinusoidal and in the vertical direction. The variables x and 0 describe the spring extensional and pendulum angular motions, respectively. The state of stable static equilibrium corresponds to the case in which x and 0 are zero, as indicated in Figure l(a), where the quantity Xsr = mg/k represents the spring deflection due to gravity. The first step is to derive Lagrange's equations of motion about the static equilibrium position. The position vector from the datum to the mass point and its time derivative are (see Figure l(b)) r = ( Y + l+xsr )ey + (1+ Xsr + x)ex, = I'e, + :ce~ + (I + Xsr + x) Oeo, (I) where % ex and eo are unit vectors defined in Figure l(c) and overdots represent derivatives with respect to time. The kinetic and potential energies have the expressions It will prove convenient to introduce the following notation: Ix = 1 + xsr , 6 = g/It, u = x/It, Y t ( t ) = Y( t ) / l l , 09] = k/m. (3) In this notation, a modified Lagrangian, Lt, can be written as follows: Lt = ( l ]m l2 ) (T - V) ={{ 1;':2 + ti 2 + (I + u)XO 2 + 2 I;'1 [-t~ cos 0 + (1 + u) 0 sin 0] - 26[Y t + (1 + u) (1 - cos 0)] - 092 t [(62/09~) + u2]}. (4) Lagrange's equations for the spring extensional motion and the pendulum angular motion can be written in the general form . d-t~-~-/-'~u --0' dt~ aO ] - t O Inserting equation (4) into equations (5), one obtains the equations of motion: / / + 0 9 ] u = ( 1 + u ) 0 2 - 6 ( I - c o s 0 ) + Yt cos0, (1 + u)20+ 2(1 + u ) \u2022 0 + ( l + u ) ( 6 + ];t) sin 0 = 0. (6) Since the support motion is assumed sinusoidal, one may let 1~1 = 2ecos2t. Then, upon cancelling (1 + u) in the second of equations (6), the resulting pair of equations is /i + ml 2 u = (1 + u) 02 -- 6(1 - cos 0) + 2~ cos 2t cos 0, (7a) (1 + u) 0 + 2fi0 + (6 + 2e cos 2t) sin 0 = 0. (7b) At this point, a pause to discuss some qualitative aspects of equations (7) is in order. For = 0, equations (7) describe a swinging spring [6]. Alternatively, for co a -+ oo and for small 0, equation (7b) becomes the well-known Mathieu equation (see references [1-3]). Equation (7b) has static equilibrium positions at 0 = 0 and 0 = n. These two positions are indicated by the respective positiveness or negativeness of 3, since shifting 0 by n effectively changes the sign of 6 in equation (7b). The sign of e is immaterial. Returning to the definition of 6, equations (3), one can write 092]6 = 1 + l /xsr and henceforth assume g, k and m, and thus 092 and Xsr, to be positive. Recalling the definition of the spring free length 1, one may note that it can be positive or negative. I f l / x s r < -1 , one has 6 < 0 and oscillations of equation (7b) are about 0 = re. I f l[xsr = -1 , 6 is undefined since the effective pendulum length/1 is zero. Otherwise 6 > 0 and oscillations are about 0 = 0. For - 1 < l /xsr < 0, one has 0 < o9 2 < 6 while for l /xsr > 0 one has 6 < 092. The case of 6 = 09 2 is evident when the spring free length, 1, is zero. Returning to equations (7) and letting 0 be small, such that sin0'-\" 0 and cos0 ~_ 1, one obtains the linearized equations / /+ 09t2u'-\" 2ecos2t, (1 + u ) O + 2 a O + ( 6 + 2 e c o s 2 t ) O = O . (Sa, b) So far, no dissipation has been included in the equation describing spring motion. I f damping had been taken into account, only the steady-state solution of equation (8a) would be of consequence for large values of t. Then, if dissipative effects are neglected, the spring motion can be approximated as u -~ eu~, u~ = (2 cos 2t)/(09~ - 22), 09~ # 2 2." ] }, { "image_filename": "designv11_32_0000449_jahs.45.118-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000449_jahs.45.118-Figure1-1.png", "caption": "Fig. 1. Split-torque, face-gear transmission from ART program (Ref. 1).", "texts": [ " A grinding procedure was developed based on a continuous grinding method using a worm grinding wheel. Prototype carburized and ground ATSl9310 steel face gears were fabricated as palt of this program. The objective of this work is to describe the preliminary results of the cxperimental tests performed on the carburized and ground AISI 9310 steel face gears. Face gears wele tested in the NASA Glenn spiralbevel-gearlface-gear facility. Basic face-gear design, test facility, setup procedures, testing procedures, and test results are described. Face Gear Applications in Helicopter Ttansmissions Figure 1 shows the split-torque, face-gear transmission developed during the U.S. A m y Advanced Rotorcraft Transmission (ART) program (Ref. 1). For this configuration, an involute spur gear drives both an upper face gear and lower face gear. These face gears areconnected to spur gears which drive a large bull gear. By splitting the power flow in these two paths, smaller components can be utilized which leads to reduced weight. Compared to spiral-bevel gears, face gears allow the useof asimpler, less expensive, involute spur pinion" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001991_ip-nbt:20050003-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001991_ip-nbt:20050003-Figure2-1.png", "caption": "Fig. 2 Schematic representations a Electrode modified with CD guest b Electrode modified with CD c Nanoparticle stabilized with CD guest d Nanoparticle stabilized with CD", "texts": [ " Based on the observed increase in the thermal stability of enzymes modified with CD, with no loss of enzymatic activity, the immobilization of enzymes on metallic surfaces, based on the same principle, was selected by us as a new approach. For this, two approaches were followed: (i) Self-assemble sulphur-containing CD on silver or gold surfaces and then immobilize the native enzyme on it through supramolecular interactions. (ii) Self-assemble sulphur-containing CD on silver or gold surfaces and then immobilize the enzyme, previously modified with a typical CD guest. For these two approaches, self-assembled monolayers (SAMs) of the sulphur-containing CD or CD guest can be formed on either an electrode bead or a nanoparticle (Fig. 2). For these procedures, two types of sulphurcontaining CD (on the primary rim) were obtained: perthiolates and polydithiocarbamates [28\u201330]. In the latter case, a complete substitution with dithiocarbamate groups, NCSS , could not be achieved once all the hydroxyl groups had been previously transformed into amino groups. Polydithiocarbamate-CDs were only used for self-assembly on silver electrode surfaces. The selected CD guest was adamantane (Ada), which is characterised by an inclusion constant of about 104 (moldm 3) 1 in b-CD, which is about two orders higher than that for Trp and Phe [24]" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002339_j.jsg.2005.11.006-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002339_j.jsg.2005.11.006-Figure2-1.png", "caption": "Fig. 2. Slip between incompressible layers constrained to remain in contact.", "texts": [ " Parallel folds, in particular, are usually found in the upper levels of the Earth\u2019s crust, typically in the upper part of an orogenic belt, and this observation supports the use of elasticity theory to study the deformation (de Sitter, 1964). The model is essentially that of two extended elastic beams, held in contact by overburden pressure, but which can slip over each other. If we consider incompressible layers of thickness t, with bending stiffness EI, embedded in a soft foundation of stiffness k per unit length and compressed by a load P (see Fig. 2), and follow classical Euler beam theory, the total potential energy, over the half-wavelength L, for small vertical deflections w, can be written as (Budd et al., 2003): V Z \u00f0L 0 EI \u20acw2KP _w2 2 Ck w2 2 Ccmqt _wj j dx (1) where dots denote differentiation with respect to the axial coordinate x. Here the first term is the bending energy in the two layers, the second is the work done by the total load P, the third is the work done in the foundation and the fourth is the work done against friction" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001608_j.medengphy.2004.04.005-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001608_j.medengphy.2004.04.005-Figure2-1.png", "caption": "Fig. 2. Labeled schematic (a) and photograph (b) of small-scale loading machine following assembly.", "texts": [ " The selected scanner model has a maximum data collection rate of 10 samples per second (10 Hz). This is more than sufficient to load mouse bones at a rate of approximately 0.1 mm/s. If faster collection is required, Vishay makes a scanner capable of 10 kHz collection rate (6000 Series); however, the price is significantly higher. Strainsmart software accompanies the scanner ($ 1175.00) and can efficiently be navigated through on-line tutorials and the accompanying manual. The assembled system is illustrated in Fig. 2. The goal of assembly is a machine that is stable during loading and can reproducibly be assembled and torn down. To attach the milling machine table to the linear slide, base plates were fabricated from 19 mm thick aluminum plate ($ 750.00). To reproducibly align the two aluminum plates, a recess was machined on the surface of the milling table (horizontal) plate such that the linear slide (vertical) plate would repeatably align. To maintain alignment of the slide relative to the vertical plate, aluminum pins in a \u2018L\u2019 configuration were pressed into the plate such that the slide rests against the orthogonal pin placement and a rectangular cutout through the bottom of the plate enables attachment of the controller cable", " If the assembly is overtightened, the sensing junction can be overloaded. For load cells on the scale of this loading machine overloads (particularly bending or side loads) slightly more than 25 N can cause irreversible damage. To avoid this, the load cells must be carefully tightened (finger tightened) in the studs and a slight gap should be visible. This will ensure that the cell has not been damaged during setup, but will enable slight \u2018wobbling\u2019 of the upper fixture if bumped. To minimize the wobbling, fixtures should be small and lightweight, stud connectors Fig. 2 (continued ) should be short and loads applied should be small. Thus loads in the order of 150 N should probably not be used on this system given this limitation; and, importantly these loads should be applied vertically. If the specimen being tested is not symmetrically aligned with respect to the loading machine, the bending moment can bend the load cell connector and damage the cell. Furthermore, the linear slide has a specified load that it can safely lift when oriented in a vertical position" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002457_cdc.2005.1582362-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002457_cdc.2005.1582362-Figure2-1.png", "caption": "Fig. 2. The trapezoidal closed path on the sphere.", "texts": [ " Then, the kinematic model which represents the relationship between \u03b7\u0307 and \u03b1\u0307f is as follows [2]: \u23a1 \u23a3 \u03b1\u0307f \u03b1\u0307o \u03c8\u0307 \u23a4 \u23a6 = \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a3 1 0 \u03c1 cos vf cos \u03c8 \u2212\u03c1 cos vf sin \u03c8 sin vf 0 1 \u2212\u03c1 sin \u03c8 \u2212\u03c1 cos \u03c8 0 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a6 \u03b1\u0307f , (2) 0-7803-9568-9/05/$20.00 \u00a92005 IEEE 1445 where \u03c1 is the radius of the sphere. For simplicity, a target point is assumed to be the origin of \u03b7 and \u03b1\u0307f is assumed to be able to controlled directly. Hence, the initial state of \u03b1f is assumed to be the origin. Consequently, the control problem is reduced to be the regulation of \u03b7\u0303 := [ \u03b1T o \u03c8 ]T \u2208 R 3 (3) by iterative closed paths on the sphere. The closed path on the sphere for the regulation is shown in Fig. 2 (initial condition: \u03b1f = 0, \u03c8 = \u03c0). In the upper, the left figure shows the closed path along the path of \u03b1f : Af \u2192 Bf \u2192 Cf \u2192 Df \u2192 Ef (Af ) which is characterized by the parameters \u03b81 and \u03b82. Then, the right figure shows the path of \u03b1f : Ao \u2192 Bo \u2192 Co \u2192 Do \u2192 Eo, which is generated by the left closed path. The thick arrow, i.e. \u2206\u03b1\u2032 o, is the incremental distance of \u03b1o by the left closed path. On the other hand, the lower left figure shows the case where the upper closed path is rotated through the parameter \u03d5 about the x\u2032- axis" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003816_iccms.2010.10-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003816_iccms.2010.10-Figure1-1.png", "caption": "Fig. 1 Global coordinates and local coordinates", "texts": [ " However, the motion of AUVs can be simplified into two planes while in weak maneuver condition: the horizontal plane and the vertical plane. Only the motion in horizontal plane will be discussed in this paper. Based on the recommendation of International Towing Tank Conference (ITTC) and the Society of Naval Architects and Marine Engineers (SNAME), we establish two reference frames. a fixed inertial frame of reference E \u2212 \u03be\u03b7\u03c2 (global coordinates), and a body-fixed coordinates (local coordinates) o xyz\u2212 , shown as Fig. 1. According to rigid-body dynamics theory, the general mathematical model of an AUV is given by [5, 6] ( ) ( ) 2 2 ( ) ( ) G G H P G G H P z G G H P m u vr y r x r X X m v ur x r y r Y Y I r m x v ur y u vr N N \u23a7 \u2212 \u2212 \u2212 = + \u23aa\u23aa + + \u2212 = +\u23a8 \u23aa + + \u2212 \u2212 = +\u23a1 \u23a4\u23aa \u23a3 \u23a6\u23a9 (1) Where m is the mass of the AUV; X, Y, N are forces and moments, and H, P represent respectively the vehicle hull and propeller. Gx , Gy are the coordinates of the gravity center of the AUV. The hydrodynamic force HX , HY and the hydrodynamic moment NBH B are the complicated functions of the AUV 978-0-7695-3941-6/10 $26" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003304_1.2783152-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003304_1.2783152-Figure2-1.png", "caption": "Fig. 2. Motion of angular momentum. Note that by the right hand rule the torque due to the normal force about the center of mass points out of the page in the same direction as DL.", "texts": [ " Reuse of AAPT content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 142.132.1.147 On: Tue, 11 Aug 2015 08:06:04 432 The Physics Teacher \u25c6 Vol. 45, October 2007 V = wZ cos a. (3) The assumption of steady-state spolling means that the center of mass remains fixed while the point of contact moves in a circle whose radius is r = R cos a. The angular velocity wD and hence the angular momentum L, remain constant in magnitude and describe a cone, which maintains a constant angle a with the surface as shown in Fig. 2. In the space of angular momentum, the tip of the angular momentum vector L traces a horizontal circle of radius L cos a with an angular frequency equal to wZ. It follows that the magnitude of the rate of change of L is simply (4) \u2206 \u2206 L t L= w aZ cos . The magnitude of the torque about the center of mass is (5)\u03c4 = =\u22a5r F R Mg( cos ) .a Assuming the disk to be uniform, the magnitude of the angular momentum about the disk diameter is L = \u00bc MR2 wD. According to the equation of motion, Eqs. (4) and (5) are equal and we obtain (6)MgR MRcos cos " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003889_j.cogsys.2009.12.003-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003889_j.cogsys.2009.12.003-Figure5-1.png", "caption": "Fig. 5. Sketch of the stereo camera system combining an omnidirectional camer path. (For interpretation of the references to color in this figure legend, the re", "texts": [ " While the interpretation of the omnidirectional camera images is done in a similar way by almost all robot soccer teams we extended the optical system of our robots by a second camera to obtain a stereo system. In contrast to approaches which use two omnidirectional cameras of the same type in a stacked setup (Gluckman, Nayar, & Thoresz, 1998; Kawanishi, Yamazawa, Iwasa, Takemura, & Yokoya, 1998; Matuszyk, Zelinsky, Nilsson, & Rilbe, 2004) we combined the omnidirectional camera with a perspective camera that observes the area in front of the robot. Fig. 5 illustrates our setup (Voigtla\u0308nder, Lange, Lauer, & Riedmiller, 2007). The advantage of this setup is that we can combine the 360 view of the omnidirectional camera with the long and narrow field of view of the perspective camera. Similar to peripheral vision in the perception of humans the omnidirectional camera offers information of a large area with small image resolution while the perspective camera provides higher resolution images with smaller aperture angle similar to foveal vision. Additionally, the robot can calculate the distance to objects in the overlapping part of the fields of view of both cameras" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002076_vppc.2005.1554564-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002076_vppc.2005.1554564-Figure2-1.png", "caption": "Fig 2. Stator Iron", "texts": [ " To obtain simple, but physically significant, expressions for the network of the thermal resistances that describe the heat conduction across the general component, some more assumptions are made along with those considered by Mellor [1, 3]. They are as follows: 1. The fluid circulated is incompressible with constant properties 2. Negligible kinetic and potential energy and flow work changes. 3. Fully developed conditions at the tube outlets. 4. Boundary layer approximations are assumed to be applicable all through the tube. 5. Constant temperature around the surface of the tube. The thermal resistance for typical TEFC motor used by Mellor [1] for stator Iron is described in equations (1, 2, 3, 4 and 5) as shown in fig 2. R3 L 6 \u03c0\u22c5 kla\u22c5 r1 2 r2 2 \u2212 \u22c5 := 1( ) R4 1\u2212 4 \u03c0\u22c5 klr\u22c5 L\u22c5 s\u22c5 r1 2 r2 2 \u2212 \u22c5 r1 2 r2 2 + 4 r1 2\u22c5 r2 2\u22c5 ln r1 r2 \u22c5 r1 2 r2 2 \u2212 \u2212 \u22c5:= 2( ) R5 1 2 \u03c0\u22c5 klr\u22c5 L\u22c5 s\u22c5 1 2 r2 2\u22c5 ln r1 r2 \u22c5 r1 2 r2 2 \u2212 \u2212 \u22c5:= 3( ) R6 1 2 \u03c0\u22c5 klr\u22c5 L\u22c5 s\u22c5 2 r1 2 \u22c5 ln r1 r2 \u22c5 r1 2 r2 2\u2212 1\u2212 \u22c5:= 4( ) C2 cl \u03c1 l\u22c5 \u03c0\u22c5 L\u22c5 s\u22c5 r1 2 r2 2 \u2212 \u22c5 2 := 5( ) All the holes are modeled by taking the equivalent cross sectional area. The heat that is pulled out by the circulating liquid in the holes is modeled by adding a lumped heat sink which is represented by a current sink at the stator iron node in the model" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003954_10402001003642759-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003954_10402001003642759-Figure2-1.png", "caption": "Fig. 2\u2014Model configuration displaying orientation of load and defining variables \u03b8, \u03c6, and xd.", "texts": [ " The SIFs are calculated by using a displacement correlation technique as described by the equations: KI = E 4(1 \u2212 v2) \u221a 2\u03c0 r (u1 \u2212 u2) [3] KII = E 4(1 \u2212 v2) \u221a 2\u03c0 r (v1 \u2212 v2) [4] KIII = E 4(1 \u2212 v2) \u221a 2\u03c0 r (w1 \u2212 w2) [5] Quadratic elements are required by the displacement correlation method for calculating SIFs because the insertion of a quar- 1 The neglect of the traction term for contacting crack faces is not mentioned in Desault Ssytemes (30). ter point element greatly increases the accuracy of the model without a dramatic increase in mesh density. To reduce the size of the problem we utilize a technique referred to as submodeling, where we apply displacements to the boundary of a small cracked block to simulate its being a part of a much larger halfspace (Desault Systemes (30)). The contact load is applied to the surface with FORTRAN user subroutines DLOAD (and UTRACLOAD) for ABAQUS (see Fig. 2). We apply this load up until the edge of the crack but not over the crack, because this would cause the applied pressure to be inaccurate (Rice (33)). Also, crack closure would result (Fujimote, et al. (35)) and the model would then require a contact algorithm on an already large fracture model with quadratic elements that would be accurate enough to yield crack tip displacements. Crack Geometry Surface cracks can have a variety of shapes. Cone cracks have received much attention in the literature (Mackerle (36))" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001435_jjap.43.5273-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001435_jjap.43.5273-Figure7-1.png", "caption": "Fig. 7. Schematic cross-section of the ZnO hexagonal microtube.", "texts": [ " On the other hand, due to the nesting layered structure near the prismatic facets, the microtubes may have a much wider hexagonal hole such that d < dc may occur. As a result, the guidance of the optical field parallel to the plate of Si substrate may cease near the prismatic facets and the radiation of light from the sidewalls may allow. Radiation loss near the prismatic facets can be estimated by studying the modal characteristics in the direction parallel to the prismatic facets of the ZnO hexagonal microtubes. Figure 7 shows the cross section of the microtube, which can be assumed to be a hexagonal slab waveguide oscillator with ZnO of refractive index n1 as the core region and air of refractive index nair as the cladding regions. The modal characteristics of the hexagonal slab waveguide oscillator can be investigated through the study of the loss and phase of the corresponding tilted slab waveguide. In the diagram, it is assumed that the incident field excites the outgoing wave inside the tilted waveguide. The incident field, Ein, and the outgoing field, Eout, can be written as Ein\u00f0x0; z0\u00de \u00bc fm\u00f0x0\u00de exp\u00f0 j mz 0\u00de; \u00f03a\u00de Eout\u00f0x; z\u00de \u00bc fm\u00f0x\u00de exp\u00f0 j mz\u00de; \u00f03b\u00de where j \u00bc ffiffiffiffiffiffi 1 p , fm, whose base system consists of sine and cosine functions, is the normalized mth order TE mode and m is the corresponding propagation coefficient" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000364_robot.1988.12028-Figure14-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000364_robot.1988.12028-Figure14-1.png", "caption": "Figure 14: Liftability Windows for Three-Point Grasp.", "texts": [ " Similarly, if the normal intersects Q4 and P4 or 54, the point belongs to B4 or J, respectively. Any point whose normal passes through TW and P3 or 53 belongs to T or J respectively. Figure 13 shows the liftability regions for the object. Notice that for the two-point initial grasp considered, T is only one orientation of contact against the vertex and thus is unusable. Including another contact in region, I, allows T to grow. The line of action of the new contact force, f5, defines four new points of interest, 915. 453, 954, and 9sg (see Figure 14). The translation window now becomes the closed line segment lying between q l g and qsg. As before, the windows Q3 and 4 4 lie above and below TW. The other windows are delimited by the points 93 and 94, where 9 3 is the lower of the points 913 and 453 and 94 is the higher of 914 and 954. Points whose normals pass through Q3 and 4 4 are assigned to liftability regions just as described above, but normals passing through TW are treated differently. There are two cases: 915 on the right of TW or on the left" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003760_(asce)0893-1321(2009)22:4(331)-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003760_(asce)0893-1321(2009)22:4(331)-Figure3-1.png", "caption": "Fig. 3. Coordinate systems and forces", "texts": [ " ,n 1 The investigation in this paper focuses upon a fixed wing flying vehicle as shown in Fig. 2 Vinh 1993 . Here force T is the thrust from the engine along the flying vehicle fuselage. The angle is the angle of attack. Force L is the aerodynamic lift which is normal to the direction of velocity v and in the symmetric plane lift-drag plane of the flying vehicle fuselage. Force D is the aerodynamic drag against the direction of velocity v. The relationship of the forces is shown in the coordinate systems in Fig. 3. Point mass M is the origin of two coordinate systems: the local-horizon system x \u2212y \u2212z and the wind-axis system x1\u2212y1 \u2212z1. The two rotations from x \u2212y \u2212z to x1\u2212y1\u2212z1 are the heading angle about x and flight-path angle about negative z1 . The coordinate r in the figure is measured from the center of the Earth. The location of M is expressed by the topocentric Earth surface Cartesian coordinates x ,y ,h , where x axis is parallel to y axis; y axis is parallel to z axis; h=r\u2212rE, where rE is the radius of the Earth" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002603_0022-4898(73)90138-9-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002603_0022-4898(73)90138-9-Figure3-1.png", "caption": "FIG. 3. Measured and calculated interface pressures.", "texts": [ " Wheel / / Soil surface her d~ss~ Element A ~ mainly to slip J ~ - ~ - ~ / Element B ~ ~ ~/~ '~Energy loss due | ~\" tO distortion ~ D ~ - of soil FTG. 1. Energy dissipation in substrate due to interaction. (2) Pressure gauges fixed to the wheel contact surface. Since the filst system is not reliable in view of the physical displacement of the embedded gauges, the second method is more commonly used. By and large, the pressure gauges will only sense pressures acting directly on them (i.e. direct normal compressive pressures). Figure 3 shows a comparison between measured and theoretically computed normal pressure at the interface--using measurements of subsoil performance [2]. Except for a clear and distinct separation of soil from the contact surface in region A as shown in Fig. 3, the pressures on the wheel surface should either be positive (compressive) or negative (tension). However, since the pressure gauges can only sense compressive performance, due either to: (a) Compressive wheel action into soil--soil is in passive state, (b) Active soil action on to contact surface in rebound action as wheel begins to unload in its forward motion, it is evident that tension values are not recorded. The tension values can occur due to adherence of soil to wheel surface because of and in addition to the slow rebound characteristics of soil--i", " The casting of analytical formulations is not unlike those developed for the grouser problem--using the stress characteristic approach, assuming a direct relationship between stress and strain rate. By physically measuring subsoil deformation with time (as is possible in controlled soil bin tests) it is apparent that with appropriate constitutive relationships and associated flow laws, the instantaneous stress field beneath a moving wheel can be mapped. The forcing function at the boundary--i.e. wheel-soil interface can thus be obtained. Figure 3 shows the calculated pressure distribution obtained directly by strain-rate measurements in the soil (i.e. response function determination) and calculating the impulse function producing the observed strain-rates. The seemingly abrupt stress contour at the two ends is a deficiency of the analytical model--which treats the stress situation implicitly in terms of a discontinuity across the limit failure characteristic. A less abrupt contour appears to be a more realistic appreciation of stress or pressure at the interface. Figure 3 demonstrates the possibility of tension values in soil being developed in view of unloading of the soil during passage of the wheel. As pointed out earlier, this phenomenon might not be directly detected by pressure gauges embedded in the wheel. The limitations and constraints of the analytical model are thus traceable directly to the requirements of limit equilibrium theory and the constraints associated with specification of the constitutive relationship for the subsoil. Energy models for analysis and prediction of vehicle-soil interaction performance will rely on one's ability to measure (or determine) response function performance" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001927_s026357470500158x-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001927_s026357470500158x-Figure5-1.png", "caption": "Fig. 5. \u201cN\u201d Adaptive Models with Switching Between the Models.", "texts": [ " Each of these models, as we discussed, have different initalizations, i.e. different estimates for the parameters.These initial parameters are updated at each instant for each model to obtain the actual plant parameters after some time. This approach is illustrated in Figure 4. In the experiments, we will consider two cases. In the first case, N identification models, each of which is being updated at each instant, will be used and a switching process will occur between these models according the cost (performance) function given in (17). This is illustrated in Figure 5 for the 3 identification models case which is also discussed in reference [12]. In the second case, N models are kept fixed and there is an additional model which is continuously adapting and switching between the fixed models based on the cost function given in (17). This case is illustrated in Figure 6 for a 3 fixed and a single adaptive model. In this section, the experiments conducted in this study and their results will be presented. Also the results of these experiments will be compared with each other" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002892_1.5061067-Figure9-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002892_1.5061067-Figure9-1.png", "caption": "Figure 9: LC Ti-6Al-4V airfoil capsule, (a) CAD drawing, and (b) as-consolidated simplified part.", "texts": [ " Thermally induced porosity (TIP) testing, metallography and density measurements were among the techniques used to verify complete consolidation of the powder. These manufacturing technologies also verified the integrity of the LC structure with the HIPconsolidated powder and its ability to uniformly deform at high temperature and pressure. LC Ti-6Al-4V Airfoil Capsule An airfoil capsule was designed to prove the concept for laser consolidation to build tooling for net-shape HIP. The airfoil capsule contains a twisted airfoil in the middle with each end connected to a saddle surface that caps on a cylinder (Figure 9a). This shape creates significant challenges for the existing laser consolidation process because of large overhangs. In order to develop laser consolidation procedures with reduced technical challenges, the airfoil capsule was simplified by replacing the saddle surface with a flat surface. Laser path planning was performed as per the simplified design. Laser consolidation of Ti-6Al-4V alloy was successfully performed to build the airfoil capsule in the following sequence: starting from the middle airfoil, then the flat flanges on the two ends of the airfoil and finally two cylinders on the flanges. The initial trial demonstrated that the laser consolidation procedures are feasible and the as-consolidated simplified LC Ti-6Al-4V airfoil capsule looks good (Figure 9b). Based on the results from the initial trial, the demonstration airfoil capsule with two saddle flanges was further investigated. Laser path was re-designed based on the demonstration airfoil capsule shape. Laser consolidation of Ti-6Al-4V alloy was successfully performed to build up the middle airfoil, saddle flanges Page 166 Laser Materials Processing ConferenceICALEO\u00ae 2007 Congress Proceedings impeller. on the two ends of the airfoil and two cylinders on the flanges. Figure 10a shows an overall view of the LC Ti-6Al-4V demonstration airfoil capsule, while Figure 10b shows the intersection between the airfoil and the saddle flange" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002142_bf03546353-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002142_bf03546353-Figure2-1.png", "caption": "FIG. 2. Geometry of Multiple Flexible Link System.", "texts": [ " In this section, we demonstrate the use of OCEA for generating equations of mo tion for multibody systems comprised of flexible elements. Toward this end, we de velop recursive expressions for kinetic and potential energy functions for a series of linked flexible beams. Since we are not considering rapid angular motions of the beams, we model the beams using Euler-Bernoulli assumptions. It is assumed that the first link is pinned without translation, and successive links are joined with pins as shown in Fig. 2. Up to this point, we have not discussed the choice for gen eralized coordinates which is an important matter for automating the process. Make note in Fig. 2 that we choose absolute angular coordinates, which are measured with respect to a common frame, in this case the horizontal. Note the Xi axis con nects the tips of the flexible members; thus for this special choice of reference frames for each beam, the elastic deformation of each domain vanishes at the ends of that domain. 262 Griffith, Turner, and Junkins (20) (24) The main development of this section is a recursion for the kinetic energy of the (p + l)th link of the form which will used in forming the system-level Lagrangian, given by Tp+ 1 = ~ (Lp+1 PP+l(xp+l)rp+l(xp+l, t) \u00b7 rp+l(xp+l) dxP+1 2 Jo where Pp+l(Xp+l) is the mass density distribution and rp+l(xp+l, t) is the velocity ex pression for the (p + 1)th link", " First we look at simulation of the motion for flexible beams linked in an open-chain topology. In the OCEA based code, we define the kinetic and potential energy for the first link with equa tions (35) and (36), respectively. For the second link and so on (p = 1 and so on) we define the kinetic and potential energy by equations (30) and (34). The system is comprised of three beams, each with mass of 12 kg, length of 10m, and stiffness (EI) of 14 X 103 Nm2 \u2022 The beams are initially oriented with angles { (J\\, (h, (h} = { 3 2 7T , 3 2 7T , 3 2 7T} as shown in Fig. 2. All initial deflections are zero with the exception of the midpoint deflection of the third beam, which is q 3,1 = 0.01 m. All initial velocities are zero with the exception of the angular velocity of the third beam (03 = 0.5 rad/sec). With the ability to quickly generate models and solutions for the motion, a con siderable number of analyses are readily available. Here, we show results for the rigid body and flexible contributions to the kinetic energy of the individual links as shown in Figs" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003722_j.jmatprotec.2009.01.018-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003722_j.jmatprotec.2009.01.018-Figure7-1.png", "caption": "Fig. 7. Machining process simulation for a Kaplan blade.", "texts": [ " Using the developed computer simulation software, the real machining environment of large blade and machining processing can be simulated and geometrical error of tool path can be verified, and whether collision between the moving components and blade/fixtures can be checked with the simulation software. As it is an extremely complex machining process for a large blade, combining with the developed computer simulation techniques, the machining strategy and tool path planning parameters and cutting parameters can be further optimized. The function of the developed software for simulation machining of large hydro turbine blades includes: (1) tool path simulation and verification for cutting; (2) machine processing simulation and verification for collision. Fig. 7 shows a snapshot during machine processing simulation of a large Kaplan blade. 8. Examples for digital manufacture of large blades The above-mentioned digital manufacture techniques have been used in manufacturing of both the large Francis and Kaplan hydro turbine blades by us. As an example, 5-axis machining of a large Kaplan blade is shown in Fig. 8, and its 3D model is shown in Fig. 2. This blade is for Gaobazhou Hydro Power Station in China and its diameter of runner is \u00d85800 mm (hereafter is called Example No" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003806_icelmach.2010.5608274-Figure11-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003806_icelmach.2010.5608274-Figure11-1.png", "caption": "Fig. 11. Magnitude of the eighth harmonic of magnetic flux density.", "texts": [], "surrounding_texts": [ "The four-pole energy-saving small induction motor with core made from the non-oriented silicon steel M600-50A was examined. The supply voltage was 230 V for the frequency 50 Hz. Stator windings were delta connected. The number of series turns of stator windings was 368. The external diameter of the stator core was 120 mm, the internal diameter is 70.5 mm, and stator core lengths is 102 mm." ] }, { "image_filename": "designv11_32_0002400_j.mechmachtheory.2006.01.005-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002400_j.mechmachtheory.2006.01.005-Figure5-1.png", "caption": "Fig. 5. Brush model.", "texts": [ " However, an apparent speed difference or creep does occur between the drive wheel\u2019s outer diameter and the belt when a traction force is applied. This apparent velocity is also know as the creep ratio d and is defined as follows: d \u00bc vb xR1 vbj j ; \u00f016\u00de where x is the angular velocity of the drive wheel. The creep ratio is related to the shear angle by the following equation: oc ox \u00bc d h . \u00f017\u00de To establish a relationship between the creep ratio and shear stress distribution in the stick-zone, the Maxwell model is combined with a brush model that describes shearing effects. The brush model depicted in Fig. 5 is a simplified representation of the belt cover in the contact region. It consists of rigid elements that hinge and are held in place by a torsion spring at their base. The behaviour of the torsion spring is also based on the Maxwell model analogous to the spring element in Fig. 3. By replacing the modulus of elasticity E, stress r and strain e in Eq. (1), (2) and (6) with the shear modulus G, shear stress s and shear angle c respectively equations are derived that describe the behaviour of the brush elements" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000364_robot.1988.12028-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000364_robot.1988.12028-Figure7-1.png", "caption": "Figure 7: Vertex Liftability Regions.", "texts": [ " Therefore, as the hand squeezes more and more tightly, the weight of the object is overcome, so it must rise. The second contact point need not occur on an edge of the polygon. It may occur on the kth vertex, in which case the contact angle, y 2 . is free to vary between the inward normals of edges k and k-1 (see Figure 6), which in turn allows the moment arm, t2, to vary according to Substituting equation (11) into equations (4) and (5) allows us to determine the liftability regions of a vertex. Figure 7 shows the edge of the second finger against the vertex in the jamming region, J. Tilting the finger clockwise or counter-clockwise eventually changes the contact to region B4 or B3 respectively. Thus for a vertex, we see that the liftability regions are defined as partitions of the range of possible contact ang le s . 2.3 Translat ional Lift-off The first goal of grasping is to break all contact with the support. With this in mind, it makes most sense to use the translation region in planning the initial grasp" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001195_s0263574700003593-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001195_s0263574700003593-Figure3-1.png", "caption": "Fig. 3. Cylinders with ellipsoidal cross-section.", "texts": [ " The objective function x \u2022 (C \u2022 x) = \u00a3*_! (sk \u2014 tk) 2 is positive semi-definite, and the minimization problem can therefore be solved using a quadratic programming method, such as Lemke's method.1415 Consider now the case where one of the components making up the object is a cylinder, rather than a convex polyhedron. We begin with a cylinder of height h, 0d(t) and whose height is d(t). Even when the frequency of rotation varies, d(t) is a signal of the form (1) with constant coefficients 0C, 0,5 Exact disturbance cancellation can, in theory, be achieved by letting 00(t) = 0*, 0,(t) = 0*. Since the nominal parameters are unknown, the control strategy is to use adaptive algorithms to adjust the parameters so that they converge to their nominal values. Let the nominal and adaptive parameter vectors be (Z:) (3) vector defined in (4), and WF (t) is the filtered regressor vector defined as WF (t) = P(s) [w(t)1 (7) P(s) is the estimate of the plant P(s)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000050_s0094-114x(00)00007-0-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000050_s0094-114x(00)00007-0-Figure1-1.png", "caption": "Fig. 1. The schematic of the cutting mechanism.", "texts": [ " It represents the boundary between stable and unstable motion. In the cutting mechanism it is the force which transforms the regular rotating motion of the leading element to oscillatory motion. The direct Liapunov method of stability is applied to prove the obtained previously solution. The pre-buckling and post-buckling motions are also discussed in the paper. The motion is obtained by solving the di erential equation of motion for various values of the cutting force. The scheme of the mechanism is shown in Fig. 1. The mechanism contains a leading bar O2C which is connected to the link CB. This bar is connected with a slider-shaped mechanism which contains the bars DE and O1A, and a slider. The rotating slider is hinged via a linear rotational spring. The bar DE is the working element of the mechanism. At the end of the working link a cutting tool is \u00aexed. A constant torque M acts on the leading element. The cutting tool acts on the working piece with a force P. Let us introduce the notation AD f, AB b, BE e, O1A a, BC r, O2C g, O1D h: 1 The angle from O1D to the vertical is a const: The angle position of the link 3 is c, and of the driving element 1, which rotates around O2 is y: The angles c and y are not independent. The mechanism is a systems with one degree-of-freedom. Using the geometrical relations in Fig. 1 it is F c, y A0 A1cos y\u00ff A2sin y 0, 2 where A0 g2 \u00ff r2 z21 z22 , A1 2gz1, A2 2gz2, z1 L\u00ff f\u00ff b sin c a , z2 f\u00ff b cos c a , and f h cos c a2 \u00ff h2sin2c q : 3 Eq. (3) describes the length variation of the link 3 as a function of the position c: The working element periodically changes its length and angle if the input velocity is constant. To satisfy the requirements of such a motion, some constraints to parameters of mechanism exist. For the working element to move oscillatory and the leading element to rotate, the relation between the parameters of length has to be L gRf r: 4 The mechanism is a one-degree-of-freedom autonomous system" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001933_05698190590948232-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001933_05698190590948232-Figure2-1.png", "caption": "Fig. 2\u2014Structure sketch of latest high-speed test rig: 1, base; 2, auxiliary bearing; 3, test gland; 4, test case; 5, bearing house; 6, coupling; and 7, high-speed motor with variable frequency.", "texts": [ " Presented at the 59th Annual Meeting in Toronto, Ontario, Canada May 17-20, 2004 Final manuscript approved December 14, 2004 Review led by Jim Netzel The main target of research on oil-film-lubricated spiral-groove face seals is to develop noncontacting spiral-groove face seals with zero leakage and long life, mainly for use in high-speed turbocompressors of the oil refinery and petrochemical industries. So, the development of a high-speed test rig is very important and essential. Figure 1 is a drawing of the early high-speed test rig (Wang, et al. (2)), where a two-stage speed-increasing gear box was used. Figure 2 is the structure sketch of latest high-speed test rig, where a high-speed variable-frequency motor with rotating speed up to 20,000 r/min is used. This has reduced noise in the laboratory and increased the driving torque. Figure 3 is a drawing of the early test spiral-groove face seal. It is a face-to-face, double seal with a closed circulation system of sealing oil using a self-circulating screw pump. Figure 4 shows the principle of the supporting system for the test rig. It consists of a sealing-oil system and a sealed-gas system" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000558_romoco.2002.1177105-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000558_romoco.2002.1177105-Figure5-1.png", "caption": "Figure 5:", "texts": [ " 4 we show two robots (denoted using digits) and two target points (denoted using letters). Robot 1 has lower priority and is assigned to its nearest target point A because it is positioned father to the desired formation. Robot 2 has higher priority and is assigned to the target point B. Robot 2 moves straight to the target point B. Robot 1 movies straight to the target point A, however, it periodically checks if its motion may violate forbidden area of robot 2. When such situation occurs robot 1 suspends its motion. At fig. 5 we present simple example for desired formation with nine target points and nine robots. The initial positions of robots cause that planned trajectories are not crossed, but when dimensions of robots are sufficiently big there can Occur collision of robots 1 and 2 with robot 9. In accordance with previously described method robots 1 and 2 suspends its motion when they may violate forbidden area of robot 9. Robot 9 has highest priority and has right of way before all other robots. At fig. 6 wepresent similar example" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001777_ejc.11.157-166-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001777_ejc.11.157-166-Figure1-1.png", "caption": "Fig. 1. Membership functions.", "texts": [ "1) can be approximated by the following TS fuzzy model: E\" _x\u00f0t\u00de\u00bc Xr i\u00bc1 i \u00f0Ai\u00fe Ai\u00dex\u00f0t\u00de\u00feB2u\u00f0t\u00de\u00feB1w\u00f0t\u00de\u00bd , x\u00f00\u00de\u00bc0 z\u00f0t\u00de\u00bcC1x\u00f0t\u00de y\u00f0t\u00de\u00bcC2x\u00f0t\u00de where i are the normalized time-varying fuzzy weighting functions for each rule, i \u00bc 1, 2, x\u00f0t\u00de \u00bc xT1 \u00f0t\u00de xT2 \u00f0t\u00de xT3 \u00f0t\u00de T , w\u00f0t\u00de \u00bc wT 1 \u00f0t\u00de wT 2 \u00f0t\u00de wT 3 \u00f0t\u00de T , A1\u00bc 2 10 0 1 1 1 1 0 1 2 64 3 75, A2\u00bc 2:9 10 0 1 1 1 1 0 1 2 64 3 75, B1\u00bc 0:1 0 0 0 0:1 0 0 0 0:1 2 64 3 75, B2\u00bc 0 0 1 2 64 3 75, C1\u00bc 0:1 0 0 0 0:1 0 0 0 0:1 2 64 3 75, C2\u00bcJ, E\"\u00bc 1 0 0 0 \"1 0 0 0 \"1\"2 2 64 3 75, A1\u00bcF\u00f0x\u00f0t\u00de,t\u00deH11 and A2\u00bcF\u00f0x\u00f0t\u00de,t\u00deH12 : The plot of themembership functions is given in Fig. 1. Assuming F(x(t),t)\u00bc 1, we have H11 \u00bc H12 \u00bc 0 0 0 0 0:3 0 0 0 0 2 64 3 75: Employing the results given in Lemma 3.1, it is easy to see that when \"1 < 0:01 and \"1\"2 < 0:000001, the LMIs become ill-conditioned and the Matlab LMI solver yields the error message, \u2018\u2018Rank Deficient\u2019\u2019. 4.1. Case I- (t) are Measurable In this case, x1\u00f0t\u00de \u00bc \u00f0t\u00de is assumed to be measurable, i.e., J\u00bc [1 0 0]. This implies that i is available for feedback. Using the LMI optimization algorithm and Theorem 3.1 with \u00bc 1, \u00bc 1, \"1 \u00bc 0:001, and \"1\"2 \u00bc 0:0000001, we obtain X0 \u00bc 3:8436 30:1349 29:5868 0 20:3660 4:5210 0 0 39:9028 2 64 3 75, Y0 \u00bc 1:6508 4:8682 0:0287 0 0:6315 0:4624 0 0 9:8302 2 64 3 75, A\u030211 \u00bc 10:3879 9:0898 0:4133 1:8593 10:6090 1:6114 0:0001 0:0001 0:4243 2 64 3 75, A\u030212 \u00bc 10:3879 9:0898 0:4133 1:8593 10:6090 1:6114 0:0001 0:0001 0:4243 2 64 3 75, A\u030221 \u00bc 10:6722 9:0898 0:4133 1:8591 10:6090 1:6114 0:0001 0:0001 0:4243 2 64 3 75, A\u030222 \u00bc 9:7722 9:0898 0:4133 1:8591 10:6090 1:6114 0:0001 0:0001 0:4243 2 64 3 75, B\u03021 \u00bc 6:4883 0:0059 0:0001 2 64 3 75, B\u03022 \u00bc 6:6304 0:0059 0:0001 2 64 3 75, C\u03021 \u00bc 0 0 25:9274\u00bd , C\u03022 \u00bc 0 0 25:9330\u00bd The resulting fuzzy controller is E\" _\u0302x\u00f0t\u00de \u00bc A\u0302\u00f0 \u00dex\u0302\u00f0t\u00de \u00fe B\u0302\u00f0 \u00dey\u00f0t\u00de u\u00f0t\u00de \u00bc C\u0302\u00f0 \u00dex\u0302\u00f0t\u00de where A\u0302\u00f0 \u00de \u00bc X2 i\u00bc1 X2 j\u00bc1 i jA\u0302ij, B\u0302\u00f0 \u00de \u00bc X2 i\u00bc1 iB\u0302i and C\u0302\u00f0 \u00de \u00bc X2 j\u00bc1 jC\u0302j with 1 \u00bc M1\u00f0x1\u00f0t\u00de\u00de and 2 \u00bc M2\u00f0x1\u00f0t\u00de\u00de: 4" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002304_004-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002304_004-Figure1-1.png", "caption": "Figure 1", "texts": [ " (23) This equation is solved for K and then the velocity correction is made using Eq.(21): K = \u2212I ( t3q\u0307 + 1 2 t2q )2 . (24) Hence the one-step velocity correction is \u0394 q\u0307 = I t3q\u0307 + 1 2 t2q . (25) Thus, at end of each time step in the numerical integration, the value of the conserved quantity is approximately zero. Example2 A pendulum of particle mass m and length l is forced to rotate about a vertical axis with a constant angular velocity \u03a9 . The pendulum angle \u03b8 is measured downward from the horizontal axis \u03b7, as shown in Fig.1. The system is described by Lagrange\u2019s equation of the form d dt (\u2202L \u2202\u03b8\u0307 ) \u2212 \u2202L \u2202\u03b8 = 0 . The Lagrangian function is L = T \u2212 V = 1 2 ml2\u03b8\u03072 + 1 2 ml2\u03a92 cos2 \u03b8 + mgl sin \u03b8 . The corresponding motion equation of the system is ml2\u03b8\u0308 \u2212 m(gl \u2212 l2\u03a92 sin \u03b8) cos \u03b8 = 0 . After simplifying it, we have \u03b8\u0308 \u2212 (g/l \u2212 \u03a92 sin \u03b8) cos \u03b8 = 0 . Assume that g/l = 4 m/s2 and \u03a9 = \u221a 10 rad/s, then substitute these values into Eq.(27), we obtain \u03b8\u0308 + (10 sin \u03b8 \u2212 4) cos \u03b8 = 0 . (28) This second-order equation can be converted into two first-order equations and integrated numerically under the initial conditions \u03b8(0) = 0 and \u03c9(0) = 0" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001578_acc.2004.1383649-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001578_acc.2004.1383649-Figure3-1.png", "caption": "Fig. 3. Steerable Nips with Paper Buckle", "texts": [ " Section I1 will describe the nonholonomic constraints, kinematic model, and dynamic model of the steerable nips mechanism. The control strategy is derived in section 111. Simulation results will be shown in section IV. Finally, conclusions and some comments regarding the control performance are stated in section V. 11. KINEMATIC AND DYNAMIC MODEL OF THE STEERABLE NIPS MECHANISM The steerable nips is illustrated in Figs. 2 - 3. The steerable nips moves a sheet on a flat surface. Figure 2 represents an initial sheet position once the two nips are in contact with the sheet. Figure 3 represents a sheet position while it is being tracked. The left comer of the sheet, point C, will be used to track the position of the sheet. The angular orientation of the sheet is 4. Note that while the paper buckles, point C remains on the flat surface since the buckle occurs only between points 1 and 2. For this reason point C does not move perpendicular to the sheet. 4n2 It is assumed that when the sheet buckles, the sheet is still transversally stiff so rotation is possible. This is illustrated in Fig. 3 where any line perpendicular to the line that connects points 1 and 2 drawn on the buckle surface is parallel to the flat surface. A . Notation Figure 4 shows a schematic representation of the modeling variables for the steerable nips system. This system has two independent steering wheels, located at points 1 and 2. These steerable wheels are separated by a distance 26. Three coordinate frames are defined to describe the position and orientation of the paper: A fixed global coordinate system denoted (jf, if, k,), and two local frames ( j l , i l ,k l ) and (j2,f2,kZ) attached to wheel 1 and 2 respectively" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001428_j.cam.2003.06.009-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001428_j.cam.2003.06.009-Figure2-1.png", "caption": "Fig. 2. Inductor with a source of electromotive force emf ; i and its cut Ci; @C+i and @C\u2212 i are the traces of both sides of Ci on @ c.", "texts": [ ", its terminals, give no contribution because n \u00d7 e = n \u00d7 es = 0 on them. Thus, using (12), one has \u3008n \u00d7 es; h\u2032\u3009 e = \u3008n \u00d7 es; ci\u3009 e = \u3008n \u00d7 es;\u2212grad qi\u3009 e = \u3008grad qi \u00d7 es; n\u3009 e = \u3008curl (qies); n\u3009 e \u2212 \u3008qi curl es; n\u3009 e : Using then the Stokes formula for the &rst integral and seeing the second integral vanishes (if the thickness of emf ; i is small enough), one has \u3008n \u00d7 es; ci\u3009 e = \u222e @ e qies \u00b7 dl = \u222e @ i es \u00b7 dl = Vi (13) because only the part i of the oriented contour @ e in contact with @C+i gives a nonzero contribution (Fig. 2). Consequently, for the test function h\u2032 = ci, (8) becomes @t( h; ci) + ( \u22121curl h; curl ci) c =\u2212Vi; (14) which is the natural weak circuit relation for massive inductor i, in which current Ii is strongly de&ned through constraint (9) on h. A similar treatment can be done for stranded inductors. The basis functions of hs in (10), i.e., the unit source magnetic &elds hs; i, lead to, when used as test functions h\u2032, @t( h; hs; i) + Is; i ( \u22121js; i ; curl hs; i) s; i =\u2212Vi; (15) which is the natural weak circuit relation, of form (11), for stranded inductor i" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003434_6.2008-4505-Figure12-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003434_6.2008-4505-Figure12-1.png", "caption": "Figure 12 Sketch of test article gaps as viewed from OD to ID for fully open seal without end flange or overlapping top foils.", "texts": [ " Test Method and Descriptions American Institute of Aeronautics and Astronautics 092407 4 Six different configurations of proof of concept foil face seals were fabricated in order to assess the impact of flow path radial length, axial preload and surface velocity on leakage. The six test articles are shown in Figure 5 through Figure 10. Two 9-inch OD thrust foil bearings, two 4.37-inch OD and two 3.82-inch OD configurations were fabricated providing different L/Ro ratios, angular gaps between pads and different flow paths. For each test seal, the outer periphery of the compliantly supported foil pads was open to atmosphere, thereby presenting a leakage path along the radius as opposed to the closed ends shown in Figure 3. Figure 11 and Figure 12 schematically show the tested configurations with the open ends and the primary flow paths. The importance of the open ends for these initial tests was to determine the baseline resistance to flow due to the total axial gap (htotal) in the angular segments between pads, the gap beneath the bump foils (hb) and the gap between the top smooth foil and the disc (hfilm), all without the end flanges and secondary seal elements to restrict flow. This would allow for an assessment of critical design parameters for the fundamental seal shape, such as an assessment of the importance of L/Ro ratio", "5 American Institute of Aeronautics and Astronautics 092407 5 The preliminary model used to assess leakage flow is presented in equation 1 below. 3 0 9/4 4/7 14 )(7.1 \u239f\u239f \u23a0 \u239e \u239c\u239c \u239d \u239b \u23a5 \u23a6 \u23a4 \u23a2 \u23a3 \u23a1 \u0394= h h P L Dq new\u03c0 Equation 1 The above equation is based on the Reynolds flow equation but has been simplified so that the influence of the critical parameters and their impact on design could be readily evaluated. As seen in the above equation, the key parameters are the axial gap, which is, in reality, comprised of both the total gap beneath the seal surface (hbump) and the gas film height (h film) (See Figure 11 and Figure 12). Since flow is affected by the ratio of film height to total gap to the 3rd power, this parameter will be crucial to reducing the leakage flow through the seal once the ends of the hydrodynamic compliant foil pads are designed to close off the radial flow, as shown in Figure 3. It should also be noted that the angular radial gap was not included in the preliminary analysis above. In the final design, the radial angular gap will be eliminated in the hardware by having the pads overlap each other", " Each of these observations was as expected, confirming the hypothesis that hydrodynamic effects would be at work in the seal design to reduce leakage by providing an additional resistance to flow. For example, a review of the leakage flow model (equation 1) shows that flow is inversely proportional to path length (L) and is reduced by reductions in the ratio of axial gap height to the third power. What is not shown in this closed form Reynolds equation is the influence of the hydrodynamic pressure generated as a function of surface velocity (see Figure 11 and Figure 12). In essence, the hydrodynamic generated pressure will act to reduce the effective gap between the disk and the top smooth foil and will put an additional resistance to leakage flow, thereby, reducing total leakage flow factor. Thus, given the trends observed and the compilation plot of all static tests shown in Figure 37, it is highly probable that large face seals having flow factors approaching and even less than 0.01 will be possible. American Institute of Aeronautics and Astronautics 092407 11 IV" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003316_07ias.2007.149-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003316_07ias.2007.149-Figure6-1.png", "caption": "Figure 6 Arrangement of axial position sensor, (a) X-Y cross-sectional view, (b) Y-Z cross-sectional view", "texts": [ " More analysis of this equation is shown in Section V. Because of the inner impeller structure, it is inconvenient to install axial position sensor directly in the flow path. Instead, four hall sensors located on the inner stator surface and a ring PM mounted on the rotor are utilized to measure rotor axial position. The ring PM provides magnetic flux to the sensors. These sensors are placed 90 degrees from one another to detect variations of magnetic field caused by rotor movements. Sensor arrangement is shown in Fig. 6. Since both axial and radial movements affect the magnetic field measured by the sensors, signal processing is required to extract axial position from sensor feedbacks. Magnetic flux density measured by the hall sensors vs. axial displacement when the rotor is located at the center of the air-gap is calculated first. Because all four sensors detected the same flux density, the resulting curves overlapped one another. For comparison, this curve is designated as the \u2018reference\u2019 curve and plotted in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000457_978-3-642-55848-1-Figure7.82-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000457_978-3-642-55848-1-Figure7.82-1.png", "caption": "Fig. 7.82. P-channel MOSFET. (a) The circuit symbol, (b) The bond graph representation", "texts": [ " It also can be used for additional control ofMOSFETS [9]. The electrical circuit symbol used for n-channel MOS (NMOS) is shown in Fig. 7.8Ia. Voltage polarities and the current direction correspond to normal operation. The corresponding bond graph component is shown in Fig. 7.81b. It is assumed 7.4 Modelling Semiconductor Components 283 that power flows into the component at the gate, bulk, and the drain ports; and flows out at the source port. Polarities of p-channel MOSFETs (PMOS) are just the opposite (Fig. 7.82a). Similarly, the port power flow senses of the corresponding bond graph compo nents also are reversed (Fig. 7.82b). The NMOS component can be created using the n-channel MOSFET button of the Electrical Component palette (Fig. 7.2). The text MOS is just a label used for reference to the component and can be changed at this stage or later. The p channel component can be created from an n-channel component by reversing the power flow direction of all ports. It also is possible to change only the base and bulk ports. In this case, the drain and source of the n-channel MOSFET effectively change places. The n-channel MOSFET model (Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001569_s0022-0728(81)80591-8-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001569_s0022-0728(81)80591-8-Figure1-1.png", "caption": "Fig. 1. Cyclic vo l t ammet ry of n i t rosodurene (T). Est imated concent ra t ion of the m o n o m e r i c form: 0.5 raM. Elec t ro ly te : DMF/0 .1 M Bu4NBF 4 in the presence of act ivated alumina. Reference electride: Ag/AgI / I - 0.1 M. Sweep rate: 100 mW s -~. Working electrode: s ta t ionary Hg. (a) T alone; (b) T + 3.2 mM n-BuBr; (c) T + 6.5 mM n-BuBr.", "texts": [ " Free radical formation by electron transfer may also be obtained electrochemically by means of an electron transfer to sulphonium salt cations R 1R 2 ~R a possessing a rather low acidity, such as VII. C12H2% J C12H25 ~ X7~ The reactivity of RX compounds (I--VII) towards T - in the vicinity of the electrode or in solution, was followed by cyclic vol tammetry at different sweep rates and also by using ESR spectroscopy coupled with electrolysis in situ in order to trace the nature of the reaction leading to the disappearance of T - (e.g. alkylation or protonation). Adding RX derivatives to nitrosodurene does not bring a noticeable increase to the current of T (Fig. 1). However, the disappearance of T - is followed by the decrease of the anodic current of the cyclic voltammogram. The reactivity of organic iodides (I) and (II) with T - is fast but n-butyl chloride (V), known to be difficult to reduce, does not react. On the other hand, the ESR method in situ does confirm the possible reactivity of these RX compounds. For high reactivity the spectrum of the trapped radical appears alone (Fig. 2). In the case of a much lower reactivity, the simultaneous presence of T= and TR\" may be noticed near the interface: Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure2.3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure2.3-1.png", "caption": "Fig. 2.3. Tube design", "texts": [ " The displacement in the device is caused by the contraction in the material being perpendicular to the direction of polarization and electric field application. The maximum travel of the laminar actuators is a function of the length of the sheets, while the number of sheets arranged in parallel will determine the stiffness and force generation of the ceramic element. Laminar actuators are easily integrated in conventional composite layers. The monolithic ceramic tube is yet another form of piezo actuator. Figure 2.3 shows a design structure. The surface of a tube is partitioned into four regions and they are connected along with one end of the tube to electrodes. Thus, it becomes possible to apply voltages to the tube to initiate motion in various directions. For example, when an electric voltage is applied between the outer and inner diameter of a thin-walled tube, the tube contracts axially and radially. A variety of chemical and materials processing applications use ceramic tubes. Ceramic tubes are also used to fabricate electrical parts for high voltage or power applications such as insulators, igniters or heating elements" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000624_s0022-5193(89)80100-6-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000624_s0022-5193(89)80100-6-Figure3-1.png", "caption": "FIG. 3. Directions of tangential, normal and binormal unit vectors.", "texts": [ " Since in this case the cell body itself is long and narrow, a similar effect to that on the sinusoidal filament might operate on the swimming spirillum. The effect is greater when there are two parallel boundaries close to the filament. The power dissipated by the model cell was calculated. Scaled average power over one cycle of the flagellar bundle kPt(l~f32) was 4.03 x 102. About 37% of the total power was dissipated by the body. F O R C E D I S T R I B U T I O N O N T H E C E L L The force distribution on the cell was calculated in directions tangential, normal and binormal to the cell centreline (illustrated in Fig. 3). These were compared with force distributions obtained using Lighthill's optimal resistance coefficients (Lighthill, 1976) and tangential, normal and binormal velocities calculated using the solutions for U and IT (This is essentially similar to Higdon's approach, 1979a.) The results are shown in Fig. 4. Generally the agreement is good, with the largest discrepancies being in the regions of high forces. This implies that body-flagellar interactions and long distance effects of the flow of fluid around the cell, which resistive force theory does not take account of, are not of great importance" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000170_0005-2736(86)90240-3-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000170_0005-2736(86)90240-3-Figure2-1.png", "caption": "Fig. 2. Scheme of the measuring chamber: cells deposited on the surface of a wedge are collected in a microfunnel by suction. Constant flow of the bathing solution is obtained with strips of filter paper between vessel A, measuring chamber B and vessel C. Chamber B is filled to cover glass with bathing solution and is open at the sides.", "texts": [ " Individual cells were immobilized in extremely fine microfunnels, which were pulled and blown from glass capillaries (WP-Instruments, New Haven, CT) with a microforge essentially as described in Ref. 9. However, the neck of the microfunnel was reduced to 7-10 /~sn. The growth of P. humboldtii cells in short chains proved to be of significant advantage, because individual chains were firmly anchored by the smaller cells inside the neck of microfunnel (Fig. 1). Yeast cells in a drop of cell suspension were allowed to sediment on the slope of a wedge located in a pelxi-glass measuring chamber (Fig. 2), a modified version of a measuring cell used by 373 Takeda and co-workers [10]. After the chamber was filled with bathing solution (see below), individual cell chains were sucked into the microfunnel. The microfunnel was advanced by means of a Leitz micromanipulator. The microfunnel and the measuring microelectrode (see below) were operated under a Leitz Dialux microscope which was fitted with a longworking-distance objective (20 x ), resulting in 250 x magnification. Potential measurements. Glass micropipettes were pulled with a vertical puller (D" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002598_s11340-007-9089-x-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002598_s11340-007-9089-x-Figure1-1.png", "caption": "Fig. 1 Split-disk tensile test", "texts": [ " Although the testing of flat specimens may be possible for determining their axial-direction material properties, flat specimens often cannot be obtained readily for determining their circumferential or \u201choop\u201d direction properties. Thus, the use of ring-shaped test specimens is desirable for determining the hoop-direction tensile properties of cylindrical composites. Of particular interest is an affordable ring test method capable of accurately determining both the tensile strength and tensile modulus of these composites. Currently the only standardized ring test method for composite materials is the split-disk tensile test, described in ASTM Standard D 2290 [1] and shown graphically in Fig. 1. In this test method, the composite ring specimen is placed over the outside diameter of a steel split-disk fixture and a separation force is applied to the disk halves with a convention load frame. The resulting separation of the disk halves produces a tensile loading of the composite ring specimen. The tensile strength of the specimen is determined by dividing the applied load at specimen failure by twice the average cross-sectional area of the ring. Using strain gages mounted on the outside surface of the ring specimen, the modulus of elasticity may also be determined in the hoop-direction" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001900_1.1850943-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001900_1.1850943-Figure1-1.png", "caption": "Fig. 1 Schematic of a brush seal", "texts": [ " Example results from this code are presented that show the bending behavior of initially hexagonally packed brush seals under model imposed pressure loads acting on the bristle tips. The effects of rotor incursions into the bristle pack, increase of the pressure load, and changes in the lay-angle and Young\u2019s modulus are also shown. The results illustrate the expected bending behavior observed in real brush seals. Procedures for coupling SUBSIS with CFD models are also currently under investigation. DOI: 10.1115/1.1850943 Conventional brush seals comprise of a dense pack of bristles held between a narrow front plate and a backing ring, as shown in Fig. 1. Over the past 20 years, these advanced seals have emerged to be a very promising technology for gas-path sealing applications in turbo-engines. However, despite much experimentation and the fact that brush seals have successfully operated in jet engines, their behavior is far from being fully understood, and advances are still required if brush seals are to be more generally used. Wear, which occurs as bristle tips contact the rotating parts, is a particular problem. There are, therefore, considerable potential benefits in better understanding and possibly controlling the factors that influence wear", " At present the model neglects the effects of static and kinetic friction due to the backing ring and/or rotor surface, although these effects are important and should be addressed in later versions. Bristle bending predictions are presented here for a typical brush seal geometry, and qualitative comparisons with previous results are discussed. Note that, although the brush seal is modeled here as a linear bristle pack, rather than a circumferential one, lengths in the width X and height Z directions are referred to as the circumferential and radial directions, respectively, as shown in Fig. 1. Bristles are identified with the coordinates (Xi , j ,k ,Y i , j ,k ,Zi , j ,k) of points along their centerline, and each bristle is subdivided into JULY 2005, Vol. 127 \u00d5 583 005 by ASME 016 Terms of Use: http://www.asme.org/about-asme/terms-of-use Download K 1 elements, each of length L/(K 1). The distance from the fixed bristle root is denoted by k (k 1) . A bristleoriented coordinate system (x ,y ,z) is also considered, and bi , j ,k denotes the point k along the centerline of the bristle with fixed root at position (xi , j ,yi , j)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000965_0005-2736(85)90037-9-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000965_0005-2736(85)90037-9-Figure1-1.png", "caption": "Fig. 1. A cross-sectional illustration of the high-pressure cell used for membrane conductance measurements is presented. A, Port closure bolt; B, O-ring seal; C, rear compartment access; D, O-ring seal for pressure vessel lid; E, nylon filler; F, membrane aperture; G, Teflon cup; H, stirring magnets; I, nylon filler; J, high*pressure port for gas entry; K, drive magnet; L, belt-driven shaft; M, stainless steel pressure vessel; N, light holder; O, O-ring seals; P, sapphire window; Q, miniature lamps; R, spring contact; S, electrical feedthrough for lamps; T, lamp input lead; U, front chamber access for membrane formation; V, fused quartz window. The Ag/AgC1 electrodes and pressure transducer are not illustrated.", "texts": [ " A motor driven oil pump delivered a rising column of oil to a high-pressure reservoir. The rising oil compressed the gas above it, typically He. The gas transmitted the pressure through a 2 m length of high pressure capillary tubing to the test cell containing the membrane under study. The system was precharged to cylinder pressure (10-15 MPa) with He, then isolated for further pressurization using the oil pump. The test cell containing the teflon (E.I. du Pont de Nemours, Inc., Wilmington, DE) chamber in which membranes were formed is illustrated in Fig. 1. Pressure was contained by a heavy walled stainless steel vessel fitted with a bolted, O-ring sealed stainless steel lid. The vessel was fitted with an oriented single-crystal sapphire window (Adolf Meller Co., Providence, RI) and miniature lamps (Model No. 718, Miniature Lamp Works, Chicago, IL) mounted internally to permit viewing of the membrane. Membranes were formed by inserting a brush laden with membrane forming solution through the open front port shown in Fig. 1. Both front and rear ports were sealed prior to pressurization. Pressure was measured using a bonded silicon strain gauge (Model 8511-10K, Endevco, 345 Inc., San Juan Capistrano, CA) threaded into a side port of the cell. Teflon-coated stirring bars, driven by a rotating magnet mounted externally, could be used to agitate the solutions bathing the membrane.\" Electrical measurements Electrical contact with the membrane was provided by Ag/AgC1 electrodes of 1 cm 2 area (not shown in Fig. 1) immersed in the adjacent aqueous 346 phases. Hermetic feedthroughs mounted in the lid of the pressure vessel (Type 24916-19501; AstroSeal, Inc., South El Monte, CA) provided external connections to the electrodes and to the internally located miniature lamps. Voltage pulses for membrane conductance measurements were produced by a microprocessorbased programmable pulse generator built in our laboratory, using a system design kit (SDK-85) available from Intel Corp., Santa Clara, CA. It could provide up to eight output pulses per cycle, each having independently programmable duration and amplitude" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002007_icarcv.2004.1469485-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002007_icarcv.2004.1469485-Figure3-1.png", "caption": "Fig. 3 Obstacle-navigation process", "texts": [ " Power department can provide the structure data information of obstacles. Fig. 2 shows the sketch of mechanical system of the mobile robot. The mobile robot has two arms (forearm and rear-am) and a bcdy. There are two grippers on the top of two arms respectively and a running wheels on the top of body. In attention, there is a wheel on every gripper and when a gripper grasps the wire, it can move along the overhead ground wire back\u2018 and forth using the wheel. The process of obstacle-navigation is shown in Fig. 3. The obstacle-navigation principle is \u2018step by step\u201d. Firstly, the gripper on rear-arm grasps the wire and the forearm elongate to navigate obstacles. In the second step, the gripper of the forearm grasps the wire and the running wheels get off from the wire. Two grippers continue to move forward, and the body can move across the obstacles. Finally, the running wheel tums over the wire and grasps it. The gripper of rear-arm loosens and navigates the obstacles or moves to a appoint position to grasp the wire" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000735_0167-2789(89)90262-5-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000735_0167-2789(89)90262-5-Figure2-1.png", "caption": "Fig. 2. Curves in the Ct C3 parameter plane at which bifurcations to a trefoil knot occur.", "texts": [ " This corresponds to the special case in which the original diffusion reaction equation has equal diffusion coefficients for all of its variables. In this special case, eqs. (4.1) reduce to the system of equations + + a,)g + + ~..2.2 0, 2'~0~ = : 2 _ ro 2 = 2Xo(iCoa 3 + al)g + g2. ( 4 . 2 ) With the simple rescaling of variables g = foX, Cl = al, C3 = roaa, ~2 _ Ko 2= p2, the equations simplify further to (x + (c,-c,)x-c:)f + = o, x 2 + 2((73 - C1)x \"- p2 = 0. ( 4 . 3 ) It is not difficult to tint, solutions of these algebraic equations. In fig. 2 are shown the four curves in the C t C 3 parameter plane on which eqs. (4.3) have solutions with ~ = 3/2 (i.e., p2= 5/4). Although the curves appear to have intersections, they do not, since the values of x along each curve are different. For example, of the two curves shown in fig. 1 with C 3 positive, one (the one which is double valued when viewed as a function of C~) has x negative, while the second curve (the one which is monotone increasing as a function of C~) has x positive. These four curves in the C1 C~ parameter plane are the curves at which torus-knot bifurcations occur. This leads us to the following observation (wh/ch is simply a statement of the Hopf bifurcation theorem [5, 14]): Proposition 4.3. Emanating from every point in the C 1C 3 parameter plane along the curves (4.3) is a family of m/n torus knotted solutions of eqs. (2.4). Before we calculate the direction of bifurcation it is worthwhile to see how large the region of possible bifurcation points is. If we vary the parameter p in eqs. (4.3) the curves shown in fig. 2 sweep out a region in the C~ C3 parameter plane. The envelope of the family determines the bounda~y of the region containing bifurcation points, and since the rational values of ~t densely pack the real line, so also the curves at which there are bifurcations to toms knots densely pack the interior of this region of the C 1 C3 parameter plane. In fig. 3 are shown the curves from fig. 2 with x > 0, as well as the envelopes which encompass this family of curves. The region covered in fig. 3 is more than half of the Ct C3 parameter plane, so when x is allowed to be negative as well, the C~ C3 parameter plane is completely covered by this family of curves, and we conclude that: Proposition 4.4. The C l C 3 parameter plane is densely packed with torus-knot bifurcation points. This is close to, but not quite the same as. a statement that there is a nontrivial torus knot at every point of the Ct C 3 parameter plane", " Although it is possible to do this calculation in general, the resulting expressions are so complicated that they are of no value, at least in helping to understand qualitative features of the solution. This calculation was automated using the alge. braic programming language REDUCE and the above perturbation calculation was repeated for a range of values of \"to. The most significant result from these calculations was the determination of the direction of bifurcation across the critical parameter curve. Fig. 4 is a sketch of the critical curves from fig. 2 with \"to > 0, with an arrow +5cos - ~ + t - ~ s i n ~ -+ t - 0 , or that x = t to leading order in e. Next, to calculate the coordinate amplitude a(t), we note that 1 + a(t) = R(x). Ro(t), so that a(t) -eA(~cos( 5x-~- t ) + s i n ( 5 ; - - - t) +Ssin ~-+t +~cos g + t , or to leading order in e a(t) = EA(~ cos-~ + 6s in -~ ) . (4.8) pointing in the direction of nontrivial bifurcation for selected values of ~'o- Bifurcations in the upper-half plane are to right-handed knots, wh;le bifurcations in the lower half plane are to lefthanded knots" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001578_acc.2004.1383649-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001578_acc.2004.1383649-Figure1-1.png", "caption": "Fig. 1. Steerable Nips Shematie", "texts": [ " INTRODUCTION Some high speed color printers require that sheets he accurately positioned so that colors can he accurately placed on the sheet. To accomplish this goal a steerable nips mechanism has been proposed as an actuator. This actuator is located at the end of the copier\u2019s paper path. The steerable nips permit a more swift correction of lateral errors. This is a challenging mechatronic problem especially when sheets must move at high speeds. The steerable nips mechanism is schematically depicted in Fig. 1. The problem of controlling paper trajectories with steerable nips is similar to the control of two-wheel robots, such as the one studied in [I]. However, the control law proposed in [I] fails to account for singularities that arise when the steering angle of the wheels approach zero. Also, in the case of the two-wheel robot, three inputs are needed to follow a reference trajectoty. This is not the case with steerable nips, where four inputs are needed due to the flexibility of the paper. The system model has four inputs, the first and second inputs rotate wheels one and two respectively" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000453_bf00790139-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000453_bf00790139-Figure2-1.png", "caption": "Fig. 2. Model of the rotor with its shaft as a standard solid", "texts": [ " This rotates in a viscous medium reacting on the motion of the rotor by a force proportional to the absolute velocity of the geometric disk center G where c is a suitable damping coefficient. The oil film in the bearings is not only an elastic but also a damped component. The viscoelastic properties of the support material are also a source of energy dissipation. The bearings in our structural model are replaced by massless Kelvin-Voigt bodies. Isotropie identical bearings are assumed, and characterized by two parameters, the stiffness coefficient k b and damping coefficient cb. Analogous shaft properties will be described by the standard solid (Fig. 2) which is a 3-parameter solid consisting of two springs (external and internal rigidity k and xlc, resp.) and one dashpot (damping constant b). This latter one represents the internal friction which may be caused by the viscosity of the shaft material and/or by dry friction between the hubs and the bent shaft. Both friction forces appear, while deformations of the shaft are nonstationary. A plane motion of the disk has been assumed, so that the journals line A1B1 is parallelly displaced in space and a cylindrical axode is circumscribed (Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002338_j.jmatprotec.2006.03.081-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002338_j.jmatprotec.2006.03.081-Figure5-1.png", "caption": "Fig. 5. The traverse section of the welding layers and definitive trajectori", "texts": [ " The distance mong the trajectories of two consecutive weld beads, odd dii r even dpp, is also constant and equal to half of the width of a eld bead (L/2). For all the points located in the damaged surface si,j(o, w) nd belonging to the initial trajectories of the weld beads, the disance t in relation to the original surface ri,j(u, v) is determined n the direction of his respective unitary normal vector. The maximal distance tm, among these points and to the orignal surface ri,j(u, v) is obtained by the verification of the largest istance t among all the points. Furthermore, the number of layrs of welding nc, Fig. 5a, is determined through the following quation: c = ceil ( tm + 0.5 h hmed ) (1) Where: hmed is the medium height of the weld layer (mm), h s the ripple of the weld layer (mm) and ceil is the function that eturns the smaller integer greater than the number considered. The definitive welding trajectories, for each layer (cs = 1, ,. . ., nc), are determined starting from the displacement of the o 8 o m and position and orientation of the welding trajectories of each layer (b). oints belonging to the corresponding initial trajectories, in the irection of their respective unitary normal vectors, as shown in ig", " A definitive welding traectory for a determined layer is formed only by the displaced nd corresponding points that satisfy the following relation: > hmed(cs \u2212 1) (2) Each welding layer is accomplished in the direction o of the amaged surface si,j(o, w). The weld beads are executed with onstant welding speed of vs and only in the opposite direction f w, by moving the origin of the system of coordinates of the orch 0t \u2212 xtytzt over the position of the points belonging to their efinitive trajectory. During the deposition welding automated process, the weldng torch\u2019s reference system 0t \u2212 xtytzt is oriented in the direcions xt, yt and zt, for the respective unitary vectors vt, vb e vn, s shown in Fig. 5b. . Experimental evaluation .1. Description of the test specimen To validate the proposed methodology, the test specimen shown in Fig. 6a as built in a CNC milling machine. Its geometry and material are similar to ypical damaged surfaces found in rotors of hydraulic turbines. The geometry of the test specimen was defined based in a clay mold conormed from a real damaged surface of one of the blades of the Turbine #2 of alto Oso\u0301rio hydroelectric plant. The extreme dimensions of the cavity that repesents the damaged area are 160 mm of length, 120 mm of width and 8" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002860_jmes_jour_1973_015_022_02-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002860_jmes_jour_1973_015_022_02-Figure1-1.png", "caption": "Fig. 1. Full journal bearing", "texts": [ " Angle by which the boundaries of pressure zone deviate from the line + = 0 and + = 6 at the beginning and at the end, respectively. axial direction. (2j- l)T/2. - a m 2 - (K2am2 +Pn2)/B2. Rotation about y\u2019-axis in counterclockwise direction (when looking towards the origin). Eccentricity ratio (e/c). Extent of film. Absolute viscosity. Rotation about x-axis in counterclockwise direcAngle measured from line of centres in circumtion (when looking towards the origin). ferential direction. 2 FILM THICKNESS FOR SKEWED AXES In terms of skew components, the transformation (Fig. 1) from the bearing fixed axes (x,y, z) to the journal fixed axes (x\u2019, y\u2019, 2\u2019) is represented by the following equation: cos 6 sin 6 sinu sin 6 cos u x 1;;1=1 0 cos u -sin u (1) -sin 6 cos 6 sin a cos 6 cos u I I I The equation of the journal surface contour at any section with respect to the journal fixed axes is Substituting the values of x\u2019 and y\u2018 from equation (1) into equation (2) ( x cos 6+y sin 6 sin u+z sin 6 cos u ) ~ Equation (3) represents the journal surface when the bearing centre 0 and journal centre 0\u2019 are coincident", " Considering the journal centre at 0\u2019, the equation of journal surface becomes [ x cos S+(y+e) sin 6 sin u+z sin 6 cos uI2 ~ \u2019 ~ + y \u2019 ~ = R2 . . . . (2) +(y cos u-z sin u ) ~ = R2 (3) +[(y+e) cos u-z sin uI2 = R2 (4) As the skew angles u and 6 are very small, sin u and sin 6 may be taken as u and 6 respectively and cos u and cos 6 may be taken as 1. Also, neglecting the terms containing squares and products of small quantities, equation (4) reduces to Changing equation (5 ) in cylindrical co-ordinates by substituting x = r cos ,9; y = r sin B, noting that B = (90-4) (Fig. 1) and solving for r r = -(z6 sin +-zu cos ++e cos +) x2+2~z6+y2+2ey-2yzu--R2 = 0 . (5) f d(z6 sin 4-zu cos ++e cos Journal Mechanical Engineering Science Vol15 No 2 1973 at UNIV CALIFORNIA SAN DIEGO on March 23, 2016jms.sagepub.comDownloaded from 125 ANALYSIS OF HYDRODYNAMIC JOURNAL BEARING WITH AXES SKEW Taking positive value and neglecting the terms containing squares and products of the small quantities I = -(zS sin 4-20 cos ++e cos $)+R . r denotes the distance of a point on the journal surface, from the origin 0" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000679_00022660110366854-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000679_00022660110366854-Figure1-1.png", "caption": "Figure 1 Notation used to describe missile", "texts": [ " The missile is open loop stable, but has insufficient damping and has non-minimum phase transfer function. The guided missile model described in this section is based on a modified version that is given in Hartman and Grebing (1990). The behavior of a rigid body guided missile may be described as follows: _x t A A x t bu t 1 y t cT t x t 2 e t y t \u00ff yref 3 where x t 2 R3 is the state variable, u t is the scalar control input, y t is the controlled scalar output variable, e t is the scalar output error: u elevator command (radians) y vertical acceleration m=sec2 az in Figure 1 x1 pitch rate (radians/sec) q in Figure 1) x2 angle of attack (radians in Figure 1) x3 elevator deflection angle (radians) in Figure 1) e error between output and desired set point yref A and A are nominal system matrix and parameter variation matrix, respectively. The aim is to find a controller to control the vertical acceleration y subject to the following conditions: (1) For a set point change in yref , the percentage overshoot in y 10 per cent, and the steady-state error 5 per cent. (2) The elevator deflection angle x3 should be limited to jx3j 20 . The elevator deflection angle rate _x3 should be limited to j _x3j 600 =sec" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001519_j.matdes.2004.09.005-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001519_j.matdes.2004.09.005-Figure2-1.png", "caption": "Fig. 2. (a) Tool set. (b) AA5454 forged discs at room temperature and for m = 0.35.", "texts": [ " AISI 5454 aluminium alloy was chosen as the working material for the experiments and its mechanical and chemical descriptions are given in Table 1. Polygonal discs were machined from the alloy sheet having a thickness of 20\u201315 mm as illustrated in Fig. 1(a). Each of them had the same height and cross-sectional area. The aluminum discs were fully annealed for about 2.5 h at 450 C and then furnace cooled. Experiments for open-die forging of regular polygonal discs were carried out in a 110 ton PLC controlled hydraulic press at room temperature and for slightly oily conditions. In Fig. 2(a), the picture of simple flat tooling and in Fig. 2(b) few polygonal forged discs are shown. The specimens were cold forged at ram speed of 0.5 cm/s by giving various deformations from 2% to about 50%. No special lubricant was used, but the tool surface had some oily condition and was not cleaned or dried, so the upsetting took place in its natural laboratory conditions. The ring tests were carried out and friction factor for experimental/tooling environment was determined as m = 0.35 using the calibration charts as proposed by Male and Cockroft [21]" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003875_10402000903312349-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003875_10402000903312349-Figure3-1.png", "caption": "Fig. 3\u2014Coordinate systems.", "texts": [ " [1] yields the unit normal vector of d as follows (n)a = ma (\u03b8, \u03c6) . [2] By means of the classical approach of differential geometry, Eq. [1] also yields the two principal curvatures of d and its corresponding principal directions as follows k1 = \u2212 1 \u03c1 , k2 = \u2212 sin \u03c6 \u03c1 sin \u03c6 + p , (g1)a = na (\u03b8, \u03c6) , (g2)a = ga (\u03b8) . [3] In the process of generation, the two fixed coordinate systems \u03c3 o2(o2; io2, jo2, ko2) and \u03c3 o1(o1; io1, jo1, ko1) denote the initial positions of the cutter pedestal and the DTT worm blank as shown in Fig. 3, respectively. Unit vectors io2 and jo2 are all in the midplane of the mating worm gear. Unit vectors ko2 and ko1 separately lie along the axes of the cutter pedestal and the worm roughcast, which are perpendicular to each other. The shortest distance between them is the distance from point o1 to o2, and |o1o2| = a. The two movable coordinate systems \u03c32(o2; i2, j2, k2) and \u03c31(o1; i1, j1, k1) are rigidly connected to the cutter pedestal and the DTT worm blank in the first enveloping, respectively", " [3], [9], [10], and [14], it is possible to obtain the curvature interference limitation function (Dong (9)) in the first enveloping as d = \u03bbd (g1)o2 \u00b7 (Vd1)o2 + \u00b5d (g2)o2 \u00b7 (Vd1)o2 + d\u03d5; where (gm)o2 = R [ko2, \u03d5d] (gm)2 = g(m) ox io2 + g(m) oy jo2 + gmzko2, g(m) ox = gmx cos \u03d5d \u2212 gmy sin \u03d5d, g(m) oy = gmx sin \u03d5d + gmy cos \u03d5d, m = 1, 2; \u03bbd = k1 (Vd1)o2 \u00b7 (g1)o2 + (\u03c9d1)o2 \u00b7 (g2)o2 , \u00b5d = k2 (Vd1)o2 \u00b7 (g2)o2 \u2212 (\u03c9d1)o2 \u00b7 (g1)o2 ; (\u03c9d1)o2 \u00b7 (gm)o2 = \u2212g(m) oy + gmz / i12, (Vd1)o2 \u00b7 (gm)o2 = \u2212g(m) ox ( yod / i12 + zd ) + g(m) oy xod / i12 + gmz (xod + a) . [15] The curvature parameters of 1 along (g1)o2 and (g2)o2 can be represented as follows k(1) \u03be = k1 \u2212 \u03bb2 d / d, k(1) \u03b7 = k2 \u2212 \u00b52 d / d, \u03c4 (1) \u03be = \u2212\u03bbd\u00b5d / d. [16] DTT WORM GEAR TOOTH FLANK AND MESHING FEATURE PARAMETERS OF DTT WORM PAIR In the second enveloping, the two stationary coordinate systems \u03c3o1 and \u03c3o2 denote the initial position of the DTT worm and its mating worm gear as shown in Fig. 3, respectively. The moving coordinate systems \u03c31 and \u03c32 are separately associated with the DTT worm and its mating worm gear. While the worm rotates around its axis, its helicoid also forms a one-parameter family of surfaces, { 1}, in \u03c3o1. From Eqs. [12] and [13], the vector equation of { 1} and its unit normal vector can be separately represented in \u03c3o1 as{( r\u2217 1 ) o1 = R [ko1, \u03d51] (r1)1 = x\u2217 o1io1 + y\u2217 o1j o1 + yodko1 d (\u03c6, \u03b8, \u03d5) = 0 , [17] x\u2217 o1 = (xod + a) cos (\u03d51 \u2212 \u03d5) + zd sin (\u03d51 \u2212 \u03d5) , y\u2217 o1 = (xod + a) sin (\u03d51 \u2212 \u03d5) \u2212 zd cos (\u03d51 \u2212 \u03d5) ; (n\u2217)o1 = R [ko1, \u03d51] (n)1 , [18] where R[ko1, \u03d51] is the rotary transformation matrix around ko1 axis" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003082_s10659-007-9145-x-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003082_s10659-007-9145-x-Figure2-1.png", "caption": "Fig. 2 Conformal mapping of Galin\u2019s problem", "texts": [ " After this a new function s(z) is introduced s z\u00f0 \u00de \u00bc w2 z\u00f0 \u00de w1 z\u00f0 \u00de ; \u00f03\u00de which maps some curvilinear quadrangle region S onto the upper half-plane of the complex plane and a Riemann-Hilbert problem for function w1(z) was formulated. Solution of this problem depends on the conformal mapping s(z). Having difficulties with mapping the original region S onto the upper half-plane of the complex plane, Galin approximated S by some other region using the following conformal mapping x \u00bc s1 z\u00f0 \u00de \u00fe i is1 z\u00f0 \u00de \u00fe 1 : \u00f04\u00de He showed that his approximation of S (the hatched region in Fig. 2) is quite good and concluded that s(z)\u2248s1(z). Moreover, using this approximation he determined that the coordinate a of the stick-slip boundary is defined by equation Z1 0 dxffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 x2\u00f0 \u00de 1 a=l\u00f0 \u00de2x2 r ,Z1 0 dxffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 x2\u00f0 \u00de 1 1 a=l\u00f0 \u00de2 x2 r \u00bc 2 artan \u03c1=ln\u03ba: \u00f05\u00de Here, the parameter \u03ba is related to the Poisson\u2019s ratio \u03bd as k \u00bc 3 4n: \u00f06\u00de Finally, examining the location of the stick-slip boundary depending on the coefficient of friction, Galin resolved when the total stick and total slip solutions have to be used", " Furthermore, this solution does not include neither explicit expressions for contact stresses nor explicit expressions for the functions w1(z) and w2(z). Galin mentions that to find an exact mapping of the curvilinear quadrangle S onto the upper half-plane of the complex plane one needs to find the integrals of the Fuchsian differential equation (linear differential equations that have regular singular points are known as Fuchsian differential equations) with respect to the function s(z) of the desired conformal mapping s00 \u00fe 1 \u03b1=\u03c0 z \u00fe 1 \u03b1=\u03c0 z 1 \u00fe 1 \u03b1=\u03c0 z a s0 \u00fe 1 \u03b1=\u03c0\u00f0 \u00de 1 2\u03b1=\u03c0\u00f0 \u00de z \u03bb\u00f0 \u00de z z 1\u00f0 \u00de z a\u00f0 \u00de s \u00bc 0; \u00f07\u00de where \u03b1=\u2220B1A1D1 (see Fig. 2), and \u03bb is an accessory parameter that is unknown a priori. Fuchsian equation (7) is also known as Heun\u2019s equation, see, e.g., Ronveaux [15]. It is known that conformal mappings of curvilinear polygons are governed by Fuchsian equations, see, e.g., Nehari [14]. It is also known that there is no general solution procedure for the Fuchsian equation (7) since the accessory parameter \u03bb and the free point a are not known a priori and should be determined as a part of the solution. Primarily because of the difficulties associated with finding parameters a and \u03bb, Galin did not pursue solution of (7) and used the conformal mapping (4) for the region that approximates the curvilinear quadrangle S" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000750_1.1454102-Figure10-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000750_1.1454102-Figure10-1.png", "caption": "Fig. 10 Bolt preload induced initial displacement", "texts": [ " Good agreement in both result comparisons was found, as discussed below. All of the results presented here were obtained using a time step corresponding to one degree crank angle. The piezoviscosity effect was neglected. In Fig. 2 two journal orbits are plotted in a polar diagram ~rigid bearing model and elastic reference bearing model!. In each orbit four points corresponding to four crank angles ~0 deg, 180 deg, 360 deg, 540 deg! are marked. The dashdot bounding circle e/c51 is also plotted. A comparison with the results published in @5# ~Fig. 10 of @5#! exhibits a good agreement. The small differences in the elastic bearing orbit may result from Fig. 3 Cyclic variation of minimum film thickness for the rigid and the reference elastic bearing compared to Mc Ivor results JULY 2002, Vol. 124 \u00d5 489 s of Use: http://asme.org/terms Downloaded F the different element order ~first order fluid and structural solid elements used in the reference bearing model, 6436 node fluid mesh!. In Figs. 3 and 4, respectively, the minimum film thickness and the peak film pressure are plotted versus the crank angle, superimposing the rigid reference bearing solution, the elastic reference bearing solution and the results shown in @5#", " Therefore, in the range ~60 percent\u2013100 percent! nominal bolt preload, the peak film pressure and the minimum film thickness variations may be regarded as linear functions of the bolt preload changes. In Table 1 the absolute minimum film thickness in the cycle is listed. Experimental results from @23# are also reported. Columns 1 and 2 show rigid model results. The results in column 2 refer to a rigid analysis with a fixed non cylindrical bearing clearance variation as determined by a 100 percent bolt preload. Figure 10 presents a three-dimensional plot of this initial displacement, with a f 52000 magnification factor. The cycle power loss values corresponding to columns 1, 3\u20136 of Table 1 are reported in Table 2. In calculating the total power loss with Eq. 14 ~see appendix!, the Couette term was evaluated considering the cavitated film as completely void-filled ~Eq. 17!, or \u2018\u2018striated\u2019\u2019 ~Eq. 18!, or completely void-free ~Eq. 16!. rom: http://tribology.asmedigitalcollection.asme.org/ on 05/14/2015 Term The bolt preload applied to the model of the Ruston and Hornsby big end bearing influences perceptibly the results of the simulated EHD lubrication, increasing the absolute minimum film thickness and the cycle power loss, while reducing the maximum value of peak film pressure and the mean value of oil film thickness" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003889_j.cogsys.2009.12.003-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003889_j.cogsys.2009.12.003-Figure2-1.png", "caption": "Fig. 2. A robot of the team Brainstormers Tribots without paneling exhibits the 2007.", "texts": [ " Although these devices are passive and only put a small force on the ball they have been shown to improve ball handling considerably. Some teams developed active dribbling devices that are able to control the ball even if the robot is moving in backward direction (de Best et al., 2008). While the before mentioned robot equipment is similar in almost all teams, the robots of different teams differ in the overall configuration of these devices. As example, the configuration of the team Brainstormers Tribots is shown in Fig. 2. Since the physical properties of a robot limit the cognitive abilities in scene understanding and behavior execution the co-development of both, the mechanical setup of the robots and the algorithms and concepts of cognition is one of the key issues in robot soccer and is one of the major differences to classical forms of research. One of the teams participating in the RoboCup middlesize-league is the team Brainstormers Tribots which has been initiated in 2002 in our research group. The team is composed out of master, bachelor, and Ph.D. students and the number of members varies between eight and fifteen. It is one of the most successful RoboCup teams of recent years becoming world champion in 2006 and 2007 and winning the technical challenge in 2006, 2007, and 2008. In parallel to developing the robot hardware depicted in Fig. 2 the team was creating the control software containing software modules for visual perception, geometric and dynamic representation of the environment, robot behavior, inter-robot communication, hardware drivers, and monitoring. The growth of the control software from 40,000 lines of code to 150,000 lines of code within 6 years reflects the increasing complexity of the robot behavior, the requirement of better perception and representation of the environment, and the desire to increase the autonomy of the robots incorporating self-surveillance and self-calibration approaches (Lauer et al" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001820_j.1934-6093.2004.tb00189.x-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001820_j.1934-6093.2004.tb00189.x-Figure1-1.png", "caption": "Fig. 1. The bleed air and moment of reaction control system (RCS).", "texts": [ " The exhaust nozzles on the turbo-fan engine can be simultaneously rotated from the aft position forward about 100 degrees. Therefore, the aircraft is allowed to maneuver in conventional wing-borne flight, jet-borne flight, and under even nozzle breaking. The thrust vector produced by the throttle and nozzle enables two-degrees-of-freedom control in the roll-yaw plane. In order to allow lateral maneuverability during jet-borne operation, the aircraft also has a reaction control system (RCS) to provide a moment around the aircraft center of mass as shown in Fig. 1. By restricting the aircraft to jet-borne operation, i.e., thrust directed toward the bottom of the aircraft, we have simplified the dynamics which describe the motion of the aircraft in the vertical-lateral directions, i.e., the motion of a planar V/STOL (PVTOL) aircraft. The aircraft states are the position of the center of mass, (X, Y ), the roll angle \u03b8, and the corresponding velocities, ( X , Y , \u03b8 ). The control input is the thrust directed toward the bottom of aircraft U1 and the moment around the aircraft center of mass U2. If the bleed air from the reaction control valves produces a force which is not perpendicular to the pitch axis, i.e., the angle \u03b1 \u2260 0 shown in Fig. 1, then there will be a coupling effect between the angle rolling moment and lateral moving force. Let the amount of lateral force induced by the rolling moment be denoted by \u03b50; then, we have the aircraft dynamics written as 1 0 2 1 0 2 2 sin cos cos sin , mX U U mY U U mg J U \u03b8 \u03b8 \u03b8 \u03b8 \u03b8 \u2212 = \u2212 + \u2212 = \u2212 + \u2212 = \u03b5 \u03b5 (1) where mg is the gravity force imposed on the aircraft center of mass and J is the mass moment of inertia around the axis extending through the aircraft center of mass and along the fuselage" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000270_iros.1998.724666-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000270_iros.1998.724666-Figure2-1.png", "caption": "Figure 2: Model of soft finger being pushed onto a rigid plane. The contact area is assumed to be circu-", "texts": [], "surrounding_texts": [ "1 Introduction\nRealistic modeling of anthropomorphic soft fingers for grasping and manipulation plays an important role in robotics. There are very little work done in the modeling of contact mechanics in soft finger, however [Howe et al. 1988, Kao and Cutkosky 19921. Nevertheless, the contact mechanics is not a very new field. Hertz first studied contact mechanics based on contact between two linear elastic materials in 1882 [Hertz 18821. He also conducted experiments using glass and found the radius of contact is proportional to the normal force raised to the power of 1/3. Experimental work using various kinds of rubber were performed by Schallamach [Schallamach 19693. Kinoshita [Kinoshita e t al. 19971 studied the growth of contact area as a function of the applied normal force for the human finger. Cutkosky and Jourdian [1987] tested compliant materials to come up with the ideal skin for artificial robot fingers. In [Howe et al. 1988,\nKao and Cutkosky 19921, initial model of soft fingers were proposed with both theoretical and experimental results.\nIn this paper, we study the contact mechanics through theoretical modeling and experimental validation. Assuming that the materials of anthropomorphic soft finger (for example, rubber, silicone, and the human tissue [Fung 19931) are nonlinear elastic, we derive the relationship between the normal force and contact area. While the linear elastic model for contact area [Hertz 18821 is a viable assumption for some materials, it is not sufficient for the study of the contact mechanics for most anthropomorphic soft fingers. For soft finger materials, like rubber and silicone among others, the rate of increase of the contact area reduces as the normal force increases. This is a property which is also observed among the human fingers. Using the constitutive relation for the nonlinear elastic materials, we derive a relationship which expresses the radius of contact as a function of the applied normal force. Based upon the theory, we experimentally determine the growth of contact area with respect to the normal force for both anthropomorphic soft fingers as well as human fingers. Through experiments, we validated the theoretical model; that is, the radius of contact is proportional to the normal force raised to the power y which ranges from 0 to 4 for anthropomorphic soft fingers. The Hertzian contact model [Hertz 18821 corresponds to the case where y = $.\nFinally, the limit surface is constructed for soft finger based on the proposed contact mechanics model. The limit surface [Howe et al. 1988, Kao and Cutkosky 19921 represents combination of tangential force and moment at the contact of soft finger beyond which slipping occurs. It represents critical values of allowable force and moment, (ft,m), that can be sustained by the contact before macro sliding takes place. When the moment is zero, it corresponds to the case of the Coulomb friction or point contact. Results of numer-\n488 0-7803-4465-0/98 $10.00 0 1998 IEEE", "ical interaction are also presented.\n2 Theoretical Background\n2.1 Linear elastic model\nMore than a century ago, Hertz [Hertz 18821 studied the growth of contact area as a function of the applied normal force N based on linear elastic model. He also conducted experiments using a glass spherical lens against a plan glass plate. Using the experimental results with 10 trials, he concluded that the radius of contact is proportional to the normal force raised to the power of $. That is,\na = c N S (1)\nwhere a is the radius of contact, N is the normal force, and c is a proportional constant. The result is consistent with the contact mechanics he derived based on linear elastic materials. The proportional constant is also approximately equal to the theoretical prediction [Hertz 18821.\nlar. 2.2 Nonlinear elastic model\nIn this paper, our objective is to extend the linear elastic contact mechanics model to include nonlinear materials which represents more realistic soft fingers.\nFor incompressible nonlinear elastic materials, the 3-D constitutive relation is given by the following\nthe derivative of ui with respect to the j t h orthogonal coordinate in the Cartesian coordinates, and ui is the infinitesimal displacement. In addition, the stress equilibrium requires that\n( 6 ) dU.. dX; equations [Hutchinson 19831 2 3 = 0 J\n(2) Let us first consider a nonlinear elastic sphere of radius l& being pushed onto a rigid plane as shown in Figure 1. The boundary conditions at the surface of the sphere in the cylindrical polar coordinates are (3)\nat = on = 0 for r > a (no contact) (7) The Von Mises stress is\nae = /3 -s. 2 z3 .s.. t3 ~ = d - ( l & - 4-1 l& - where ut and (T, denote the tangential and normal stresses, respectively, a is the radius of contact area, for r < a (in contact) 3 1 1 (8) -(aij - - ( T , + ~ & ~ ) ( ( T ~ ~ - - a k k & j ) 2 3 3 (4)\nThe strain components are U is the displacement of the spherical surface in the contact zone, and d is the displacement in the contact\n1 dui duj zone at r = 0. The force balance requires that -> E . . - -(- + a3 - 2 axj axi\nwhere k is a constant with stress unit, n is the stress exponent depending on the material (n 5 l), 2 is", "Using the following dimensionless variables\nwe can obtain\nAfter substitution and reduction, we can derive\na = c ~ * (14)\nFor linear elastic materials, the constant n is equal to 1. Thus we have the Hertzian model\na = c N i (15)\nEquation (15) is a special case of equation (14) for linear elastic materials in contact. In general 0 5 n 5 1; therefore, the exponent in equation (14), defined as y, is\n1 0 5 7 5 - 3\nwhere y = 71 2n+l. If y = 0, the radius of contact is constant and independent of the normal force. This corresponds to the case of an ideal soft f inger where the full contact area is reached once the contact is made, and subsequent increase in the normal force does not change the area of contact.\n(16)\nvertical pole. An electronic scale is placed under the fingertip with the tray vertical to the lateral axis of the finger. The fingertip can be moved with the knob of the translation stage. When the finger comes in contact with the surface of the tray, a normal force is developed between tray and finger which is displayed on the electronic scale. The area of contact is measured directly from the finger imprint. The surface of the fingertip is coated with very fine toner powder which gives a clean and vivid imprint with a very clear circumference on white paper. The recording paper is placed upon the plexiglass tray and is replaced every time a different normal force is applied. Multiple finger imprints at the range of normal force from 0 to 90N are printed and the circular areas of contact are measured. All the artificial fingers used in this experiments have spherical asperities. In order to ensure that the surface roughness of the tray does not affect the finger print for the particular range of forces (0 to 90N), two different tray surfaces were tested - a metallic and a plexiglass. The results show that there was no significant change in contact area occured under identical loading conditions. A least squares curve fitting algorithm is used to fit the experimental data to provide an empirical relationship between the normal forces and areas of contact.\n3.1 Experimental results 3 Experimental Setup\nFigure 3 shows the experimental setup used for the investigation of different soft finger materials. The artificial finger is mounted on a linear stage through a\nExperiments using various fingertip materials are conducted with the apparatus described in Figure 3, and the results are summarized in Figure 4. The experiments were performed using a substrate with\n490" ] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure1.1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure1.1-1.png", "caption": "Fig. 1.1. Air bearing", "texts": [ " They are implemented in high-precision manufacturing devices such as high speed turning and milling machines, as well as non-manufacturing devices such as high performance magnetic memory disk file systems, high definition large scale projection televisions, and video cassette recorders. These applications call for highly precise positioning, which poses a challenge since it is also to be accomplished at high speed. To achieve the required specifications, air-bearing is typically employed. The characteristic of interest in air-bearing is its low asynchronous error motion making it possible to achieve high rotational accuracy. The disadvantage, however, is its low stiffness and damping ability. Figure 1.1 shows the working diagram of an air-bearing, where pressurized air is used to maintain the gap between the rotating and the static parts of the machine (e.g. spindles). To achieve high stiffness, a hybrid solution involving the integration of air-bearing with conventional oil bearing has also been developed. Lasers, in particular excimer lasers, are today widely used for micromachining of different kinds of materials due to their unique pulsed ultra violet (UV) emission. They have been used of in research laboratories since 1977 and about 10 years later they were successfully introduced into industrial processing and manufacturing" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-FigureA.1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-FigureA.1-1.png", "caption": "Fig. A.1. Optics and accessories for linear measurements", "texts": [ " In servo control systems, a position measurement is usually inferred directly from the encoder (or equivalent position measurement device) for the motor. However, due to inherent encoder calibration errors, there will inevitably exist some mismatch between the encoder measurement and the actual position. The laser system would be able to address this situation by giving the end user an assessment of the linear profile of the motor performance. The optics required to obtain the linear measurements are given in Figure A.1 (Appendix A). The set-up for a linear measurement is as shown in Figure 5.6. An angular measurement is concerned with the measurement of the angular displacement (tilt) of the moving part (on which the angular reflector is mounted) from the ideal position. This angular displacement may vary with the linear travel distance of the moving part. The primary causes of an angular deviation include the physical guide imperfections and possibly cogging related effects. The optics and accessories used for the angular measurement are rather similar to those used for linear measurements" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002666_elps.200700443-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002666_elps.200700443-Figure2-1.png", "caption": "Figure 2. Photograph of the assembled chamber. The front plate is Plexiglass, behind this is a dialysis membrane, Teflon spacer, then the back plate which incorporates the platinum electrodes.", "texts": [ " BPB and Mb (M1882, from equine heart) were from Sigma\u2013 Aldrich. Reagents used to prepare buffers were of the highest purity available. Bare silica (spherical, 5 mm) was from Phase Separations, polyacrylamide (spherical, 45 mm) from BioRad (Biogel P-6 Extrafine) and Sephadex (20\u2013180 mm) was from Fluka. The focusing chamber was essentially as described previously [9], except that the size was reduced as were the number of electrodes: 2.1 in. long 21-pin connectors were used in place of 2.5 in. long 50-pin connectors. The chamber (Fig. 2) was formed from two blocks of transparent Plexiglass\u00ae (polymethylmethacrylate) and a 3.2 mm thick black Teflon (PTFE) spacer. The front block had a channel 57 mm long, 1 mm wide and 0.5 mm deep machined into it (the separating channel) and \u2018screw-in\u2019 connections for external 1/16 in. tubing. The spacer contained a slot to act as the coolant channel, 67 mm long, 1 mm wide on the front side (to a depth of 1.6 mm) and 1.6 mm wide at the back (for the remaining thickness 1.6\u20133.2 mm). The rear block contained a central channel 1" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001775_robot.2004.1308051-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001775_robot.2004.1308051-Figure2-1.png", "caption": "Fig. 2 Planar 5R manipulator moving on a straight line", "texts": [ " A potential may also be used to penalize joint variables exceeding geometric joint limitations. The potential b b b b with a,.Pa (q,~,,,) = -DaPa(s,pU,)a,~Sa (q,Pc,). The 1 1 J ( ) .- H (1 - e-('?\"/9E,& )/ (1 - - a q . - U e l ) (16) approximates a Heaviside function of height Ha with edges at zkq;,, for r going to infinity. It is increasing with a speed according to r when approaching the limits *qku of joint a. Its gradient is in addition to V,U considered in the PPC algorithm. VI. EXAMPLES A simple but illustrative example is the planar 5R manipulator in Fig. 2. The object linings are the isosurfaces 6, = 0, i.e. the boundaries determined by the shape functions; rectangles in this case. The order is rn = 3. The precision goal for the geometric tracking of the desired EE configuration is ~d = lo-'. The task is to move the EE along the depicted straight line with a constant velocity of 4 m/s while turning the EE about -90'. The target path C(t ) is sampled with a time step At = 10 ms. Black dots on the objects refer t o sensor points. Each sensor on the obstacles measures the potential of all five manipulator bodies" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002939_s11071-007-9215-4-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002939_s11071-007-9215-4-Figure5-1.png", "caption": "Fig. 5 Stable equilibrium space of rtip", "texts": [ " Now we consider that the offset \u03b81off is in the rage of 0 \u2264 \u03b81off \u2264 \u03c0/4 corresponding to the measurement restriction of the after-mentioned experiments. Since the maximum value of \u03b82 is \u03c0/2 for any values of \u03b81off and \u22172 0 , the minimum value of rtip is realized in the case of \u03b81off = \u03c0/4 and \u03b82 = \u03c0/2 as shown in Fig. 4 (a)\u2032; the minimum value is rtip =\u221a l2 0 + l2 1 + l2 2 + \u221a 2l0(l1 \u2212 l2)/(l0 + l1 + l2) and we define the value as rmin. Thus, it is obvious that the reachable area of the tip of the free link is the gray zone in Fig. 4. From Equation (8), we can obtain stable equilibrium surfaces of rtip depending on \u03b81off and \u22172 0 as in Fig. 5. The upper surface is connected to the lower on the junction line at \u03b81off = 0. In order to change the distance rtip from the maximum value at the point (c) in Fig. 5 to the minimum at the point (a)\u2032, rtip needs to go through the junction line to reach the lower surface on which the point (a)\u2032 exists. Therefore, we first increase \u22172 0 as the arrows indicate in Fig. 6 (from (c) to (a) through (b)). Then, by keeping the excitation frequency constant and varying the offset of the excitation \u03b81off from 0 to \u03c0/4 (from (a) to (a)\u2032 along the arrows in Fig. 7), the minimum value of the distance rtip = rmin at the point (a)\u2032 can be realized. The magnitude of the minimum value for the Springer parameters of the after-mentioned experimental apparatus is rtip = 0" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003122_j.sna.2008.11.029-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003122_j.sna.2008.11.029-Figure6-1.png", "caption": "Fig. 6. Finite element model of the shot-put sensor.", "texts": [ " (6), we obtain UZ = UI 4 G(\u03b51 \u2212 \u03b52 \u2212 \u03b53 + \u03b54) (7) In like manner: UX = UY = UI 4 G(\u03b51 \u2212 \u03b52 + \u03b53 \u2212 \u03b54) (8) It can be found that auto decoupling is possible if \u03b51 = \u03b54 and \u03b52 = \u03b53. 4.2. Finite element analysis Statics analysis is to study the displacement and strain under the constant payload. With the definite payload, strain of the sensor is determined by the geometrical structure of the elastic body. Finite element analysis is conducted to investigate the stress distribution of the sensor. The geometrical model of the shot-put sensor is shown in Fig. 6. For the upper part, the elastic membrane with the diameter of 32 mm is fabricated by aluminium alloy (LY12). Its elastic module, Poisson\u2019s ratio and density are 280 GPa, 0.3 and 2.7 \u00d7 103 kg/m3. The compensated mass with the diameter of 26 mm is fabricated by yellow brass, whose density is 8.5 \u00d7 103 kg/m3. SOLID45 is used for the three-dimensional modelling of solid structures in which the threedimensional solid-continuum eight-node element is adopted. The theory of elastic mechanics can be used to the constitutive behavior of the sensor" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001172_nafips.1996.534733-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001172_nafips.1996.534733-Figure3-1.png", "caption": "Figure 3 Balance beam system", "texts": [ " At the end of forward pass, output of GeNFIS is compared with the desired output and an error term E is computed by squaring the difference, and the modifiable parameters of MFs are updated by using backpropagation algorithm. 3 A Nonlinear Dynamic System One of the major objective of this work is to develop a neuro-fuzzy controller and to apply it in an experimental setup suitable for academic environment. In order to meet this objective a fluid beam balancing system is used as a test bed of non-linear dynamic system for this work. The basic problem of the balance beam system is to balance a beam containing two fluid tanks, one at each end, by pumping the fluid back and forth from the tanks [8]. Figure 3 shows the schematic diagram of the fluid beam balancing system. The beam is comprised of a wooden plank clamped on top of a shaft about which it can rotate. The shaft is supported by two low friction bearings, and at the one end of the shaft a potentiometer is connected to measure angular position of the beam. The center of the mass of the complete system is above the center of rotation. This feature makes the system unstable. 21 1 1 2 3 height voltage NL N NL NM NS -- NL NL __- 2 NS MN Control effort is created by pumping water between two plastic tanks, thereby creating a moment due to weight imbalance" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002002_t-ed.1977.18852-Figure11-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002002_t-ed.1977.18852-Figure11-1.png", "caption": "Fig. 11. Reflective Type I11 B-on-W reflex system.", "texts": [ " 7, if identical lenses are used for S and P (or P l ) , and if they are arranged to be equidistant from the LV, then folding the system about the LV will put the light source L on top of the stop and S on top of P (or P l ) . In this manner, a single lens performs both as a telecentric schlieren lens and as the projection lens. For a W-on-B system, this arrangement can be made to work by replacing the opaque center stop by a small 45\u201d mirror. The light can then be brought in from the side, as in Fig. 11, and since the mirror is imaged onto itself by the lens and the reflective LV, no light reaches the screen when the LV is not written [ 111. In Fig. 11 the small mirror has been placed slightly off-axis so that light specularly reflected by the LV misses the mirror and reaches the screen. Light from written areas of the LV is prevented from reaching the screen in this B-on-W arrangement by an aperture. For a reflective B-on-W system, the arrangement of Fig. 11, or the equivalent of Fig. 7(b) (i.e., with an additional projection lens element beyond the stop), is probably the best choice. For a W-on-B system, however, there is a problem with this arrangement that is hard to correct. The DEWEY: PROJECTION SYSTEMS FOR LIGHT VALVES 927 illuminating beam diverges from the 45\u201d mirror and is partially reflected by the lens surfaces. This reflected beam diverges around the stop and appears on the screen as a luminous \u201cdonut,\u201d the center being shadowed by the stop" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003876_2013.38674-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003876_2013.38674-Figure3-1.png", "caption": "FIG. 3 General view of active vibrationcontrol system showing hydraulic pressure supply (9), accumulator (7), cylinder (3), feedback rack (2), and potentiometer (1), vertical guide (4), electrohydraulic servo valve (6), distribution manifold (5), return hose (10), and batteries to energize feed back pententiometer (8).", "texts": [ " A conventional hydraulic cylin der having approximately 1 sq. in. cross-sectional area and 6 in. of ex tension was used as the actuator. In operation the cylinder moves the seat upward as the tractor drops into a furrow and downward as it moves over a ridge, thus counteracting the vertical motion of the tractor. The seat was attached to the top end of a verti cal guide to which the cylinder was also mounted so that moments would TRANSACTIONS OF THE ASAE 1970 not be transferred to the relatively small cylinder piston rod (Fig. 3) . Also shown in this figure are the physi cal relationship of the components to each other. The c h a s s i s - m o u n t e d vibrometer which was used as a detector of vibra tional motion consisted of a springsupported se i smic mass m o u n t e d around a vertical shaft on a linear bearing with freedom to move verti cally (Fig. 4 ) . In order to effectively sense position for low frequency, the mass was sprung very softly having a natural frequency of about 0.5 Hz. To circumvent the problems of large spring deflections commonly associated with such a low natural frequency, a lever was used so that the spring could be attached to a short arm and the mass to a long arm" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000275_ias.2000.882133-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000275_ias.2000.882133-Figure5-1.png", "caption": "Fig. 5 - Rotating fields and air gap flux.", "texts": [ " In the present paper, as described in section 111, a specific high frequency (400 + 1200 Hz) common mode voltage component will be generated, that produces a small but measurable common mode current component owning useful information on the position of the air gap flux. III. THE PROPOSED TECHNIQUE An additional low amplitude (10 + 20 V) three phase high frequency (400 Hz < fh < 1200 Hz) voltage component vshf is added to the stator voltage V , of a standard induction motor, in order to generate a high frequency rotating field Fh,, that is superimposed to the main rotating field F,. Due to the high frequency and the low amplitude of the additional voltage, Fhf is noticeably lower than F,. As shown in Fig. 5, composition of Fhf , rotating at angular speed wh = 2nfh, with the main field F,, rotating at angular speed w, < a h , produces an oscillation of the saturation level that depends on the relative position of the two fields. In fact, the saturation level will be increased when the high frequency field is aligned and in phase with the main field, will be decreased when the high frequency field is opposite to the main field, while almost no variation of saturation from the level stated only by the main field will occur when the two fields are orthogonal. Let us now consider Fhfd and Fhh, the components of F h f along two orthogonal rotating axes d, q , with the d axis aligned with F, ,as shown in Fig. 5. The oscillation of the saturation level is only due to Fhfd , that modulates the main field, while the Fhfq component does not influence the saturation level as the iron paths are saturated on the d axis. As F h f and F, respectively rotates at angular frequency U), and &, F,,,d is oscillating at a =Q - a, ,and the saturation level also oscillates at such an angular frequency. Due to the oscillation of the saturation level, the zero sequence component & of the air gap flux, which is normally dominated by the third harmonic component, will also include an additional component &hf, whose angular frequency is @ , irrespectively of load and speed levels, at steady state as well as in dynamic transients" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002092_1-4020-3393-1_14-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002092_1-4020-3393-1_14-Figure4-1.png", "caption": "Fig. 4. Example of Cartesian generalized coordinates", "texts": [ " At the textbook level, the works of Dimentberg [41], Beyer [40] and Fischer [34] are excellent introductory texts to the topic. Recent reviews of dual algebra kinematics are due to Wittenburg [42] and Angeles [43]. - Cartesian generalized coordinates. The absolute position of each body is independently located by a set of Cartesian generalized coordinates (3 for planar motion, 6 for spatial motion). Kinematic constraints between bodies are then introduced as algebraic equations among coordinates. Constraint expressions are numerous, but involve only the absolute coordinates of adjacent parts. (e.g. Fig. 4). With the purpose of avoiding singular configurations, some authors (e.g. [12, 14, 17, 24, 28]) prefer the definition of the spatial attitude of a body in terms of Euler parameters (4 coordinates) instead of Euler angles (3 coordinates). Computer codes using these coordinates require only a minimal amount of pre and post processing. A substantial number of nonlinear constraint equations is involved. Coefficient matrices are large but sparse. It is advisable to take advantage of this condition in order to increase the numerical efficiency of the code", " 6, the links coordinate-transformation matrix takes the form [34] 2 With this approach, the coordinate \u03b82 is not involved. [ T\u0302 ]i i+1 = \u23a1\u23a3 cos \u03b8\u0302i \u2212 cos \u03b1\u0302i sin \u03b8\u0302i sin \u03b1\u0302i sin \u03b8\u0302i sin \u03b8\u0302i cos \u03b1\u0302i cos \u03b8\u0302i \u2212 sin \u03b1\u0302i cos \u03b8\u0302i 0 sin \u03b1\u0302i cos \u03b1\u0302i \u23a4\u23a6 (8) The closure condition of the slider-crank chain is expressed by the matrix product[ T\u0302 ]1 2 [ T\u0302 ]2 3 [ T\u0302 ]3 4 [ T\u0302 ]4 1 = [I] (9) where [I] is the unit matrix. The constraint equations (4) and (5) follow by equating appropriate elements of the final matrix products. Using Cartesian generalized coordinates, with reference to the nomenclature of Figure 4, the scleronomic constraints are expressed by the following equations \u03a81 \u2261 X (1) A0 \u2212X (4) A0 = 0 (10) \u03a82 \u2261 Y (1) A0 \u2212 Y (4) A0 = 0 (11) \u03a83 \u2261 X (2) A \u2212X (3) A = 0 (12) \u03a84 \u2261 Y (2) A \u2212 Y (3) A = 0 (13) \u03a85 \u2261 X (3) B \u2212X (4) B = 0 (14) \u03a86 \u2261 Y (3) B \u2212 Y (4) B = 0 (15) \u03a87 \u2261 Y (4) B = 0 (16) where X(i) P , Y (i) P are the absolute coordinates of point P on the ith body. Such coordinates are related to the generalized Cartesian coordinates by the transform{ X (i) P Y (i) P } = [ cos q3i \u2212 sin q3i sin q3i cos q3i ]{ x (i) P y (i) P } + { q3i\u22122 q3i\u22121 } (17) Using the natural coordinates (see Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003739_gt2009-59285-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003739_gt2009-59285-Figure1-1.png", "caption": "Figure 1: FPTPGB-C with flexure pivot and compliant beam structures created by wire-EDM, photo adopted from [13]", "texts": [ " Much information about early stage pioneering work on tilting pad gas bearings can be found in these literatures. However, these conventional tilting pad gas bearings used spherical seat pivots which must consider assembly tolerance stack-up and pivot wear issues due to contact forces and sliding of mating components. Very tight tolerance and non-compliant bearing pads in radial direction created major technical hurdles including thermal managements, damage due to debris, etc. Flexure pivots (Figure 1) are monolithic structures created via wire-EDM (electro-discharge machining) and do not have tolerance stack-up due to assembly or pivot wear, thus identifying it as an easily made, simple and reliable design. While flexure pivot tilting pad bearings have been used in oillubricated machinery, the technology is especially suited to oil-free applications where clearances are smaller and sensitivity to tolerances is higher. There have been recent investigations of flexure pivot tilting pad gas bearings (FPTPGBs), including hybrid applications (hydrodynamic and hydrostatic) [2, 8] and tilting pads with radial compliance [1, 9, 10]", "org/about-asme/terms-of-use Down larger than the manufactured bearing clearances while at operating conditions [10, 12]. FPTPGBs have better rotorbearing stability than air foil bearing, which is recognized as the most common oil-free gas bearing. However, due to rigid pad surface in radial direction, the current FPTPGBs have a limited speed range, not being able to accommodate shaft centrifugal and thermal growth. To address this issue, Sim and Kim [1, 9, 10] investigate FPTPGBs with a radial compliance mechanism (FPTPGB-C) that permits rotor growth to exceed the original bearing clearances. As shown in Figure 1, the simple design of FPTPGB-Cs manufactured by wire-EDM permits a designer to control the pad properties (i.e. tilting and radial stiffness) by selecting the appropriate dimensions of the flexure pivot web and compliant beam. In the present work, experimental results for high speed operation of FPTPGB-Cs are presented to demonstrate the potential of the technology and for comparisons with simulations. Furthermore, the investigation of dampers in series with compliant beam is discussed as a method to stabilize an unstable rotor-bearing system" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001608_j.medengphy.2004.04.005-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001608_j.medengphy.2004.04.005-Figure8-1.png", "caption": "Fig. 8. Schematic (a), compression testing of trabecular and cortical bone block properties and novel tissue-engineered scaffolds (b), in vivo loading of mouse limbs in either A-P or M-L orientations (c), in vitro, in situ and ex vivo modeling with the addition of an environmental chamber (d), and tension testing (e) or bend testing (f) of single osteons.", "texts": [ " Furthermore, as in our system, this pricing does not include test fixtures, but the commercial systems generally include a computer and technical support. Given the simplicity of operation in our system, technical support beyond what is available with manuals is not necessary. As we noted earlier, while our system does not provide feedback, the system is acceptable for loading relatively rigid objects such as long bone and could easily be expanded to accommodate a variety of research interests. For example, as illustrated in Fig. 8, the system could be expanded to four-point bending (8a), compression testing of trabecular and cortical bone block properties and novel tissue scaffolds (8b), in vivo modeling of mouse limbs in either A-P or M-L orientations (8c), in vitro, in situ and ex vivo modeling with the addition of an environmental chamber (8d), and tension testing (8e) or bend testing (8f) of single osteons, to name a few practical examples. Finally, the system enables both fracture and fatigue testing. However, in the event of the latter, the fatigue cycle must be defined in terms of displacement and not load" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000558_romoco.2002.1177105-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000558_romoco.2002.1177105-Figure7-1.png", "caption": "Figure 7:", "texts": [ " Then robots 4,s and 6 are assigned to the robots D, E and F. Finally robots 7.8 and 9 are assigned to the target points G, H and 1. The succession of motion of robots is reverse: robot 9 with highest priority moves first, then robots 8, 7 and so on; point B. When we lay some additional condition for shapes of trajectories we can assure that formation building will be executed without bypass maneuvers. Mentioned condition is that the function of distance between robot and target point must decrease in whole range. At fig. 7. we present example in which planned trajectories may looks a little chaotically, however, they was planned using previously described methods. Desired formation may be successfully reached tracking these trajectories. 4 Nonholonomic robots discussion In this section we discuss possibility of use of target assignment strategy with nonholonomic robots. At figure 8 two robots are shown (denoted using digits) and two target points (denoted using letters). Robot 1 is assigned to the target point A and robot 2 (with higher priority) to target point B" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002461_j.jbiomech.2006.04.013-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002461_j.jbiomech.2006.04.013-Figure1-1.png", "caption": "Fig. 1. Schematic of simple shear test configuration for planar soft tissue. (A) Clamp, (B) metal plate, (C) set screw, (D) sand paper, and (E) soft-tissue specimen.", "texts": [ " After the adipose tissue was removed, specimens were cut from a uniform thickness region (average thickness is 2.1570.3mm) of porcine skin. Three softtissue specimen geometries (5 5, 5 3.75, 5 2.5 cm) were prepared for the tests. These geometries allowed the effect of different aspect ratios on the strain field distribution during simple-shear tests to be investigated. Finally, low Young\u2019s modulus specimen cross grating (Liou, 2005) was put on soft-tissue specimens after the specimen was cut. A set of custom-made clamps were used to hold specimens for simple-shear tests (Fig. 1). One clamp was fixed on an optical bench and another clamp was mounted on a step motor driven linear stage. Specimens with the aforementioned three different aspect ratios were mounted on the clamps with two clamping prestrains (0.15 and 0.3). These are engineering strains computed based on average undeformed specimen thickness of 2.15mm (the negative sign was omitted). Specimens extended 15mm into each clamp, so there was enough area to be clamped. Uniform clamping prestrain was applied by tightening the three set screws in each clamp" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003743_isie.2010.5637684-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003743_isie.2010.5637684-Figure2-1.png", "caption": "Fig. 2. Presentation of the current vector I in different reference frames", "texts": [ " After 100ms from the start in open loop the EKF or UKF observers are activated to operate in parallel. To minimize the transient states after switching between control strategies it was necessary to provide continuous voltages and currents of the machine. Thus, it was necessary to determine the inverted Park\u2019s transformation of the components of the voltage and current vectors from the reference frame rotating synchronously with the current vector (with the xy axis) to the \u03b1\u03b2 stationary reference frame (Fig. 2). Next, using the Park\u2019s Transformation, the vectors were transformed to the reference frame rotating with the rotor flux (with the dq axis). The obtained voltage vector components in dq reference frame decreased by the decoupling components are applied as the output of the integral terms of the currents regulators. The values of the proportional terms are equal to zero to reduce the transient states. Determined component of the current vector in the q axis is applied as the output of the integral term of speed regulator and its proportional term are equal to zero" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000610_ip-d:19830007-Figure9-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000610_ip-d:19830007-Figure9-1.png", "caption": "Fig. 9 VSS responses for slow null space dynamics a System output b Null space variable a time response c Null space trajectory", "texts": [ " Sb, and as expected is oscillatory. The state diagram for the range space is shown in Fig. 8c, illustrating the switched modes of Fig. 7c. If the null space operator is now changed so that m1 contains the fastest eigenvalue m* = (2.154 1 0) (82) the range space eigenvalues are then given by \\2 = \\ 3 = -0 .4226 (83) The response should be of the same format as Fig. 7c, but with much slower eigenvalues. This will tend to increase the excursions around the null space and reduce the frequency of oscillation. This is confirmed in Fig. 9a, which shows a large oscillation superimposed on the first-order null space eigenvalue. Fig. 9b, showing the range space dynamics, shows a slowing in frequency as expected. The range space state diagram of Fig. 9c still exhibits the predicted form of Fig. 7c. 4 Conclusions It has been shown that by treating the variable-structure control system as an extension of state feedback with a switched-gain vector Akf, the dynamics of the state trajectory onto the desired switching function can be described. The description of the switching function dynamics a have also been extended to a reduced-state switching control system where the dynamics of the switching function become second order. As more states are taken out of the operator mf, more eigenvectors will have to remain outside the null space, and the order of the range space dynamics will increase" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003297_j.rcim.2008.07.002-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003297_j.rcim.2008.07.002-Figure2-1.png", "caption": "Fig. 2. The concave tooth of the spherical gear.", "texts": [ " In order to underline the originality of this paper, it should be pointed out that in the former approach the convex teeth are the cones, while the profile of the concave teeth is the conjugate tooth surface of the cone. In this paper the concave teeth are the cones, while the profile of the convex teeth is the conjugate tooth surface of the cone. With just this small change, the machining properties are improved dramatically. ll rights reserved. For concave teeth the cone tooth profile with a tooth profile angle of a is used. Fig. 2 shows the axle section. ABCD stands for the profile of the concave cone teeth. CD is the bottom of the cone, O0 is the tip of the cone. The addendum circle coincides with the pitch circle. Rf1 is the radius of the dedendrum circle. Given that the hypotenuse length of AB is S, then O0O \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 \u00fe S 2 2 s S 2 ctga (1) In Fig. 2, the equations of the tooth profile of the concave tooth section BD are x1 \u00bc u sin a; y1 \u00bc O0O\u00fe u cos a (2) On the pitch circle, we have x2 1 \u00fe y2 1 \u00bc R2 umax \u00bc \u00f0O 0O1\u00de cos a\u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 \u00f0O0O1\u00de 2 sin2 a q (3) For the same reason umin \u00bc \u00f0O 0O1\u00de cos a\u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 f1 \u00f0O 0O1\u00de 2 sin2 a q (4) uminpupumax (5) In substance, the spherical gearing of ratio 1 is equivalent to two pitch spheres of the same size rolling against each other in space", " There is one tooth at the center, six teeth uniformly distributed on the first parallel and 12 teeth are uniformly distributed on the second parallel. All the teeth are uniformly distributed on a pitch ball. On the first parallel y \u00bc y(1) \u00bc 151. On the second parallel y \u00bc y(2) \u00bc 301. The addendum radius of the concave gear Ral \u00bc 36.00 mm and the addendum radius of the concave gear Rf1 \u00bc 29.25 mm. The addendum radius of the convex gear Ra2 \u00bc 42.00 mm and the addendum radius of the convex gear Rf2 \u00bc 35.25 mm. In Fig. 2, the larger the value of S, the thicker the convex tooth root, and the greater the strength. However, if the value of S had been too big, the top of the concave tooth will be pointed. So that we choose S \u00bc 7.3978; therefore the top of the gear would not become too pointed. In the meantime the convex tooth will have enough strength. In order to prevent the convex tooth from becoming too pointed and to satisfy the requirements of the contact ratio, the profile angle of the concave tooth should not be too big. It is calculated that a \u00bc 121 would be the most appropriate size. According to our calculations, every pair of convex teeth and concave teeth engages an area f \u00bc 0.2236-0.1029 rad. Since this area is larger than 15, the gearing can act continuously. The convex tooth surface is a curved rotational surface. The sectional profile of the axle is shown in Fig. 2. According to Eq. (3), thus umax \u00bc 17:7909 According to Eq. (24), on the undercutting limited point, thus uc \u00bc 17:7042 Since uc4umax, there is no undercutting. Spherical gearing is the key part of a robot\u2019s wrist. As shown in Fig. 1, the two balls are the pitched surfaces; the centers of the balls are the revolving centers. On the two spherical surfaces, there are concave and convex teeth, respectively, which can engage so as to mesh meshing with each other. So that the spherical gear transmission is realized" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003763_b924100k-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003763_b924100k-Figure1-1.png", "caption": "Fig. 1 Schematic illustrating the flow reactor set-up used to evaluate the in situ electrochemical regeneration of an immobilised NAD(H) 1 in the presence of an immobilised enzyme.", "texts": [ " It was therefore envisaged that by packing the conducting biocatalytic material into a continuous flow reactor, product isolation and biocatalyst re-use would be more efficient compared to the use of a batch reactor; where biocatalytic material could be lost upon filtration and vessel transfer. It was also postulated that as substrates and products are constantly supplied to, and more importantly removed from, the reactor that this would prevent product accumulation and a thermodynamic resistance against the forward reaction.2 As Fig. 1 illustrates, the proposed reaction set-up involved placing a conducting material into a packed-bed, through which a solution of (rac)-2-phenylpropionaldehyde 3 would be passed in order to undergo selective reduction. Maintaining the system under a potential would therefore ensure in situ electrochemical conversion of the spent NAD+ 2 to NAD(H) 1, increasing regeneration efficiency cf. electrode based systems. Using this approach, initial investigations centred on the use of a silica-vanadium oxide hybrid xerogel, as it had been shown to be electrically conducting by Park et al", " Evaluation of CPG-PPy 14 for enzyme immobilisation Having demonstrated an enhancement in the formation of NAD(H) 1 in the presence of CPG-PPy 14, the material was subsequently evaluated as a solid support for the separate immobilisation of HLADH 6 and NAD(H) 1, affording CPGPPy-HLADH 15 and CPG-PPy-NAD(H) 16 respectively, prior to investigating the co-immobilisation of HLADH 6 and NAD(H) 1. As Scheme 3 illustrates, enzyme 6 and co-factor 1 immobilisation was achieved utilising CPG-PPy 14, derivatised with 3- glycidoxypropyltrimethoxysilane (GPTS) 17 to afford the epoxidefunctionalised CPG-PPy 18. The material 14 (0.08 g) was subsequently dry-packed into a flow reactor (5 mm i.d. x 5 cm (long) Fig. 1) and in the first instance a solution of HLADH 6 in phosphate buffer (pH 7) pumped through the reactor (1 ml min-1) for a period of 24 h. Any unbound enzyme was then removed from the reactor upon purging with phosphate buffer (pH 7.0, 1 ml min-1, 24 h) to afford a packed-bed containing CPG-PPy-HLADH 15. Scheme 3 Schematic illustrating the protocols used to immobilise HLADH 6 and NAD(H) 1. To evaluate the immobilised enzyme 15, the continuous flow reduction of (rac)-2-phenylpropionaldehyde 3 (2.6 \u00a5 10-4 mM) was performed in the presence of a solution of free NAD(H) 1 (8" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002892_1.5061067-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002892_1.5061067-Figure1-1.png", "caption": "Figure 1: Design of the IN-625 demonstration piece.", "texts": [ " The microstructures of the LC samples were examined using an Olympus optical microscope as well as a Hitachi S-3500 scanning electron microscope (SEM). A Philips X\u2019Pert X-ray diffraction system with Mo tube was used to identify the phases of the LC samples. A 100 kN Instron Mechanical Testing System was used to evaluate the tensile properties of the LC samples. LC IN-625 Demonstration Pieces A net-shape IN-625 part was initially designed to demonstrate the capability of the laser consolidation process (Figure 1). It consists of 5 portions: (a) cylinder #1 (3 mm thick), (b) cylinder #2 (2 mm thick), (3) a conical top on a short cylinder (0.81 mm thick), (4) a circular fin (2 mm thick), and (5) substrate disk (50 mm in diameter and 9.4 mm thick). Laser consolidation of IN-625 was performed with a 5- axis motion system to build the demonstration piece on a 1020 steel substrate in the following sequence: cylinder #1, cylinder #2, conical top on a short cylinder and finally the circular fin. A hole with a diameter of 8 mm was pre-drilled in the middle of the substrate to allow the release of the loose powder inside the part after laser consolidation" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003662_s12239-009-0025-1-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003662_s12239-009-0025-1-Figure1-1.png", "caption": "Figure 1. Vehicle dynamic model. Figure 2. Error in trajectory tracking.", "texts": [ " The proposed methodology was tested by using a multibody dynamics vehicle model in the ADAMS program and a MATLAB Simulink model. This paper is organized as follows. In section 2, the basic kinematic model of a vehicle system is introduced. Section 3 explains the derivation of the error function, and section 4 describes a predictive controller with feed-forward and feedback control vectors. Section 5 shows the simulation method and the control process in detail, and section 6 provides the simulation results and conclusion. The bicycle model shown in Figure 1 is an approximate model (Park and Heo, 2005) for a four-wheel drive vehicle system which represents a low-velocity vehicle system without slipping in the tires. By means of geometrical relations, this model can be used to easily extract the control vectors and their relation to the vehicle\u2019s condition. To control a vehicle system, two types of vectors, steering-angle \u03b4f and velocity of the front wheel \u03c5f , are generally considered. The output state variables are defined as the vehicle velocity \u03c5 and yaw velocity in a plane" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002598_s11340-007-9089-x-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002598_s11340-007-9089-x-Figure2-1.png", "caption": "Fig. 2 Pressurized ring test", "texts": [ " Thus although the split-disk tensile test has been shown to produce artificially low values of tensile strength, it appears capable of producing accurate measurements of tensile modulus for composite ring specimens. A second method for ring testing of composite specimens is the pressurized ring test. The primary advantage of this test method is the uniformity of the pressure distribution produced on the inner surface of the ring specimen. Cohen et al. [4] developed an internally pressurized ring test apparatus that applies internal pressure to the composite ring specimen through the pressurization of an internal bladder. As shown in Fig. 2, the inflatable bladder is placed in the cavity between the composite ring and an internal steel plug. The inner steel plug, bladder, and ring specimen are clamped or pressed between two steel plates to prevent the expansion of the bladder in the axial direction of the ring. The bladder is pressured using hydraulic fluid and produces an internal pressure in the ring specimen. Although the pressurized ring test provides an excellent method for tensile strength and modulus determination of composite ring specimens, it is not without disadvantages" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003891_bit.260110305-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003891_bit.260110305-Figure3-1.png", "caption": "Fig. 3. Longitudinal section of the outer case and locking nut. See Fig. 1 for key to materials.", "texts": [ " This is again heated as previously described to cure the resin. If the threaded rod is made from brass, care must be taken to ensure no brass is uncovered inside the electrode because copper acts as a poison to the system by being deposited on the cathode surface. Earlier electrodes had the top and main body sections screwed together but this caused some difficulty in fitting the anode and thus the model described has the top held in place with 3 small set screws. The outer case is constructed from $ in. I.D. stainless steel tube (Fig. 3). This is a standard size tube and thus the electrode can be fitted into stainless steel fermentors using the normal industrial pipe fittings. The hole a t the bottom end of the case must be large enough for the cathode and membrane to slide through easily without causing any damage to the membrane. The membrane is held in place by a neoprene 0 ring. The outer case tightens down on this 0 ring thus preventing any electrolyte leakage. The anode is made by soldering a piece of Analar lead foil (B", " Figure 2 shows the cathode to be convex in shape, and this has been found to be necessary because if the cathode is flat, the weight of the large volume of eIectrolyte presses the membrane away from the surface of the cathode, thus making the electrode very sensitive to turbulence (Fig. 4). This sensitivity is probably due to the length of the diffusion pathway between membrane and cathodal surface being altered by the turbulence. BIOTECHNOLOGY AND BIOENGINEERING, VOL. XI, ISSUE 3 LONG-LIVED OXYGEN ELECTRODE 329 The outer case (Fig. 3) is fitted over the membrane and the locking The electrode should now be filled with electrolyte nut tightened. and checked for leakage. The main electrolytes used by other workers are listed in Table I. 330 J. S. G. BROOKMAN These electrolytes have all been tested in the electrode described, and of these only the potassium chloride and dipotassium hydrogen orthophosphate gave a linear response to the high oxygen tensions, and were also heat sterilizable. The optimum concentration for both of these electrolytes was found to be a molar solution" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002031_978-1-4020-2249-4_27-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002031_978-1-4020-2249-4_27-Figure5-1.png", "caption": "Figure 5. A numerical example for a 3R manipulator with al=lu; a2=lu; a3=lu; d2=3u; d3=2u; ul=n/4; u2=n/4: a) cross-section boundary curve f; b) a zoomed view", "texts": [ " It is possible to observe that the derivatives fr, fz, and fw of the cross-section boundary curve meet at the 3 singular points Dl, Cl and C2. Their coordinates can be computed as the zeros of the set of the f derivatives. Their coordinates are: Dl=[3.82, 6.62]; Cl=[1.87, 7.12]; C2=[3.09, 7.16]. The nature of those characteristic points has been checked by Eq.(9). It has been verified that Cl and C2 are cusps, since g is equal to zero, and Dl is a double point, since g is greater than zero. In Fig.5 the workspace boundary of a cuspidal manipulator is shown . with f, fr , fz, fw plots. (u is the unit length, angles are expressed in radians) An algebraic formulation has been presented for a Cartesian representation of the boundary workspace of 3R manipulators. The cross section boundary curve and boundary surface are of 16-th degree and fully cyclic. Geometric singularities of the cross-section boundary curve are identified as delimiting ring void and 4-solution regions. Numerical examples have been presented to outline the practical feasibility of the proposed formulation" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003648_iccas.2010.5669710-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003648_iccas.2010.5669710-Figure1-1.png", "caption": "Fig. 1 Bicycle Model of 4WS.", "texts": [ " The characteristics of vehicle can be analyzed by linear model of 2 degree of freedom(bicycle model). It is verified through experiments [4],[5]. In linear model, we can substitute both right and left wheels by single equivalent wheel on centerline axle of the vehicle. so, easily figure out dynamic performance of the car ignoring many factors such as motion of suspension, transition of lateral force, and negative and positive acceleration. Herein 2 degree of freedom are a yaw and a lateral displacement. Fig. 1. shows the 2 degrees of freedom model which shows the general linear model. Motion equation of linear model is equation (2.1) and Matrix form is equation (2.2). ( ) ( ) ( )x t Ax t Bu t= + (2.1) 11 12 11 12 21 22 21 22 f r a a b b a a b b \u03b4\u03bd \u03bd \u03b3 \u03b3 \u03b4 \u23a1 \u23a4\u2212\u23a1 \u23a4 \u23a1 \u23a4\u23a1 \u23a4 \u23a1 \u23a4 = + \u23a2 \u23a5\u23a2 \u23a5 \u23a2 \u23a5\u23a2 \u23a5 \u23a2 \u23a5 \u2212\u23a3 \u23a6 \u23a3 \u23a6\u23a3 \u23a6 \u23a3 \u23a6 \u23a3 \u23a6 (2.2) Elements of matrix A and B shows equation (2.3). 978-89-93215-02-1 98560/10/$15 \u00a9ICROS 1125 11 12 2 2 21 22 11 12 21 12 ( ) ( ) , ( ) ( ) , , , r f f f r r f f r r f f r r f r f f r r c c c l c l a a m m c l c l c l c l a a J J c cb b m m c l c lb b J J \u03c5 \u03c5 \u03c5 \u03c5 \u03c5 + + = \u2212 = \u2212 \u2212 \u2212 \u2212 \u2212 + = = = = = = \u2212 (2" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000457_978-3-642-55848-1-Figure9.9-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000457_978-3-642-55848-1-Figure9.9-1.png", "caption": "Fig. 9.9. Prismatic joint", "texts": [ "8 by a resistive element R. It is important also if there is an ac tuator that drives the bodies about the junction axis, as is often the case in robot ics. Otherwise it can be simply removed from the model. 1 In which case the lower bonds in the model of the joined bodies in Fig. 9.3 should be removed as well. The Prismatic Joint The prismatic joint connects two bodies - one containing a straight slot and other that has a part that fits precisely into the slot and can slide in it without rotation (Fig. 9.9). The rotation is usually prevented by the form of the slot and the body sliding in it, e.g. both having rectangular cross sections, or by the use of a keyway. 1 This holds for planar motion of the bodies only, for in that case the rotation axis is or thogonal to the plane of the motion. The analysis of a prismatic joint is done in a similar way to the body motion in Sect. 9.2.1. We define a joint Ax'y' coordinate frame that is fixed in one of the bodies, e.g. the one with the slot (Fig. 9.9). As the origin A of the frame, a conven ient point on the centreline of the slot is chosen, for example, it can be the mid point. The x-axis is directed along the slot axis and the y-axis is orthogonal to it. The other point, B, used for representing the joint also is chosen on the slot centre line, but belongs to the other body. We assume that at these points the joint is connected to the bodies. They corre spond to the ports of the prismatic joint component. Like other body connections, there is a force vector and a moment acting on the joint at one port, and the reac tions of other body at the other port. Likewise the ports flow consists of the veloc ity vectors of the corresponding junction points and the common angular velocity of the joined bodies. The position vectors of point B and A, with respect to the base frame (not shown in Fig. 9.9), are related by (9.16) where r'AB is the relative position vector of B with respect to A, expressed in the frame of the joint, i.e. r~B = (X~B ) (9.17) The rotation matrix R of the joint frame with respect to the base frame (Sect. 2.7.3) is given by R = (c~s~ - Sin~) SIn~ cos~ (9.18) 338 9 Multibody Dynamics Thus Eq. (9.16) reads _ (X~B COS <1\u00bb rB-rA + , . X AB sln (9.19) Here X'AB represents the joint displacement coordinate and is the angle of the slot axis to the base x-axis. Both of these can change with time" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000457_978-3-642-55848-1-Figure9.46-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000457_978-3-642-55848-1-Figure9.46-1.png", "caption": "Fig. 9.46. Revolute joint in space", "texts": [ " The problem of modelling manipulators as multi body systems is only one part of it; there is also the problem of the control of such complex space systems, particularly when there are interactions with the environ ment. The bond graph method is a good candidate for solving such multi disciplinary problems. Revolute Joints Revolute joints have already been discussed in Sec. 9.2.2. The basic difference with those discussed earlier is that, because bodies connected by a revolute joint can move in three-dimensional space, the axis of the joint is not confined to spe cific motions but can move freely. To describe this effect, we analyse the bodies A and B connected by a revolute joint, as shown in Fig. 9.46. The bodies could, for example, be two links of a robot manipulator joined by a revolute joint. We as sume that the z-axis of the coordinate frame OAXAYAZA of body A is directed along the joint axis. We assume further that there is a body B frame OsxsYszs. The pre cise positions of the frames are not prescribed and in a specific multibody system they can be defined as is most convenient, e.g. using the Denavit-Hartenberg con vention [9]. The frame Oxyz is the base frame. Let P be the centre point of the revolute joint used as the reference connection point" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002238_s00170-006-0517-3-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002238_s00170-006-0517-3-Figure4-1.png", "caption": "Fig. 4 Meshed state graph of a pair of point-line meshing gear", "texts": [ " Equations of the involute curve of the point-line meshing gear can be stated as: x \u00bc r 1 2 r\u2019 y00\u00f0 \u00de sin 2 t cos\u2019\u00fe r\u2019 y00\u00f0 \u00de cos2 t sin\u2019 y \u00bc r 1 2 r\u2019 y00\u00f0 \u00de sin 2 t sin \u2019\u00fe r\u2019 y00\u00f0 \u00de cos2 t cos\u2019 9>>>= >>>; Equations of the transition curve of the point-line meshingcan be written as: x \u00bc r x1\u00f0 \u00de cos\u03d5\u00fe x1tg\u03bb sin\u03d5 y \u00bc r x1\u00f0 \u00de sin\u03d5\u00fe x1tg\u03bb cos\u03d5 9>= >; x1 \u00bc x0c \u00fe cos\u03b2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u03c1f cos\u03b2 2 y0c y1 2s ; tgr \u00bc x1 x0c y0c y1 \u03c1f cos\u03b2 2 y0c y1 2 When a pair of point-line gears are meshing, the meshing process includes two parts: part I is that the involute parts of the two gears mesh each other, forming line contact, with the weight right on the end face; and part II is that the involute of small and big gear wheels are in contact with the transition curve, forming point gearing. 1. Point-line meshing gear transmission fits basic law of tooth outline meshing When the point-line meshing gear is meshing, its mesh line N1N2 becomes the inside tangent of two basic circles, and when it is diving, as shown in Fig. 4, the big and small wheel\u2019s beginning mesh point is B2, and termination mesh point is J(B1) (point of intercession of the involute on big gear and the transition curve). So line meshing is formed between B2 and J, and point gearing is formed at the termination mesh points, while the mesh point moves parallel along the direction of the axis. All contact points of the common normal pass through the pitch point P, whose meshing accords with the basic law of tooth profile meshing. 2. The condition of continuous transmission If the involute tooth profile of the small gear wheel and the above parts of the big gear wheel\u2019s point J achieve continuous transmission, we must satisfy: B2J B1\u00f0 \u00de > Pb or B2J Pb > 1 Under general circumstances, it can be fashioned as helical or spur tooth" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000457_978-3-642-55848-1-Figure7.31-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000457_978-3-642-55848-1-Figure7.31-1.png", "caption": "Fig. 7.31. The independent voltage source. (a) The circuit symbol, (b) The bond graph rep resentation", "texts": [ "3 Models of Circuit Elements 243 The model presented above is linear with constant values of the impedances. It could be modified in a way that is similar to that of the simple inductive compo nent. Voltage and Current Sources The independent voltage source is a two-terminal component that generates a voltage across its port (electromotive force) independently of the current drawn from the source. The circuit symbol used for such a component is shown in Fig. 7.3la. The bond graph component representing the independent voltage source is given in Fig. 7.31 b. It is a two-port component with a half-arrow showing the sense of power deliv ery. The model used for independent voltage source components is similar to other bond graph models of circuit components and consists of an effort junction and a source effort component (Fig. 7.32). Likewise, an independent current source is a two-terminal component that gen erates a current that is independent of the voltage across its terminals. The electri cal circuit symbol used for such a component is shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003014_med.2007.4433818-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003014_med.2007.4433818-Figure2-1.png", "caption": "Figure 2: Stacked Board Design", "texts": [ " The autopilot is fully interfaced / integrated with Simulink and it is capable of handling several types of communication protocol, accepting various ranges of analog sensor input, data acquisition by including additional memory, measuring altitude and forward speed through on board pressure sensors, and allowing for releasing control of the physical system to either a master computer, or a human pilot. In order to both minimize size and allow for custom analog and MEMS sensor to be developed for use with the autopilot, a stacked board design consisting of a main board and a secondary daughter board is implemented as shown in Fig. 2. The daughter board may be used for inclusion of application specific hardware. This is a necessary requirement for micro air vehicles because the small payload capacity requires extremely small on board sensors to be utilized. When a mini-ITX or PC-104 type processing system is used, a second board, the secondary safety board, is designed to allow for this second processor to act as the \u201cmaster\u201d. The master processor and autopilot communicate through a standard USB connection. This custom daughter board allows for master processor to take control of half the servos for camera pan and tilt control" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000641_1527-2648(200103)3:3<111::aid-adem111>3.0.co;2-z-Figure22-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000641_1527-2648(200103)3:3<111::aid-adem111>3.0.co;2-z-Figure22-1.png", "caption": "Fig. 22. Standard container after 5 days etching in 30 % HNO3.", "texts": [ " The HIP-cycle and the parameters are shown in Figure 21. 4.2.4. Electrochemical Leaching of Dummy Material After the forming process the container must be removed and the dummy material leached out. In order to apply only a single leaching step the capsule material, the inserts and the pore forming powders must be dissolvable in the same chemical etchant. First experiments with a standard unalloyed steel container showed that simple etching with hot 30 % HNO3 takes too long. A standard container is shown in Figure 22 after first etching trials. To increase the efficiency of this working cycle, the etching process was supported by an electrochemical potential. To establish favorable leaching conditions, basic potentiodynamic experiments were made. The results are shown in Figure 23. The parameter of the various curves is the density in g/cm3. Iron dissolves readily at low-negative voltages, where the chromium steel is still very stable. Therefore, the best result was achieved at a voltage of \u00b10.4 V. This was experimentally corroborated with encapsulated chromium steel powders" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000364_robot.1988.12028-Figure11-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000364_robot.1988.12028-Figure11-1.png", "caption": "Figure 11: Regions I, 11, and S .", "texts": [ " It is best to illustrate the method with the following example. First, the perimeter of the object is partitioned into the regions I and I1 which are delimited by the points on the curve whose normals are vertical. The region, I, is the set of curve segments for which all normals have a component in the negative x-direction, excluding the curve segment between the supporting contacts. The region, 11, is the remaining set of curve segments, again excluding the segment between the support contacts (see Figure 11). Second, the lines of action of the forces, f3, f4, and mg, are divided into seven liftability windows by the line of action of f l . at the points 413. 414, and q ig . The J windows are closed half lines beginning at their respective q points, while the Q and P windows are open half lines. The remaining point, q l g . is the only element of the most important window, the translat ion window, TW (see Figure 12). Third, the regions J , B3, B4, and T are defined by considering the possible contact normals of the points in region 11" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002561_bf02986203-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002561_bf02986203-Figure5-1.png", "caption": "Figure 5. A simply connected monotile that R)rces hexagonal parquet layers that can be stacked to fill space. Top, bottom, and tiling views.", "texts": [ " The f igure clearly shows, however , that the h e x a g o n a l pa rque t til ing can still be formed. Connected 3D Monotile The co lor -match ing rule r equ i r ed for the hexagona l pa rque t tile can also be i m p l e m e n t e d with a s imply c o n n e c t e d mono t i l e in three d imens ions . The s imples t w a y to do it is to p r o m o t e the mul t ip ly c o n n e c t e d 2D monot i l e on the right in Figure 4 to a 3D p a r a l l e l e p i p e d wi th sha l low p ro t rud ing rods and grooves , as s h o w n in Figure 5. The comple t e til ing is a s tacking of ident ica l h e x a g o n a l pa rque t layers. The lowest permi t ted i sohedra l n u m b e r for the space-f i l l ing 3D tiling is the one in w h i c h the layers are in per fec t registry. This can be forced, if des i red , by p lac ing b u m p s on the rods at the pos i t ions c o r r e s p o n d i n g to the disk centers in the monot i le of the left pane l of Figure 4 and co r r e spond ing dents in the bo t tom of the pa ra l l e l ep iped . Note that the pattern of disks in Figure 4 is , zot a t r iangular lattice, so the registry is indeed forced" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003272_09544100jaero270-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003272_09544100jaero270-Figure1-1.png", "caption": "Fig. 1 The dynamics of the PVTOL aircraft", "texts": [ " The states of this PVTOL aircraft include the position of centre of mass, (X , Y ), the roll angle, \u03b8 , and their corresponding velocities, (X\u0307 , Y\u0307 , \u03b8\u0307 ). The control input is the thrust directed to the bottom of aircraft Ut and the moment around the aircraft centre of mass Um. In the case of the air bleeding from the reaction control valves or ducts producing force which is not perpendicular to the pitch axis, there will be a coupling effect between the angle rolling moment and lateral moving force. Let the ratio of lateral force induced by rolling moment be denoted by \u03b50, then the aircraft dynamics as shown in Fig. 1 can be written as [3]\u23a7\u23aa\u23a8 \u23aa\u23a9 \u2212mX\u0308 = \u2212 sin \u03b8Ut + \u03b50 cos \u03b8Um \u2212mY\u0308 = cos \u03b8Ut + \u03b50 sin \u03b8Um \u2212 mg J \u03b8\u0308 = Um (1) where mg is the gravity force imposed in the aircraft centre of mass and J the moment of inertia around the Proc. IMechE Vol. 222 Part G: J. Aerospace Engineering JAERO270 \u00a9 IMechE 2008 at The University of Iowa Libraries on June 28, 2015pig.sagepub.comDownloaded from axis through the aircraft centre of mass and along the fuselage. Let the first and second statements in equation (1) be divided by m, and the third one by J , and the varying quantities of mass and moment of inertia denoted by m = mo(1 + \u03b4m), J = Jo(1 + \u03b4J)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001128_ias.1997.643075-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001128_ias.1997.643075-Figure1-1.png", "caption": "Fig. 1. 8/6 SRM", "texts": [ " Hence it includes the effect of saturation and has a very good accuracy. In addition, it offers a good dynamic response and has an excellent self-learning capability. Computer simulations are performed to prove the validity of this algorithm. Experimental results are provided to demonstrate the working of the proposed self-tuning controller. 11. THE SELF-TUNING CONTROL PRINCIPLE A. Basic Principle Of Operation SRM is a doubly salient, singly excited reluctance machine. A typical SRM of 8/6 configuration is shown in Fig. 1. Fig. 2 shows the classical power converter circuit, with two switches and two diodes per phase, typically used with a SRM. The measured phase inductance profile, under unsaturated condition, of an 816, 0.6 kW SRM drive is shown in Fig. 3. This profile can be approximated With a Fourier series. For simulation purposes, this s e ~ e s can be simplified by considering only the first two terms Fig. 3 also shows the approximated inductance plot where 0\" corresponds to the unaligned position and 180\" corresponds to the aligned position, measured in electrical degrees" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001615_tpas.1981.316711-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001615_tpas.1981.316711-Figure2-1.png", "caption": "Fig. 2 Combined space and time phasor diagram of nth frame. Definition of DtQnaxes as real and imaginary axes.", "texts": [ "l, it is clear that: -f f ) =k I n a n -f I = I 1 f where 0 ff f V 2 = 13 2 f (4) As the DnQn axes are each rotating at wn r/s, the rule for expressing a magnetic flux phasor, bj (in the jth frame) by k (in the kth frame), is through the relationship: O. exp jiw t = tD exp j w.t I k j J Wb (5) Basic RelationshipEs of FlUXL Voltage and Current Phasors -fAs is well known, the field flux vector, tn which rotates at wn r/s in thea-aairgap space, induces a voltage En in the three phase stator. The voltage produces the stator current In , and ultimately a stator flux vector $aa which also rotates at the same speed. In the Dn-Q n frame, therefore, one finds a static diagram involving the phasors and-as shown in Fig.2. As explained by Fitzgerald, Kingsley, and Kusko [7], the phasor En lags bfby 90 degrees and is given by the expression: (6)E = -j kb wrl n As the voltage frequency isw% , the stator phase current is: -a -a( T In = (En- En)/ a(j wn) (7) - T where Za(jwi ) and En are respectively the impedance and voltage of the stator circuit equivalent as shown in Fig.3(a). These equivalents are based on the frequencies w>. Usually ET is nonzero, because the stator circuit is connected to some bus voltage. However, E2 = E3 0", " Bilateral Torque Coupling The torque component which couples bilaterally to the source oscillations of the rotor must have the same frequency Wv. Substituting eq.(9) and (10) into eq.(11), one finds that the relevant terms are f + f3) x a and $.fx( 2a + -)* However, the first term makes no contribution to damping, because it is not in time phase with the rotor velocity. This leaves: kT( ,, XI f X -.) =k k If aD2-aD3)s V + (a +, )Cosw t Q2 Q3 'V (12) Using eq.(2) as the time reference, the damping torque component which is in phase with the velocity has the coefficient: AT =k k I OD (Da) ed e a f D2 D3 Referring to Fig.2, the term, a a 1al a2 aj a 1~D2 D3 kcI2 2 3Co 31 (a) 8 'I6r (13) (14) In particular, when the stator is and R-L-C circuit in series as shown in Fig.3(b), a a%= -akbkceVIfR wo + W ~D-4~ 2 2 2D2D3 ~~~R +[(w +w )L - 1/(w +w )C] 0 IV 0 V d8 dt kef X w - W 0 V 2 2 R +[(w-w )L -l/(w-w)Cv0 V 0 V (15) Clearly when (\u00a2D2 -4D3)>.0, the damping torque component becomes unstable. A PhXsical Intelkretation of Electromechanic- kt'X (O3. 3 a77 -W-<~~~~~ I~~~~~~~d IA' 1Di 4- <7 Wvt wV t wt WVt At this point, it is instructive to draw a physical pict_pre of the damging torque component based on (bl x\u00a22) and (l X\u00a23) of eq" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-FigureA.13-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-FigureA.13-1.png", "caption": "Fig. A.13. Optics and accessories for diagonal measurements", "texts": [ " As the tool is traversed along a body diagonal of the work zone, all axes must move in concert in order to position accurately along the diagonal. Diagonal measurements are useful in machine tool acceptance testing or in a periodic maintenance program to assess quickly the condition of a machine. Therefore, linear measurements along the work zone diagonals can provide a quick assessment of the overall positioning accuracy. The HP 10768A diagonal measurement kit is an optical accessory to the HP5529A laser measurement system. A schematic of the accessories is shown in Figure A.12. Figure A.13 shows the typical optics used for a diagonal measurement. A typical set-up for a diagonal measurement is shown in Figure A.14. The accuracy associated with laser measurements are also affected by several factors usually relating to the set-up, optical deformation and also environmental conditions. The main factors will be described. The perpendicular distance between the measurement axis of a machine (the scales) and the actual displacement axis is called the Abbe\u0301 offset. As a result of the Abbe\u0300 offset which is inevitably existent, an Abbe\u0301 error occurs when there is an angular displacement of the moving part during its translation" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001466_tmag.1982.1061888-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001466_tmag.1982.1061888-Figure3-1.png", "caption": "Fig . 3 - Armature End Windings and End Region Boundary Patches", "texts": [], "surrounding_texts": [ "341\nWhen P is on-the f i lgment AB o r o n - i r s e x t e n s i o n , i . e . , when e i t h e r 5=0, o r 5 '=0 or t2E2- ( t .E )2z0 , t he cu r ren t f i l amen t AB has no con t r ibu t ion_ , i . e . , h . . =O. Hence (5) i s s i n g u l a r i t y - f r e e s i n c e h i j v a n i s h e s a t t h e s i n g - u l a r i t y p o i n t s . The f i e l d i n t e n s i t y due to a l l t h e cu r ren t - ca r ry ing conduc to r s i so f cour se 1 3 yethod of Approach -- The method of s i n g u l a r i t i e s is u t i l i z e d f o r s o l v -\ni n g t h i s e l e c t r o m a g n e t i c f i e l d p r o b l e m . To s a t i s f y boundary condi t ion ( l ) , f i c t i t i ous \"magne t i c cha rge\" is d i s t r i b u t e d L o n a l l the mater ia l -body sur faces . Denote t h e f i e l d i n t e n s i t y v e c t o r d u e t o t h e s u r f a c e - d i s t r i b - u t e d f i c t i t i o u s m a g n e t i c c h a r g e s by I& _and t h a t d u e t o a l l the cu r ren t - ca r ry ing conduc to r s by HJ. We have then\ni = vr$ = 8, + 8, and\nwhere @ is a s c a l a r p o t e n t i a l f o r t h e r e s u l t a n t f l u x - i n t e n s i t y f i e l d , M(Q) t h e s t r e n g t h o f t h e f i c t i t i o u s magnetic charges and r p ~ the d is tance be twgen a f i e l d p o i n t P and a cha rge po in t Q on S . While Hi can be e v a l u a t e d d i r e c t l y by the Biot-Savart law, HM can be ob ta ined o n l y a f t e r t h e M(Q) d i s t r i b u t i o n is known. An i n t e g r a l e q u a t i o n is fo rmula t ed to de t e rmine the s t r e n g t h s o f t h e M d i s t r i b u t i o n s u c h t h a t b_oundary cond i t i o n (1) i s sa t i s f i_ed . The f lux dens i ty-B can then be eva lua ted by B = pH and the force by F = J x B , where v i s t h e m a g n e t i c p e r m e a b i l i t y f o r t h e r e g i o n Y and J t h e c u r r e n t c a r r i e d by a conductor.\n--- F i e l d I n t e n s i t y --Due to Current-Carrying Conductors\nThe cur ren t -car ry ing conductor is d i s c r e t i z e d i n t o a number of s t r a i g h t l i n e s e g m e n t s a l o n g i t s c e n t e r l i n e , and each segment is represented by a c u r r e n t f i l a m e n t . Consider one of the f i laments AB as shown i n Fig . 2. The\nf i e l d i n t e n s i t y at a f i e l d p o i n t P induced by t h i s f i l a m e n t i s given by the Biot-Savart law:\nR - - .I d t x r\ni\\ r where J i s t h e c u r r e n t , c = a, t h e p o s i t i o n v e c t o r f o r P f r o m a n y p o i n t a l o n g t h e s t r a i g h t l i n e b e t w e e n A and B , a n d t h e s u b s c r i p t s i and j i n d i c a t e t h e c o n t r i - bu t ion is-d-ue tg t h e j th-segment of the i th conductor . Denoting AP by 6, PB by 6' (see Fig. 2) and performing t h e i n t e g r a t i o n f o r ( 4 ) y i e l d s\nIn t eg ra l Equa t ion for Magnetic Charge Strength Determina t ion\nThe a s s u m p t i o n o f i n f i n i t e p e r m e a b i l i t y f o r t h e m a t e r i a l b o d i e s i m p l i e s t h a t t h e f i e l d - i n t e n s i t y pot e n t i a l w i t h i n t h e b o d i e s is cons t an t , because the re i s no H f i e l d e x i s t i n g w i t h i n them. Consequent ly , the normal component of H on t h e i n t e r i o r s i d e o f S ( i n s i d e t h e material bodies) is zero :\nHere P i s a p o i n t on S , and the term 2\"M i s deduced from the Gauss f lux theorem. Consider the normal component of H on t h e e x t e r i o r s i d e o f S ( i . e . , i n t h e reg ion V , see F ig . 1). We have\n(E .E)p = 8,.Mp - 1 M(Q) - .L dS + 27M(P) (9) a\nS a N P rPQ S u b t r a c t i n g (8) from (9) y i e l d s\n(G-a), = 471M(P) (10)\nwhich shows tha t - the normal component of the resu l tan t f i e l d i n t e n s i t y H on t h e e x t e r i o r s i d e o f S i s e x a c t l y e q u a l t o 471 times t h e lgc_al magne t i c cha rge s t r eng th . S u b s t i t u t i n g (10) f o r (H.N)p i n (9) y i e l d s\nwhere\nK(P,Q) = - - a 1 a N r\nP PQ is t h e k e r n e l o f ( 1 1 ) . E q u a t i o n (11) i s a Fredholm i n t e g r a l e q u a t i o n o f t h e s e c o n d k i n d f o r t h e unknownM. The equa l -po ten t i a l boundary cond i t ion of t h e s u r f a c e S is thus \"bu i l t - i n to ' ' ( 11 ) by the subs t i t u t ion o f (10) i n t o ( 9 ) .\nS i n g u l a r i t y Removal\nTo remove t h e s i n g u l a r i t y e n c o u n t e r e d i n (ll), t h e Gauss f lux theorem i s u t i l i z e d . D e n o t e t h e t r a n s p o s e o f t h e m a t r i x K(P,Q) by K(Q,P)\nK(Q,P) = - - a 1 3N r Q PQ\nThe i n t e g r a l\nr e p r e s e n t s t h e t o t a l f l u x due t o a \" s i n k \" a t P on S e n t e r i n g t h e r e g i o n V through the remainder of S . When P i s on t h e o u t e r s u r f a c e ( S o ) , ao=2a and ain=O; when P i s on one o f t he inne r su r faces (S in ) , a0=4a and ain=-2r. Thus f o r e i t h e r P on S o o r on S i n ,\nj K(Q,P)dSQ = 2 s S\nWith the a id o f (15 ) , (11) can be wr i t t en in a s i n g u l a r i t y - f r e e f o r m", "342\nI t e r a t i o n Formula for Magnet ic Charge Strength Determination\nAn i t e r a t i v e s o l u t i o n p r o c e d u r e similar t o t h o s e employed by t h e writers e lsewhere i s adap ted fo r so lv - ing (16) [12 ,13 ,14 ,15] :\nwhere k i s t h e number o f t h e i t e r a t i o n . When Q=P, t h e in tegrand of (17) is set e q u a l t o z e r o . I t can be shown t h a t t h e l i m i t o f the in tegrand of (17) is ze ro when Q approaches P . I n add i t ion (17 ) can be shown t o be uniformly convergent by mathematical induct ion. S p a c e l i m i t a t i o n p r o h i b i t s p r e s e n t a t i o n h e r e o f t h e d e t a i l e d p r o o f s .\nSOLUTION PROCEDURES\nd e v e l o p e d f o r c a l c u l a t i n g t h e magnet ic f i e l d i n t h e end A comprehensive computer program package has been r eg ion and the e l ec t romagne t i c fo rces on t h e end windings . Its execut ion i s i n t h r e e s t e p s . F i r s t , t h e end-region boundary descr ipt ion and the end-winding l o c a t i o n s are entered and processed. Second, a magn e t i c c h a r g e d i s t r i b u t i o n on the boundary is ca l cu la t ed . Th i rd , t he in s t an taneous 3-D f l u x p a t t e r n a n d f o r c e d i s t r i b u t i o n are c a l c u l q t e d .\nGeometry I n p u t s\nThe s u r f a c e S shown i n F i g . 1, on which the magn e t i c c h a r g e s a r e t o b e d i s t r i b u t e d , is d i v i d e d i n t o small pa t ches , each w i th cons t an t cha rge s t r eng th . On each pa tch a r e p r e s e n t a t i v e p o i n t i s chosen where the boundary condi t ion w i l l be enforced . The pa tch area a c t s as a w e i g h t i n g f a c t o r i n t h e c a l c u l a t i o n , a n d t h e sur face normal a t t h e r e p r e s e n t a t i v e p o i n t d e f i n e s t h e p a t c h o r i e n t a t i o n . The axisymmetr ic boundary surface i s d i v i d e d i n t o s e c t o r s c o r r e s p o n d i n g t o t h e number of s l o t s i n t h e a r m a t u r e . S u r f a c e - p a t c h g e n e r a t i o n i s c o n d u c t e d i n d e t a i l f o r o n l y o n e o f t h e s e s e c t o r s . P a t c h e s f o r t h e r e m a i n i n g s e c t o r s are then genera ted s i m p l y b y r o t a t i n g t h e b a s i c set. I n t h i s p a p e r on ly the e f f ec t o f t he a rma tu re end wind ing cu r ren t s is cons i d e r e d . S i n c e a l l the windings a re assumed to have t h e same shape, only one winding, called \"#l conductor\", is input for conductor geometry genera t ion . The conduc to r i s r ep resen ted by t h e l i n e a r c u r r e n t - f i l a m e n t s a long i t s c e n t e r l i n e . The complete model of surface pa tches and conductor loca t ions is checked v isua l ly through a 3-D g r a p h i c a l c a p a b i l i t y .\nMagnet ic Charge Calculat ions\nThe magnet ic charge d is t r ibu t ion on the magnet ized boundary i n r e s p o n s e t o a l l the a rmature end winding c u r r e n t s i s o b t a i n e d b y s u p e r p o s i n g t h e d i s t r i b u t i o n o f c h a r g e t h a t a r i s e i n r e s p o n s e t o e a c h s e p a r a t e cond u c t o r c u r r e n t . Each o f t h e s e d i s t r i b u t i o n s i s obt a i n e d b y r o t a t i n g a n d s c a l i n g t h e s o - c a l l e d \" b a s i c so lu t ion\" , which i s t h e c a l c u l a t e d d i s t r i b u t i o n a r i s i n g i n r e s p o n s e t o ill c o n d u c t o r c a r r y i n g u n i t y c u r r e n t . T h i s b a s i c s o l u t i o n is ob ta ined by s o l v i n g t h e i t e r a - t ion formula (17) . Thg ngrmal f lux induced by armature elld wind ing cu r ren t s , H j *Np i n (17) , is obtained from (.?).\nFie ld and Force Calcu la t ions ___- The e l e c t r o m a g n e t i c f i e l d i n t h e e n d r e g i o n i s ob ta ined by summing t h e e f f e c t s o f a l l t h e c u r r e n t car ry ing conductors and the boundary magnet ic charges . The n o r m a l f i e l d i n t e n s i t i e s on the boundary pa tches a r e c a l c u l a t e d d i r e c t l y by (10) . The electromagnefi_c f o r c e s a c t i n g on the conduc to r s a re ob ta ined f rom JxB. A pos tp rocesso r has been des igned to d i sp l ay the 3-D\nf i e l d and f o r c e r e s u l t s i n s e v e r a l d i f f e r e n t ways f o r a number of s p e c i f i e d v i e w i n g c r o s s s e c t i o n s .\nNUMERICAL RESULTS\nTest-Case Generator Description\nA Westinghouse-manufactured generator, which i s a two-pole 3 -phase tu rb ine-genera tor a ted a t 850 NVA a t 24 kV, was s e l e c t e d f o r t h i s t e s t ca l cu la - t i on . F igu re 3 shows t h e 4 2 computer-generated a rma tu re co i l w ind ings o f co i l p i t ch 1 7 / 2 1 and 13 ,650 end-region boundary patches. Each coil consists of 69 l i n e s e g m e n t s f o r t h e p a r t o u t s i d e of t he i ronboundary . A s i n d i c a t e d i n t h e s o l u t i o n p r o c e d u r e s , t h e a x i s y m - metr ic boundary i s d i v i d e d i n t o 42 s e c t o r s and only 325 pa tches in one sec to r a re ac tua l ly gene ra t ed and s t o r e d . z\nF igu re 4 is a p l o t o f t h e mmf wave of armature r e a c t i o n f o r t h e c a l c u l a t e d i n s t a n t o f time when t h e\nc u r r e n t i n p h a s e A ( a b s e c t o r number 1) has a maximum p o s i t i v e v a l u e . The d i s c r e t e c o n d u c t o r c u r r e n t d a t a show seven s lo t s pe r phase , and the re is a p h a s e d i f - f e r e n c e i n mmf between top and bottom conductors of a g i v e n s l o t e q u i v a l e n t t o a f o u r - s l o t s h i f t . T h e s e", "343\nt h e i n i t i a l v a l u e f o r M(P). Twen ty - s ix i t e r a t ionswere n e c e s s a r y t o o b t a i n t h e f i n a l c o n v e r g e d s o l u t i o n w i t h i n 1% t o l e r a n c e f o r c h a n g e s b e t w e e n s u c c e s s i v e i t e r a t i o n s o v e r t h e s i g n i f i c a n t p a r t s o f t h e b o u n d a r y . The f i e l d i n t e n s i t y d i s t r i b u t i o n s f o r t h e 81 conduc tor are shown i n F i g s . 6 and 7 f o r r a d i a l i h d t r a n s - ve r se v i ewing p l anes a t '3 = 225' and i = 1.917 f t , r e s p e c t i v e l y . The c a l c u l a t i o n p o i n t s are a t t h e c e n t e r s\n.................... .................... .................... 1 d::::::::::::::::: . . . . . . . . . . . . . . . . .\n. . . . . . . . . . . . . . . . . . , ( ( , . 1 . . . . . . . . . . . . . . . . . ( I ( . . . . . . . . . . . . . . . . . . ,...... ........... ......,- .......... .(,,.,....... ......... .. 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -\n0 . (ROTOR) R(sT,rroRP = 225aQ0\n0. 1.50 3. 4.50 6.\nS o l u t i o h a t a Transverse Cross Sect ion\nf in i t e -d imens ion conduc to r , where th i s ca l cu la t ion may no t be phys i ca l ly mean ingfu l . The f i e i d c a l c u l a t i o n , however, i s e x a c t when t h e c a l c u l a t i n g p o i n t i s r i g h t a t t h e c e n t e r o f t h e c o n d u c t o r , d u e t o t h e s i n g u l a r i t y f r e e f o r m u l a (5) u s e d f o r t h e a c t u a l c a l c u l a t i o n .\nInstantaneous Armature Reaction\nAny i n s t a n t a n e o u s f l u x f i e l d o f t h e a r m a t u r e r eac t ion can be ob ta ined from t h e b a s i c s o l u t i o n . F o r t h e i n s t a n t o f time shown i n F i g . 4 , t h e c a l c u l a t e d f i e l d i n t e n s i t y d i s t r i b u t i o n s are shown i n F i g s . 8 and 9. The symbols are similar t o t h o s e u s e d i n F i g s . 6 and 7 e x c e p t t h a t t h e c o n d u c t o r c r o s s i n g p o i n t s a r e\n.................... .................... .................... .................... .................... .................... ........................ ........................\nh W LI N v ( ? -\nC v)\n.-(\n0 = 225.0\" (ROTOR) (STATOR)" ] }, { "image_filename": "designv11_32_0001226_cdc.2001.980739-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001226_cdc.2001.980739-Figure1-1.png", "caption": "Figure 1: Differential drive two wheel vehicle (a), and underactuated planar link (b).", "texts": [], "surrounding_texts": [ "= 2(x1 sin(8) - x2 cos(8)) - 6(sl cos(8) + x 2 sin(0)) VI = r1u1 - r2212(21 sin(0) - x 2 cos(8)) 212 = r 2 u 2 the system equations (3) can be converted into the nonholonomic integrator 21 = V I , 2 2 = v 2 , i 3 = z l v 2 - 22211. Thus we can design controls for the nonholonomic integrator and apply them to the kinematic mobile robot. We will use this example to demonstrate configuration tracking with (CM) systems. 3 Controllability The systems we are considering here fall into the class of control affine nonlinear systems with drift: (5) m ..\" x = f(x) + Si ( . )Ui i= 1 where x E M, hf is a smooth n-dimensional manifold and U E Rn'. For a complete treatment of nonlinear accessibility and controllability, the reader is referred to [la, 221. We will state the relevant definitions here for reference. Definition 3.1 The system (G) is controllable i f for any two equilibrium points p , q E M , there exists a finite time T and control functions U : [O,T] + E%\"L such that x(0) = p and x(T) = q. The system (G) is small time locally controllable (STLC) if for every fo r equilibrium point p E M and T > 0, the set reachable from p in time T contains p in its interior. From [23], we have the following result for (CI) systems. Proposition 3.2 (Sussmann [23]) Given any driftfree controllable nonlinear system (l), the cascade input system (CI) is both controllable and STLC. Controllability results for (CS) and (CM) systems are not as strong as for (CI) systems, however, each of these classes is fully accessible. Under certain conditions, STLC can also be shown. Proposition 3.3 Given any drift-free controllable nonlinear system (l), the cascade state system (CS) as fully accessible. Proof: In order for a nonlinear system to be accessible, we simply need to show that the Lie Algebra Rank Condition (LARC) is satisfied at all p E 11.1. Define z = [tT, x\"]\", and rewrite the overall system equations in the form Straightforward calculations show that As long as the original drift-free system is controllable, these vector fields will span R\" x R\" at all points. 0 Proposition 3.4 Any cascade state system (CS) fully accessible with Lie brackets of order no more than four is STLC. Proof: For i = 1,. . . , m let 6; be the number of occurrences of the vector fields g; and So be the number of occurrences of the vector field f in a Lie bracket B. From [ 2 2 ] , we refer to a bracket B as bad if do is odd and each Si is even and good otherwise. A sufficient condition for a system to be STLC is that all bad brackets a t an equilibrium point p are linear combinations of good brackets of lower degree. From the previous proposition, we see immediately that the only bad brackets of degree less than four are those of degree three with i = j and 60 = 1 or 3. However, in those cases the bad brackets are identically zero ([si , gi] z 0 and f(p) G 0). 0 Proposition 3.5 (Reyhanoglu et al. [20]) A cascade mechanical system (CM) is fully accessible i f each nonlinear state equation is nonintegrable. Proposition 3.6 (Reyhanoglu et al. [20]) If a (CM) system is fully accessible with the brackets from all equilibrium points. {Si, [f,g;I, [S j , [f,Sill, [f, [S j , [ f , s i l l I l , then it is S T L C While we do not have a general controllability statement for (CS) and (CM) systems, we will see in the next section that when the drift-free portion of the system is controllable, we can always perform configuration tracking. 4 Trajectory Tracking As shown in [5, 16, 17, 181, amplitude-modulated sinusoidal controls can be used to generate motion in the constrained states of a drift-free nonholonomic system. We refer the reader to the references for details and state the basic result here. For readability, we will sometimes suppress explicit time dependence. Proposition 4.1 Given the twice differentiable functions xd( t ) E R\" and a controllable, drift-free nonholonomic system (l), there exist w-parameterized controls of the form ui\"'(t) = Y ; ( x d , i d ) + c*.;j(xd,kd) sin(Xijwt) + ~ i j ( ~ d , cos(pijwt) (7) 2(n--m) j=l 2(n-m) j=1 such that, f o r matched initial conditions and with respect to an C2 norm, limw--too x(W)(t) = xd(t) . 2, I Note that for each state xi such that xi = ui, we will have ~i = x d , i . Example: Consider the nonholonomic integrator j.1 = ul , k2 = u2, 23 = zluz - x2u1 and the controls ul(t) = i d , l + f is in(wt) uz(t) = i d , 2 - f i P ( t ) cos(wt) (8) where p( t ) = k d , ~ -zd ,1&,2 + ~ d , 2 & , ~ . Integrating each of the controls once by parts and assuming matched initial conditions leads t o 1 1 X l ( t ) = Z d , l ( t ) - - cos(wt) fi fi z2(t) = xd,a(t) - -,b(t) sin(wt) The third state then evolves according to To eliminate the integral terms, we use a version of the Riemann-Lebesgue lemma: Lemma 4.2 (Riemann-Lebesgue [9]) Let f be of bounded variation on [a, b] and let 4 E [0,27r]. Then limw+oo s,\" f ( t ) cos(wt + 4 ) d t = o ($1 . In the limit as w becomes large, we have d W ) ( t ) M xd(t). Now we will show how a result of this form for a driftfree system can be extended to our classes of secondorder systems to produce configuration tracking. Corollary 4.3 ((CI) Configuration Tracking) Given a controllable (CI) system, three times differentiable functions X d ( t ) and approximate tracking controls (7) for the system x = G(x)u, define 2 ( n - m ) + ~ i j w c ~ i j ( z d , i ) cos(Aijwt) j=1 2(n-m) - h j U f l i j ( x d y k d ) sin(pijwt). (9) j=1 Denote by [[, x](~) the solution to (CI) for the controls dw). Then for matched initial conditions and with respect to the C2 norm, limw+oo d W ) ( t ) = z d ( t ) . -0.5' I 2, I 4 I O 20 30 40 20 t An example of tracking using these controls with the system (nhi-ci) is shown in Fig. 2 for w = 25. The plot shows the actual position trajectories as solid lines overlaid on dashed lines representing the desired trajectories. The higher order terms that we discarded while constructing our control law will cause the introduction of a constant error in the matched initial conditions at the velocity level. As w becomes large, the error will decrease. Corollary 4.4 ((CS) Configuration Tracking) Given a controllable (CS) system, three times differentiable functions xd( t ) and approximate tracking controls (7) for the system i = G(<)u, define 2 (n- m) j=1 w,!\"'(t) = 7 ( 2 , 2 d ) + a i i j ( 2 d r 5 d ) sin(/\\ijwt) 2(n-m) + P i j ( i 2 , Z d ) cos(pijwt). (10) j=1 Denote by [ E , XI(*) the solution to (CM) for the controls d W ) . Then for matched initial conditions and with respect to the C2 norm, limw-+h? x(\")( t ) = xd( t ) . Proof: Directly using the result from Prop. 4.1 gives One additional integration and the assumption x(0) = &(O) gives and the result follows in the limit w + 03. U An example of tracking with these controls for the system (nhi-cs) is shown in Fig. 3 with a frequency of w = 10. Thc dashcd line represents the desired signals, and the solid line shows the system response. To demonstrate how trajectory tracking for drift-free systems can be extended to (CM) systems, we will restrict our attention to the class where Q , U ~ E Rp, p < m, xnl E Rn-p, u,,~ E Rm-', and the subscripts 1 and nl refer respectivcly to states that are linear and nonlinear. Results for the general case can be stated, but the corresponding proofs are beyond thc scope of this text. Corollary 4.5 (( CM) Configuration Tracking) Given a controllable ( C M ) system with G(x)v of the form (ll), three times differentiable functions xd(t) and approximate tracking controls (7') for the system (ll), define 2(n-m) U:;) = 2d,L,i + X i j w a i j ( Z d , i d ) cos(/\\.@) j = 1 2 (7L - m) j=1 - pi jwpi j ( z d , i d ) sin(pijwt) 2(n-m) ( w ) wnl ,k = ~ k ( z d , i d ) + n k j ( z d , i d ) sin(/\\kjwt) j = 1 2(n-m) j=1 + P k j ( Z d , i d ) cos(pkjWt) (12) where i = 1 , . . . , p , k = p + 1,. . . ,m, and zd = [ x d , l , x d , n l ] . Denote by [ E , XI('\") the solution to (CM) for the controls dW). For matched initial conditions and with respect to the C2 norm, limw+m x(w)(t) = xd(t) . Proof: Integrate the controls assume matching initial conditions to get twice by parts and 2 ( n - m ) j=1 which is exactly the result obtained by integrating the portion of controls (7) corresponding to ul in (11). When z d = [zd,~, ~ d , ~ l ] in v2,)h., we recover the controls (7) corresponding to unl, and G(zl)vnl = k d , n l + o (i) . In order to have the desired result of G(zl)v,l = 2 d , n ~ + o (i) , we simply choose Zd = [zd,~, 2 d , n l ] . Two final integrations assuming matched initial conditions gives the stated result. 0 The underactuated link in the plane (4) is a (CM) system of the type in Cor. 4.5. Using the controls (8) with ( 5 ) , the drift-free system (3) can track [zld, x2d, B d ] with u1 = y(t) + w + sin(wt) - wbm(t),(t) cos(wt) u2 = &(t) - w h ( t ) cos(&) where y = il + i z q , rn = is - (&I - i l zz) , 17 = zd,, sin(0d) - z d , ~ COS(&), z1 = zd , l cos(6') + z6,2 sin(O), z3 = 29 - B d q . Modifying the kinematic controls as shown in the corollary gives us v1 = y ( t ) + wf sin(ut) +ufm(t)y( t )cos(wt) vz = i d ( t ) +ufm(t)s in(wt) where we make the substitutions q = id,lsin(ed) - f d , 2 cos(&) and z1 = i d , j cos(6') + Xd,z sin(0). An example of these controls for w = 10 is shown in Fig. 4. 5 Conclusion Given the reduction of a mechanical system t o the ca.. cade of a drift-free nonholonornic system and a set of integrators, we have shown for some such classes how amplitude-modulated sinusoidal controls can be constructed t o achieve configuration tracking. The general case of (CM) systems was not presented here, hut will be handled in subsequent work. Finally, the type of controls presented here do not take into account bounds on actuator amplitude or frequency As the frequency is increased to produce greater tracking accuracy, physical actuators will quickly reach performance limits. Simultaneously handling limits on tracking errors and limits on actuators is a topic of current research." ] }, { "image_filename": "designv11_32_0000050_s0094-114x(00)00007-0-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000050_s0094-114x(00)00007-0-Figure2-1.png", "caption": "Fig. 2. Two special positions of the cutting mechanism.", "texts": [ " Let us assume the motion of the mechanism whose parameter values are: b 0:3, e 0:5, a 1:3, g 0:2, r 0:25, a 0:75: For these values a mechanism is formed for which the angle of the working tool varies in the interval c1 20:796473: The motion of the mechanism can be divided into two periods: working and return strokes. The \u00aerst interval is realized for the angles from g1 to g2 and the second from the angle g2 to angle g1,which correspond to the case when the leading element and the element 2 are in line, (see Fig. 2). The angle g is de\u00aened as g y\u00ff g1: Where g1 3:9052: Let us analyze the in\u00afuence of the parameter M on buckling properties of the working element of the mechanism. The parameter M is varied in the interval from 0 to 0.1. In Fig. 3(a) the case M 0 is considered. For this case the primary equilibrium path is always stable. There is a symmetric stable branching point for l 0: For M 0:001 the static buckling force is ls 0:0782 and the exact dynamic buckling force is lD 0:0413 (see Fig. 3(b)). It can be concluded that the dynamic buckling force is positive for MR0:001: It means that the buckling occurs in the cutting regime" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001182_robot.2002.1014767-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001182_robot.2002.1014767-Figure7-1.png", "caption": "Figure 7: No antipodal points. Neither the ray of N ( t a ) nor the ray of N(ta) intersects the segment S.", "texts": [ " Under conditions (i)-(v), testing if the ray extending N(t , ) , or simply called the ray of N( t , ) , intersects S can be done by checking whether the cross products (a(&) -a(t,)) x N(t,) and (a ( sb ) - a(t,)) x N ( t , ) have different signs. ,Proposition 5 Suppose S is convex and 7 is concave. Assume that the two antipodal angles 6(s,) and 6(Sb) have the same sign. No antipodal points exist on S and 7 if neither the ray of N(t,) nor the ray O f N ( t b ) intersects S. Proof For simplicity, we assume that N(s , ) points vertically upward, as shown in Figure 7. Under condition (v), S and 7 must lie on the same side of the two tangent lines L, and Lb of S at sa and Sb, respectively. Suppose neither of the rays of N(t , ) and N(tb) intersects S. Because N(t , ) does not intersect s, t, is either to the right of S or to its left. If t , is to the right, condition (v) determines that the segment 7 cannot cross the line containing N(t , ) to its left. So 7 lies entirely to the right of the segment S, as shown in Figure 7(a). But all normals on S point to the left. Thus no antipodal points exist. If t , is to the left of S, then 6(s,) > 0. Since 6(Sb) has the same sign, 6(Sb) > 0. Then S and 7 must lie on different sides of the line containing N(tb) as in Figure 7(b). Apparently, they cannot have antipodal points either. 0 eration when the ray of N ( t , ) intersects S. Lemma 6 Suppose S is convex and 7 is concave. And suppose the ray of N ( t , ) intersects S. In the above iteration, si < si+l and no antipodal points exist in (s i , si+l] and ( t i , ti+l] for all i 2 0. The proof of the lemma is by induction in a way similar to the proof of Lemma 3. Following Lemma 6, the sequence {si} defined by is monotonically increasing. If there exists at least one antipodal point on S, the sequence { s i } will converge to the first such point s* from sa" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure7.1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure7.1-1.png", "caption": "Fig. 7.1. Sign convention for plane structure", "texts": [ " However, it is useful to look at a two-dimensional problem first before extending the problem to a three-dimensional one. Generally, machine structures are stationary. Therefore the sum of the forces and moments acting on it must be zero, which is in accordance with Newton\u2019s second law. In mathematical form,\u2211 Fx = 0, (7.1)\u2211 Fy = 0, (7.2)\u2211 Mz = 0, (7.3) where Fx and Fy are the forces in the x- and y-axis, respectively, while Mz is the moment about the z-axis where the z-axis is pointing out of the page. For a plane structure, we will make use of the sign conventions as depicted in Figure 7.1. Since the static determinacy of a structure is a twofold issue, it is possible to proceed without first considering the support. Each structural configuration can be tested to verify whether the plane structure satisfies the equation 2j = m + 3, (7.4) where j denotes the number of joints and m denotes the number of members; then, there are three possible cases, namely, 1. If 2j = m + 3, then the structure is statically determinate 2. If 2j > m + 3, then the structure is unstable 3. If 2j < m + 3, then the structure is statically indeterminate The three conditions are depicted in the Figure 7", " Therefore, for a space-structure to be rigid, every plane-structure that makes up the space-structure must be rigid in its own right. This is one reason to have a good understanding of plane structural rigidity. Since machine structures are stationary, the sum of the forces and moments acting on it must be zero; which is in accordance with Newton\u2019s second law. Mathematically, this implies \u2211 F = 0, (7.5) \u2211 M = 0, (7.6) where F and M are three-dimensional force and moment vectors, respectively. The sign conventions as depicted in Figure 7.1 will be used. As before, each structural configuration can be tested to verify if the planestructure satisfies the equation 3j = m + 6, (7.7) where j denotes the number of joints and m denotes the number of members; then, there are three possible cases, namely 7.1 Mechanical Design to Minimise Vibration 203 2. If 3j > m + 6, then the structure is unstable 3. If 3j < m + 6, then the structure is statically indeterminate In the plane-structure, the triangle is the basic shape, which is rigid and statically determinate" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002168_3-540-29461-9_104-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002168_3-540-29461-9_104-Figure7-1.png", "caption": "Fig. 7. Examples of mechanical planks", "texts": [ " In order to move from one column of glass to another in the right-left direction, a specially designed ankle joint gives a passive turning motion to the suckers. This joint is located between the connecting piece which joins the vacuum suckers with the Y cylinder and the plank beneath it to which 4 vacuum-suckers are attached (shown in Fig. 6). In order to meet the requirements of the lightweight and dexterous movement mechanism, considerable stress is laid on weight reduction. All mechanical parts are designed specifically and mainly manufactured in aluminum. Figure 7 shows some examples of the mechanical planks. A PLC is used for the robot control system (shown in Fig. 8), which can directly count the pulse signals from the encoder and directly drive the solenoid valves, relays and vacuum ejectors. FX2N-4AD which is added to the system can identify the ultrasonic sensor signals and other analog sensors. The control and monitoring of the robot is achieved through the GUI to allow an effective and user friendly operation of the robot. The communication interface between the PLC and the controller of the following unit is designed to synchronize the following movement of the cables" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000061_s0257-8972(01)01531-6-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000061_s0257-8972(01)01531-6-Figure4-1.png", "caption": "Fig. 4. Plans of the induced-currents and Lorentz-forces in a volume element at the surface and in an element within the melt.", "texts": [ " Due to the small size=\u00d8js0 of the melting pool and the relatively low velocities of the liquid material, an influence on the MF can be neglected and, above that, the electric field can be expressed by means of the gradient of the electric potential in Eq. (1) w2x Within the melt, where differences of the electric potential are negligible with respect to the induction of the Lorentz-forces, these volume forces can be approximated according to Eqs. (1) and (2) by the relation (3): B Ewx 2f ;ys w B (3)L e y 0C F D G0 Therefore Lorentz-forces in a constellation, according to Fig. 3, act in the opposite direction of the velocity components that are perpendicular to the MF lines (see Fig. 4). At the surface of the melting pool, gradients of the electric potential normal to the surface have to possess such a magnitude that current density vectors are forced in a surface tangential direction. Hence, a physical impossible current flux over the surface is avoided. The Lorentz-force at this location is described by Eq. (4): B E0 \u2260w f sys B (4)L e 0 \u2260xC F D G0 If a transport variable, like the alloying element concentration, but also impurities or gaseous inclusions, is transported convectively, a distinct influence on the distribution within the melt is expected depending on the MF strength" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001820_j.1934-6093.2004.tb00189.x-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001820_j.1934-6093.2004.tb00189.x-Figure2-1.png", "caption": "Fig. 2. The dynamics of the planar V/STOL (PVTOL) aircraft.", "texts": [ " Let the amount of lateral force induced by the rolling moment be denoted by \u03b50; then, we have the aircraft dynamics written as 1 0 2 1 0 2 2 sin cos cos sin , mX U U mY U U mg J U \u03b8 \u03b8 \u03b8 \u03b8 \u03b8 \u2212 = \u2212 + \u2212 = \u2212 + \u2212 = \u03b5 \u03b5 (1) where mg is the gravity force imposed on the aircraft center of mass and J is the mass moment of inertia around the axis extending through the aircraft center of mass and along the fuselage. To simplify the notation of the PVTOL aircraft dynamics (1), the first and second equations in (1) are divided by mg, and the third one by J. Let x := \u2212X/g, y := \u2212Y/g, u1 := 1U mg , u2 := 2U J , and \u03b5 := 0 J mg \u03b5 ; then, we have the normalized PVTOL aircraft dynamics as shown in Fig. 2: 1 2 1 2 2 sin cos , cos sin 1, . x u u x u u u \u03b8 \u03b8 \u03b8 \u03b8 \u03b8 = \u2212 + = + \u2212 = \u03b5 \u03b5 (2) The term \u201c\u22121\u201d denotes the normalized gravity acceleration. The coefficient \u201c\u03b5\u201d denotes the parasitic coupling effect between the lateral force and rolling moment, which results in the non-minimum phase characteristic. Note that the possible parasitic yaw/rolling coupling and aerodynamic effects are neglected for the sake of simplicity. The nonlinear PVTOL model (2) is rewritten as an uncertain LPV system with state-space dependence on the measurable varying roll angle \u03b8 and uncertain coupling parameter \u03b5: 1 2( ( ) ( )) ,x A x B B u D\u03c5 \u03c5 \u03c5 \u03b8 \u03b8= + + +\u03b5 (3) where x\u03c5 = (x, x , y, y , \u03b8, \u03b8 )T and u = (u1, u2)T" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002167_1434461000166-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002167_1434461000166-Figure7-1.png", "caption": "Figure 7. A. Mastigonenes drawn on the flagellum of Paraphysomonas vestita in the hypothesised orientation. Mastigonemes that appear to be crossing are not necessarily doing so, as the movement is 3-dimensional. The open arrows indicate the direction of the flow; the closed arrows indicate the velocity components parallel and normal to the flagellar axis. B. A transect of the flagellum at the position marked on A, showing the suggested movement perpendicular to the C-plane of the flagellum (circles) with mastigonemes (straight lines). The open arrows indicate the direction of the flow.", "texts": [ " Mastigonemes are too small for observations with a light microscope, so we can only guess how they are oriented in living organisms with respect to the direction of movement of the flagella. We assume they are oriented in two rows placed on opposite sides of the flagellum in the C-plane; this seems the most likely interpretation of published TEM photographs (e.g. Thomsen et al. 1981), and also gives the fluid dynamical estimates that accords best with observations (e.g. Holwill and Sleigh 1967). The observed flow pattern can be explained if we assume the mastigonemes to be positioned within the C-plane (Fig. 7A). As described for Ochromonas (e.g. Jahn et al. 1964), movements in the C\u2013plane would then result in the fluid being pulled along the flagellar axis. When looking at Figure 7A, movements in the S-surface would result in the flagellum being moved in and out of the plane of the paper and so in the mastigonemes being moved sidewise (Fig. 7B). The mastigonemes are thus moved together, like a surface. If the flagellum is capable of generating a flow with such movements, the mastigonemes must change orientation during the flagellar beat. If the top row of mastigonemes tilt towards the movement as seen in Figure 7B, the surface formed by the mastigonemes would push the fluid down and to the right when moving to the right in the S-surface, and down and to the left when moving to the left (Fig. 7B). There are no inertial effects at very low Reynolds numbers, so all fluid motions are reversible and the horizontal fluid motions in Figure 7B cancel each other out in the course of an oscillation. The resulting fluid motion would thus be reduced to a velocity component normal to the axis of the flagellum seen from the C-plane. The flagellum would produce a flow both in the forward and backward stroke. This together with the constant movement of fluid by the lower part of the flagellum explains that there are no observable instabilities in the flow pattern at the time scale of 8 ms. Whether the movement is circular, as shown in Figure 7B or a Figure of 8 (which automatically would produce the tilting), is impossible to say. At any given point along the flagellum, the flow would be a sum of the flow components normal and parallel to the axis of the flagellar waveform seen from the C-plane. Along the proximal part of the flagellum, the largest amplitude is in the C-plane (Fig. 2A), and the flow would thus mainly follow the axis of the flagellum. In the distal part of the flagellum, the largest amplitude is in the S-surface (Fig. 2B) and the flow would be almost normal to the flagellar axis of the C-plane (Fig. 7A). As we cannot be sure of the orientation of the mastigonemes, the above is only a hypothesis, but it accords with observed flow patterns. Bacterial flagella are of comparable diameter to the mastigonemes of eukaryotic cells. It has been possible to study the movements of individual bacterial flagella by fluorescent labelling of the cells and filaments (Turner et al. 2000). In the future, such methods might also make possible a more precise study of the function of the mastigonemes. However, the assumption that the mastigonemes are oriented within the C-plane is supported by observations on the movement of particles near the flagellum" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003496_6.2007-1806-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003496_6.2007-1806-Figure1-1.png", "caption": "Figure 1: Square membrane model for finite element analyses. Crease elements are represented by a single row of elements.", "texts": [ " Second, an experimental analysis is outlined to provide validation of the numerical results. Third, physical explanations are provided addressing the numerical and experimental observations. Finally, a discussion concludes the paper. II. Dynamic Response of Creased Membrane: Numerical Analysis Numerical simulation is performed using the nonlinear finite element code ABAQUS. As numerical analysis is computationally expensive with material nonlinearity, a reasonably smaller square membrane model with side dimension of 125 mm is considered. The numerical model, as shown in Figure 1, is a square Kapton film with thickness of 25 micron (1 mil). Corner loads are applied to the membrane using a 15 mm wide load spreader (rigid bar elements). The membrane surface is modeled using standard membrane elements, M3D4, available in ABAQUS. The load spreader is modeled using rigid elements. A local roller boundary condition is assigned at the center node of each load spreader, which allowed in-plane translation along the loading direction. The numerical model is under self-equilibration due to the loading configuration" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002855_07ias.2007.334-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002855_07ias.2007.334-Figure8-1.png", "caption": "Figure 8. Mode 2 of the stator with piezoelectric excitation, 8200 Hz", "texts": [ " Vibratory acceleration spectra of the yoke frame and the end shields have multiple spectral lines due to different part of them (bolt, teeth \u2026). Vibration sources (aerodynamic, mechanical and magnetic) create forces on stator. The spectrum of these forces excites resonance of the stator but also resonances of yoke frame and end shields. III. NOISE REDUCTION BY ACTIVE CONTROL Principle of active compensation with piezoelectric actuators is to generate one controlled source of vibration [5], [8]. Piezoelectric actuators located to the stator boundary layer (Figure 8.) create adequate force on stator in order to compensate the modal structure strain. In figure 8. piezoelectric inserts generate modal forces which correspond to mode 2 resonance of structure. The final deformation is the result of the forces composition generated by on the one hand, mechanical, aerodynamical and magnetic sources and on the other hand by piezoelectric actuators. Figure 9. is an E.F. comparison between the spectrum of the vibratory acceleration measured in stator for different piezoelectric voltage. Stator is excitated by two different ways. A sinusoidal magnetic excitation (5 kPa amplitude) applied to stator teeth" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000819_al-120023612-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000819_al-120023612-Figure1-1.png", "caption": "Figure 1. Cyclic voltammograms of (A), (B), and (C) electrodes in phosphate buffer solutions (pH 7.4). Scan rate: 20mV s 1. Electrode surface area\u00bc 0.07 cm2.", "texts": [ " In the two first cases same amount of ferrocene was dissolved in the binding paraffin oil, then mixed with graphite powder or graphite and zeolite. It needed to be oxidized at the surface of the electrode before reacting with the reduced form of (GOx)red generated after reaction with b-glucose. In the third case the ferricinium cation was incorporated in the frame of the zeolite at the right oxidation state for immediate reaction with the reduced form of GOx. In this case the binder was free of any product. Figure 1 displays the cyclic voltammograms for the three modified electrodes in phosphate buffer solution in the absence of glucose. Electrodes (A) and (B) contain the same amount 1744 Serban and El Murr of ferrocene and therefore should exhibit the same cyclic voltammogram if the amount of the electroactive species is the only important factor governing the electrochemical behavior of the two electrodes. Figure 1 shows that electrode (B) exhibits higher peak currents that can be attributed to higher hydrophilicity of (B) surface due to the presence of NaY zeolite. Such a high hydrophilicity permits a higher oxido-reduction rates due to an easier ion exchange between the electro-active species and the solution or to a better penetration of the electrolyte support in depth of the electrode. For comparison purpose, several (B) and (C) type electrodes were respectively prepared with different amounts of NaY and exchanged zeolite FcHY" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000219_20.877668-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000219_20.877668-Figure1-1.png", "caption": "Fig. 1. The effect of the interaction field on the direction of magnetization.", "texts": [ " The total magnetic energy of a single domain is given as: (1) where the first and second terms are anisotropy energy and interaction energy, respectively, and are the angles of magnetization and applied field from the easy axis, and is the modified applied magnetic field defined as follows: (2) The stable direction of the magnetization of the particle is calculated from the energy minimum conditions, which are expressed as follows by introducing the normalized field defined as : (3) The solutions of (3) are easily found by using the Newton\u2013Raphson method, and in the case that more than one solution exists, the direction of the magnetization will be the smallest angle from the easy axis [5]\u2013[8]. The direction of the magnetization, hence, strongly depends on the easy axis. In the modeling, the easy axis of the current status should be memorized for next calculation. The effect of the interaction field on the solution of (3) is shifting and rotation of the asteroid curve as shown in Fig. 1. The single domain particle changes its easy axis to the nearer direction from the direction of magnetization between the direction of the original easy axis and negative direction of the original easy axis when the applied field satisfies the following condition [8]: (4) where . After the direction of the magnetization is decided, the component of the magnetization of the domain parallel to the applied field is computed using the following equation: (5) The coercive force, , and interaction field, , can be found easily at the Preisach plane as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000001_s0389-4304(01)00108-4-Figure14-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000001_s0389-4304(01)00108-4-Figure14-1.png", "caption": "Fig. 14. Results of friction measurements in each portion.", "texts": [ "7Nm, which corresponds to the average torque in the camshaft valve system, the overall timing chain friction is attributed 13% to guide R friction, 27% to guide L friction and 60% to other frictions (chain and sprockets). We established a technique for accurately measuring sliding loss in the timing chain and guides of an engine. Measurements by this technique have led us to conclude as follows: (1) Overall timing chain friction accounts for 16% of overall engine friction. (2) Breakdown of this timing chain friction is: 13% guide R friction, 27% guide L friction, and 60% other friction (chain and sprockets) (see Fig. 14). [1] Ushijima, K. et al., Development of a Method of Analyzing Engine Bearing Friction Loss (in Japanese), Proc. of JSME 71st Annual Meeting, Vol. D, No. 930\u2013963, pp. 332\u2013334. [2] Soejima, M. et al., Studies on Measurement Method of Total Friction Loss of Internal Combustion Engines (in Japanese), JSME Int. J. Series B (1994). [3] Kato, A., Yasuda, Y., An Analysis of Friction Reduction Techniques for Direct-acting Valve Train Systems (in Japanese), Proc. Autumn Convention of JSAE, Vol. 924, pp" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003802_tpas.1967.291730-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003802_tpas.1967.291730-Figure7-1.png", "caption": "Fig. 7. Conversion design-230-kV tangent structure.", "texts": [ " The most common pole sizes are 60 and 65 feet, class 2 and 3. The spans average about 660 feet. Pole spacing is 13 feet. Conductor size is 266.S kemil ACSR 26/7. In the sixth edition of the National Electric Safety Code ground clearance requirements were reduced so that 230- kV conductors can now be at about the same level as that required for 115-kV conductors under the fifth edition. This simplified the structure modifications and reduced the cost significantly. Conversion Modifications The converted tangent structure design is shown in Fig. 7. The actual changes and modifications were as follows: 1) The existing 26-foot double plank crossarms were raised two feet to compensate for one additional insulator and 1.5 feet additional sag in the new 795 kemil ACSR 24/7 conductor. The horizontal spacing of the conductors was not changed. 2) To maintain vertical spacing, the shield wires were also raised two feet and supported by ridge irons. The shielding angle is 290. There was no change in the shield wire size or in the sag. 3) Four braces were added to the structure top assembly to support the increased vertical load and to strengthen the structure for transverse loading" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001487_j.mechmachtheory.2004.05.004-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001487_j.mechmachtheory.2004.05.004-Figure3-1.png", "caption": "Fig. 3. A point-line as a point in T5.", "texts": [ " The image points of point-lines of R3 fill the whole space of T5. A point-line with h \u00bc 0 has the same coordinates as that of the coaxial oriented line. Observing Eq. (9), one may find that all point-lines associated with the same line can be expressed as a linear function of h: A\u00f0h\u00de \u00bc A\u00f00\u00de \u00fe hu \u00f0 1 < h < 1\u00de; \u00f014\u00de where A\u00f00\u00de \u00bc \u00f0a1; a2; a3; a01; a02; a03\u00de represents a point of the Klein Quadric, and u \u00bc \u00f00; 0; 0; a1; a2; a3\u00de represents a point of T5. The geometric interpretation of Eq. (14) is a hyperline through point A\u00f00\u00de along the direction of vector u (Fig. 3). Therefore, we have the following property. Property 3. All point-lines associated with the same oriented line of R3 can be mapped to points of the same hyperline of T5. Consider two positions A\u0302, B\u0302 (dual vectors) of a point-line as shown in Fig. 4. The unit line vectors a _ and b _ are coaxial with A\u0302 and B\u0302, respectively. Taking any point on the common perpendicular of A\u0302 and B\u0302 as the reference point, the representations of A\u0302 and B\u0302 read A\u0302 \u00bc exp\u00f0ehA\u00dea _ ; \u00f015\u00de B\u0302 \u00bc exp\u00f0ehB\u00deb _ : \u00f016\u00de The inner, cross, and geometric products of A\u0302 and B\u0302 are as follows: A\u0302 B\u0302 \u00bc exp\u00bde\u00f0hA \u00fe hB\u00de \u00f0a _ b _ \u00de; \u00f017\u00de A\u0302 B\u0302 \u00bc exp\u00bde\u00f0hA \u00fe hB\u00de \u00f0a _ b _ \u00de; \u00f018\u00de A\u0302B\u0302 \u00bc exp\u00bde\u00f0hA \u00fe hB\u00de \u00f0a _ b _ \u00de: \u00f019\u00de As dual vectors, A\u0302 and B\u0302 have the following relationship [23]: A\u0302B\u0302 \u00bc A\u0302 B\u0302\u00fe A\u0302 B\u0302: \u00f020\u00de The dot and cross products of the two unit line vectors a _ and b _ are [30]: a _ b _ \u00bc cos h\u0302; \u00f021\u00de a _ b _ \u00bc s _ sin h\u0302; \u00f022\u00de where h\u0302 \u00bc h \u00fe es is the dual angle subtended by the two point-line axes, and s _ is the unit line vector along the common perpendicular referred to as the common-normal axis" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001763_025-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001763_025-Figure1-1.png", "caption": "Figure 1. Methods for fatigue testing by rotation of a bent fibre: (a) free biaxial rotation; (b) rotation over a pin, with a single drive; ( c ) biaxial rotation over a pin; (d ) diagrammatic representation of nature of deformation, transformed so that fibre alignment is constant, instead of rotating (the cross-section at A remains stationary but the end B is moved round a circle, without rotation of the cross-section itself).", "texts": [], "surrounding_texts": [ "Recent investigations (Cali1 and Hearle 1977, Goswami and Hearle 1976, Hearle and Lomas 1977, Hearle and Vaughn 1970, Hearle and Wong 1977, Lyons 1962) have shown that the rotation of a bent fibre leads to progressive breakdown and ultimate failure through the development of multiple splits in a way which is similar to the most common form of wear in ordinary use. The method is therefore a useful way of studying fibre fatigue. Three basic forms of apparatus have been used. For very coarse monofilaments, the fibre can be bent freely and clamped so that both ends can be rotated together, as in figure l(u). In order to get reasonably rapid fatigue, it is necessary to have a radius of curvature of the order of ten times the monofilament diameter; and it has not proved possible to scale down this form of apparatus to obtain a small enough radius of curvature to test typical textile fibres with diameters of the order of 10 pm. Consequently, we adopted the method of forcing a small radius of curvature by passing the fibre over a pin or wire under some tension. In the first form of apparatus, figure l(b), the fibre was rotated from one end and tensioned by a hanging weight. In later forms, figure I(c), the fibre was driven from both ends and tensioned in other ways. Present addresses : t Instituto de Pesquisas Technologicas do Estado de Sao Paulo S/A, Sao Paulo, Brazil. $ University of Tennessee, Textiles and Clothing Department, College of Home Economics, Knoxville, Tennessee 37916, USA. 0022-3727/80/040725+ 10 $01.50 0 1980 The Institute of Physics 725 726 S F Calil, B C Goswami and J W S Hearle If the fibre were perfectly elastic, and if there were no frictional or air resistance to rotation, then the fibre deformation would be pure bending about an axis which is rotating in the material as illustrated in figure l(d), which is transformed so that the material alignment of the fibre is fixed. Consequently the only deformation would be cyclic bending strains. However, in practice, considerable torsional deformation is observed. Other tests (Hearle 1975, Jariwala 1974) in simple repeated bending have led to failure along the planar surfaces of kink bands at angles of about 45\" to the fibre axis-a form of breakage which is quite different from the multiple splitting of biaxial rotation. It therefore appears that the shear stresses, arising from the torque, are important in promoting failure, in conjunction with the bending stresses. The present paper is concerned with the observation and origin of the torque. 2. Experimental observations In experiments with rotation over a pin, as in figure l(b), reported by Hearle and Wong (1977), considerable real twist develops in the fibre as the rotation of the weight lags behind the rotation of the driving clamp. An example is shown in figure 2(a) (plate). This twist was attributed to friction between the fibre and the pin surface and to viscous drag (and initial inertial drag) impeding the rotation of the weight. However, the level of twist was quite high, and must have been increased by the effects to be discussed in this paper. With biaxial rotation over a pin, as in figure l(c), the results of Calil and Hearle (1977) show a marked false twist effect. More details of this work will be reported elsewhere, but an example is shown in figure 2(b) (plate). Real twist is impossible since the two clamps are geared together. However the rotation of the centre point of the fibre lags behind the rotation of the clamps giving right-handed twist on one side and left-handed twist on the other, as shown in figure 2(b). Frictional drag between the fibre and the surface of the pin would give rise to an effect of this sort. The forces and moments would vary in the way indicated in figure 3 with the torque being zero at the centre point and rising to a constant value where the fibre leaves the pin. This variation in torque would explain the fact that in coarse fibres the splitting occurs in opposite senses in two separated positions where the torque is higher. Torque in fatigue testing ofjibres 727 When there is rotation over a pin, there is clearly an external frictional force which would cause torque to develop, although, on reflection, the levels of twist developed appear to be high, especially as tensions are low and the surface damage caused by any friction is very slight. However, even when there is no solid surface involved, as in figure l(u), there is still evidence of high twist. The material used for these studies was 66 mg m-1 (600 denier) nylon 6 monofilament with a breaking load of 2.7 kg and a breaking extension of 60 %. The monofilaments were rotated at 200 rpm in a standard atmosphere of 65% RH and 20\u00b0C. Test results are shown in figure 4 (plate). Figure 4(a) shows early damage after 400 cycles; figures 4(b) and (c) show the increased splitting after 7240 cycles; and figures 4(d) and (e) show the two ends of a monofilament which has failed completely after 28 000 cycles. The mounting of the monofilament, as in figure l(u), does not give uniform bending but instead gives the greatest bending curvature at the centre. The compression on the inside of the bend will lead to yielding through the formation of kink bands. Progressive damage will lower the bending resistance, intensify the bending locally, and so concentrate failure at the centre of the specimen. There may be some heating, but this is not large. Following the formation of kink bands, the torsional shear stresses leads to splitting and final failure. However the present paper is not concerned with the details of the failure situation but with the origin of the false-twist effect, with opposed torque coming in from either end, when it cannot be explained by external frictional drag. All the illustrations show the strong false-twist effect, indicating a considerable lag in rotation of the central portion and it seems unlikely that this could be caused solely by the air drag at the low speeds used. A similar false-twist effect is reported in earlier studies (Hearle and Vaughn 1970, Lyons 1962)." ] }, { "image_filename": "designv11_32_0002400_j.mechmachtheory.2006.01.005-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002400_j.mechmachtheory.2006.01.005-Figure2-1.png", "caption": "Fig. 2. Rigid cylinder rolling on a curved visoelastic surface.", "texts": [ " The three parameter Maxwell model, consisting of a single Maxwell element in series with a spring, suffices for a conventional conveyor belt because the contact surface between the belt and idler can be described by a line contact. With a constant contact length throughout the contact zone the model only has to match for a single frequency of excitation, making a good approximation possible by tuning the time constant of the single Maxwell element to this frequency. However, as a result of the curved running surface in the E\u2013BS, there exists an elliptical contact zone. Due to the varying contact length in the elliptical patch, the model has to match for a range of frequencies. Fig. 2 shows how the model represents the belt passing over an idler or drive wheel. A rigid cylinder rolling with angular velocity x is pushed onto a curved viscoelastic surface moving with the belt velocity vb, which results in the elliptical contact patch. To match the model with the rubber\u2019s viscoelastic properties within the excitation range, additional Maxwell elements are introduced. An array of Maxwell elements approximates the viscoelastic behaviour each consisting of a spring with stiffness Ei and a dashpot with a damping coefficient gi, as illustrated in Fig", " In the stick-zone only the rubber surface deforms due to the applied traction, while in the slip-zone the rubber surface also slides over the wheel\u2019s surface because the friction limit has been reached. To determine the placement of the zones, friction is modelled according to the Coulombs d\u2019Amonton\u2019s law: js\u00f0x; y\u00dej 6 lr\u00f0x; y\u00de; \u00f011\u00de where l is the friction coefficient. To solve this equation, the pressure distribution r(x,y) in the contact plane is determined first, by defining the deformation of the viscoelastic surface in the direction of the z-axis (see Fig. 2). For this calculation an assumption, also used by Johnson [3], is made that the shear stress does not influence the normal stress distribution. If the contact zone is small compared to the curvatures of the rolling cylinder and rubber surface (so x R1 and y R2), and the cylinder is pressed into the surface with a distance z0, then the deformation of the contact surface can be described as follows: w\u00f0x; y\u00de \u00bc z0 x2 2R1 y2 2R2 with z0 \u00bc c2 2R2 . \u00f012\u00de Under steady state conditions with a constant belt speed vb\u00f0dx dt \u00bc vb\u00de, using a Winkler foundation with thickness h and the deformation equation (12) \u00f0e \u00bc w\u00f0x;y\u00de h \u00de, the differential equation (6) for each Maxwell element can be written as ori ox ri Ei givb \u00bc Ei x hR1 " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000364_robot.1988.12028-Figure9-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000364_robot.1988.12028-Figure9-1.png", "caption": "Figure 9: Translation Region for an Edge.", "texts": [ " The particular solution of equation (1) in which we are interested is the one for which the third and fourth contacts break, which can be stated as Removing the third and fourth columns from W and noting that the first and fifth contact angles are equal, we can solve equation (1). Substituting the result into inequality (12) yields sin(w1 - w2) > 0 (13) t5 > o (14) tg sin(yr1 - y~ 2) + t5 COS(Y2) te s i n ( ~ 1 - ~ 2 ) < o . cos(w1) C O d V 1) < t2 < cos(yr1) ( 1 3 These inequalities define the translation, T, region in which squeezing with the second finger causes the object to translate along the first finger breaking both support contacts. In Figure 9, the translation region is indicated by the double bold line. An interesting property of translation regions is that the internal grasp force required to lift the object is constant throughout T for a given edge. The translation region for a vertex is determined by substi tuting equation (1 1) into inequalities (13). (14) and (15) (see Figure 10). 2.4 Graphical Construction A graphical method to determine the liftability regions of any planar curve with or without vertices for two- and three-point initial grasps has been developed based on the above analysis" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003008_j.mechmachtheory.2007.05.001-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003008_j.mechmachtheory.2007.05.001-Figure5-1.png", "caption": "Fig. 5. Optimal grasps on a bottle for different manipulation tasks.", "texts": [ " Then b\u03021 \u00bc b\u03022 \u00bc b\u03023 \u00bc 0:0724p and the contact positions r1 \u00bc \u00bd 6:764 0 18:820 T; r2 \u00bc \u00bd 6:764 16:299 9:410 T; r3 \u00bc \u00bd 6:764 16:299 9:410 T, and r4 \u00bc \u00bd 20 0 0 T. Running Algo- rithm 3 w.r.t. wb ext, we obtain grasp bGb (Fig. 4b) at / \u00bc 0;w \u00bc 0, and h \u00bc 0, for which Q\u00f0bGb;wb ext\u00de \u00bc 0:8321. At that time, b\u03021 \u00bc b\u03022 \u00bc b\u03023 \u00bc 0:0724p, and r1 \u00bc \u00bd 6:764 0 18:820 T; r2 \u00bc \u00bd 6:764 16:299 9:410 T; r3 \u00bc \u00bd 6:764 16:299 9:410 T, and r4 \u00bc \u00bd 20 0 0 T. The required CPU times are 113.08 min and 126.21 min. Example 2. The object O to be manipulated is a bottle (Fig. 5), which consists of an intercepted ellipsoid E and the spherical extension H of a hexahedron. The origin of frame FO is selected at the center of E. The piece of surface E can be formulated in frame FO as E \u00bc conv \u00bd a cos c1 cos c2 a cos c1 sin c2 b sin c1 Tj p=6 6 c1 6 p=6; 062 6 2p n o where a \u00bc 10 mm and b \u00bc 20 mm. The vertices of the hexahedron are v1 \u00bc \u00bd 12 16 12 T; v2 \u00bc \u00bd 12 16 12 T; v3 \u00bc \u00bd 12 16 12 T; v4 \u00bc \u00bd 12 16 12 T v5 \u00bc \u00bd 8 12 50 T; v6 \u00bc \u00bd 8 12 50 T; v7 \u00bc \u00bd 8 12 50 T; v8 \u00bc \u00bd 8 12 50 T The radius of its spherical extension is r0 = 2 mm", " Then rp \u00bc \u00bd/ cos w / sin w 10 T; np \u00bc \u00bd 0 0 1 T; op \u00bc \u00bd 0 1 0 T; tp \u00bc \u00bd 1 0 0 T where / 2 \u00bd0; 8 and w 2 \u00bd0; 2p\u00de. The steps of /;w, and h are taken to be 2, p=8, and p=12, respectively. By Algorithm 1 we find 110 feasible grasps on the bottle with the CPU time of 184.65 min. Suppose that the external wrench wext \u00bc \u00bd fx fy fz mx my mz T is limited by fx 2 \u00bd 2; 1 ; fy 2 \u00bd 1; 1 ; fz 2 \u00bd 3; 1 ;mx 2 \u00bd 1; 1 ;my 2 \u00bd 1; 1 , and mz 2 \u00bd 1; 1 . Thus the external wrench set W a extis given by the convex hull of 64 points in the wrench space. Using Algorithm 3, we find the optimal grasp bGa (Fig. 5a) with Q\u00f0bGa;W a ext\u00de \u00bc 0:9844 at / \u00bc 4;w \u00bc p; h \u00bc p=2. Then b\u03021 \u00bc b\u03022 \u00bc b\u03023 \u00bc 0:0614p; r1 \u00bc \u00bd 11:326 0 18:576 T; r2 \u00bc \u00bd 11:179 15:777 18:567 T; r3 \u00bc \u00bd 11:178 15:778 18:567 T, and r4 \u00bc \u00bd 4 0 10 T. Changing the limitations of fx into fx 2 \u00bd 1; 2 , we have another set W b ext. Running Algorithm 3 again yields the optimal grasp bGb (Fig. 5b) with Q\u00f0bGb;W b ext\u00de \u00bc 0:9844 at / \u00bc 4;w \u00bc 0; h \u00bc p=6. Then b\u03021 \u00bc b\u03022 \u00bc b\u03023 \u00bc 0:0614p, r1 \u00bc \u00bd 11:177 15:779 18:567 T; r2 \u00bc \u00bd 11:177 15:779 18:567 T; r3 \u00bc \u00bd 11:326 0 18:576 T, and r4 \u00bc \u00bd 4 0 10 T. The CPU times for yielding bGa and bGb are 118.70 min and 128.64 min, respectively. In Example 1, bGa and bGb are geometrically equivalent, but by Algorithm 2 we see Q\u00f0bGa;wb ext\u00de \u00bc 1:1020 > Q\u00f0bGb;wb ext\u00de \u00bc 0:8321 and Q\u00f0bGb;wa ext\u00de \u00bc 1:1022 > Q\u00f0bGa;wa ext\u00de \u00bc 0:8322. Both Q\u00f0bGa;wb ext\u00de and Q\u00f0bGb;wa ext\u00de are over unity" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002359_s00332-005-0700-y-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002359_s00332-005-0700-y-Figure7-1.png", "caption": "Fig. 7. (a) Eigenfunction shapes for subsequent pitchfork bifurcations. (b) Mode of instability of the trivial solution at BP1, displacement in plane (e1, e3).", "texts": [ " Note that these solutions are fully three-dimensional since they have nonzero projections in both the x2 = 0 and x1 = 0 planes; see Figures 5(c) and 5(d). Figure 6 depicts the evolution of the eigenvalues of largest real part of the trivial solution. We first show the evolution of the eigenvalues along the trivial solution branch from first pitchfork bifurcation BP1 at \u03c9 = 1.14 to the third at \u03c9 = 11.4. We found that the trivial branch is indeed stable up to BP1, and that at each subsequent pitchfork, an additional eigenvalue crosses into the right-half plane. Figure 7 depicts the eigenfunctions corresponding to the zero eigenvalue at BP1, BP3, and BP5 where the tether buckles into the (e1, e3)-plane. This indicates the mode of static instability of the whirling solutions as indicated in Figure 7(b) for BP1. As can be seen in the figures, there is a rotation around d2 (\u03b12 = 0), which is parallel to e2 at the straight configuration, inducing the displacements into (e1, e3)-plane. An equivalent 528 J. Valverde, J. L. Escalona, J. Dom\u0131\u0301nguez, and A. R. Champneys explanation can be made using points BP2, BP4, and BP6, but in this case, the unstable eigenvalue corresponds to nonzero \u03b11. Tracing paths with increasing \u03c9 of either of the symmetrically related branches (labelled 1) that bifurcate from the trivial solution at BP1, we expect at least initially that the nontrivial whirling solutions are stable, because the pitchfork is supercritical" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003779_0369-5816(65)90138-9-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003779_0369-5816(65)90138-9-Figure6-1.png", "caption": "Fig. 6. Notation for spherical part of shell.", "texts": [ " The constants A and B can be evaluated using any suitable stress distribution, provided this assumed stress field nowhere exceeds any of the chosen yield surfaces of section 2, e.g. / a t x = l , Q = 0 , M x = M c , N o = N c , (12) a t x : 0 , Q : Q ' , M x : M ' c , NO : N c . T where Mc, M c, N c a r e the a p p r o p r i a t e va lues of the m o m e ~ s and t h ru s t on the y ie ld sur face . S i m i l a r l y for the s p h e r i c a l p a r t of the she l l , equ i l ib r ium equat ions with the notat ion of fig. 6 become\" N 0 sinq~ + Q cosq~= \u00bdPR sinq) , s i n e + N 0 sin~0 + d~(Q s i n g ) = p R s i n ~ , (13) N, dM\u00a2 de sin(p + (Mq) -Mo)cosq ) - Q R sinq) = 0 . In o r d e r to mee t the r e q u i r e m e n t s govern ing the use of the y ie ld su r face , MO must be e l i m i - nated f rom the t h i rd equation. Two poss ib l e ways of achieving th is may be dev i sed by set t ing: a) M O = 0 , (14) b) MO = M~o \u2022 (15) In t roduct ion of the condi t ion (14) in the equ i - l i b r i um equat ions (13) and in tegra t ing l eads to: Q = (\u00bdPR -No)cp + C , =R(\u00bdPR " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000119_027836402761393360-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000119_027836402761393360-Figure2-1.png", "caption": "Fig. 2. The connection between a finger and the object.", "texts": [ " The algorithms suggested in the next section are introduced via an egg-shaped object manipulation. The x, y and z coordinates of the surface points (Goodwine 1999) shown in Figure 1 are parameterized by the equation c(u, v) = (1+ u \u03c0 ) cos u cos v (1+ u \u03c0 ) cos u sin v 3 2 sin u , u \u2208 (\u2212\u03c0 2 , \u03c0 2 ) v \u2208 (\u2212\u03c0, \u03c0), (1) where u and v are the parameters of the surface. Let us turn our attention to a robot hand equipped with four fingers. Each finger has three degrees of freedom. The relation between a finger and the object is illustrated in Figure 2. The frame Kp denotes the palm frame and it is the inertial frame in the manipulation system. The object frame Ko is fixed to the object. Without loss of generality, we assume that the origin of the object frame Ko coincides with the origin of the palm frame Kp. Let the vector \u03c9o denote the angular velocity of the object frame relative to the palm frame, as seen from the palm frame. Similarly, let vo denote the linear velocity of the object frame relative to the palm frame, as seen from the palm frame" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003779_0369-5816(65)90138-9-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003779_0369-5816(65)90138-9-Figure2-1.png", "caption": "Fig. 2. Yield polyhedron.", "texts": [ " (8) This y ie ld locus has the o r ig in of coo rd ina t e s as a c en t e r of s y m m e t r y . I t has uniquely d e t e r - mined suppor t ing p lanes at a l l po in ts except those on the p a r a b o l i c a r c s (4) and (5), the s e g - ment CD, and the poin ts obtained f rom these by s y m m e t r y with r e s p e c t to the or igin . An exact y ie ld locus for a sandwich she l l , if M 0 and N O a r e t aken to r e p r e s e n t the y ie ld m o - ment and the y ie ld fo rce of the sandwich she l l , was d e s c r i b e d by Hodge [9] and is shown in fig. 2. If, however , M 0 and N O a r e given the va lues c o r r e spond ing to a so l id she l l , th is po lyhedron r e p r e s e n t s an approx ima t ion to the exact y ie ld locus of fig. 1. The c o r r e spond ing f a c e s of the po lyhedron l ie in the fol lowing p lanes : face I n O = 1 II n O - n x = 1 H I n x - m x = - 1 I V 2 n 0 - n x + m x = 2 V 2 n 0 . n x - m x = 9 (9) face I nO = 1 II n O - n ~ o = 1 III m ~ o = l i v n \u00a2 = 1 Other p l anes can be obtained by s y m m e t r y with r e s p e c t to the or ig in " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001489_jahs.28.13-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001489_jahs.28.13-Figure1-1.png", "caption": "Fig. 1 Test specimen configuration for previous (Ref. 13) testing.", "texts": [ " In addition to the analytical investigations, many photo el as ti^\"-^^ and strain s ~ r v e y ~ ~ \" ~ ~ ' ~ ' ~ investigations have been undertaken to evaluate gear tooth stresses. Unfortunately, the vast majority of the research (both analytical and experimental) accomplished to date has concentrated on the gear teeth themselves without regard to the blank configuration. This has been demon~trated'~~J\"0 be inadequate for lightweight thin rimmed gears. In order to better understand this phenomena, a brief photoelastic program\" was undertaken using a simple segment model (Fig. 1). The results of this testing, summarized in Fig. 2, clearly indicated that the root stresses become much more significant as the gear rim thickness was reduced. As the backup (rim) thickness was reduced on this simple specimen, however, it began acting more like a beam. Thus while the 13 Specimen Design In order to accurately evaluate the effect o f rim thickness, three different pitch diameters combined with three rim thicknesses were evaluated, as summarized in Table 1. Our earlier testing\" indicated that the problem is related to the combination of rim thickness and diameter rather than rim thickness alone" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002455_tmag.2005.862760-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002455_tmag.2005.862760-Figure5-1.png", "caption": "Fig. 5. Magnetic flux patterns of the actuator with no currents and with 2 A currents.", "texts": [ " Kinematics Analysis The equation for the motion of the armature is (2) where is the magnetomotive force, is the mass of the moving components including the armature and the beams, is the spring\u2019s stiffness, and is the viscous damping coefficient. C. Electrical Analysis For the electrical circuit, the governing equation is (3) Combining (1), (2), and (3), the mathematical model for the actuator is established and has been solved by using the discrete time marching and finite-element method. Here, we omit the details of our computational method; the reader is referred to the literature [6] and [7]. The magnetic field distributions with and without electrical currents are presented in Fig. 5. It is evident that the polarized magnetic field directly passes the four air gaps while the driving magnetic field moves along the arms of the armature. The static characteristics of the actuator can be calculated and are shown in Fig.6. Itsdisplacement remains linearwithin the rangeof 1.5 A, and goes into saturation when the current exceeds the range. The actuator\u2019s simulated step responses are shown in Fig. 7, in which (a) shows the influence of the mass and (b) shows the spring stiffness. It can be seen that when the mass of the moving parts decreases, the rising time decreases correspondingly; thus, it is confirmed that reducing the mass of the armature is an effective way to improve the actuator\u2019s dynamic quality" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003997_1.4002089-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003997_1.4002089-Figure4-1.png", "caption": "Fig. 4 Modeling of normal contact force: \u201ea\u2026 elastic foundation model and \u201eb\u2026 Hertz\u2019s contact model", "texts": [ " In order to generate the look-up contact table, the nonconformal contact condition that guarantees the point and tangency conditions between two bodies in contact are imposed as follows 10 : Ck qw,swrk = rP w \u2212 rP r t1 w \u00b7 nr t2 w \u00b7 nr k = 0 19 For given lateral displacement ywt and yaw angle wt of the wheelset defined with respect to the trajectory coordinate system 11 , one can directly obtain surface parameters that determine the location of contact points, the contact angle, the rolling radius, etc. That is, ywt wt \u2192 s1 wk s2 wk s1 rk s2 rk , k = 1,2, . . . 20 Since the location of contact point is determined by the off-line look-up table and the contact condition is not imposed on the equations of motion, the normal contact force needs to be determined by elastic contact formulations. There are two different ways of determining the normal contact force. In the first approach, as shown in Fig. 4 a , the normal contact force is determined using the compliant force between the rail and track foundation by assuming rigid wheel/rail contact, while in the second approach, as shown in Fig. 4 b , Hertz\u2019s contact force model is used to determine the normal contact force. These two approaches are conceptually different in a sense that the local deformation on the wheel and rail contact surface is considered or not. 3.1 Elastic Track Foundation Model. In the elastic track foundation model, each rail is assumed to be supported by elastic foundation ballast and sleepers and each rail is allowed to displace from their initial positions in the lateral and vertical direc- tions. By modeling the track foundation stiffness and damping JANUARY 2011, Vol" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001332_iecon.1998.722910-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001332_iecon.1998.722910-Figure5-1.png", "caption": "Fig. 5: Polar plot of C,=G,ii +j G,I, n, = 0; 0,4; 1", "texts": [ " excitation the stator resistance voltage drop is equal to the stator voltage xs. Now a speed difference between model and machine can lead to considerably different stator fluxes, and the simple rule of sign for the transfer function Gil is no longer valid. A simple change of the sign of the transfer function at operating points with G,1> 0 does not solve the problem, because it cannot avoid the zero-crossing of the gain of speed estimation at a stator frequency not equal to zero. To analyse the behavior of the stator current difference at low stator frequencies Fig. 5 shows the polar plot of the complex transfer function G_,=Gi(( +j Gil with n, as parameter for three different rotor frequency factors n, = 0; 0,4 and 1. The polar plots-are circles starting at the coordinate origin for n, = 0. For n, = 0 the corresponding diameter has the direction of the imaginary axis. For n, # O the circles are rotated around the origin. Between their origin diameter vectors d and the negative imaginary axis there are the angles 6 ($ and 6, for n, = 0,4; d2 and 6, for I n, = 1, respectively)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003809_3.3120-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003809_3.3120-Figure2-1.png", "caption": "Fig. 2 Optimum switching surface, rate-limited.", "texts": [ " The switching surface is obtained by noting that switching occurs at a state for which n = 0. Thus, setting n = 0 in (26-28), we obtain 0-43 - 2r2 + rf = 0 (29a) oo, we obtain sinhr/, coshr/ ~ erf/2 and sinhr2, coshr2^eT2/2 or a(qi + g3) ~ \u2014 eTf/2)erz and 1 \u2014 crg2 ~ \u2014 erf/2 + er2" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001665_sensor.1995.717182-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001665_sensor.1995.717182-Figure2-1.png", "caption": "Figure 2. Side view of the flying machine.", "texts": [ " The magnetic torque makes the soft magnetic wire parallel to the alternating magnetic field because the magnetic moment of the wire is held in the axial direction by the shape magnetic anisotropy. Note that the wire is not a weight for balance. As a result, we can flap the wing and can control the attitude of the flying machine without any cables or guides at the same time. In order to produce lifting force, we fabricated the wing with two hinges; the polyimide hinge and the polyethylene hinge as shown in Figure 2. The polyethylene hinge is very flexible and bends downward easily but the (structure makes the hmge hard to bend upward. During the down stroke the magnetic wing presses downward the polyimide wing and they move together. On the other hand, during the up stroke the polyimide wing bends downward at the polyethylene hinge. As a result, drag during the up stroke is smaller than that during the down stroke and lifting force is produced. The hard magnetic film was prepared by coating Fe base magnetic powder to a thickness of 4 pm on a 7.5-pm-thick PET substrate. We obtained the magnetic wing by pasting these two hard magnetic films together. The size of the magnetic wing was 10 mm in length and 2 mm in width. The size of the polyimide wing was 10 mm square and 7.5 pm in thlckness. The body was a 50-pm-diameter amorphous CoFe-Si-B wire with length of about 20 mm. The polyimide wing was connected on the under surface of the magnetic wing by a polyethylene hinge as shown in Figure 2 . This polyethylene hinge was about 8 pm in thickness. The wing was attached to the body of the amorphous wire by a 7.5-pm-thick polyimide hinge. The mass of a wing was about 2.5 mg and that of the body was about 0.2 mg. The total mass of this flying machine was 5.3 mg. The applied magnetic field was produced by a helmholtzcoil whose gap was 40 mm. RESULTS AND DISCUSSIONS Lifting Force of The Wing At the beginning, we examined the motion of the flapping wing attached on a fixed body. Figure 3 shows the motion of the wing when the altemating magnetic field of 500 Oe at 10" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure4.21-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure4.21-1.png", "caption": "Fig. 4.21. Three-degree-of-freedom structure", "texts": [ " In more demanding applications, coupling and disturbances along the X and Y direction and load change which can be fairly asymmetrical in nature, may have to be adequately addressed. In this section, an adaptive control scheme is designed based on a physical model, which is able to adaptively estimate the model parameters without much a priori information assumed. Although there are various configurations of H-type gantry stages, many of them are intrinsically similar. A typical gantry stage may be considered as a three-degree-of-freedom servo-mechanism, which can be adequately described by the schematics in Figure 4.21. Two servomotors carry a gantry on which a slider holding the load (e.g., the tool) is mounted. One motor yields a linear displacement x1 (measured from origin O), while the other yields a linear displacement x2. Ideally x1 = x2, but they may differ in practice owing to 4.4 Adaptive Co-ordinated Control Scheme 117 different dynamics exhibited by each of the motors, and also the dynamic loading present due to the translation of the slider along the gantry. The central point C of the gantry is thus constrained to move along the dashed line with two degrees of freedom. The displacement of this central point C from the origin O is denoted by x. The gantry may also rotate about an axis perpendicular to the plane of Figure 4.21 due to the deviation between x1 and x2, and this rotational angle is denoted by \u03b8. The slider motion relative to the gantry is represented by y. It is also assumed that the gantry is symmetric and the distance from C to the slider mass center S is denoted by d = w+v. With this formulation of the gantry stage, it is imminent to proceed with the dynamic modeling of the gantry stage. Let m1, m2 denote the mass of the gantry and slider respectively, l denotes the length of the gantry arm, I1, I2 denote the moment of inertia of the gantry arm and slider respectively, (we assume that I1 = m1(l/2)2, I2 = m2( l 2 + y)2) and X = [x \u03b8 y]T , where x = x1 + x2\u2212x1 2 (refer to Figure 4.21). The positions of mi, i = 1, 2 are given by 4.4 Adaptive Co-ordinated Control Scheme 119 xm1 = x, (4.1) ym1 = 0, (4.2) xm2 = x + dcos\u03b8 \u2212 ysin\u03b8, (4.3) ym2 = ycos\u03b8 + dsin\u03b8, (4.4) which lead to the corresponding velocities as vm1 = [ x\u0307 0 ] , (4.5) 120 4 Co-ordinated Motion Control of Gantry Systems vm2 = [ x\u0307 \u2212 d\u03b8\u0307sin\u03b8 \u2212 y\u0307sin\u03b8 \u2212 y\u03b8\u0307cos\u03b8 y\u0307cos\u03b8 \u2212 y\u03b8\u0307sin\u03b8 + d\u03b8\u0307cos\u03b8 ] . (4.6) Thus, the total kinetic energy may be computed as K = 1 2 m1v T m1vm1 + 1 2 m2v T m2vm2 + 1 2 (I1 + I2)\u03b8\u03072 = 1 2 (m1 + m2)x\u03072 + 1 2 (I1 + I2 + m2y 2 + m2d 2)\u03b8\u03072 + 1 2 m2y\u0307 2 \u2212 x\u0307\u03b8\u0307m2[dsin\u03b8 + ycos\u03b8] \u2212 x\u0307y\u0307m2sin\u03b8 +\u03b8\u0307y\u0307m2d, (4" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure7.8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure7.8-1.png", "caption": "Fig. 7.8. Basic space-structure - the tetrahedron-structure", "texts": [ "7) where j denotes the number of joints and m denotes the number of members; then, there are three possible cases, namely 7.1 Mechanical Design to Minimise Vibration 203 2. If 3j > m + 6, then the structure is unstable 3. If 3j < m + 6, then the structure is statically indeterminate In the plane-structure, the triangle is the basic shape, which is rigid and statically determinate. In a space-structure, the basic form for rigidity and statically determinant is the tetrahedron, which is depicted in Figure 7.8. Adding a new non-coplanar joint to the three existing joints of a triangular plane-structure derives the tetrahedron-structure. This new joint is connected to the existing joints with three new members. By following this procedure, rigid and statically determinate space-structure can be derived. Other space-structures are shown in Figures 7.9 and 7.10. It is also noteworthy that the members are connected with ball-joints. 1. If 3j = m + 6, then the structure is statically determinate Thus far, the approach to obtain the tetrahedron space-structure from the triangle plane-structure, the pyramid from the tetrahedron, and the box from the tetrahedron has been illustrated" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003714_13506501jet667-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003714_13506501jet667-Figure2-1.png", "caption": "Fig. 2 Three-body abrasive set-up [8, 37]. 1-counterface, 2-BOR load lever, 3-load cells, 4-specimens, 5-dead weights, 6-sand hopper", "texts": [ " According to the standard test (ASTM B 611), the prepared composite was machined into small specimens of size 20 mm \u00d7 25 mm \u00d7 58 mm and tribological tests were conducted on 25 mm \u00d7 58 mm apparent contact area.Three different orientations of fibres, with respect to the sliding direction of the counterface, were considered. These orientations were parallel, anti-parallel, and normal (P-O, AP-O, and N-O, respectively). A schematic diagram illustrating these orientations is presented in Fig. 1(d). The high-stress 3B-A wear experiments were conducted using an ASTM B 611 machine as shown in Fig. 2. The tests were performed against a stainless steel (AISI 304) counterface. Further information on the developed machine is given in [8, 37]. Sand was collected from a beach in Melaka state, Malaysia. The sand particles were sieved (in the size range of 370\u2013390 \u03bcm, 650\u2013750 \u03bcm, and 1200\u2013 1400 \u03bcm), cleaned, washed, and then dried in an oven for 24 h at 40 \u25e6C (see Fig. 3). The sand flow was fixed at a rate of 4.5 g/s. The 3B-A tests were conducted at a rotational speed of 100 rpm corresponding to 1", " Before and after the tests, the prepared samples were cleaned by a dry soft brush. A Setra weight balancer (\u00b10.1 mg) was used to determine the weights of the specimens before and after tests and then the weight loss was calculated. Wear rate at each operating condition was determined using equation (1) Wr = W N (1) where Wr is the wear rate (mm3/Nm), W is the weight loss (mg), and N is the applied load (N). During the tests, the friction force was measured by the load cell, which is fixed in the middle of the lever (see Fig. 2). The composite surface morphology was studied using scanning electron microscopy (SEM) (JEOL, JSM 840). Before using the SEM machine, the composite surfaces were coated with a thin layer of gold using an ion sputtering device (JEOL, JFC-1600). Each tribological test was repeated three times and the average of the measurements was determined. JET667 Proc. IMechE Vol. 224 Part J: J. Engineering Tribology at East Carolina University on April 25, 2015pij.sagepub.comDownloaded from The wear rate of the KFRE composite and neat epoxy (NE) versus the applied load is presented in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000140_s0025579300015230-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000140_s0025579300015230-Figure3-1.png", "caption": "Figure 3. A typical Stokeslet streamline pattern in the plane y = 0.", "texts": [ " From (34), (50) and (51) the values of /x = cos 6 at which flow reversal takes place on r = 1 are found by solving the equation (55) A numerical solution of (55) shows a single point of flow separation in the half-plane

1), which translates without rotation parallel to the x-axis with velocity Vi. The axis of translation is assumed to be a principal axis of resistance of the particle, and Fi, Fx,i denote the viscous drag forces experienced by the particle in the presence of the sphere and in an everywhere unbounded fluid. If a denotes a typical dimension and h = c \u2014 1 measures the distance of a suitable centre Q of the translating body from the surface of the sphere, then according to Brenner [9] ^ o ( t 3 ) - ( 5 6 ) where e = a/ b and the drag factor kx is defined by fc" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003789_13506501jet718-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003789_13506501jet718-Figure1-1.png", "caption": "Fig. 1 Sketch of the journal bearing and the frame of reference", "texts": [ " Finally, the new model is employed to analyse dynamic responses of the low-pressure rotor\u2013bearing model of a 200 MW turbine set. 2 REYNOLDS EQUATION AND PRESSURE DISTRIBUTIONS The hypothesis of iso-viscous Newtonian lubricating liquid in journal bearings has been assumed. Considering the plane that is normal to the rotor axis is taken in the middle of one of the bearings, a fixed reference frame OXY is assumed in this plane with its origin in the centre of the bearing. A Z coordinate axis, normal to the XY -plane with origin in O, is given as shown in Fig. 1. A right-hand frame of reference OXYZ is assumed. With respect to this reference frame, the two-dimensional Reynolds equation expressed in the cylindrical coordinates system is given as in references [16] and [17] 1 R2 \u2202 \u2202\u03b8 [ h3 12\u03bc \u2202p \u2202\u03b8 ] + \u2202 \u2202Z [ h3 12\u03bc \u2202p \u2202Z ] = \u03c9 2 \u2202h \u2202\u03b8 + \u2202h \u2202t (1) where p is the fluid film pressure, \u03c9 is the angular rotational speed, \u03bc is the dynamic viscosity of the fluid, and R is the journal radius (m). The film thickness h and the squeeze velocity of the film \u2202h/\u2202t are given, respectively, as h(\u03b8 , t) = C \u2212 X cos \u03b8 \u2212 Y sin \u03b8 (2a) \u2202h \u2202t = \u2212(X\u0307 cos \u03b8 + Y\u0307 sin \u03b8) (2b) where (X ,Y ) are the displacement components of the journal centre O\u2032, (X\u0307 , Y\u0307 ) are velocities of journal centre O\u2032, and C is the bearing radial clearance" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003447_iros.2007.4399022-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003447_iros.2007.4399022-Figure6-1.png", "caption": "Fig. 6. Examples where Z is singular", "texts": [ " Theorem 1 enables us to skip combinations of B whose bM = 0 in the calculation of possible contact forces when Z is nonsingular. In other words, nonsingularity of Z is a sufficient condition to skip some unnecessary virtual slidings. We can reduce the computation when this sufficient condition holds. For example, if each of fingertip links of all the fingers has only one contact point and Z is nonsingular for each, the number of the combinations of B to be considered is reduced from (2M \u2212 1) to 2M\u2212N . Z is singular only in special cases as shown in Fig. 6. We implemented the procedure presented in Section IVB for calculating the set of possible indeterminate contact forces as a program on Linux. The program uses cdd [7] for solving (30) and (32). Because of the page limitation, we present a few simple numerical examples. The computation times for the examples are measured on a PC with Pentium4\u20133.2GHz. The friction coefficient is set to 0.5 in all the contact points. Let us consider the case of Fig. 3. The parameters are as follows: wext = [0, \u22121, 0]T , \u03c4 = [1, \u22121]T p1 = [\u22120" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003377_ijvas.2007.016408-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003377_ijvas.2007.016408-Figure1-1.png", "caption": "Figure 1 2D schema representation", "texts": [ " The increasing demands for safety require accurate tools to represent states and parameters of the vehicle. These accurate representations need a lot of precise and expensive sensors, which means that an important diagnosis system should be implemented to avoid false data. To avoid these problems, which are the problems of expensive sensors and the complicated diagnosis system required, robust virtual sensors are proposed. These virtual sensors are based on a non-linear model which can be found by applying the fundamental principles of dynamics at the centre of gravity (Shraim et al., 2005) on Figure 1: with wind 1 2 3 4 1 2 3 4 cos( )( ) cos( )( ) sin( )( ) sin( )( ) LF F F F F F F F F F \u03b4 \u03b4 \u03b4 \u03b4 = + + + + \u2212 + \u2212 + \u2211 x f r f r x x x x y y y y and 1 2 3 4 1 2 3 4 sin( )( ) sin( )( ) cos( )( ) cos( )( ) SF F F F F F F F F \u03b4 \u03b4 \u03b4 \u03b4 = + + + + + + + \u2211 f r f r x x x x y y y y 2 1 1 2 1 2 1 1 2 2 3 4 3 4 4 3 3 4 {cos( )( ) sin( )( )} {sin( )( ) cos( )( )} {sin( )( ) cos( )( )} {cos( )( ) sin( )( )}. I F F F F F F F F F F F F F F F F \u03b4 \u03b4 \u03b4 \u03b4 \u03b4 \u03b4 \u03b4 \u03b4 = \u2212 + \u2212 + + + + + + \u2212 + + \u2212 + \u2212 Z f f f f f r r r r r t x x y y L x x y y L x x y y t x x y y \u03c8 (3) The model representing the dynamics of each wheel i is found by applying Newton\u2019s law to the wheel and vehicle dynamics Figure 2: In this paper, the task is to design virtual sensors (observers) for the vehicle to estimate the states, parameters and forces which need expensive sensors for their measurement" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000449_jahs.45.118-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000449_jahs.45.118-Figure3-1.png", "caption": "Fig. 3. NASA Glenn spiral-bevel-gearlface-gear test facility.", "texts": [ " This configuration allows a large power capacity in a relatively small package. Assuming a full size production design, this concept has an estimated weight savings of 25-percent compared to a modern technology conventional design. These two examples show the potential benefits for the use of face gears in helicopter transmissions. Test Facility The experiments reported in this report were tcsted in the NASA Glenn spiral-bevel-gedface-gear test facility. An overview sketch of the facility is shown in Fig. 3(a) and a schematic of the power loop is shown in Fig. 3(b). The facility operates in a closed-loop arrangement. A spur pinion drives a face gear in the test (left) section. The face gear drives a set of helical gears, which in turn, drive a face gear and spur pinion in the slave (right) section. The pinions of the slave and test sections are connected by a cross shaft, thereby closing the loop. Torque is supplied in theloop by a thrustpiston which exertsanaxial force on oneofthe helical gears. A75 kW (100 hp) DCdrive motor,connected to theloop by V-belts and pulleys, controls the speed as well as provides power to overcome friction" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003739_gt2009-59285-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003739_gt2009-59285-Figure2-1.png", "caption": "Figure 2: FPTPGB-C geometry, adopted from [13]", "texts": [ " As shown in Figure 1, the simple design of FPTPGB-Cs manufactured by wire-EDM permits a designer to control the pad properties (i.e. tilting and radial stiffness) by selecting the appropriate dimensions of the flexure pivot web and compliant beam. In the present work, experimental results for high speed operation of FPTPGB-Cs are presented to demonstrate the potential of the technology and for comparisons with simulations. Furthermore, the investigation of dampers in series with compliant beam is discussed as a method to stabilize an unstable rotor-bearing system. Figure 2 shows the schematic of a general FPTPGB-C. The inertial frame coordinate system is indicated by (X,Y,Z), where X is in the direction of gravity loading, and Z is parallel to the rotor rotation vector. Eccentricities of the rotor from the bearing center are eX and eY. Pad deflections relative to the bearing are given by tilting and radial coordinates. The masses of the rotor and pads are denoted mR and mp, respectively, and pads also have tilting mass moment of inertia ip. Pad tilting stiffness is k, and pad radial compliance is characterized by radial stiffness k and damping c" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000621_rob.4620070104-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000621_rob.4620070104-Figure1-1.png", "caption": "Figure 1. Spatial accelerations and forces of a single rigid-body.", "texts": [ " If two points A and B are &kUy connected then fe=L (17) 64 Journal of Robotic Systems- 1990 @A = ole (19) where PA,B denotes the position vector from point B to A. If the linear and angular velocities of point A are zero, then the linear and angular accelerations of points A and B are also related: From Eqs. (14)-(22), the propagation of the spatial forces, velocities, and accelerations can be performed: Note that as follows: = obi,jobj,k. The axis of joint i (5) is represented by a spatial vector If joint i is revolute, and if joint i is sliding. Consider link i as a single rigid body accelerating in space (Fig. 1). Using Newton's and Euler's laws, the spatial force acting on its center of mass and the spatial acceleration of its center of mass can be related as where mi is the mass of link i and Ji is the second moment of tensor) of link i about its center of mass. Ici is a 2 x 2 tensorial (26) mass (inertia matrix which Fijany and Bejczy: Manipulation Inertia Matrix 65 represents the spatial inertia of link i with respect to its center of mass and describes the relationship between the spatial force and acceleration at the center of mass" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002001_1.3453240-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002001_1.3453240-Figure3-1.png", "caption": "Fig. 3 Pressure distribution for a long, porous bearing for various values of Co. E = 0.75, 12<1>1/c3 = 0.25,,., = constant", "texts": [], "surrounding_texts": [ "H. D. Conway Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, N. Y. he Lubrication Flexible Jouraa a Long, Porous, earing Solutions are obtained for the pressure distributions in porous, flexible long bearings. The oil is assumed to have a viscosity which is either (a) constant or (b) varying with pressure according to the law JJ = i]0e aP. Finally, a method is given whereby the pressure distribu tions in porous, flexible bearings can be found approximately from the corresponding values for non-porous bearings. The limits of validity of the approximation are investi gated. I n t r o d u c t i o n Porous material bearings are very commonly used, particularly for lightly loaded applications. An important reason for their popu larity is that they require no external lubrication and consequently they can be used in inaccessible locations. One of the very first theoretical studies of porous bearings was that of Morgan and Cameron [l] .1 This analytical work was further in vestigated and extended by Cameron, Morgan and Stainsby [2]. The latter research indicated that porous metal bearings will run under fully hydrodynamic conditions below a certain critical load provided there is a sufficient supply of oil. Above this critical load, the eccen tricity ratio approaches unity, inferring that the shaft touches the inner surface of the bearing and consequently hydrodynamic lubri cation ceases. The analysis of porous metal bearings was further extended by the researches of Rouleau [3], Sneck [4], Murti [5], and Cusano [6]. Rou leau [3] gave the analysis of narrow, press-fitted porous metal bearings by assuming that the thickness of the bearing was small. Sneck [4] compared the performances of porous and nonporous bearings at moderate eccentricity ratios. Both Murti [5] and Cusano [6] showed that solutions for the pressure distributions in porous, rigid journal bearings could be obtained in cylindrical coordinates, and relaxed the assumption of small bearing thickness. All the above journal bearing investigations were based on the as sumption that the bearing shell is rigid. The effects of bearing flexi bility on the oil film thickness and hence on the lubrication of the journal itself were ignored. Recently the effects of flexibility on lu brication for long and short impervious bearings were studied by Conway and Lee [7], [8]. In impervious bearings there is no normal component of the oil velocity across the interface of the oil film and the bearing shell. 1 Numbers in brackets designate References at end of paper. Contributed by the Lubrication Division for publication in the JOURNAL OF LUBRICATION TECHNOLOGY. Manuscript received by the Lubrication Division, November 10,1976; revised manuscript received April 18,1977. However, this is not the case in porous bearings. The effect of both bearing porosity and flexibility has recently been investigated by the authors for short bearings [9]. As an alternative approach, the investigation is extended here to the case of long porous bearings. The bearing material is again as sumed to be both porous and flexible. This is considered appropriate because although porous bearings are usually lightly loaded, they are also flexible, with a modulus very much lower than that of the solid metal [10]. The stress-strain curve for a typical porous metal is given by Cameron in [10]. This curve is linear up to the quite large stress of 104 psi (6.9 X 107 Pa) with a small effective modulus of about 1.2 X 106 psi (8.27 X 109 Pa). We would expect similar behavior in porous ma terial bearings. The peripheral length of bearings is usually much larger than their thickness, and the bearing shell can frequently be considered as a thin tube surrounded by a relatively rigid housing. It follows that the re sponse of the bearing can be modelled as a Winkler foundation [7], where in the latter is replaced, analytically, by a series of springs which can deflect independently of one another. To consider the validity of such a foundation model, the following simple experiment was performed. A large, thin, flat slab of porous material was compressed by a flat indenter of width equal to the slab thickness. It was observed that the comparison of the slab was largely confined to the material directly under the indenter, the material at short distances away being virtually unaffected. This indictes that the Winkler model is a reasonable one, provided the bearing shell thickness is not too thick. Since the thickness of the bearing shell is already assumed small in adopting the Winkler model, it is in keeping to assume that the pressure gradient in the shell is linear across the material of the bearing, and is zero at the outer surface of the bearing shell. This greatly simplifies the analysis. The shaft and housing are both assumed rigid and their deforma tions are ignored. These are reasonable assumptions in conventional design. Other assumptions which are used to analyze the long, porous bearing may be stated as follows: (1) The lubricant is Newtonian and is incompressible. Journal of Lubrication Technology OCTOBER 1977 / 449 Copyright \u00a9 1977 by ASME i li of , , w. c. l l 01 ll l i l n l lutions tained essure tributions us, l xible i gs. T sumed e cosity ich ther stant ying th press rding e 1) 1)o aP. a ly, thod en reby ssure distrib s rous, l xible ings und roximately cor espon l es -porous i gs. its lidity f e roximation invest . t t . 1 .1 r . ll i iti l t i iti l l i t r i ffi i nt l f il. t i riti l l , t tri it r ti r it , i f rri t t t ft t t i er s rface f t e eari a c se e tl r a ic l ri cation ceases. r , itt t t i it ti . t ti l ti t i t i ti i , i i j l ri l t i i li ri l r i t , r l t ti f ll ri t i . t lf t i ti l t i i i t i , . t 1 r. , , 1 l i i l t t l . . i r is li t t it l r str l04 7 l i 6 9 l ~odel t tl it f ll t . ~ n d t i t i i t ll t . i i i t t i l r l i r l , r i t ri ll t ic ess is t t t ic . tl i li i t l i . t f l : t Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/26/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use (2) The problem is an isothermal one. (3) End leakage for the bearing is ignored. (4) The pressure p is zero at a point denoted by 0 = o. Also p = dp/dO = 0 at 0 = 'Y > 180 degrees. These are so-called Reynolds' conditions. (5) The flow in the oil film satisfies Reynolds' equation appropriately modified for the porosity of the shell. (6) The oil flow in the porous shell is governed by Darcy's law. (7) The permeability is constant. (8) The pressure is continuous across the porous bearing. (9) The normal component of the velocity across the porous boundary is continuous. Analysis (a) Constant Viscosity Oil. Assume that the flow in the porous shell in Fig. 1 is governed by Darcy's law if> of> ql = --- 71 0/ where if> is the permeability, 71 is the viscosity and f> is the pressure in the porous medium. Denote qx, qy, and qz as the respective flows in the x, y, and z directions of the medium. Then continuity of flow in the latter gives a a a - (qx ) + - (qy) + - (qz) = 0 ox oy oz or to the peripheral length of the bearing, it is reasonable to express the pressure gradient across the matrix in Cartesian coordinates. In ad dition it is also reasonable to assume that of>/oy is linear across the porous matrix ofthe bearing shell. Finally of>/oy is zero at the outer surface of the shell, since there is no radial flow of oil there. These ~ (_!. Of\u00bb + ~ (_!. Of\u00bb + ~ (_!. Of\u00bb = 0 ~ 71~ ~ 71~ ~ 71~ (1) assumptions can be expressed as Since the axial pressure gradients in a long, porous bearing are much smaller than the circumferential ones, the term involving the former is neglected. Also if> and 71 are assumed to be constants, so that equa tion (1) reduces to the two-dimensional Laplace equation. The well known Reynolds' equation for a thin film [1) is given as ~ (h 3 OP) + ~ (h 3 OP) = 6U (dh) + 12(Vh - Vol ox 71 ox OZ 71 OZ dx (2) (3) Under steady load, V h = 0 at y = h, the surface of the shaft. In addi tion Vo is the oil velocity into the porous shell at the inner bearing surface y = o. From Darcy's law Vo can be written in the form Thus equation (3) becomes ~ (h 3 OP) + ~ (h 3 OP) = 6U(dh/dx) + 12!. of> I ox 71 ox OZ 71 OZ 71 oy y=o (4) Since op/oz is neglected compared with op/ox for a long bearing, equation (4) reduces to ~ (h 3 OP) = 6U (dh) + 12!.. of> I ox 710 ox dx 710 oy y=o where 71 = 710 for a constant viscosity oil. Since the thickness of the bearing shell is usually small compared C~ = Co/(1 + 12if>t/c 3 ) of> of> I -=w(y+t)and- =0 oy oy y=-t (5) where w = w(x) and Vo = - !. of> I = - !. wt 71 oy y=o 71 From equation (5) and (2), we obtain 02f> 02f> -=--=-w ox 2 oy2 Since the pressure is continuous at the interface of the oil and the bearing shell, it follows that f> I y=o = P and equation (4) becomes a (h 3 OP) U (dh) if>t 02p (6) ox 710 ox = 6 dx - 12 710 ox 2 or d [h 3 dP] (dh) if>t d 2 p dO 710 dO = 6UR 1 dO - 12 710 d0 2 since dx = RldO. Taking into account the radial compression of the bearing shell and using the Winkler foundation hypothesis, the equation of the oil film thickness is written as (7) h = c(1 + \u20ac cosO) + pt(1 - vij)/E (7) where Vo = a quantity between Poisson's ratio v (tangential stress = 0) and [2v2/(I- v\u00bb)1/2 (tangential strain = 0) [7). Substituting (7) into E = e/c c = radial clearance in bearing e = eccentricity h = film thickness E = modulus of elasticity of bearing R 1 = inner radius of the bearing E* = d(1 + 12if>t/c 3 ) v = Poisson's ratio of the bearing p = pressure in the oil film f> = pressure in the porous medium p = pc 2/6 U7IoR 1 t = thickness of bearing shell Co = 6U7IoRlt(1 - vij)/Ec 3 450 / OCTOBER 1977 R2 = radius of the shaft U = peripheral velocity of shaft a = constant in 71 = 710e cxP a = 6a7l0URdc2 'Y = value of 0 where p = dp/dO = 0 Vo = a quantity between v (tangential stress = 0) and [2v2/(I- v\u00bb)1/2 (tangential strain = 0) 71 = viscosity if> = permeability Transactions of the ASME Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/26/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use (6) !!.- [(h 3 + 12<1>t) d P ] = 6T/oUR1 [-e sinll + t(I- vg) dP / E ] dll dll dll and integrating the above equation from 'Y to II dp = 6T/oURde(cosll- cos')') + pt(I - vg)/E) dll [h 3 + 12<1>t) (8) We next introduce a nondimensional parameter p = pc 2/6UT/oRl and equation (8) reduces to p(lI) = f O [E(COS~ - cos')') + CopW) d~ (9a) Jy [(1 + E cos~ + COp(~))3 + 12<1>t/c3) where Co = 6T/oUR 1t(I - vg)/Ec 3. Since from the Reynolds' conditions 56 (dp/dll)dll = 0, it follows that Sa y [E(COS~ - cos')') + CopW) d ~=O o [(1 + E cos~ + COp(~))3 + 12<1>t/c 3) By adding (9a) and (9b), we finally obtain p(lI) = f O [E(COS~ - cos')')+ CopW) d~ Jo [(1 + E cos~ + COp(~))3 + 12<1>t/c 3) (9b) (10) Equation (10) gives the formal solution for the pressure distribution in a long, porous bearing. In order to compute the integral in (10), a trial value of')' is first assumed. Then values of E, CO and 12<1>t/c 3 are selected and p(lI) found from (10). The restraint equation (9b) is then checked to see if it is satisfied. If it is not, another value of')' is assumed and the procedure repeated until it is. For small values of E and Co, (10) can be expressed in the approxi mate form -() So\u00b0 [E(COS~ - cos')') + CopW) d p II \"\" ~ o [(1 + 3E cos~ + 3CopW) + 12<1>t/c 3) Two new parameters E* and C~ are now introduced such that E* = E/(I + 12<1>t/c3), C~ = Co/(I + 12<1>t/c 3) and the approximate form of the pressure is written as p(lI) '\" f O [E*(COS~ - cos')') + C~pW) d~ (11) Jo [1 + 3E* cos~ + 3C~pW) Equation (11) is seen to have the same form as the corresponding one for impervious bearing. It follows that the results obtained by Conway and Lee [7) for impervious bearings will also apply, approximately, for porous bearings provided that E and Co in [7) are redefined as E* and C~ respectively. The validity of this approximation will be in vestigated. As mentioned above, equation (10) can be solved numer ically for an assumed value of ,)\" and the trapezoidal method used to obtain non-uniform step sizes required for accurate representation. Thus equation (10) is written as p(O) = 0 () ; _---\"[....:E(.:..co_s~IIJ'-\u00b7 -_c_os_')'c.,:)_+_C.::!op;....(:.,.IIJi,:.\u00b7).!..)o.t.,j_ P II; = L j=l [(1 + E cosllj + Cop(lIj))3 + 12<1>t/c 3) If error\"\" 0 for an assumed')' = liN and if p(n)(IIN) = p(n)( ')') = 0, then the iteration is assumed complete and the test satisfied. (b) Variable Viscosity Oil. In this analysis the viscosity is assumed to vary with pressure according to the equation T/ = T/oe cxp where C/ is a constant. Continuity of flow in the bearing matrix gives \u00b0 \u00b0 - (qx) + - (qy) = 0 ox oy which leads to [ -C/ (OP)2 + 02p ] + [-a (OP)2 + 02p ] = 0 (12) ox ox 2 oy oy2 As before, the thickness of the shell is small compared to the periphery of the bearing, and op! oy is assumed linear across the matrix and zero at y = -to Then op 02p -= w(y + t) and-= w oy oy2 (13) where w = w(x). Again, at the interface of the oil film and the bearing shell, the pressure is continuous and p = p !y=o. Substituting (13) into (12), we have w(I - C/wt 2) = - -- C/ -[ 02p (OP)2] ox 2 ox (14) In practice C/wt 2 is a small quantity, typical values of C/ being 0.00124 cm2/kg at 25\u00b0C and 0.0006 cm2/kg at 100\u00b0C [11). Thus it is reasonable to expect that awt 2 \u00ab 1. This has the effect of greatly simplifying the analysis. Hence equation (14) can be written in the approximate form w \"\" _ [02P _ a (OP)2] ox 2 ox (15) Since Reynolds' equation allowing for the presence of the porous medium is ~ [h 3 OP] _ 6U (dh) + 12 ~ op I ox T/ ox dx 1] oy y=O Substituting (15) into (16), we have !!.- [(h 3 + 12<1>t) dP] = 6U (dh) dx T/ T/ dx dx where T/ = T/Oe cxP\u2022 The oil film thickness is and h = c(I + E cosll) + pt(I - vg)/E dh dp - = -e sinll + t(I - vg)/E dll dll Substituting (18) into (17) gives dp 6T/oUR1[E(cosll- cos')') + pt(l - vg)/E) -= eap dll [h 3 + 12<1>t) (16) (17) (18) (19) i= 1,2, ... ,N-I Introduce the non-dimensional pressure p = pc 2/6UT/oRl and (19) reduces to where N = number of subintervals and and O. = {(t::.llj + t::.llj+l)/2 J t::.11;/2 j = I,2,(i - 1) j = i N ')' = L t::.llj j=l For the iteration procedure, (10) is expressed as ; [E(cosll\u00b7 - cos')') + Cop(n-l)(II'))o' p(n)(II;) = L J J J j=l [(1 + E cosllj + Cop(n-l)(lIj))3 + 12<1>t/c3) Here n denotes the number of iterations required to satisfy the con vergence test as follows. Set error = r;a~2,,, N_l!p(n)(II;) - p(n-l)(II;j!. Journal of Lubrication Technology p(lI) = f O [E(COS~ - cos,),) + CopW) eapd~ J'Y [(1 + E cos~ + COpW)3 + 12<1>t/c3) (20) where Co = 6UT/oRlt(1 - vg)/Ec 3 and a = 6C/T/oURdc 2 Since 56 (dp/dll)dll = 0, it follows that Sa y --!..::[ E..:..:( c...:.o.:..:s~,--.....:...co~s..!..')':....) _+_C-\"o!....p..:..:(~\"\") '---- -d eCXP ~ = 0 o [(1 + E cos~ + CopW)3 + 12<1>t/c3) (21) Equation (20) can then be expressed as -(II) SaO [E(COS~ - cos')') + CopW) -p = ecxPd~ o [(1 + E cos~ + CopW)3 + 12<1>t/c 3) (22) Equation (22) gives the formal solution for the pressure distribution in a long, porous bearing for an oil having a variable viscosity T/ = OCTOBER 1977 / 451 Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/26/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use ,.,oe\"p. The computation of the integral in (22) is similar to that in (10). Values of E, CO, IX and 12<1>t/c3 are selected and a trial value of)' is assumed. We then find j5 from (22) and check to see if equation (21) is satisfied. If it is not, another value of)' is assumed and the process repeated. Similarly the approximate solution for an oil having pressure dependent viscosity can also be obtained by introducing E* = e!(1 + 12<1>t/c 3) and C~ = Co/(l + 12<1>t/c3) such that -(0) 50 0 [E*(COS~ - cos),) + C~j5W] -d p = e\"P ~ \u00b0 [1 + 3E* cos~ + 3C~j5W] (23) It follows once again that the impervious results obtained by Conway and Lee [7] for the pressure-dependent viscosity case will also apply, approximately, to the porous bearings provided E* and C~ replace E and Co, respectively. Results and Calculations Before performing a numerical analysis, a value of the nondimen sional term 12<1>t/c3 is required, the permeability being assumed constant. Various porous metal bearings have permeabilities ranging from 15 X 10-12 in2 (100 X 10-12 cm2) to about 300 X 10-12 in2 (2000 X 10-12 cm2) [10]. Thus for a bearing material having = 1500 X 10-12 cm2, t = 0.508 cm and c = 2.54 X 10-3 cm, 12<1>t/c3 is about 0.54. Thus values of 12<1>t/c 3 = 0.25 and 1.0 were used in the calcula tions. Graphs of normalized pressure j5 = pc 2/6Uwfi 1 were plotted using the numerical scheme previously outlined. Typical plots for constant viscosity oil and 12<1>t/c3 = 0.25 and 1.0 are given in Fig. 2, 3, 4, and 5 for values of eccentricity ratio E = e/c of 0.5 and 0.75, respectively, and with various values2 of Co = 6U,.,oR1t(1 - va)/Ec 3. It is observed that, for fixed values of eccentricity ratio, the normalized pressures p reduce with increasing values of 12<1>t/c3 from 0.25 to 1.0, particu larly for the smaller Co values. It is also observed that, for fixed values of Co, the normalized pressures increase with increasing values of E from 0.5 to 0.75, particularly for smaller values of 12<1>t/c3. It was already concluded by Conway and Lee [7] that the normal ized pressures for non-porous long bearings are quite sensitive to 2 For a rotational speed N = 1500 rpm, t = 0.2 in (0.50S em), ~o = 3.3 X 10-6 Rey. for SAE 30 oil at 160\u00b0F, Rl = 1 in (2.54 em), E = 106 psi (6.S9 X 109 Pal, \"0 = 0.3, c = 10-3 in (2.54 X 10-3 em), the constant Co is about 0.57. 452 / OCTOBER 1977 variations in the value of the parameter Co. As observed from Fig. 2, 3, 4, and 5, a similar behavior is found for both porous and impervious bearings, especially for larger values of eccentricity ratio. It is also seen that, for fixed values.of E and Co, the normalized pressures for a porous bearing are smaller than those for a corresponding nonporous one. The reductions in the normalized pressure increase with increase in the value of the permeability. Transactions of the ASME Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/26/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use Typical plots for E = 0.2 and 0.3, 12t1>t/c 3 = 1.0 and for various values of Co are given in Fig. 6 and 7 in order to compare the exact results for porous with the approximate ones obtained from the im pervious solution. As observed from Fig. 6 and 7, it is seen that the results obtained in [7] may also apply, approximately, for porous bearings provided E and Co are substituted by E* and C~, respectively. However, the comparison becomes increasingly poorer beyond E* = 0.15 as seen from Fig. 7. Nevertheless the approximate solution is good provided the values of E* and C~ are small. Journal of Lubrication Technology Finally graphs of normalized pressure p for an oil having a pres sure-dependent viscosity3 11 = 110eCiP are given in Fig. 8 for E = 0.5, Co = 0.2, and a = 6Ci110URt/c2 = 0,0.2,0.4 and 0.6. A typical comparison of the exact pressure distributions in porous, flexible bearings is made in Fig. 9 with the approximate distributions obtained from the non porous solution. Referring to the variable viscosity results given in Fig. 8 and 9, it is seen that the larger the value of a, the larger will be the normalized pressure. A comparison made between the exact solution for porous bearings with the approximate one obtained from the impervious 3 For a pressure-dependent viscosity oil with a = 0.0008 cm2/kg, N = 1800 rpm, viscosity ~ = 5 X 10-6 Rey. for SAE 30 oil at 140\u00b0F, Rl = 1 in (2.54 em), c = 10-3 in (2.54 X 10-3 em), the constant a is about 0.3. OCTOBER 1977 / 453 Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/26/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use solution shows good agreement for small values of f* and C~, even for an oil having variable viscosity. Finally it is concluded that the effects of flexibility for porous bearings are more significant than those for impervious ones, par ticularly for bearing materials having high porosity. Based on the normalized pressure curves shown in the above figures, it is also 454 j OCTOBER 1977 concluded that the effects of deformation should not be ignored for Co> 0.5 for constant viscosity oils and for a > 0.3 for variable viscosity oils with Co = 0.2. For large values of Co, the effects of variable vis cosity will be more pronounced. References 1 Morgan, V. 1'., and A. Cameron, \"Mechanism of Lubrication in Porous Metal Bearings,\" Institution of Mechanical Engineers-Proceedings, 1957, pp. 151-157. 2 Cameron, A., V. T. Morgan and A. E. Stainsby, \"Critical Conditions for Hydrodynamic Lubrication of Porous Metal Bearings,\" Institution of Me chanical Engineers-Proceedings, Vol. 176, No. 28, 1962, pp. 761-770. 3 Rouleau, W. 1'., \"Hydrodynamic Lubrication of Narrow Press-Fitted Porous Metal Bearings,\" Journal of Basic Engineering, TRANS. AS ME, Vol. 85,1963, pp. 123-128. 4 Sneck, H. ,I., \"A Mathematical Analog for Determination of Porous Metal Bearing Performance Characteristics,\" JOURNAL OF LUBRICATION TECHNOLOGY, TRANS. ASME, Series F, Vol. 89, 1967. 5 Murti, P. R. K., \"Pressure Distribution in Narrow Porous Bearin!!s,\" JOURNAL OF LUBRICATION TECHNOLOGY, TRANS. ASME, Serie~ F, Vol. 93, 1972, pp. 512-513. 6 Cusano, C., \"Lubrication of Porous Journal Bearings,\" JOURNAL OF LUBRICATION TECHNOLOGY, TRANS. ASME, Vol. 94, 1972, pp. 69- 73. 7 Conway, H. D. and H. C. Lee, \"The Analysis of the Lubrication of a Flexible Journal Bearing,\" JOURNAL OF LUBRICATION TECHNOLOGY, TRANS. ASME, Oct. 1975, pp. 599-604. 8 Conway, H. D. and H. C. Lee, \"The Lubrication of Short, Flexible Journal Bearin\"s,\" to appear in JOURNAL OF LUBRICATION TECH NOLOGY, TRANS. ASME. 9 Mak, W. C., and H. D. Conway, \"Analysis of a Short, Porous, Flexible ,Journal Bearing,\" to appear in the International Journal of Mechanical Sci ences. 10 Cameron, A., The Principles of Lubrication, Wiley 1967, pp. 543- 559. 11 Tipei, N., Theory of Lubrication, Stanford University Press, 1962, pp. 30-31. Transactions of the ASME Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/26/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use" ] }, { "image_filename": "designv11_32_0000890_1521-3919(20020901)11:7<739::aid-mats739>3.0.co;2-i-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000890_1521-3919(20020901)11:7<739::aid-mats739>3.0.co;2-i-Figure1-1.png", "caption": "Figure 1. (a) A right-handed helical ribbon. (b) A cut and flattened portion of a helical ribbon. The vertical side of the rectangle is parallel to he helical axis and is one period long (AB \u00bc h). The horizontal side corresponds to the circumference of the helix (BC \u00bc 2 ). The height of the ribbon is \u00bc DE, whereas T \u00bc AD is the height parallel to the helical axis. Equation (27) follows from the similarity of triangles ABC and ADE.", "texts": [ " The transformation of 0 lmjk under the symmetry operations Mxy, Mxz, Myz, I, C2 x = MxyMxz, C2 y = MxyMyz and C2 z = MxzMyz (together with E, these are the symmetry operations of the D2h point group) can be worked out with the help of Equation (12) and (13): Mxy ) 0 l; m;j; k; Mxz ) 0 l;m; j;k; Myz ) 0 l;m; j;k; I ) 0 l; m;j; k; Cx 2 ) 0 l; m; j; k; Cy 2 ) 0 l; m; j; k; Cz 2 ) 0 lmjk \u00f024\u00de The sought pseudoscalar may be constructed on the basis of these results: lmjk \u00bc 1 2 0 lmjk 0 l; m;j; k 0 l;m; j;k \u00fe 0 l; m; j; k \u00bc Re\u00f0 0 lmjk\u00de Re\u00f0 0 l; m;j; k\u00de \u00f025\u00de It is easy to check that lmjk is indeed invariant under T, R, and C2, and changes sign under M and I. Most of the mathematical results in the previous sections are general and applicable to any helical structure. Here I will illustrate them in case of helical ribbons (see Figure 1a), for which its is possible to obtain exact analytical solutions. Let us consider an infinite ribbon of zero thickness and height s, which is wound about an imaginary cylinder of radius a = 1 (this sets the length unit) to give a continuous helical structure of period h. The parametric equations for the helical surface are: x \u00bc cos t \u00fe 2 h u y \u00bc sin t \u00fe 2 h u z \u00bc h 2 t 8>>>>< >>>>: \u00f0 1 a t a 1;0 u T ; \u00fe for R; for L\u00de: \u00f026\u00de where T is the height of the ribbon parallel the helical axis (see Figure 1b): T \u00bc 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h2 \u00fe 4 2 p : \u00f027\u00de The density of the helix is equal to infinity within the ribbon and zero elsewhere. We have: \u00f0r; #; z\u00de \u00bc \u00f0r 1\u00de S2 T=h # 2 h z ; \u00f0\u00fefor L; for R\u00de \u00f028\u00de where SW (x) is the periodic \u201cbox car\u201d function (period = 2p): SW\u00f0x\u00de \u00bc 0; for a x a W 2 and W 2 a x a ; 1; for W 2 a x a W 2 : 8>< >: \u00f029\u00de The helix becomes an achiral cylinder when the ribbon is tightly wound with h = T, or \u00bc 2 h= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h2 \u00fe 4 2 p " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure5.5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure5.5-1.png", "caption": "Fig. 5.5. Six degrees of freedom for a machine axis", "texts": [ " The accuracy and precision of a multi-axis machine is determined primarily by the geometrical properties of the machine. Thus, to analyse fully the 5.3 Overview of Laser Calibration 135 machine\u2019s positioning accuracy, it is necessary to measure the following geometrical characteristics (each of which contributes to positioning accuracy and precision at any point within the workzone of the machine): \u2022 The six degrees of freedom for each measurement axis, \u2022 Squareness between measurement axes, \u2022 Parallelism between measurement axes. The six degrees of freedom for each motion axis are depicted clearly in Figure 5.5. The squareness and parallelism of travel between two or more axes characterise the relative orientation among the axes. Both measurements can be accomplished by performing two straightness meausrements, with the squareness measurement approach requiring more optics such as the 900 reference (the optical square). Most of these geometrical characteristics can be duly obtained using a laser measurement system. Linear measurements refers to the actual distance translated by the moving part when it is controlled to move in a straight line" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003416_sice.2008.4654878-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003416_sice.2008.4654878-Figure1-1.png", "caption": "Fig. 1 Experimental system", "texts": [ " The effectiveness of the designed system is shown by experiment. The contents of this paper will be written as follows. In Section 2, principle of the Peltier element, modelling of the aluminum plate with the Peltier element are described based experiment. Meanwhile, problem setup is given. Section 3 describes the operator based nonlinear temperature controller of the thermal process by using operator theory. In Section 4, experimental result is shown. The experimental system on a thermal process of the aluminum plate with a Peltier element is shown in Fig. 1, and the model of the system is given in Fig. 2. Further, model of the aluminum plate with Peltier element is shown in Fig. 3, where S1 is a Peltier element and another side (bottom) is a sensor to measure temperature of the aluminum plate between the Peltier element and the sensor. The definitions of parameters of the thermal process are given in Table 1. In the following, model of the thermal process shown in Fig. 3 is derived. State variable is defined as follows. T0 \u2212 Tx = y(t) Based on the result in [5], a differential equation in regards to heat conduction is obtained as follows" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002893_1.5060985-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002893_1.5060985-Figure6-1.png", "caption": "Figure 6: Manufacturing of a revolution geometry (left) CAD drawing, (middle) 2D profile with the different manufacturing steps and vertical orientation indicated, (right) manufactured part.", "texts": [ " Manufacturing considerations become very important on real parts and it is especially important to consider a manufacturing process to overcome the constraints induced by the process itself. In order to illustrate this one, two different geometries are described hereafter. The first geometry is a revolution part with the possibility to built a casing-like structure. In fact, a profile can be defined and the part is generated by a two-dimensional movement of the laser head and a rotation and the table supporting the part. As the shape implies a large overhung angle in respect to the substrate, it is required to build the structure in different steps. As presented in figure 6, seven steps have been necessary with a different inclination of the rotating table for each step. Another example is a demonstration part that will be used for the functional tests. The part is massive, exhibiting a triangular shape with two vertical structures on each side. The holes, impossible to build, have been filled. Page 27 Laser Materials Processing ConferenceICALEO\u00ae 2007 Congress Proceedings Thus, starting from a small substrate, the part will be built in 5 steps. First, the main axis is built, then each side, and finally the structure located on each side" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001217_tasc.2003.813065-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001217_tasc.2003.813065-Figure2-1.png", "caption": "Fig. 2. SMB: composed of the PM rotor, the cryostat, and six HTSC bulks", "texts": [ " But the characteristics of measurement results were against the prediction derived from cause-A and B. Namely, the degradation was remarkably enhanced when the levitation force of the SMB increased [2]. Such an enhancement cannot occur due to cause-A and B, because the degradation by the inhomogeneous magnetic field of the PM rotor should be independent of the levitation force [3], [4]. For explaining such \u2018anomalous\u2019 characteristics of the rotation speed degradation by the SMB, we noticed the shape of the HTSC stator. It consists of the cryostat and six HTSC bulks as in Fig. 2. The magnetic field distribution made by the six bulks is periodic in the circumference direction in each 60 degrees, because the shielding current does not flow across the boundaries between HTSC bulks. Looking from the rotating PM rotor, the magnetic field becomes like the AC field. As a result, the eddy current is induced in the PM rotor by this magnetic field. So this is the third mechanism of the rotation speed degradation (cause-C). As one of the techniques to suppress the rotation speed degradation due to the cause-C, we proposed the advanced PM rotor with many insulator thin films to reduce with the eddy currents. The SMB equipment has the AMB, the SMB and so on as shown in Fig. 1. The SMB is composed of the PM rotor, the cryostat and six HTSC bulks (Fig. 2). The cryostat is made of SUS304 stainless steel, and the HTSC bulks are YBCO. The outer and inner radius of the HTSC bulks are 34.4 mm and 24.4 mm, the height is 30.0 mm. The thickness of the cryostat is 1.0 mm. When the SMB is used, the cryostat is filled with nitrogen liquid, and the HTSC was cooled soaking in it. As the HTSC stator moves by a motor in direction from mm to mm, the relative position between the PM rotor and the HTSC stator can be changed. Another motor accelerates the PM rotor\u2019s rotation" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001209_tia.2003.808977-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001209_tia.2003.808977-Figure3-1.png", "caption": "Fig. 3. Relative positions ofv , i , , and \u0302 in the regenerating mode (P = 1, ! > 0). (a) (k) < \u0302(k); (k) < 0 Multiple shot view of vectors v , i , , and \u0302 when R > 0. (b) v\u0302 (k) R\u0302 i\u0302 (k) < 0) i(k) < 0 Due to R T i with R > 0, \u0302 (m+ 1) leads \u0302 (m).", "texts": [ " Applying a Euler algorithm, we obtain that for Since by Corollary 2, we obtain that for all . Therefore, the result follows from (17). In this section, we repeat the same procedure for the motor in the regenerating mode. Since the proving processes in this subsection are very similar to those in the previous section, we omit proofs here. Lemma 4: Assume that the motor is running in a positive direction with negative -axis currents, i.e., and for . Assume that . If , there exists an integer such that satisfies for . Remark: As shown in Fig. 3(a), lags behinds . Thus, with , contributes to increasing faster than . Lemma 5: Assume that . If , , there exists an integer such that for . Remark: One can check the inequality from Fig. 3(a). Claim 2: Assume that , , and are rotating at the same angular speed and that and . Assume that . Further, if , , then . Remark: See Fig. 3(b) for proof. Corollary 3: Assume that , , and are rotating at the same angular speed and that their magnitude does not vary drastically. Assume that . Further, if , , then there exists an integer such that for . Lemma 6: Assume that , , and are rotating at the same angular speed and that and . Further, if , , then there exists an integer such that for . Remark: Note that by the above Corollary. Thus, for . Hence, the result follows from (17). 1) Motoring Mode : , and : Fig. 4 shows the simulation results which support Lemmas 1, 2, and 3" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001694_j.talanta.2004.11.027-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001694_j.talanta.2004.11.027-Figure1-1.png", "caption": "Fig. 1. Schematic representation of PbO2-parafin pH-sensor in different supports. (1) Copper wire and grafite support: (A) support, (B) paraffin membrane, (C) Teflon tape, (D) electric contact region. (2) Copper plate: (E) paraffin membrane, (F) support, (G) epoxi resin, (H) electric contact wire. (3) Other support materials.", "texts": [ " he membranes were spread on different support materials uch as graphite (2-mm diameter rod, Rayovac Corporation), old (3-mm diameter rod, Aldrich), tungsten (4-mm diameer rod, Aldrich), antimony (4-mm diameter rod, Aldrich) and opper (6.35-mm diameter rod, Aldrich) by dipping the suport material into the melted composite at a temperature near araffin melting point. The paraffin was kept in the melting tate only for a few seconds. Membranes with almost uniorm thickness (0.2\u20131 mm) and surface area approximately .5 mm2 were obtained. Teflon tape was used for isolation f the support material rods. The schematic representation of he sensors is shown in Fig. 1. Aliquots of the 60 mmol L\u22121 sulfuric acid solution were dded in a 50-mL potentiometric cell with 25 mL of ional potential ranged from 1253 to 1276 mV. The linear pH ange for the analytical curves was 1.2\u20137.5. The electrodes resented fast response time to the solution pH (a few secnds). The Pb2+ response forecast in Eq. (2) was verified at pH .2, resulting in a slope of 25.5 mV/decade. The potentiometric response associated with the halfeaction of reduction of PbO2 Eq. (1) is shown in Eq. (3) or the 75% (w/w) PbO2 membrane" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001401_robot.2003.1242217-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001401_robot.2003.1242217-Figure4-1.png", "caption": "Fig. 4. The experimental setup", "texts": [ " Nevertheless, as apparent from Fig 3B, Mk enjoys the same ill-conditioning property as that of the inertia matrix M. As a result, the acceleration can be always computed and the simulation may proceed smoothly even if the system works in the vicinity of the singular position. This is evident form the plot of constraint error in Fig.2B showing that the proposed method is always able to maintain the constraint condition within the specified tolerance. VIII. EXPERIMENTAL RESULTS In this section, we report comparative experimental results obtained from a constraint mechanical system shown in Fig. 4. The arm which was used for these experiments was a planar robot arm developed at CSA with three revolute joints which are driven by geared motors RH8-6006, RH-11-3001, and RH-14.6002 from Hi-T Drive. The robot joints are equipped with optical encoders, while an AT1 force sensor (gamma type) is installed in the robot wrist. The robot endpoint is connected to a slider by a hinge (global joint), as illustrated in Fig. 4, and the robot motion in Y-axis is thereby constrained. Let the position and orientation of the robot. endpoint be presented by {z,y,B}. Then from the topology of the kinematics, the constraint equation and the reduced-dimension coordinate can be specified by = y(q) - yo = 0 - where yo = -0.27m - and OT = [z(q),B(q)], respectively. In this experiment, the position feedback gains are Gp = 480 and GD = 45, which corresponds to 3.5Hz bandwidth of the closed loop system. While the force feedback gains are GF = 3, and GI = 0" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000288_20.105041-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000288_20.105041-Figure6-1.png", "caption": "Figure 6. Permanent magnet motor", "texts": [], "surrounding_texts": [ "The calculation of the global values force and torque is the direct aim of many applications of computational magnetostatics based on the finite element method. Among many formulations the Maxwell stress method and the virtual work principal are the most popular methods. Other methods such as the equivalent magnetizing current, magnetic charge method have been also used. The accuracy of the force calculation of these methods depends upon that of the local field where will be carried out the line (2D) or the surface (3D) integration of Maxwell stress, the surface (2d) or the volume (3D) integration over the elements deformed due to the virtual displacement. The number of elements over the integration path is very small in comparison with the total number of elements. That means these methods use only a tiny amount of the computed field without regard of the fact that the finite element method minimizes the global energy of the field. The state of the local field has the contribution to minimize the global energy, and in the same sens the accuracy of the local field is also determined by the whole field. It would be perfect in the force calculation if every point had its contribution, not only a small part of the field. One new method developed recently by the authors shows in theory and in practical applications that we can determine the local field with the analytical accuracy by subtracting from the original FE solution the field of the so-called Discretization Current Sheet (DCS) [l]. With the help of this technique the flux density over the integral contour of Maxwell stress and then the force can be calculated with analytical accuracy. METHOD - _- In magnetostatic field the global force acting on the body m may be expressed as [2] where the C is a contour enveloping the body m in region free of the source and magnetic material, B the flux density, n' and f a r e unit vector in the normal and tangential direction of the contour C. A new method developed by authors permits to calculate the flux density B on the contour C with the analytical accuracy. The method has been presented in detail in [3]. The force and the torque calculation by the present method can be described in following steps: 1. solve the problem by finite element method with a mesh of first order and calculate the flux density Bopp on the contour C. 2. calculate the Discretization Current Sheet (DCS) at all borders of element by: where Jdis is the Discretization Current Sheet, J,, the exciting current of coils and Jm the equivalent current sheet of hard magnets. 3. calculate analytically the flux density BdlS produced by all Jd,s on the contour. The field Be, is now more accurate than Bapp. 5 . calculate the force with the help of (l), where the flux density takes Be, from (3). The accuracy of the force calulcation by this method can be verified by: comparing with analytical solution verification of the force and the torque balance in a system verification of physical and mathematical laws comparing with experimental results The first comparison can only be done for a very simple problem. The third verification can be, for example, the independance of the integral contour on the force. 0018-9464/91$01.00 (D 1991 EEE IEEE TRANSACTIONS ON MAGNETICS. VOL. 27, NO. 5, SEPTEMBER 1991 The distance between bars is 100mm, the dimension of the bar 20 x 20mm, the current density in bars 2.5 x 105A/m2. The force between the bars, calculated with a mesh of about -47 nodes by Lorentz's formulae, the normal Maxwell stress method and the new method here presented, is given in Table 1. An analytical solution may be computed for this example and gives out a comparison reference. The accuracy of the present method is better than the classic Maxwell stress method and even also better than reliable Lorentz's formulae. The method verifies also the balance of the forces: the sum of the forces on two bars is almost zero. The improvement of accuracy is dramatic. 4255 The second illustration problem is the same as the above by only inserting an iron bar (pr = 1000) unsymetrically between the conductor bars (Figure 2). The forces calculated on two different contours are given in Table 2. The indice 1 and 2 denotes the first and the second contour respectively. The column fine is the force calculated by normal Maxwell stress method with a mesh of about 10 times more nodes (4661 nodes). The results show us that the force calculated by the present method is independant of the integral contour choice and the balance of the forces within the system is always verified. That proves, on other side, that the accuracy of this method is very high. The accuracy of the present method in a coarse mesh is even not achievable by a fine mesh with 10 times more nodes. APPLICATION The field in the air gap of an attraction-type levitation magnet (Figure 3) has been computed using the method developed by authors in [3]. 4256 After the computation of the field over a contour by this method, the force calculation based on Maxwell stress method will be car- ried out. The levitation and guidance force of the magnet have been calculated by the present method for different laterial displacements. For the purpose of comparison we use three different meshes, with 880, 1200 and 3400 nodes respectively and forces are also calculated by classic Maxwell stress and the virtual work method. The results are given in Figure 4-5. With the fine mesh the levitation force obtained by three different methods agrees very well one another. The guidance force calculated by Maxwell stress method has a small oscilation and at the instable balance position (d=O) a considerable error. With the coarse mesh the guidance force after Maxwell stress and virtual work method has an inacceptable error and agrees not a t all with the physical explication. The guidance force calculated with the present method has a correct evaluation about the lateral displacement although the error is still important. The levitation force after this method is very smooth and after two other methods an oscilation. A similar result can also be obtained with a middle fine mesh. IEEE TRANSACTIONS ON MAGNETICS, VOL. 27, NO. 5, SEFTEMBER ~~ 1991 4257 CONCLUSION The accuracy of the force calculation by Maxwell stress method _____~~~ can be dramatically improved. The local field on the stress contour is obtained from the original FE solution by subtracting the field of all Discretization Current Sheet (DCS). Every field point has the contribution in the force calculation. The results show that the new method is independant of the contour. The contour can be laid on the surface of iron and that permits to calculate the surface force density. REFERENCE [l]. G.Henneberger, Ph.K.Sattler, D.Shen: Achievement of analytical accuracy in the computation of magnetostatic field b y finite element method , CEFC\u2019SO Toronto. [2]. T.TLnhuvud, K.Reichert: Accuracy problems of force and torque calculation in FE-systems, IEEE Trans. Magnetics, Vo1.24, No.1, Jan. 1988." ] }, { "image_filename": "designv11_32_0002041_fuzz.2001.1009036-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002041_fuzz.2001.1009036-Figure1-1.png", "caption": "Fig. 1. Membership functions of the input linguistic variables (\u0302E f", "texts": [ " and x, is Ah and U is B' THEN yi = C; + ~1x1 + + C ~ X , + c ~ + ~ u (11) A e f(x, U, 0) = OT7(x, U) (16) where ~ ( x , U) is a pl x pz x with its ( j l , j , , . . . , j , , m) element given by a x p , x M dimensional vector ~(jl.jz,... , j , ,m) (x, U) = ( fi pBm (U) j1=1 2 . * * jn=l F m=l E [(iip,j,(zi))pBm(U)] =l (17) i=l and Q = [,g(l..- .1,1), . . . , ,g(p~ ,.- ,P\" , M ) ] E RPI x...XPn x M The membership functions of linguistic variables of U have the form of a triangle and are placed evenly throughout the whole defined space U, as shown in Fig. 1. The space U, can be decomposed into several subspaces U t (a = 1,2 , . . . , M - 1). If U exists in subspace U t , all membership function of linguistic variable of U given by r U - a , 1 a,-1 - U a,-aa,++l m = a a,-1 -am m = a + l (18) I o otherwise where a, is a constant satisfying &(a,) = 1. in U?. we have Substituting (18) into (16)and considering that U exist Using( 19) and (20), if we choose the control law fyx, U, e) = and the adaptive law for updating parameter vector 8 6 = YfeTPbg(x, U) (24) then form (22), we have 1 1 - 2 (\u0302E f (19) V = - -eTQe + eTPb6f + -&fit (25) In order to reduce the tracking error, we require that V 5 0" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003825_j.triboint.2010.02.018-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003825_j.triboint.2010.02.018-Figure1-1.png", "caption": "Fig. 1. Sectional view of the tri-taper bearing.", "texts": [ " However, this bearing is akin to three tapered land composite thrust bearings arranged around a bearing circle. There are three lubricant supply grooves, equispaced at 1201 apart, around the bearing periphery. Each of the three sections consists of equal lengths of the bearing base circle and a section offset from the base circle, such that, it merges smoothly with the base circle and provides a predetermined depth at or near to the lubricant supply groove. The sectional view of the tri-taper journal bearing is shown in Fig. 1. The basic differential equation for pressure distribution in the bearing clearance under dynamic conditions for incompressible fluid may be written as @ @x h3 @p @x \u00feh3 @ 2p @z2 \u00bc 6ZU dh dx \u00fe12Z @h @t \u00f01\u00de Using the following substitutions y\u00bc x R , z \u00bc z L , p \u00bc pC2 ZoR2 , t\u00bcopt and h \u00bc h=C \u00bc 1\u00fee cos\u00f0y c\u00de\u00feRamp Nomenclature C radial clearance (m) D diameter of the bearing (m) R radius of the bearing (m) e eccentricity (m) Fr ,F r dynamic force along radial direction,F r \u00bc FrC2=ZUR2L Ff,Ff dynamic force along f direction, Ff \u00bc FfC2=ZUR2L h,h local film thickness (m), (h \u00bc h=C \u00bc 1\u00fee cosy\u00feRamp Ramp Normalized ramp size, Ramp/C L length of the bearing (m) M,M mass parameter (kg), M \u00bcMC3o2=ZUR2L p,p film pressure (N/m2), p \u00bc pC2=ZoR2 ps non-dimensional supply pressure pa pressure at the bearing edges t time (s) U journal peripheral speed, oR (m/s) W steady state load capacity (N) W non-dimensional load capacity, W \u00bcWC2=ZUR2L Wa load capacity (N) W a non-dimensional load capacity, W a \u00bcWaC2=ZUR2L e eccentricity ratio, e/C Z coefficient of absolute viscosity of lubricant (N s/m2) y,z non-dimensional co-ordinates, y\u00bc x=R, z \u00bc z=L,y measured from the line of centres yn co-ordinate in the circumferential direction measured from centre of the groove" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001422_oxfordjournals.jbchem.a133832-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001422_oxfordjournals.jbchem.a133832-Figure2-1.png", "caption": "Fig. 2. Apparatus for the recording of streaming. (1) Stabilized power (D.C.) supply. (2) Small lamp. (3) The rotating stage of an inclined microscope and the capillary system. (4) Photocell. (5) Balanced amplifier. (6) Recorder.", "texts": [ " The microcapillary was secured against breaking during the introduction of the solution by attaching it to a cover glass. One end of the capillary was now approached by the tip of a Pasteur pipette containing the solution which was allowed to fill about onehalf of the capillary. Even wetting of both wider sides of the capillary and homogeneity of the liquid were achieved by sucking and pushing the liquid several times. The capillary was inserted inside a wider and longer capillary tube (i.d. about 1.5 mm; Fig. 2), each end of which was then sealed by a drop of water with the aid of a narrowed tip of a Pasteur pipette. This arrangement was important in order to avoid evaporation of the solution, with subsequent possible unbalancing of surface tension forces at the two ends of the solution, and to protect the capillary from atmospheric turbulences. The whole set-up was laid on a cover glass with its wet ends extending out of the glass cover. Up-Hill Streaming as a Further Test for Mechanochemical Activity\u2014Streaming was examined by following the movement of the meniscus at one end of the solution in a capillary which was mounted on a movable and rotateable stage of an inclined microscope (x 200) (Fig. 2). By rotating the stage, one could place the capillary at different inclinations. The horizontal position was taken to be the point at which passive streaming of water (due to gravity) vanished and this was defined as zero angle of rotation. After rotating by 90\u00b0, the (constant) velocity of down-hill streaming of water assumed a maximal value. At 180\u00b0, streaming stopped again while at 270\u00b0 passive streaming reached another maximum, equal to the first one and proceeding in the opposite direction with respect to the capillary", "com /jb/article-abstract/91/4/1435/787529 by G oteborgs U niversitet user on 17 January 2019 ACTIVE STREAMING OF ACTO-HEAVY MEROMYOSIN SOLUTIONS 1437 faster than at 0\u00b0 or 180\u00b0. Moreover, contrary to passive streaming, the velocity of active streaming at a given angle was not always constant and occasionally dropped down for a while to nearly zero. In order to get a continuous record of streaming we took advantage of the fact that, due to light diffraction at the meniscus, its liquid side appears brighter and therefore any movement of the meniscus leads to a change in the light intensity of the observed field (Fig. 2). A linear relationship was found between light intensity and displacement of the meniscus in the range of 0.2 mm. By displacing the stage along the direction of the capillary this range could be extended. The velocity of streaming in the microcapillary path is equal to the velocity of movement of the meniscus times the ratio of the cross-sectional areas of the capillary in its wide and narrow parts. In order to minimize fluctuations in light intensity we utilized a low power light source and covered the apparatus with a black cloth" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003998_09544062jmes1329-Figure12-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003998_09544062jmes1329-Figure12-1.png", "caption": "Fig. 12 Mesh scheme of the FEA model", "texts": [ " The disc spring stack was placed on the protrusion of the bottom fixture, with the inner rings of the spring closely aligned, and the upper fixture descended to apply the load on top of the conic surface of the springs. The setting for the maximum load stroke was 0.8 mm, equivalent to 75 per cent of the total free height of the three sets of disc spring combinations. The FEA was performed using ABAQUS with the arrangement of the disc spring model mirroring that of the actual stack in the spindle. The mesh of the FEA model is shown in Fig. 12, with a close-up of the mapped mesh at the left. The boundary constraints in the FEA model were assumed to be rigid planes at both the top and bottom surfaces of the stack. The load\u2013deflection curves for the six disc springs from both the experiment and the FEA are shown in Fig. 13. Little difference was apparent at small deflections up to around 0.4 mm. However, the difference gradually increased as the deflection increased, reaching 8.4 per cent at a deflection of 0.8 mm (75 per cent of free height) of the stacked disc springs where the Proc", " It caused a reduction in drawbar force of 4 per cent at 300 000 r/min, as shown in Fig. 16(b). High-speed gas spindle systems, which commonly run at working speeds of more than 100 000 r/min, always offer different drawbar forces to meet various cutting conditions. A considerable amount of centrifugal force exists when the spindle is running, which generates extra deformation of the disc spring that will in turn affect the drawbar force. To investigate the effects of centrifugal force, an FEA was conducted on the same model, in Fig. 12, by setting the angular velocity of the whole model as one extra boundary condition (as opposed to the earlier static analyses, which factored in no rotation). The resulting boundary condition of the angular velocity can be visualized through the arrows representing the acting directions of each angular velocity as shown in Fig. 17. The whole disc spring stack installed inside the spindle will rotate axisymmetrically with the assembly. Figure 18 shows the stress distribution of the disc springs with an initial deflection of 0" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000271_robot.1994.351376-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000271_robot.1994.351376-Figure3-1.png", "caption": "Figure 3: Two PUMA-like arms grasping an object", "texts": [ "la6 -.i4a - . u a o 0 0 0 o .a13 .si1 -.Sa9 .Sa6 - 3 1 4 0 0 0 0 o - m i o 0 0 o . iaa . i sa 0 0 0 .I91 -.158 In this case, an external wrench may be applied a torque about the z axis), as indicated by matrices Moreover, as expected, since the structure of the manipulator is more complex, the subspace of the controllable internal forces, R(F24), is larger than before, and there are more posaibihties for grasp optimisation. Caee 2. Consider now the case of two 6 dof industrial robots depicted in fig.3. Contacts are located at c1 = [2,0, -1]*, c2 = [3,0,-2IT, and the corresponding unit normal vectors are nl = [&/a, 0, -&/2]T, n2 = [-&/2,0, &/2JT. In the following, all the force vectors are expressed with respect to a reference frame b e d to the center of the object. Moreover, for the sake of brevity, matrices F3g and F34 are not reported. Assume that grippers are used to manipulate an object, i.e. contacts are of the complete constraint type. Since is,F23 and F33. b No external wrenches may be applied by this manipulation system (matrices F1g,FZg,Pgg are null), as can be easily deduced from the observation of the mechanism" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003206_jst.28-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003206_jst.28-Figure5-1.png", "caption": "Figure 5. Spring-damper model of ball impact. m, ball mass. x, displacement. k, spring stiffness. a, spring power. c, damping coefficient.", "texts": [ " Cheng, A. Subic and M. Takla based on a mathematical analysis, which makes it difficult to be coupled with other existing Finite Element Analysis (FEA) models. The second limitation is the fact that this is a single degree of a freedom model, which prevents its implementation in the simulation of impact with 3-D objects. Finally, this model was developed under low speed, which can hardly be used for the prediction of real game conditions in cricket. The model reported by Carre\u0301 et al. [15] is shown in Figure 5. In this model, both k and c are functions of vin. An equation was proposed by Carre\u0301 et al. [15] which assumes that the viscoelastic coefficient, c, is associated with the contact area, which can be expressed as: c \u00bc ppR2 \u00bc q(d x)x \u00f011\u00de where R is the radius of the contact area, d is the ball outer diameter and p and q are introduced model coefficients. The equation of motion of the system is presented as follows: m \u20acx\u00fe c _x\u00fe kxa \u00bc 0 \u00f012\u00de Subic et al. [16] developed an approximate FEA model to emulate the effects of the interaction of the cricket ball with a rigid or deformable surface" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000240_s0263574701004027-Figure10-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000240_s0263574701004027-Figure10-1.png", "caption": "Fig. 10. Vector chain for leg i [17].", "texts": [ " The calibration method introduced by Patel14 requires an introduction of a redundant leg to the hexapod, a parallel robot similar to the Stewart platform. Finally, the calibration method proposed by Daney15 also requires internal sensor measurements with position information provided by external sensors. An ideal model of a six degree of freedom Stewart Platform is shown in Figures 9 and 10. The Stewart Platform is made up of a moving platform B with coordinate frame B(x, y, z), a base platform A and six extensible legs L. In Figure 10, the joints on the base are denoted by Ai, and those on the moving platform denoted Bi, in which i=1, 2 . . . 6. The rotation matrix Aui is formed using the Roll-Pitch-Yaw Euler angles of ( x, y, z). Position vector Aq of the coordinate frame A and the rotation matrix Aui describe the transformation from the moving platform to the fixed base.16 As a result, the position and orientation of the moving platform, , is defined as [x y z x y z ]T. The complete deviation of is described by =[ x y z x y z]T with six partial deviations, ( ) , ( =1 )= x , " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000135_1.1587178-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000135_1.1587178-Figure1-1.png", "caption": "Fig. 1. (a) The n director in the SmC structure makes the angle \u03b8 with the normal z to the smectic layer. The azimuthal molecular orientation in the layer plane (xy) is specified by the angle \u03d5 or by the orientation of c director. The magnetic field H is parallel to the yz plane and makes the angle \u03b1 with the smectic layer. (b) The orientation of the c director in the field-oriented sample is shown by the arrows. The angle \u03b1 could vary by the rotation of magnets (M) or film about the x axis.", "texts": [ " \u00a9 2003 MAIK \u201cNauka/Interperiodica\u201d. PACS numbers: 61.30.Jf; 61.30.Gd; 68.55.Ln In tilted smectic liquid-crystal films, linear and point defects are formed either spontaneously or under the action of an external field [1\u20136]. Freely suspended thin (2\u2013100 molecular layers) films are suitable objects for studying these defects [7]. Such films are composed of a strictly fixed number of smectic layers parallel to the free surface. In smectic C (SmC) liquid crystals, the average orientation of the molecular long axes (n director; Fig. 1a) is tilted at angle \u03b8 with the normal z to the smectic layer. The n-director projection onto the plane of a smectic layer forms a two-dimensional (2D) field of molecular orientations, which can be described by a 2D unit vector c(xy), so-called c director [8, 9]. The defects in the layer plane are formed due to the modulation of c-director orientation. Up to now, the defects were studied mostly in electric-field-oriented polar films or in nonoriented samples. In this work, linear orientational defects were studied in freely suspended films exposed to a magnetic field", " Immediately after the preparation, the film was inhomogeneous in thickness. On holding the sample in the SmC phase for one hour, the thickness, as a rule, became homogeneous. Measurements were made on films with a strictly fixed number of smectic layers. The 0021-3640/03/7708- $24.00 \u00a9 0429 number of layers in the film was determined from the measured optical reflectance spectra [10]. The direction of a magnetic field about the film plane (polar angle \u03b1) could be changed by turning the sample or magnetic field in the yz plane (Fig. 1b). The samples were placed in a thermostatted cell. The defects were imaged in reflected polarized light using an optical microscope and a CCD chamber. We first describe qualitatively the linear and point defects that are observed in a magnetic field (Fig. 2). In the crossed-polarizer images, the c director continuously turns by an angle of 90\u00b0 upon passing through a light stripe; i.e., the linear defects in Figs. 2a and 2b with two and four stripes correspond to the \u03c0 and 2\u03c0 walls, respectively", " This differentiates the system under consideration from the others. For example, in polar smectic films, only the 2\u03c0 walls can form in an electric \u2207i\u03d5dri\u222b\u00b0 2\u03c0s= field, and only the \u03c0 walls can form in nematics in a magnetic field [8, 9]. The interaction between the orientational order and magnetic field H is described by the energy density \u22121/2\u03c7a(H \u00b7 n)2, where \u03c7a denotes the magnetic anisotropy [8, 9]. The elastic energy of the c(x, y) orientation field in a thin SmC film has the following form in an external magnetic field with the geometry shown in Fig. 1: (2) where h is the film thickness and Ks and Kb are, respectively, the 2D splay and bend elastic constants of the c director [11]. F0 is the \u03d5-independent free energy. The last two terms on the right-hand side in Eq. (2) account for the magnetic energy: A1 = 1/2sin2\u03b8sin2\u03b1 and A2 = 1/2sin2\u03b8cos2\u03b1, where \u03b1 is the angle between the magnetic field and the film plane. The 2\u03c0 periodicity of the magnetic energy for \u03b1 \u2260 0 and the \u03c0 periodicity for \u03b1 = 0 should give rise, respectively, to the 2\u03c0 and \u03c0 walls" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002040_rtd2004-66044-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002040_rtd2004-66044-Figure1-1.png", "caption": "Fig. 1 - Side view of the wagon model.", "texts": [ " The advantage of this model over the models presented before [7], is the addition of coupler forces and its degrees of freedom in addition to wagon body torsional flexibility. All parts of primary and secondary suspension systems with their nonlinear characteristics, friction between moving elements, variations in brake torque of wheels due to transportation lags, the effect of wheel flanges contact with the rail, wheel rail contact nonlinear forces, kinematics constraint of bogie center bowl, the contact forces between side pads and bogie frame, inter-wagon effects, and flexibilities of bogie and wagon body are considered in the model (Fig. 1 and 2). The considered degrees of freedom of this model come from: \u2022 16 DOF for four axles, \u2022 14 DOF for two bogie frames that includes torsional flexibilities of the bogies too, \u2022 6 DOF for the two bolsters, and \u2022 7 DOF for the car body including the car torsional flexibility. Downloaded From: http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/conferences/rtd2004/71104/ on 03/28/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 2 Copyright \u00a9 2004 by ASME The model is so constructed that can easily be used for cargo as well as passenger train studies" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002384_02286203.2006.11442380-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002384_02286203.2006.11442380-Figure2-1.png", "caption": "Figure 2. Normal and tangential interference.", "texts": [ " Differentiate the normal force in (1) with respect to d and present the results in normalized form to obtain the normalized total normal contact stiffness, K\u0303n: K\u0303n = 1 32 H \u221e\u222b h 1 (s\u2212 h)3/2\u03b2\u03c33/2 [ 204\u03b22sh(s\u2212 h)\u03c33 + 160\u03b2sh ( 3 2 sh\u2212 s2 \u2212 h2 ) \u03c34 \u2212 \u03b22(s3 + h3)\u03c33 + 40\u03b2(s4 + h4)\u03c34 + 45(5s4h\u2212 10s3h2 \u2212 s5 +h5 + 10s2h3 \u2212 5sh4) ] \u03d5(s) ds (2) where: H = 8 3 \u03c0E\u03b72A\u03b21/2 (3) \u03c3 is the standard deviation of asperity height sum of the first and second surfaces, h(d/\u03c3) is the normalized separation, and s(z/\u03c3) is the normalized height sum. For any separation, h, (2) can be integrated to obtain the contact stiffness. According to the Hertzian equations [15] the contact load between two asperities having interference w is given by: P = 4 3 E\u2032\u03b21/2w3/2 (4) where the interference w may be approximated (Fig. 2) using: w = w1 cos\u03b1 w1 = z \u2212 d\u2212 1 4 ( r2 \u03b2 ) where \u03b1 is the angle used to define the angular orientation of the line approximating the deformed boundary of the two asperities, using the mean plane of surface S1 as the reference. The tangential load then can be approximated using: Pt = 4 3 E\u2032\u03b21/2(w1 cos\u03b1)1/2 sin\u03b1 (5) Expression for tangential contact stiffness may be derived by differentiating (5) with respect to r and then summed statistically to obtain the expected total contact stiffness. For interaction of two asperities in contact: \u2202Pt \u2202r = 4 3 E\u2032\u03b21/2 ( \u2202(w1 cos\u03b1)3/2 \u2202r sin\u03b1+ (w1 cos\u03b1)3/2 \u00d7\u2202(sin\u03b1) \u2202r ) (6) where: sin\u03b1 = r/\u03b2 \u221a 4 + r2 \u03b22 (7) cos\u03b1 = 2/ \u221a 4 + r2 \u03b22 (8) The total normalized tangential contact stiffness K\u0303t can be written as: K\u0303t =H \u222b 6 128 (s\u2212 h)3/2\u03c33/2 4\u03b22(s\u2212 h)\u03c3 + 13(s3 \u22123s2h+ 3sh2 \u2212 h3)\u03c33 \u03b22 + ([ (72\u03b2(s3 \u2212 3s2h+ 3sh2 \u2212 h3)\u03c33 + 36\u03b22(s2 + sh\u2212 h2)\u03c32 ] + [ 55(s4 \u2212 4s3h+ 6s2h2 \u2212 4sh3 + h4)\u03c34)(s\u2212 h)\u03c3 ] 1 \u03b2 5 2 )] \u03c6(s) ds (9) Later in this paper the surface parameters are used in conjunction with the density function for a Gaussian distribution to examine contact stiffness and force" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002602_j.matdes.2007.03.009-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002602_j.matdes.2007.03.009-Figure4-1.png", "caption": "Fig. 4. Designed and manufactured workpiece manipulator.", "texts": [ " A workpiece holder for this type of work must not only hold but should also be able to accommodate the three-dimensional deformation of the workpiece during deformation. When the workpiece is forged, elongation occurs and the movement of the centerline of the workpiece moves vertically. This can cause severe distortions and so undesirable features. These problems appear because of the difficulty in holding the workpiece between the tools and can led to the occurrence of nonsymmetrical flow and undesirable features. To over- come these problems, as shown in Fig. 4, a workpiece manipulator is designed and manufactured for this particular work. This holder accommodates the vertical, lateral and axial movements of the workpiece during the single or multi-cycle compression\u2013rotation process. In order to avoid these features, the concept of process operating regions and limitation zones in open die forging characterized by four zones is proposed to eliminate the difficulty in measuring elongation. While pressing the workpiece between the flat tools, the horizontal centerline of the workpiece which is parallel to the press surface, changes its vertical position" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003924_iros.2010.5650335-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003924_iros.2010.5650335-Figure1-1.png", "caption": "Fig. 1. Multiple mini rotorcraft flying in formation", "texts": [ " In [20], the authors propose a robust linear PD controller considering parametric interval uncertainty. Here, the authors present a robust stability analysis and computes the robustness margin of the system with respect to the parameters uncertainty. In [21] a flight formation control based on a four integrators coordination control is presented. This approach is based on a forced consensus algorithm to achieve a multiple mini rotorcraft flight formation and tracking. This work addresses the nonlinear control for multiple mini rotorcraft flying in formation, shown in Figure 1, based 978-1-4244-6676-4/10/$25.00 \u00a92010 IEEE 634 on nested saturations and a single integrator coordination control strategy. In this approach we consider every mini rotorcraft as agents to be coordinated and follow a virtual reference. The proposed control scheme is based on the idea that lateral and longitudinal subsystems are decoupled which enable us to implement a decoupled coordination of the lateral and longitudinal subsystems. In this way, the multiple mini rotorcraft platoon can hover and thus keeping the desired formation by following a constant zero-reference" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003780_10426914.2010.490862-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003780_10426914.2010.490862-Figure2-1.png", "caption": "Figure 2.\u2014Diagram showing the weld with surfaces parallel to the: (a) cross section; (b) longitudinal section; and (c) section used for XRD.", "texts": [ " The laser was equipped with a co-axial delivery system that allowed the shielding gas to be supplied through a 5mm diameter nozzle. In addition the laser was equipped with a side gas delivery system consisting of a 3mm diameter nozzle angled at 45 to the laser beam. The samples were retained in position for welding using the jig shown in Fig. 1. The underside of the weld could be back-shielded by applying a jet of gas from below. The laser and process parameters investigated are given in Table 1. Weld cross-sections were produced by cutting the welds parallel to the surface shown in Fig. 2(a), whilst longitudinal sections were made by cutting parallel to the surface shown in Fig. 2(b). These were ground and polished, and then electrolytic etched in 10% oxalic acid. Weld quality was initially investigated by means of low magnification optical microscopes. Once the optimal parameters for a fully penetrated weld were identified, the remainder of the investigation was based on samples produced using these. A batch of welded samples were annealed by heating to 650 C for 30 minutes; then to 950 C for 45 minutes; and finally to 1025 C for 45 minutes. The samples were then quenched in nitrogen gas at 4 bar. Optical microscopy was again carried out on both as-welded and annealed samples. XRD analysis was performed on the raw material, as-welded and annealed samples. The section of the weld was made by cutting the weld parallel to the surface shown by Fig. 2(c). XRD analysis was conducted on an X-radiation diffractometer with a \u2212 2 configuration, equipped with a Cu-K radiation ( = 0 154nm) source. The scanning step was 0 02 with a dwell time of 3 seconds. The accuracy of this XRD equipment is up to 0 01 for 2 . Three as-welded samples together with three annealed samples and three samples of as-received material were tested for corrosion in a salt spray testing machine. The test was carried out according to the ISO 9227 standard, with the salt solution having 50g/l of sodium chloride and a pH between 6" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003188_j.mechmachtheory.2007.07.001-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003188_j.mechmachtheory.2007.07.001-Figure6-1.png", "caption": "Fig. 6. Relationship of conjugate surfaces and the generating surface.", "texts": [ " It follows that v\u00f021\u00de; v\u00f023\u00de and v(31) should be collinear, that is, three groups of relative motions between the surfaces R(1),R(2) and R(3) must share a same instantaneous screw axis and a same screw parameter. Based on it, we can determine the parameters of intermediate motion. Because v\u00f021\u00de; v\u00f023\u00de and v(31) are collinear, the expression can be presented by: v\u00f031\u00de \u00bc lv\u00f021\u00de; v\u00f023\u00de \u00bc \u00f01 l\u00dev\u00f021\u00de \u00f049\u00de where l is the adjust parameter. Therefore, v(3) and v\u00f01\u00de; v\u00f02\u00de must satisfy an initial condition, i.e. v\u00f03\u00de \u00bc \u00f01 l\u00dev\u00f01\u00de \u00fe lv\u00f02\u00de \u00f050\u00de Follow the previous nomenclature of symbols in Section 3.1. In addition, as shown in Fig. 6, the radius vectors r\u00f01\u00de; r\u00f02\u00de and r(3) describe the spatial position of considered point relative to the origins O\u00f01\u00de;O\u00f02\u00de and O(3) in the meshing space. Z(3) is an axis of intermediate motion, and shares a common perpendicular O\u00f01\u00deO\u00f02\u00de between Z(1) and Z(2)-axis, a3 = jO(1)O(3)j is the center distance of intermediate conjugation. Considering any arbitrary spatial motion can be deemed as a synthesis of instantaneous screw motions, thus the intermediate conjugate motion can also be considered as a screw motion" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002558_978-3-540-71364-7_29-Figure28.14-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002558_978-3-540-71364-7_29-Figure28.14-1.png", "caption": "Fig. 28.14. (a) Kinematic model of the mobile platform (b) Unit sphere representation of wheel configurations", "texts": [ " 1) Representation of wheel configuration: In order to satisfy the pure rolling and nonslipping condition, all wheel normals must be either parallel or intersect in a single point. The respective wheel configurations are called admissible wheel configuration (AWC). All AWCs can be represented on the surface of a unit sphere and can be described by using two spherical angles: the azimuth angle \u03b7 represents the direction of the translational motion and the altitude \u03b6 is a measure for the amount of rotational motion. In Fig. 28.14b the unit sphere model is illustrated. All configurations on the equator (\u03b6 = 0) correspond to pure translational motion while configurations at one of the poles (\u03b6 = \u00b1\u03c0/2) represent pure rotational motion. As an AWC does not specify the absolute speed of the platform motions, a third variable, the generalized velocity \u03c9 is introduced. From the AWC (\u03b7, \u03b6) the unit vector e(\u03b7, \u03b6) can be calculated. Including the generalized velocity \u03c9 yields the platform velocity in the Cartesian platform coordinate system:\u239b\u239d Px\u0307 Py\u0307 P\u03c8\u0307/\u03baG \u239e\u23a0 = \u03c9 \u239b\u239d cos \u03b6 cos \u03b7 cos \u03b6 sin \u03b7 sin \u03b6 \u239e\u23a0 = \u03c9e(\u03b7, \u03b6), (28" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000481_28.993169-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000481_28.993169-Figure3-1.png", "caption": "Fig. 3. Measured reluctance torque of an 80-W U-core motor.", "texts": [ " However, as a consequence of its simple construction, the U-core motor has poor performance, expressed in the following: \u2022 torque pulsations; \u2022 high stator leakage inductance; \u2022 poor utilization of PMs; \u2022 no preferred direction of rotation with uniform air gap. Rotor PMs in Fig. 2 create reluctance torque with stator salient poles. This reluctance torque should not be mistaken for a reluctance torque created by a salient rotor in a cylindrical stator, typical for hydrogenerators. Whereas rotor saliency in a hydrogenerator travels at the same synchronous speed as the stator field, the stator saliency in a U-shaped stator is stationary. Therefore, it is experienced by the rotor as torque pulsations (Fig. 3). As opposed to a hydrogenerator, in which the rotor saliency contributes to the total torque, the stator saliency of the PM motor in Fig. 2 is only a consumer of reactive power and a source of shaft vibrations. When the U-core motor in Fig. 2 is running at synchronous speed and generating pulsating torque as in Fig. 3, its rotor is accelerated and decelerated twice in each revolution, as a consequence of pulsating torque. During the acceleration phase, the motor absorbs additional power from the source, which is returned during deceleration. The motor apparent power pulsates with twice the mains frequency, which is for the source nothing but an additional reactive component of the load. Denoting by its maximum value, one can express the pulsating torque as where denotes rotor synchronous speed (s ). Neglecting slight speed changes due to pulsating torque, one can express the power needed for this pulsating torque as Assuming that power pulsates between the source and fictitious inductance at voltage level , where pulsating electrical power in is equal to , one can further write or, fictitious inductance which consumes reactive power equal to the pulsating power due to reluctance torque is inversely proportional to the amplitude of pulsating torque" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002176_11505532_4-Figure4.2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002176_11505532_4-Figure4.2-1.png", "caption": "Fig. 4.2. The geometric principle of the proposed guided path following scheme in 2D.", "texts": [ " To arrive at P, we need to positively rotate the INERTIAL frame an angle: \u03c7p( ) = arctan yp( ) xp( ) (4.3) about its z-axis, where the notation xp( ) = dxp d ( ) has been utilized. This rotation can be represented by the rotation matrix: Rp,z(\u03c7p) = cos\u03c7p \u2212 sin\u03c7p sin\u03c7p cos\u03c7p \u2208 SO(2), (4.4) used to state the error vector between p and pp( ) expressed in P by: \u03b5 = Rp (p\u2212 pp( )), (4.5) where Rp is short for Rp,z, and \u03b5 = [s, e] \u2208 R2 consists of the along-track error s and the cross-track error e; see Figure 4.2. The along-track error represents the (longitudinal) distance from pp( ) to p along the x-axis of the PATH frame, while the cross-track error represents the (lateral) distance along the y-axis. Also, recognize the notion of the off-track error |\u03b5|2 = \u221a s2 + e2. It is clear that the geometric task is solved by driving the off-track error to zero. Consequently, by differentiating \u03b5 with respect to time, we obtain: \u03b5\u0307 = R\u0307p (p\u2212 pp) + Rp (p\u0307\u2212 p\u0307p), (4.6) where: R\u0307p = RpSp (4.7) with: Sp = S(\u03c7\u0307p) = 0 \u2212\u03c7\u0307p \u03c7\u0307p 0 , (4", " Denote this angular difference by \u03c7r = \u03c7d \u2212 \u03c7p. Intuitively, it should depend on the cross-track error itself, such that \u03c7r = \u03c7r(e). An attractive choice for \u03c7r(e) could then be the physically motivated: \u03c7r(e) = arctan \u2212 e e , (4.18) where e becomes a time-varying guidance variable shaping the convergence behavior towards the longitudinal axis of P. Such a variable is often referred to as a lookahead distance in literature dealing with planar path following along straight lines [19], and the physical interpretation can be derived from Figure 4.2. Note that other sigmoid shaping functions are also possible candidates for \u03c7r(e), for instance the tanh function. Consequently, the desired azimuth angle is given by: \u03c7d( , e) = \u03c7p( ) + \u03c7r(e), (4.19) with \u03c7p( ) as in (4.3) and \u03c7r(e) as in (4.18). Since is the actual path parametrization variable that we control for guidance purposes, we need to obtain a relationship between and Up to be able to implement (4.16). By using the kinematic relationship given by (4.11), we get that: \u02d9 = Up x 2 p + y 2 p = Ud cos\u03c7r + \u03b3s x 2 p + y 2 p , (4.20) which is non-singular for all regular paths. Hence, by utilizing trigonometric relationships from Figure 4.2, the derivative of the CLF finally becomes: V\u0307\u03b5 = \u2212\u03b3s2 \u2212 Ud e2 e2 + 2 e , (4.21) which is negative definite under the assumptions that the speed of the agent is positive and lower-bounded, and that the lookahead distance is positive and upperbounded. Consequently, with the recent considerations pertaining to (4.20) and (4.21), we can state the following relevant assumptions: A.1 The path is regularly parametrized; 0 < x( ) 2 p + y( ) 2 p < \u221e \u2200 \u2208 R. A.2 The agent speed is positive and lower-bounded; Ud(t) \u2208 [Ud,min,\u221e \u2200t \u2265 0" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003164_13506501jet284-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003164_13506501jet284-Figure7-1.png", "caption": "Fig. 7 Lip seal finite element mesh", "texts": [ " The latter is formed under the lip and across the lip surface asperities by the shaft rotation. The considered seal has an elastic linear structure and the lip is considered to have, along the height hl of the contact surface, a non-axisymmetric behaviour [21]. The elastic deformation of the lip is dealt with using the finite-element method, employing elements with 20 nodes for the non-axisymmetric part, defined by the height hl, whereas using two-dimensional elements with eight nodes for the remainder of the seal structure (Fig. 7). The deformation vector, d (Fig. 8), of the seal lip that is generated by the pressure and shear stress in the fluid film is characterized by the influence matrices C1, for the radial forces, and C2 and C3, for the tangential forces. The influence matrices, C1 , C2, and C3, are calculated through juxtaposing the solutions obtained by applying a unit force, normal, circumferentially tangential, and axially tangential, respectively, to each Proc. IMechE Vol. 221 Part J: J. Engineering Tribology JET284 \u00a9 IMechE 2007 at BROWN UNIVERSITY on May 20, 2015pij" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001763_025-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001763_025-Figure6-1.png", "caption": "Figure 6. (a) Elastic stress-strain relation. (b) Curved elastic rod with vectors showing fibre direction F, curvature direction C, and moment direction M . The moment M is always a bending moment perpendicular to the plane. (c) Maximum tensile strain E+ and stress U+ and compressive strain E- and stress u- giving a moment M. (a') Stress-strain relation with hysteresis. (e ) Kesolution of moment vector showing components at ends giving torque, acting in opposite directions along fibre and so corresponding to twist in opposite directions. (f) Stress U+ and u- leading the strain 6+ and C- giving moment M in a different direction.", "texts": [ " (2) 2s This may be rewritten as: Mt=(1/4~) jr $ k f b d8 dx (3) where the origin of x is taken at the centre of the fibre length and 9 is defined as the angle of bending over a length x. The torque will be a maximum at the two ends, where the whole of the energy has to be supplied, and will decrease to zero at the centre as the length contained, and thus the integrated energy loss, is reduced. A partial explanation of the force and moment situation can be given as follows. For simplicity the diagrams in figure 6 are drawn with uniform bending curvature through 180\": this does not affect the general argument. In simple bending of an elastic rod, with a stress-strain relation as in figure 6(a), the vectors for fibre direction (F), Torque in fatigue testing offibres 729 curvature (C) and moment ( M ) will be shown in figure 6(b). The bending moment results from the fact that the rod is strained as in figure 6(c) , with the stresses in phase with the strain. Although the vectors F and C change direction, the vector M remains constant as required for equilibrium. The situation is different if there is hysteresis, as in figure 6 ( d ) ; the stress will then lead the strain as the fibre rotates, reaching a maximum first. This phase difference occurs in the plane of rotation of each bent section of fibre ax. The exact shape of the hysteresis loop is not important in the argument. The strain distribution at any instant will be the same as before, but the peak stress U+ and U- will be in a different part of the fibre circumference, as shown in figure 6 ( f ) . The moment vector will therefore be in a different direction, as shown in figures 6(e) and (f), with components in the plane of the curvature. If we then consider the moments applied at the fibre ends in the same direction so as to maintain equilibrium, we see that these have components along the fibre axis which would give rise to torque. The vectors are parallel, since both drives rotate in the same direction in space; they are however in the opposite direction along the fibre and thus give rise to torque in opposite directions. The argument in the last paragraph is not completely correct because the moments shown in figure 6(e) would not produce the bending deformation shown, since the bending moment component is reduced at the ends. It also seems very likely that the fibre will be displaced out of the plane causing a further change in the directions of the various vectors. The situation will also be complicated if the behaviour in tension and compression is different. However, the argument is adequate to indicate in a general way how the torque arises. 730 S F Calil, B C Goswami and J W S Hearle An estimate has been made of the magnitude of the effects for the experimental situation of figure l(c), which is the most important in practice" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003893_tmtt.1967.1126477-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003893_tmtt.1967.1126477-Figure3-1.png", "caption": "Fig. 3. Cavity used in tests.", "texts": [ "78 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, JUNE 1967 The imaginary component of permittivity is related to QE by where tan # is the dissipation factor. In order to test the technique, a Mylar sheet 1 mil thick was measured at 2.8 GHz. A KF of 2.21 and tan 6\u2019 of 0,0035 were found experimentally; these values show excellent agreement with the corresponding published values [3] of 2.20 and 0.003, respectively. The technique described above was used to measure the properties of a silicon monoxide (SiO) film at S-band. The cavity for these measurements is shown in Fig. 3. It is convenient to measure the real part of the permittivity with the dielectric film deposited on the end plate A of the cavity and the imaginary part with the film deposited on the post B. Plate A should be baked at a temperature exceeding the maximum temperature encountered during formation of the film. The cavity with the baked but uncoated end plate is calibrated by obtaining a curve of resonant frequency as a function of gap space. The gap space is controlled by placing washers of known thickness under surface C and a weight on surface D", " The permittivity of these materials varied between 11 and 15 (Table 1), The matching procedure was found to be independent of linewidth and magnetization but the choice of the permittivity and height of the dielectric disks was dependent on the dielectric constant of the ferrite. AH 490 380 220 55 85 450 150 175 245 55 120 \u2014 \u2014 \u2014 \u2014 15 12 14 11 13 \u2014 \u2014 \u2014 12.22 12.24 11.20 14.50 14.80 12.21 13.0 11.55 12.42 14.96 10.60 2.11 2.05 2.03 2.00 2.00 2.10 2.02 2.05 2.05 2.00 2.01 tan 6 0.0008 0.0008 0.0005 0.002 0.0005 \u2014 0.002 Figure 3 is a plot of overall height of each stack of ferrite and dielectric disks against square root of permittivity of the disks. Points 1\u20138 represent the overall height and the permittivity of the final disk for the ferrites indicated in Table I. It has been found experimentally that the disk permittivity should lie within the bounds of the limit curves shown for broadband operation. Using Fig. 3 it is possible to match a ferrite of known permittivity, lying within the range covered, by choosing a number of dielectric disks which form a \u201cstaircase\u201d as shown on the curve lying within the bounds indicated. The overall height of the combination and the dielectric constant of the final disk lie on the curve drawn through points 1-8. EXPERIMENTALRESULTS The largest bandwidth obtained was 8 percent using YIG (2) [Fig. 4(a)]; final external screw matching was applied to the circulator in order to further improve the 1\u20133 isolation characteristic", " Larger bandwidths appear possible with variation on the previously mentioned matching techniques. S. R. LONGLEYS Mullard Research Labs. Redhill, Surrey, England 3 Mr. Longley is now engaged in postgraduate studies at University College, London. Gap Spacing for End- Coupled and Side-Coupled Strip-Line Filters Two of the simplest strip-line configurations for bandpass filters are those which utilize end coupling [1], [2] (Fig. 1) and side coupling [3] (Fig. 2). For the special case of a symmetric strip line with center conductor of negligible thickness (Fig. 3), it is possible to establish expressions which explicitly relate gap spacing S to normalized bandwidth w. Generally it is found that the greater the gap width, the less important are the tolerance considerations; alternatively, a broader bandwidth may be achieved for a given tolerance. The purpose of this correspondence is to establish a criterion that will enable a designer to select the filter with the greater coupling gap for given values of ground plane spacing D, rnidband wavelength XO, and normalized bandwidth" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001578_acc.2004.1383649-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001578_acc.2004.1383649-Figure4-1.png", "caption": "Fig. 4. Two Wheel Moving Bar", "texts": [ " The angular orientation of the sheet is 4. Note that while the paper buckles, point C remains on the flat surface since the buckle occurs only between points 1 and 2. For this reason point C does not move perpendicular to the sheet. 4n2 It is assumed that when the sheet buckles, the sheet is still transversally stiff so rotation is possible. This is illustrated in Fig. 3 where any line perpendicular to the line that connects points 1 and 2 drawn on the buckle surface is parallel to the flat surface. A . Notation Figure 4 shows a schematic representation of the modeling variables for the steerable nips system. This system has two independent steering wheels, located at points 1 and 2. These steerable wheels are separated by a distance 26. Three coordinate frames are defined to describe the position and orientation of the paper: A fixed global coordinate system denoted (jf, if, k,), and two local frames ( j l , i l ,k l ) and (j2,f2,kZ) attached to wheel 1 and 2 respectively. The generalized coordinates of the system are (z, y, $,6,6'1, 02, $1, $2)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001182_robot.2002.1014767-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001182_robot.2002.1014767-Figure3-1.png", "caption": "Figure 3: l k o concave segments. Since @(sa) = 0, < 0 and e(&) = o b > 0 exactly one pair of antipodal points exists.", "texts": [], "surrounding_texts": [ "1.2 Antipodal Points Let a(u) be a closed, simple, and twice continuously differentiable curve, where u increases counterclockwise. For clarity of presentation, we assume that a is unit-speed, that is, IIa' (U) 11 = 1. All procedures in this paper are presented on unit-speed curves but can be extended with virtually no effort to (and have been implemented on) arbitrary-speed curves.\nDenote by T(u) = a'(u) the tangent of a and denote by N(u) the inward normal. We only consider that a's curvature rc is not constant.' Furthermore, K can be zero at only isolated points on the curve. In case no ambiguity arises, the parameter u also refers to the point a(.) on the curve. Two points a and b on a are called antipodal if their normals are opposite and collinear:\nN ( a ) + N(b) = 0 and N ( a ) x (a@) - a ( a ) ) = 0.\nIn Section 2 we will consider how to find antipodal points on a pair of segments of a that satisfy some restricted conditions. In Section 3 we will describe how to preprocess a to generate all such pairs. Section 4 will present some experimental results.\non 7: N ( s ) + N ( t ) = 0, orequivalently, (1)\nT ( s ) + T ( t ) = 0. (2)\nLet g(s , t ) = ~ ( s ) x ~ ( t ) . Since = ~ ( s ) x (-rc(t)T(t)) = -rc(t) # 0: by the Implicit Function Theorem, the equation g(s, t ) = 0 defines t as a function of s. We refer to t as the opposite point of s.\nA pair of points may be antipodal only if their normals do not point away from each other. We add a fifth condition:\n(v) N ( s ) . (a(t) - a ( s ) ) > 0 for d l s E (sa, sa).\nDifferentiate (2) and then plug (1) in: (rc(s) - n( t )$ )N(s ) =O.Thus~(s) -~( t ) =Oand$ = 3.\n2 Computation of Antipodal Points Two segments of a, denoted as S and 7, are defined on subdomains (sa, sa) and ( t , , t b ) , respectively. Here sa < Sb always holds. For convenience, we allow t , > t b , in which case (ta, ta) refers to the interval ( t b , t a ) . Let @(a, b) = s,\" IE du be the total curvature over (a, b) , which measures the amount of rotation of the tangent T as it moves from a to b along the curve. We assume that the following conditions are satisfied:\n(i) No intersection between S and 7.\n(ii) rc > 0 everywhere or K < 0 everywhere on both S and 7, with n = 0 possible only at s,, sa, t,, and t b .\n(iii) N(s , ) + N(t,) = 0 and N(sb) + N(ta) = 0 but neither s, and t, nor and t b are antipodal.\n(iv) -7r 5 @(sa, sa) = -a(&, t b ) 5 7r.\nConditions (ii) states that the normal rotates in one direction as each segment is traversed. Condition (iv) ensures that a pair of antipodal points cannot appear on the same segment, which does not include s, sa, t,, or t b .\nUnder condition (iii) (and (ii) and (iv)), a one-to-one correspondence exists between a point s on S and a point t\n'This excludes a circle on which any two points determining a diameter are antipodal.\n2.1 Antipodal Angle Define the antipodal angle3 6(s) as the rotation angle from the normal N ( s ) to the vector ~ ( s ) = a(t) - a ( s ) (see Figure 2). Under condition (v), 6 E (-$, $). By definition, s\nand t are antipodal ifand only ifO(s) = 0. To determine e', we first calculate the derivative:\nFrom Figure 2 we see that sin6 = N ( s ) x T ( s ) / ~ ~ T ( s ) ~ ~ . Differentiate both sides of this equation and substitute $Ilr(s)ll in. After a few more steps, we obtain\nTwo antipodal point s* and t* with 6'(s*) # 0 are called simple antipodal points.\nThe rest of Section 2 presents an algorithm to find all simple antipodal points on S and 7. This algorithm deals separately with three cases: S and 7 are both concave, both convex, or one concave and the other convex.\n2The Frenet formulas [lo, pp. 56-58] for planar curves state that\n31n [2], it is referred to as the friction angle. T'(s) = K ( S ) N ( $ ) and N'(s) = -IC(S)T(S) .", "2.2 Two Concave Segments In this case, K ( S ) < 0 and ~ ( t ) < 0; by (3), 8\u2019(s) > 0. The antipodal angle 8 increases monotonically from sa to S b .\nTheorem 1 Suppose S and 7 are concave. IfO(s,) < 0 and 8(sb) > 0 then a unique pair of antipodalpoints exists. Otherwise, no antipodal points exist.\nWhen @(sa) < 0 and @(Sa) > 0, we use bisection to find the antipodal points. Initialize (so, to) t (sa, t , ) and (s1,tl) t (sb,tb). Then evaluate s2 t and find its opposite point t 2 . If e(s2) > 0, set ( s l , t l ) t ( s 2 , t z ) ; otherwise set (so, t o ) t (s2, t2 ) . Repeat the above steps until 8(s2) approaches 0, that is, until s2 and t 2 approach two antipodal points.\n2.3 Two Convex Segments Since ~ ( s ) > 0 over S and ~ ( t ) > 0 over 7, we cannot determine the sign of O\u2019(s). Multiple pairs of antipodal points may exist on S and 7. The first pair will be found through \u201cmarching\u201d described in Section 2.3.1 if 8(s,) and 8 ( S b ) have the same sign or through bisection in Sections 2.3.2 if they have different signs. Section 2.3.3 will describe how all the remaining pairs can be found by letting the two strategies invoke each other recursively.\n2.3.1 Endpoint Antipodal Angles with the Same Sign\nThe marching strategy will rely on the following result.\nProposition 2 When S and 7 are convex, the vector r (s) rotates counterclockwise as s increases from sa to S b .\nProof ating the vector T yields We need only show that x T < 0. Differenti-\n- = --(a@) - a ( s ) ) = T(t) dr d ds ds\nSince K ( s ) , K ( ~ ) > 0, we have 1 + # > 0. Hence is in the direction of T(t). Meanwhile, from condition (v) that r(s) N ( s ) > 0 it follows that T(s ) x T ( S ) > 0 and\n0\nFigure 4 illustrates the working of an iterative method when 8(s,) < 0 and < 0. The iteration starts with s and t at SO = S b and t o = t b , respectively. From Proposition 2, as s moves towards sa, the vector T ( S ) rotates clockwise. At the ith iteration step move s from si to si+l at which the normal is parallel to si). If no such point si+l exists, stop. Otherwise, move t from ti to ti+l where N(ti+l) + N(si+l ) = 0. The iteration continues until\n~ ( t ) x T ( S ) < 0. Therefore x T ( S ) < 0.\nsi and ti converge to a pair of antipodal points, as in Figure 5(a), or they reach sa and t,, in which case no antipodal points exist as in Figure 4.\nWhen 8(s,) > 0 and (?(sa) > 0, the march starts at sa and t , and moves towards 8 b and t b , respectively, in the same manner. The method has been implemented in the procedure Ant i poda 1 -Convex- March .\nBelow we establish the correctness of the procedure when @(sa) < 0 and 8 ( S b ) < 0.\nLemma 3 In the case e(&) < 0 and e(&,) < 0 of theprocedure Antipodal-Convex-March, si > si+1 and every s E [si+l, s i ) satisfies 8(s) < 0 for all i 2 0.\nProof We use induction. That O(s0) = @ ( S a ) < 0 follows directly from the initial condition. Suppose 8(si) < 0. The normal N ( s ) rotates clockwise as s decreases from si. Also since N ( s i ) x si) < 0 and the normal N(si+l) , if si+l exists, is in the direction of ~ ( s i ) , we know that si+i < s i and\nN ( s ) x r ( s i ) < 0, for all s E (si+l, si). (4)\nBy Proposition 2, T ( S J rotates clockwise as s moves from si to si+l; hence\n(5)\nCombining inequalities (4) and (5) with condition (v) that N ( s ) - ~ ( s ) > 0 over ( S a , S b ) , we infer that\nr ( s i ) x r (s) < 0, for all s E [si+l, s i ) .\nN ( s ) x T ( S ) < 0, for all s E [si+l,si).", "O f ( s*) < 0 must hold.\nThus O(s) < 0 for all s E [si+l, s i ) .\n2.3.2 Endpoint Antipodal Angles with Different Signs\nIn this case, the two antipodal angles O(sa) and O ( s b ) have different signs. At least one pair of antipodal points exists. 0\nLemma states that the sequence * * - 9 defined by To find one pair, we use abisection procedure Antipodal-\n(6) Convex-Bisect. At the found antipodal points S* and t*, either O'(s*) > 0 or O'(s*) c 0. ,~\nis monotonically decreasing and no antipodal point exists - on [si, sb) = U:=~[S~, s l ~ - ~ ) for all i > 0. Suppose the segment S has at least one antipodal point and let s* be 2.3.3 Finding All Pairs of Antipodal Points\nsj+l -s* = f(si>-f(s*) = f ' (s*)(Si-~*)+. .* . the iteration started at s i and ended at s*. That O'(s*) < 0 and O(s*) = 0 imply O(s* - E) > 0 for small enough Below we determine f'(s*). For simplicity, denote the antipodal angle @(si) by 8i. As shown in Figure 5(b), sinei = N ( s i ) x N(si+l). Differentiating both sides of this equation with respect to si yields\ncos& 8'(si) = -tc(si)T(si) x N(si+l) + si) x (-.(si+l)f'(.i)T(si+l))\n= +si) cosei + K(si+l)f'(si)cosei. Let t* be the opposite point of s*. Hence we have\nE > 0. Therefore the interval (sa ,s * - E) contains at least one antipodal point. So we need to invoke the procedure Antipodal-Convex-Bisect(S,, s* - E,ta,t* - s), where t* - 6 is the opposite point4 of s* - E. Similarly, when O(s,) > 0 and O ( s b ) > 0, the interval (s* + E , s ~ ) contains at least one antipodal point. We need to invoke Antipodal-Convex-Bisect(s* + e, sb, t* + 6, tb) .\nSuppose @(sa) and O ( s b ) have different signs. Then S* and t* are found by Antipodal-Convex-Bisect. And O(s* -E) has the sign of O(s,) while O(s* +E) has the sign of 8(sb). The procedure Antipodal-Convex-March needs to be invoked on both intervals ( s a , s* - E) and (s* +E, sb) to search for possible antipodal points.\n.\nNote that the iteration starts at sb where O ( s b ) < 0 So O'(s*) < 0 must hold in the and never passes s*." ] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure5.11-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure5.11-1.png", "caption": "Fig. 5.11. Sources of error for a typical 3D machine", "texts": [ "10 shows an illustration of the working principles of the level sensor. The main objective behind the calibration of a machine tool or Co-ordinate Measuring Machine (CMM) is to determine its positioning accuracy, i.e., to improve the positioning accuracy of the tool within the work zone. This calibration cannot be done directly, but it can be achieved by measuring the six degrees of freedom for each of the three axes, and the squareness between X, Y and Z, for a 3D Cartesian workzone. Thus, a total of 21 sources of error needs to be calibrated as shown in Figure 5.11. This can be a time-consuming process. An assessment of the accuracy, before and after compensation, is usually done via diagonal measurements. As the tool is traversed along a body diagonal of the work zone, all axes must move in concert in order to position accurately along the diagonal. Diagonal measurements are useful in machine tool acceptance testing or in a periodic maintenance program to assess quickly the condition of a machine. Therefore, linear measurements along the work zone diagonals can provide a quick assessment of the overall positioning accuracy" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003733_1.3601523-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003733_1.3601523-Figure8-1.png", "caption": "Fig. 8(b) Contour of the contact surface", "texts": [ " Proceeding in a similar way with points situated on the front part of the contact contour of coordinate y = 0, the points of vanishing cr on the back part of the contact surface and its contour can be obtained. In order to determine the shape of the base behind the contact area with ball, Boltzmann's superposition principle is applied for a second time in the form: 4 The rolling velocity is considerably lower than the velocity of Rayleigh's waves in the base material, so that the inertial resistance can be omitted, comparing with resistance originating from viscosity. 6 Adhesion forces and other superficial interactions are neglected. Fig. 8(a) presents the adopted rectangular coordinate system. A ball of a radius a rolls without slip in the positive direction of z-axis; this is equivalent to the rotation of the ball around its horizontal central axis perpendicular to the velocity and motion of the base in the opposite direction. The base material, until the moment 9 = 0 when it enters into contact with the base at point A, is not strained; it does not correspond to reality but is a consequence of adopting as a model for the base a series of independent columns" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001744_135065004322842799-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001744_135065004322842799-Figure3-1.png", "caption": "Fig. 3 (a) Mesh of the compliant part of the lip, (b) threedimensional mesh of the lip edge, (c) junction between the two-dimensional and three-dimensional meshes", "texts": [ " The analysis of the behaviour of the seal can be made on only one period of this strip, and therefore on a rectangular cell \u2026l, b\u2020. The complexity of the model requires a speci\u00aec mesher. This one puts in connection a two-dimensional mesh for the axisymmetric part and a three-dimensional mesh for the edge of the lip. The developed mesher, which is entirely automatic, uses as inputs the coordinates of a few particular points of the seal, the height h3 of the edge and the size of the cell \u2026l, b\u2020. Figure 3 shows the resulting mesh. Thus, Fig. 3a presents a global view of a three-dimensional\u00b1two dimensional mesh, Fig. 3b points to a three-dimensional part (the lip edge) and \u00aenally Fig. 3c represents the junction between three-dimensional and two-dimensional meshing. The calculation of the compliance matrix necessary for the elastohydrodynamic (EHD) study is done by taking into account the particularities of this mesh. As an example, 2 mm of pre-load leads to a cell length b \u02c6 0.1 mm; the analysis of the defect periodicity of the lip surface gives a cell width l \u02c6 0:0125 mm; the static Proc. Instn Mech. Engrs Vol. 218 Part J: J. Engineering Tribology J02903 # IMechE 2004 at NORTH CAROLINA STATE UNIV on March 18, 2015pij", "comDownloaded from pressure \u00aeeld ps that pushes back the lip is given in Fig. 4; and, \u00aenally, a 0.5 mm height for a threedimensional part of the lip h3 is chosen. The elastohydrodynamic problem is solved on a two-dimensional mesh of this cell. The main hypothesis concerns: (a) a perfectly elastic lip seal, (b) a perfectly smooth rotating shaft, (c) a perfectly centred seal (no whipping). After elaboration of the elasticity matrix from the threedimensional\u00b1two-dimensional mesh of the structure (Fig. 3a), the Reynolds equation is solved, coupled, through the elasticity matrix, to the elastic behaviour of the seal, while controlling the cavitation. The steady state Reynolds equation for an isoviscous \u00afuid q qx rh3 qp qx \u00b4 \u2021 q qy rh3 qp qy \u00b4 \u02c6 6mU qrh qx \u20261\u2020 must be veri\u00aeed for the active zones (zones under pressure). According to the JFO (Jacobson, Floberg, Olsson) model of cavitation [16, 17], this equation is simpli\u00aeed for the non-active zones (cavitation zones), where pressure p is constant q\u2026rh\u2020 qx \u02c6 0 \u20262\u2020 where r represents the density of the lubricant-gas mixture due to the rupture of the lubricant \u00aelm" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000977_10402000108982449-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000977_10402000108982449-Figure1-1.png", "caption": "Fig. 1-Schematic diagram of double decker high precision bearing (DDHPB).", "texts": [ " BASIC CONCEPT AND PRINCIPLE OF OPERATION OF DDHPB The basic concept of the Double Decker High Precision Bearing is to use two pair of rolling-element series one riding on thc other and separated by the rotating intermediate race in bctwccn thcm. The intermediate race acts as an inner race of second scrics of rolling-elements (secondary) and outer race for the first scrics of rolling-elements (primarylfirst), however the outer lace of tlie second series of rolling-elements is mounted in the housing whcreas the inner race of first series of rolling-elements is fittcd on tlic rotating shaft like a conventional bearing. Figure 1 shows thc basic configuration of DDHPB design. Thc inncr race ofthe first series of rolling-elements of DDHPB rotutcs at tlie shaft speed, however, the intermediate race rotates at lowcr spcccl than the inner race due to frictional forces, kinematics nncl configuration of rolling- elements, and slip phenomenon occurring between the races and the rolling-elements. 'This has bcen cstablishecl both by theoretical and experimental investigations. The rotntionnl speed of the intermediate race is determined assuming that the driving torque in both rolling-element rows is cclual" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002690_j.jtbi.2007.07.033-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002690_j.jtbi.2007.07.033-Figure1-1.png", "caption": "Fig. 1. A sketch of the arrangement of a bottom heavy squirmer. Gravity acts in the g direction, while the squirmer has orientation vector e, radius a and its centre of mass distance h from its geometrical centre.", "texts": [ " For example, certain swimming algae are bottom-heavy, enabling them to swim vertically upwards (on average) in still water (see Kessler, 1986). The bottom-heaviness provides the micro-organism with a self-righting mechanism, causing it to move in a preferred direction even if temporarily advected or rotated by the flow in another direction (cf. Pedley and Kessler, 1987). The characteristic time, tC, for reorientation of a spherical bottom-heavy cell was derived by Pedley and Kessler (1987) as tC \u00bc 6m/rgh, where h is the distance of the centre of mass behind the geometry centre (see Fig. 1), m is the fluid viscosity, r is the fluid density and g is the gravitational acceleration. If one assumes values of water for m and r, and h is 10 7\u201310 6m, tC is about 0.1\u201310 s. In this study, we discuss the relation between tC and tR. Micro-organisms in a suspension may experience an unsteady surrounding flow; plankton blooms in the ocean for instance. The influence of turbulence on planktonic contact rates, plankton predation strategies and a plankton foodweb model has been discussed by one of the authors (Lewis and Pedley, 2000, 2001; Metcalfe et al", " The pairwise additivity is an approximation, but it is expected to be justified if the particle volume fraction is not too large (defining semi-dilute). Fsq is the force\u2013torque due to the squirming motion, which is calculated from superposition of the pairwise interactions between squirmers computed with the boundary element method (see Ishikawa et al., 2006). Ftor represents the external torques due to the bottom-heaviness. If the distance of the centre of gravity is h from the centre of the squirmer, in the opposite direction to its swimming direction in undisturbed fluid (see Fig. 1), then there is an additional torque of Ftor \u00bc 4 3 pa3rhe g. (4) For any concentration of particles, there is a relation between the deviatoric part of the bulk stress and the conditions at the surfaces of individual particles. This relation was derived by Batchelor (1970) as P \u00bc IT \u00fe 2mE\u00fe 1 V X S, (5) where IT stands for an isotropic term, and E is the bulk rate of strain tensor. The last term is the particle bulk stress, which is expressed as a summation of the stresslets S in a fluid occupying volume V", " Gbh is the ratio of the gravitational torque to a scale for the viscous torque, assuming that a typical angular velocity is equal to the swimming speed divided by the radius, and is defined as: Gbh \u00bc 2prgah/(mB1). If one assumes that the micro-organisms swim in water at 5 body lengths per second with their centre of mass 0.2a down from the geometric centre, Gbh is about 10 for microorganisms with radius of 12.5 mm, and about 100 for microorganisms with radius of 125 mm. Before discussing the relaxation time in a semi-dilute suspension, we analytically derive it in the dilute limit. As shown in Fig. 1, the gravitational direction is taken as y. When a solitary squirmer with the orientation vector e has an angle of y from the y-axis (see Fig. 1), the rotational velocity O(y) of the squirmer can be given as O\u00f0y\u00de \u00bc mgh sin y 8pa3m . (9) where m is the mass of the squirmer. We assume isotropic random orientation at t \u00bc 0, thus the probability density function of squirmer orientation, p(y, t), is given by p(y, 0) \u00bc 1/4p, where the normalization condition is 2p R p 0 sin yp\u00f0y; t\u00dedy \u00bc 1. p(y, t) needs to satisfy the following Fokker\u2013Planck equation: qp\u00f0y; t\u00de qt \u00bc 1 sin y q qy \u00bdsin yO\u00f0y\u00dep\u00f0y; t\u00de (10) in which there is no term representing rotational diffusion, because the squirmers\u2019 rotation is purely deterministic" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003394_peds.2007.4487699-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003394_peds.2007.4487699-Figure4-1.png", "caption": "Fig. 4. A single turn of an overlapping stator coil of a RFAPM machine.", "texts": [ " A two-dimensional linearised cross-sectional view along the nominal stator radius of only one phase of the overlapping stator coil configuration, with a sinusoidal radial flux density, a coil pitch, Oq, equal to the pole pitch, Op= 2p, a coil position a with respect to the flux density wave and a coil side with of 2A can be represented as shown in Fig. 3. For the analysis we assume that the stator thickness is much smaller than the nominal stator radius, i.e. h < rN allowing us to consider all the turns to be situated on the nominal stator radius. To begin the analysis, we start by looking at a single turn, say 1 and 1' of Fig. 3, as shown in Fig. 4. The flux-linkage for this turn at position d inside the coil, can be calculated as A1= j j Bp sin (Of) rdOdz = 4 Bp cos (ap) cos (6p) rft (1) The total flux-linkage for N number of turns, can be calculated by integrating with respect to d across the entire coil side-width (i.e. between -A and A), dividing by the coil sidewidth (i.e. 2A) to get the average flux-linkage and multiplying the result by N. The total flux-linkage for a typical coil with a wide coil side-width can thus be calculated as follows, AN = 4B cos (aP) cos (0) rLfd6 = pBpIN cos (a 2rnfkA with kA, the flux-linkage factor given by sin (AsP2) k,A=P (2) (3) The maximum coil side-width will be equal to T mechan-~Q ical degrees, i" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000956_3.19783-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000956_3.19783-Figure4-1.png", "caption": "Fig. 4 Domain of maneuverability for the load factor: a) unbounded and b) 0 bounded.", "texts": [ " This can be achieved by rotating the lift-drag plane away from the vertical plane about, V by a certain angle as shown in Fig. 3. This causes / to lie on the projection of P on the plane formed by the y2 axis and Z2 axis, as represented by A in the figure, where e=\u00b1l (24) Hence, the above optimal interior can be obtained by i.e., tan = P^/Pcos7 (25) which is equivalent to the maximum of A \u2022 /. Under this optimal condition P is expressed as P=P1i+Ak (26) that is, it is on the lift-drag plane as shown in Fig. 4a, where a=-di+lk (27) The set of vectors (i, /, k) in Eqs. (26) and (27) represents the unit vectors associated with the Mxyz system. As seen in Fig. 4a, when / varies within constraint Eq. (12), a = ( \u2014 d , l ) describes the domain of maneuverability which is the parabolic drag polar. To maximize H, I has to be selected so that at the terminus of a the tangent to the parabolic drag polar is perpendicular to P. This results in an angle /3 formed between this tangent and the z axis having the same value as the angle 0 formed between P and the x axis. Hence, atan*--. AE* (28) leads to By applying Eq. (25) to the preceding equation, we have /KPKcos (29) (30) If P, with components P7 and A, is inside the angle A7MA2, then the optimal load factor used is an interior load factor as given in Eq. (30). As seen in Fig. 4a, a necessary condition for interior n is that P7 >0, i.e., Py>0. From condition Eq. (18) interior n is used with B arc. In addition, for positive interior n it is necessary that e= l ; for negative interior n, it is necessary that e= - 1. If P is outside the angle A7MA2, then the optimal load factor used is boundary load factor, either / i = \u2014 \u00abmax or n = nmSLX, depending on whether H*>ff2 or H*2>H*lt where H*2=P- with (3D (32) If e > 0, then H*2 > //J, hence n = wmax. If e < 0, then /ff > /fj, hence n= \u2014 nmax", " Otherwise, D ow nl oa de d by U N IV E R SI T Y O F C A L IF O R N IA - D A V IS o n Ja nu ar y 30 , 2 01 5 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 97 83 516 C.-F. LIN J. GUIDANCE interior is used and n is either in the interior or on the boundary as described previously. When 0 = <\u00a3max\u00bb P m tne reduced Hamiltonian Eq .(21) becomes (33) where (34) deduce the adjoint equations of Pv and Py. For interior 0 and interiors, dt 2g+Py -f7 - cos7) Fcos7 that is, it is also on the lift-drag plane as shown in Fig. 4b. As in the first two arcs where <\u00a3 is unbounded, when / varies within constraint Eq. (14), a=(-d, /) describes the domain of maneuverability (Fig. 4b) which is the parabolic drag polar. To maximize //, / must be selected so that at the terminus of a the tangent to the parabolic drag polar is perpendicular to P. This results in an angle /3 formed between this tangent and the z axis having the same value as the angle \u00a3 formed between P and the x axis. Hence, dd (35) dt _ ____ _ JP 7 y rt> - P gnsinfainy (38) In the preceding equations the Hamiltonian integral has been used for simplification. In Eqs. (38), f=l, 0 is given in Eq. (25) and n is given in Eq. (30). For interior 0 and boundary \u00ab, if n = nSJ then the adjoint equations are given in Eqs. (38) with given in Eq. (25). Ifn=M2CL /co, then dt leads to A\u00a3* VPV If P, with components Pl and 0, is inside the angle A7AfA2, then the optimal load factor used is an interior load factor as given in Eq. (36). As seen in Fig. 4b, a necessary condition for interior n is that Pl >0, i.e., PK>0. From condition Eq. (18), interior n is used with B arc. If P is outside the angle A;MA2, then the optimal load factor used is boundary load factor, either n = nmin or \u00ab = \u00abmax defending on whether fF[>H% or H*2 >ff*> where //? and H*2 are defined in Eqs. (31), and a2 is the same as that in Eq. (32). However, now (37) From Fig. 4b, if P is above Pc, then ff* > H*> hence n = n m a x . If Pis below Pc, then H*2 0 and QsO for a finite time interval, there may exist a period of flight with B arc and n = 0 as long as nmin < 0", " At the junction of the different thrust control arcs, the switching function Pv is zero. It suffices to analyze the sign of dPv/dt at Py = 0 to determine the optimal switching. For a junction between two nonsingular thrust arcs, a C-B sequence is optimum if at the junction dP^/d^>0. For a reverse condition, a B-C sequence is optimum. In the case where dPK/d/=0 at the switching point, the optimal switching is determined upon analyzing the high-order derivative of the switching function.13 As seen in Fig. 4, if P^O at the switching point, then boundary n is used. With n on the boundary and PK = 0, by using the Hamiltonian integral we have d/V ~dt~ a//* aK /2gnsin _ gsin dn, * \\ Vcosy cosy dV (40) D ow nl oa de d by U N IV E R SI T Y O F C A L IF O R N IA - D A V IS o n Ja nu ar y 30 , 2 01 5 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .1 97 83 SEPT,-OCT. 1982 3D SUPERSONIC MINIMUM-TIME TURN TO A POINT 517 If n = ns at the switching point, then dn/bV-Q and Eq. (40) becomes Using this equation, a switching from a C arc to a B arc is optimum if 2g 2gnssm (x 2 avec kl < k2. La Fig. 6 montre l'6volution des courbes i=f(E) quand la vitesse du balayage en tension augmente, dans le cas off K1 = Kz, les autres param6tres caract6ristiques des deux r6actions d'oxydation ayant 6t6 choisis identiques fi ceux de la Fig. 5. Les variations des taux de recouvrement en fonction du potentiel sont les m~mes que pr6c6demment. On constate alors que c'est le deuxi6me pic en courant, correspondant \u2022 h la formation du deuxi6me oxyde, qui devient de plus en plus important au d6triment du premier. Malgr6 les diff6rences morphologiques entre les graphes 5 et 6, les courbes i=f(E) traduisent, dans les deux cas, le marne m6canisme r6actionnel d'oxydation de l'61ectrode. Le param6tre exp6rimental v, vitesse de balayage en tension, pr6sente donc toujours une grande importance puisque, A l'inverse du cas pr6c6dent, c'est en diminuant la vitesse du balayage en tension, que l'on pourra s6parer, sur les courbes exp6rimentales, les deux r6actions d'oxydation" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000300_rob.10066-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000300_rob.10066-Figure2-1.png", "caption": "Figure 2. System for simulation.", "texts": [ " Now, consider the function Using (21)\u2013(23), its time derivative satisfies V\u0307 s TKds 1 qP e TDeeqP e 0. Hence s L2 L , qP e L2 L , P L2 , \u0303 L2 L , and \u0303 \u21920 as t\u2192 . Since V is bounded, so are a\u0303 and \u0303r . Since s , \u0307\u0303 , \u0303 , \u0307d , \u0308d\u21920 as t\u2192 , so do r and \u0307r . Therefore, \u0303 \u0302 \u0302d\u2192PTW(\u0307r , r , ) a\u0303 0. Since q\u0303e is the solution of the stable system in (19) with \u0303\u21920, then q\u0303e\u21920. When this result is combined with \u0303 \u21920, then \u0303\u21920. Simulation results will now be presented for a system of two planar arms each with three joints that manipulate a shared object (Figure 2). Each arm has two flexible links and a third rigid link which is cantilevered to the large rigid payload. Bodies B1 , B2 , B4 , and B5 are modeled as an inboard rigid body, a homogeneous, isotropic flexible beam exhibiting inplane bending (with bending stiffness EI), and an outboard rigid body. The mass properties of each body are presented in Table I where m , c , and J are the zeroth, first, and second moments of mass relative to the inboard attachment point of the subbody and is its length. The geared actuators exhibit a lumped rotor inertia each of which is given in Table II", " Other details concerning the modeling procedure and the simulation of the exact motion equations (no large payload approximation) subject to the loop-closure constraint are discussed in ref. 8. The desired trajectory is a circle for the center of the payload with constant orientation. The center of the circle is given by c 0.3 0.75 0 T m and its radius is rc 0.15 m. The payload position around the circle is measured with the angle (t) with 0 corresponding to the \u2018\u20183 o\u2019clock\u2019\u2019 position. This angle is selected so that the first semicircle is an acceleration phase with (0) /2 (roughly the position in Figure 2), \u0307(0) \u0308(0) 0, \u0307(T) 2 /T , and \u0308(T) 0 with (t) ( /2) ( t/T) sin( t/T). The next three full circles are performed with constant angular velocity \u0307 2 /T . The last semicircle is a deceleration phase terminating with (5T) /2 and \u0307(5T) \u0308(5T) 0, with (5T t) (t), 0 t T . For the following study, T 4 s, 0.8, c1 in (15), and Kd c\u2022P( c) TMP( c) in (22), where c 4 rad/s. The value of in the adaptation law is selected to be diagonal with entries given by mm 4 cT\u0302mm where \u0302mm 0 T W \u0307d , d , d Kd 1W \u0307d , d , d dt mm " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001805_elan.200402888-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001805_elan.200402888-Figure6-1.png", "caption": "Fig. 6. Geometric and hydrodynamic conditions in the source channel, in the presence of 2 different source spacer window. Figure to scale. w: width of the source spacer window, s: thickness of the source spacer.", "texts": [ " Thus,Cb st at time t tst td/2 (tst being the accumulation time at which the SWASV stripping is done) can be determined from ip (using the calibration plot). The flux through the PLM membrane depends on diffusion conditions in the source phase, in the membrane and in the strip solution . In particular, the source spacer window may play a role by modifying the hydrodynamic conditions in the source solution [1, 19]. The effect of this factor was studied by measuring the transport of Pb and Cd at various s/w ratio of the source spacer window where s andw are the thickness of the source spacer and the width of the window, respectively (Figure 6). The time evolution of F at these two different s/w ratio (0.13 and 0.29) are shown in Figure 7A and 7B for Pb and Cd, respectively. It can be seen that the transport of lead depends strongly on the aspect ratio while the transport of Cd is independent of s/w in this studied range. This is consistent with the transport properties through the PLM of these two metals: due to the low partition coefficient of Cd between the source solution and the PLM phase, its transport has been shown to be limited by the diffusion of the metal-carrier complex in the PLM membrane [19]", " In presence of the source spacer, the time needed to clean the gel corresponds well to the theoretical time required for Electroanalysis 2004, 16, No. 10 \u00b9 2004 WILEY-VCH Verlag GmbH& Co. KGaA, Weinheim the metal ions to diffuse out of this 280 m thick gel. In contrast, in the absence of a spacer, the rinsing time is longer. When rinsing of the strip solution was stopped after 10 min, an increase of the SWASV peak current was observed. This is attributed to the fact that in such configuration, the strip solution penetrates between the strip spacer and the PLM membrane (Figure 6). The corresponding metal ion then diffuses back, slowly, in the strip compartment during the cleaning step. The systemwas testedwith naturalwater samples fromLake of Lucerne (Switzerland). The samples were filtered through 0.45 m Millipore filter immediately after sampling and 1 l of each sample were used for PLM measurements with the microcell using accumulation time of ca 1 hour. The total metal concentrations were determined by ICP-MS after acidification of filtered samples. PLM measurements were made without a source spacer with 9" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000453_bf00790139-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000453_bf00790139-Figure3-1.png", "caption": "Fig. 3. Polar plot (for ~0 = O) stable (PTS) and unstable (PTU) perturbation grajectories", "texts": [ ")] + iyb@, A;o ~ z@, A ~ ( 1 - - @)[(1 + ~)(1 + go) -- 1 ] - - (1 + z ) ( l + go + yyo@) + 1 -- z + i{vv[(1 + z) (1 + zb) -- 1] -- (1 + g)yova}. Note t ha t ~* = ~* + i~* where ~*(v), W*(v) are the coordinates of point G in the O~W sys tem during their s t a t ionary ro ta t ion with the angular veloci ty ~. These formulas m a y be t rea ted as pa ramet r i c equat ions of the curve called the polar plot in which the angular veloci ty is a pa ramete r . For very l ight damping (y ~ 1) the polar p lot is a curve similar to a circle (Fig. 3). The m a x i m u m shaft, deflection is equal to Ir -- ;~[. Let us introduce small variations in the equilibrium points (~*, ~ , a*) and observe their evolution in time. Then we substitute r = ~* + r ;0(~) = ;3 + ~(~) , ~(v) = ~* + ~(~) into (6) -- (8). Here ~(r) , ~ = 1, 2, 3 are small perturbations which must satisfy the homogeneous equations @~1 + (y~ + 2i@)~1 + ( 1 - @ + i 7 ~ ) ~ 1 - ~ 2 - ~s = 0 , (12) - - ~ + r + flur + (1 + u) r = 0. (14) They have been derived in consideration of (9)-(11) . If their solutions are non-increasing or increasing functions of time, the stat ionary motion of the rotor is either stable or unstable. At the limit of stability the perturbations preserve constant (initial) values dependent on external forcing impulses. In a polar plot the perturbat ion is interpreted as a jump of a representative point to the small orbit with an instantaneous radius of ~ and point ~* as the center (see Fig. 3). The solution of (12) - (14) may be found in the form r = Z, e i~r (r162 = 1, 2 , 3 ; Z~, 2 constants). This frequency equation yields @(,t + 1) 2 - 1 - i7~(2 + 1) 1 1 det - 1 1 + ~ +iy~v(2 + 1) 1 J = 0 . (15) - 1 1 1 + ~ + i/%~ This is a fourth-order equation with respect to L The l~outh-Hurwitz criterion applied in this case is cumbersome because of the complex character of the coefficients of the equation. Instead, another procedure will be applied. As mentioned above, the roots ~ of (15) are generally complex numbers 2 = 2R + i2r, hence " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000281_iros.1998.724592-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000281_iros.1998.724592-Figure1-1.png", "caption": "Fig. 1 The kinematic model of skid-steer type mobile", "texts": [ ",( 1) time-optimization problem for trajectory along specified paths and (2) global and local path search problem, then we propose two methods to solve each problem, using an idea of path parameter and B-spline function. Finally, we obtain quasioptimal path for the original problem, by combining the two algorithms. Numerical simulations are presented to confirm a validity of the proposed method. 2 Problem formulation Assuming no slip of two tires and defining the state variable x= (z,y,B, U,, vi,v, $T, the state equation based on the kinematics of skid-steer type mobile robots (see Fig.1) is expressed by j. = vcose (1) y = vsine (2) (3) U, = \u2018Ur (4) i i l = U1 ( 5 ) where C(z, y) is the reference point which is the center of the axle, 0 is the orientation of the robot, v is the velocity a t point C, 4 is the angular velocity of the robot, FY is the distance between two wheels, and U,., vi, U,, ui are the velocities and accelerations of right and left wheels. - 32 robots. Due to the limits of velocity for two wheels, state constraints are lor1 5 urnax, 1.61 i Vmax (8) Another state constraints due to obstacle avoidance is described as where X,(t) is the space occupied by the robot a t the time t, and X O is the one occupied by the obstacles" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001209_tia.2003.808977-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001209_tia.2003.808977-Figure2-1.png", "caption": "Fig. 2. Relative positions of v , i , , and \u0302 in the motoring mode (P = 1, ! > 0). (a) (k) > \u0302(k); (k) > 0. Multiple shot view of vectors v , i , , and \u0302 when R > 0. (b) v\u0302 (k) R\u0302 i\u0302 (k) > 0 ) i(k) > 0 Due to R T i with R > 0, \u0302 (m+ 1) lags behind \u0302 (m).", "texts": [ " Similarly, implies that the signs of the torque and the frequency of the stator flux are different, i.e., the motor will be in the regenerating mode. Lemma 1: Assume that the motor is running in a positive direction with positive -axis currents, i.e., and for . Assume that . If , there exists an integer such that satisfies for . Proof: The positive -axis current implies that the current vector leads the flux vector . Since , it follows from (4) that . It also follows from (18) and (19) that Hence, we obtain a vector diagram as shown in Fig. 2(a). Considering , one can notice from the geometrical relation that the incremental angle between the real fluxes is larger than the incremental angle between the estimated fluxes, i.e., (22) The above result holds for some period starting from Therefore, it follows that for Remark: Lemma 1 describes local phenomena starting from the initial condition at . It cannot be global since the dynamic relationship of induction motor between the voltage and the current is basically nonlinear. With the definition of , one can state the Corollary as follows. Corollary 1: Assume that . If and , then there exists an integer such that for . In Lemma 1, the sign of angle error is investigated. However, in the following Lemma, we will consider the sign of the flux magnitude error. Henceforth, we assume that for since it is very rare for to be negative. Lemma 2: Assume that . If , , there exists an integer such that for . Proof: For the convenience of proof, let us assume that in Fig. 2(a). Then, it is obvious that . Claim 1: Assume that , , and are rotating at the same angular speed and that and . Assume that . Further, if , , then . Proof: Since the above conditions satisfy the conditions of Lemma 1, inequality (22) holds, i.e., the incremental angle of is less than that of . In other words, , , and rotate by , while rotates by less amount . If we draw the vectors in the rotating frame which are synchronized with and , locates behind as shown in Fig. 2(b). From the geometrical point of view, the projection quantities of and on are the same by assumption. However, if we project the same ones on , then obviously we have the result. Remark: Due to the continuity of the dynamical system properties, the above result can be extended to the following Corollary. Corollary 2: Assume that , , and are rotating at the same angular speed and that their magnitude does not vary drastically. Assume that . Further, if , , then there exists an integer such that for " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002192_bbpc.19730771029-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002192_bbpc.19730771029-Figure1-1.png", "caption": "Fig. 1 Schematic diagram of the total reflection at a Sn0,-aqueous electrolyte interface. 6: the penetration depth, 4: the angle of light incidence", "texts": [ " The existence of the intermediate semiquinonediamine in solution (\u201cWurster\u2019s Red\u201d) is well established by its intense absorption and its radical nature in dilute solutions has been established by ESR-measurements [9]. The normal potentials of the two oxidation steps, however, are still unknown, which is probably due to the chemical \u2018instability of the diimine. RT F RT F [l-41. Principle of ATR-measurement [ 101 The attenuated total reflection technique at transparent electrodes is based on the fact, that totally reflected light also penetrates into the optical medium with the lower refractive index, as schematically shown for an SnOz/electrolyte interface in Fig. 1. The penetration depth is of the order of the wavelength and depends on the angle of incidence. The .reflected intensity is reduced, if an absorbing species is present within the range of the penetrating light beam. In the case of relatively weak absorption a simplified relationship between the absorption signal and the concentration of absorbing molecules is valid as given by [l 11 : AJ 2~ ? where AJ is the absorbed light intensity; J o the reflected light intensity, if no absorption occurs; E is the extinction coeficient; c(x) is the concentration of theabsorbing species, x is the distance from the interface; S is the penetration depth of light without absorption and @ is the angle of light incidence" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001286_s0003-2670(01)01347-2-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001286_s0003-2670(01)01347-2-Figure1-1.png", "caption": "Fig. 1. Representation of the flow cell, adapted from Taylor [12].", "texts": [ " The voltammetric measurements were made at room temperature, without thermostatic temperature control. The flow system used consisted of a Gilson Minipuls 3 Peristaltic Pump, using 1.52 mm i.d. PVC tubing in the pump and PTFE carrier tubing of 0.8 mm i.d. and 1.6 mm o.d. to deliver the solution to the voltammetric HMDE flow cell. Samples were injected by a Rheodyne four-way valve, model 5041; a 500 l loop was used for injection of the sample. The voltammetric flow cell used in this work was adapted from that developed by Taylor [12]. A schematic representation of the flow cell is shown in Fig. 1. In this cell, the glass capillary is inserted into a PTFE adapter head and the flow is directed towards the mercury drop. This adapter head allows a more reproducible repositioning of the glass capillary to be made whenever the flow cell is dismounted and then remounted. The adapter head together with the reference electrode and the counter electrode are contained in a glass cell which was filled with the solution used as the carrier stream. A drain ensures a constant level of solution to be maintained during the work", " On the other hand, the use of higher square wave frequencies decreases the interference of oxygen, because the increase of the reduction signal of oxygen is much smaller than the increase of the reduction signal of the adsorbed DMQ. The observations above were born in mind in developing a flow injection square wave cathodic stripping voltammetric method for the determination of diacetyl. The adsorption step at the HMDE is performed whilst the sample solution slug is flowing through the injection head (Fig. 1). The square wave voltammetric scan was performed also under flow conditions, as it was observed that the flow of solution caused no perturbation of the signal. Interference owing to oxygen present in the flowing solution was shown to be minimal. The length of the tube between the injection valve and the HMDE was kept as short as possible in order to minimise dispersion of the injected sample, and to keep the injected slug as intact as possible. That this was achieved is evident from the results shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003435_te.2007.906612-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003435_te.2007.906612-Figure2-1.png", "caption": "Fig. 2. Double-inverted pendulum.", "texts": [ " The topics covered are proportional-integral-derivative (PID) control design and tuning based on Bode plots, state-space feedback control based on pole-placement and LQR/LQG optimal controllers, observer design based on pole-placement and Kalman filtering, as well as state machines using the Stateflow toolbox in Simulink. Every week the students can make progress on the IP experiment, but they have not learned all the required theory to reach the final solution before the fifth week of lectures. One benefit of the IP hardware is that it can replace a series of smaller disconnected experiments. All the different controllers and the theory are connected together in this larger project. The students need all of the individual elements taught in the lectures in order to solve the overall goal of the experiment. Fig. 2 shows the hardware used in the IP experiment. The actuated joint is controlled by an electrical servomotor and the angle is measured by a digital encoder. The free joint has no actuation, but the angle of the free joint is also measured by a digital encoder. A counterbalance mass is used to counteract the gravity acting on the pendulum. A lightweight carbon fibre arm is used as the pendulum, with a steel mass of 50 g being placed at the tip as illustrated in Fig. 2. The IP is modelled as a planar elbow manipulator using the Euler\u2013Lagrange equations as in Chapter 7 of [17]. The dynamic model has the following form: (1) where, in the case of the IP experiment presented in this paper, the inertia matrix and the centripetal and Coriolis matrix both have dimensions 2 2 and both contain nonlinear functions such as and , where is the angle of the free joint. The gravity vector , the viscous friction vector and the torque input vector all have dimension 2 1. Since the IP is only actuated at the first joint, the second element of the vector is zero" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003997_1.4002089-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003997_1.4002089-Figure2-1.png", "caption": "Fig. 2 Parametrization of inde", "texts": [ " To this end, the linear stability analysis of a two-axle IRW truck is first performed, and the vibration characteristics of IRW truck are investigated with the model that considers the independent wheel rotations. The results are compared with those obtained using the multibody dynamics IRW model developed using the velocity transformation method. This multibody dynamics IRW model is used for evaluating the curving performance, and effects of the longitudinal creep forces on the dynamics of IRW are discussed. 2.1 Wheel and Rail Coordinate Systems. In this section, equations of motion of an IRW are derived. As shown in Fig. 2, two independent wheels are connected to an axle by revolute joints. The global position vectors of the axle and wheels are, respectively, defined as ra = Ra + Aau\u0304a rwk = Rwk + Awku\u0304wk, k = 1,2 1 where k=1 for the right wheel and k=2 for the left wheel. The vector R is the global position vector at the origin of body coordinate system, the matrix A is its orientation matrix, and u\u0304 is the local position vector defined in the body coordinate system. In order to determine the location of the point of contact on wheel body w, a complete parametrization of the surfaces must be used 9 " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002741_imece2007-41351-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002741_imece2007-41351-Figure1-1.png", "caption": "Fig. 1. Vericut simulation of a five-axis milling operation on a jet-engine impeller.", "texts": [ " \u03c6p j, pitch angle for flute, j \u03c6st q, , \u03c6ex q, start and exit immersion angle pair for engagement, q , at height, z \u03c8 z( ) lag angle of cutting flute at height, z , due to cutter\u2019s helix \u0394\u03b8i total angle swept out by the tool axis vector in tool path segment, i \u03b8s z( ) feed coordinate shift angle at height, z ownloaded From: http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ash \u03c9i angular velocity at tool path segment, i Jet engine impellers are flank milled on five-axis CNC machining centers as shown in Fig. 1 In order to maintain tangential contact between the ruled surface of the blade and the tapered, helical, ball-end periphery of the cutter, the flank milling process requires three translational and two rotational degrees of freedom. The jet engine impellers are made from titanium or nickel alloys due to their high mechanical and thermal strength. The thin webs of the impeller, the strength and low thermal conductivity of the workpiece material present difficulties during flank milling of the part" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000956_3.19783-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000956_3.19783-Figure3-1.png", "caption": "Fig. 3 Optimal aerodynamic force.", "texts": [ " In the domain of maneuverability, this optimal condition leads to the selection of the optimal a such that the projection of a on P is maximized. For this, the four different arcs of the aerodynamic control are 1) interior bank angle and interior load factor, 2) interior bank angle and boundary load factor, 3) boundary bank angle and interior load factor, and 4) boundary bank angle and boundary load factor. For the first two arcs where is unbounded, the aeodynamic control law requires that a, whose terminal point touches a plane which is tangent to E and concurrently perpendicular to P, be obtained (Fig. 3). In order to satisfy this optimal condition, the following procedure is considered. First, a plane which is tangent to E and contains a point in contact with the terminus of a is always perpendicular to the lift-drag plane. Therefore, in order for this plane to be perpendicular to P to satisfy the preceding optimal condition, the lift-drag plane must contain P. This can be achieved by rotating the lift-drag plane away from the vertical plane about, V by a certain angle as shown in Fig. 3. This causes / to lie on the projection of P on the plane formed by the y2 axis and Z2 axis, as represented by A in the figure, where e=\u00b1l (24) Hence, the above optimal interior can be obtained by i.e., tan = P^/Pcos7 (25) which is equivalent to the maximum of A \u2022 /. Under this optimal condition P is expressed as P=P1i+Ak (26) that is, it is on the lift-drag plane as shown in Fig. 4a, where a=-di+lk (27) The set of vectors (i, /, k) in Eqs. (26) and (27) represents the unit vectors associated with the Mxyz system" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003153_s00170-007-1028-6-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003153_s00170-007-1028-6-Figure2-1.png", "caption": "Fig. 2 a, b, Constructional solutions of the PGTs used to extend the constant power range. c An example of spindle gearbox based on the PGT of Fig. 2b", "texts": [ " In particular, the two spindle gearbox configurations used by manufacturers are studied for all the marketed range of powers and speed ratios, and the optimal designs of these configurations are given and compared for all that range. In this section we explain some important considerations that must be taken into account for spindle gearbox design. The members of PGTs are of three types, depending on their movements and links with other members. In the present work, they will be called suns, arms, and planets. Two different PGT configurations are used by spindle gearbox manufacturers. They are shown in Fig. 2a and b. In these figures, members 1 and 2 are the suns, 3 is the arm, and 4 and 4\u2032 are the planets. 2.1 Economic and operating considerations The spindle gearbox configuration of Fig. 2b has the advantage of being more interesting economically, since it does not include a ring gear. The reason is that spindle gearbox gears must be hardened, tempered, and ground to avoid high heating, and a ground ring gear is more expensive than a non-ground ring gear. Also, if the ring gear is not ground, heat buildup will occur more quickly, and this heating limits and reduces the input speed and torque. 2.2 Efficiency considerations Another interesting consideration in spindle gearbox design is that it is possible to prove that the efficiency of the reducers based on these two PGT configurations is greater if they are designed with the input being the sun member. This is why all spindle gearboxes are designed as reducer PGTs with the sun (member 1) as input and the arm (member 3) as output, as shown in Fig. 2a and b. 2.3 Planet member considerations In spindle gearbox design, it is quite important to choose an optimal number of planets for the required power and speed ratio. In this context, the number of planet members in a PGT (Np) is the number of these members that are arranged around the PGT\u2019s principal axis. For example, the commercial spindle gearbox shown in Fig. 2c has two planet members, i.e., Np=2. This number must be as small as possible to reduce the weight and the kinetic energy of the transmission, while ensuring a good distribution of the load to each of the planet gears. This number can be two, three, four, or even more, depending on the application. Whichever the case, the planets must always be arranged concentrically around the PGT\u2019s principal axis to balance the mass distribution. This section describes the constraints in spindle gearbox design", "1 Constraints involving gear size and geometry The first constraint is a practical limitation in the range of acceptable face widths b. This constraint is as follows: 9m b m \u00f01\u00de where m is the module. All the kinematic and dynamic parameters of the transmission depend on the values of the tooth ratios Znl,, where Znl is the tooth ratio of the gear pair formed by the linking members n and l. In particular, Znl is defined as: Znl \u00bc Zn Zl \u00f02\u00de For the definition of the tooth ratios to satisfy the Willis equations, Znl must be positive if the gear is external and negative if it is internal [5]. For the train of Fig. 2a, one would have to take Z14>0 and Z24\u2032<0. In theory, tooth ratios can take any value, but in practice they are limited mainly for technical reasons because of the difficulty of assembling gears beyond a certain range of tooth ratios. In this work, the tooth ratios considered for the design of spindle gearboxes are quite close to the recommendation of M\u00fcller [6] and the AGMA norm [7]. They are: 0:2 < Znl < 5 \u00f03\u00de 7 < Znl < 2:2 \u00f04\u00de where the constraint of Eq. (3) is for external gears, and that of Eq. (4) is for internal gears. In this way one also ensures that there exists no interference between the gears. Another constraint that will be imposed is on the ratio of the diameters of the gears constituting the planets (members 4 and 4\u2032): 1 3 < D4 D0 4 < 3 \u00f05\u00de Other relationships must be satisfied as a consequence of the geometry of these PGTs. For example, in the PGT of Fig. 2a the tooth ratios Z14 and Z24 are related to the radii of the gears constituting the planets. In particular, the following geometric relationship must be satisfied: R1 \u00fe R4 \u00bc R2 R0 4 \u00f06\u00de Expressing the above equation in terms of the module of the gears, it is straightforward to find that the ratio of the diameters of gears 4 and 4\u2032 conditions the value of Z14 and Z24\u2032. This ratio is: R0 4 R4 \u00bc Z14 \u00fe 1 Z240j j 1 \u00f07\u00de Likewise, for the case of the PGT of Fig. 2b one obtains the expression: R0 4 R4 \u00bc Z14 \u00fe 1 Z240 \u00fe 1 \u00f08\u00de Lastly, one assumes a minimum pinion tooth number: Zmin 18 \u00f09\u00de 3.2 Planetary gear train meshing requirements The meshing requirement for equally spaced planets with the configurations of Fig. 2a and b is given by the AGMA norm [7], and is: Z2P2 Z1P1 Np \u00bc an integer \u00f010\u00de where Z1 and Z2 are the number of teeth on members 1 and 2, respectively, and P1 and P2 are the numerator and denominator of the irreducible fraction equivalent to the fraction Z 0 4 Z4, where Z 0 4 and Z4 are the number of teeth on the planet gears (see Fig. 2): Z 0 4 Z4 \u00bc P1 P2 3.3 Contact and bending stresses The torques on each gear of the proposed spindle gearbox designs were calculated taking power losses into account. This aspect allows one to really optimize the spindle gearbox design, unlike optimization studies in which these losses are not considered [8, 9]. The procedure for determining the torques and the overall efficiency of the spindle gearbox is described in [10]. For each of the gears, the following constraints relative to the Hertz contact and bending stresses must be satisfied: sH < sHP \u00f011\u00de sF < sFP \u00f012\u00de For the calculation of the gears, the ISO norm was followed", " Various works have presented methods for the optimization of a conventional transmission [11\u201320], but only a few for the design of PGTs [8, 9]. Furthermore, none of the latter studies calculate exactly the torques to which each of the gears is subjected, since they do not consider the power losses in the different gear pairs of the PGT. This question is taken into account in the present work to ensure an optimal spindle drive gearbox design. For an optimal spindle gearbox design, the kinetic energy must be minimal. In mathematical terms, for the gearboxes designs based on Fig. 2a and b, the following objective function must be minimized: KE \u00bc 1 2 I1w 2 1 \u00fe 1 2 Np m4 \u00fe m40\u00f0 \u00dev24 \u00fe 1 2 Np I4 \u00fe I40\u00f0 \u00dew2 4 \u00f017\u00de where Ii is the moment of inertia, wi is the rotational speed, mi is the mass, vi is the translation speed (center of the gear) of member i, and Np is the number of planet gears. In Eq. (17) the energy of the arm has been neglected because this member can be designed in different and variable forms, and because it is considerably less than that of the planetary system", ", different speed ratios and powers) covering all the marketed range. Table 1 lists these designs and an alphanumeric identification code. In this code, the letter identifies the speed ratio, and the number the nominal output torque and the maximum input speed. For example, code D3 represents the spindle gearbox with a speed ratio of 4.5:1, 2,300 Nm of nominal torque, and a maximum input speed of 6,500 rpm. Tables 2 and 3 summarize the results for the optimal spindle gearbox designs based on the different constructional solutions of Fig. 2a and b, respectively. In these tables, the first column gives the specific spindle gearbox design according to the code given in Table 1. The second, third, and fourth columns give the helix angle, the module and the face width of the gears corresponding to the gear pair formed bymembers 1 and 4, respectively. The following three columns give the same information for members 2 and 4\u2032. The eighth and ninth columns give the tooth number of each member for the optimal spindle gearbox design. Finally, columns ten to thirteen give the kinetic energy, the moment of Table 2 Optimal spindle gearbox designs based on the constructional solution of Fig. 2a \u03b214 m14 (mm) b14 (mm) \u03b224\u2032 m24\u2032 (mm) b24\u2032 (mm) Z1/Z4 Z2/Z4\u2032 KE (J) J (kg mm2) Vol. (\u00d710\u22123 mm3) (mm) A1 19.5 1.5 21.00 26.1 1.25 13.95 20/ 22 88/40 47 455 452 128.3 A2 19 2 18.00 21.8 1.25 11.25 20/ 22 121/ 55 68 1,165 609 162.8 A3 30 2.5 22.50 27 2 19.20 20/ 22 99/45 248 6,318 1,617 222.2 A4 26.5 2.5 35.00 23 2 24.45 20/ 22 99/45 299 7,452 2,159 215.0 B1 29 1.5 21.00 29 1.5 13.50 18/ 18 60/24 23 204 287 102.9 B2 5 2 28.00 29.3 1.5 13.93 18/ 18 70/28 29 449 478 120.5 B3 21 2.5 35.00 29.4 2 22.50 18/ 18 70/28 87 2,030 1,165 160", "12 22/ 40 110/ 50 85 2,148 822 172.6 F2 27.8 1.5 21.00 19.7 1.5 14.90 22/ 40 121/ 55 77 3,450 1,048 192.8 F3 0 2.5 31.90 21.7 2 23.25 22/ 40 132/ 60 388 25,153 3,498 284.2 F4 20 2.5 35.00 24.6 2.5 24.75 22/ 40 110/ 50 538 34,754 4,291 302.4 inertia, the volume, and the diameter of the optimal spindle gearbox design, respectively. For example, for the A1 design (speed ratio 3:1, nominal torque 230 Nm, and maximum input speed 8,000 rpm), the optimal spindle gearbox design based on the configuration of Fig. 2a has Z1=20, Z4=22, Z2=88, and Z4\u2032=40. The helix angle of members 1 and 4 is 19.5\u00b0, the module is 1.5 mm, and the face width 21.00 mm. For the other gear Table 3 Optimal spindle gearbox designs based on the constructional solution of Fig. 2b \u03b214 m14 (mm) b14 (mm) \u03b224\u2032 m24\u2032 (mm) b24\u2032 (mm) Z1/Z4 Z2/Z4\u2032 KE (J) J (kg mm2) Vol. (\u00d710\u22123 mm3) (mm) A1 27.5 1.5 21.00 27.5 1.5 17.04 18/ 36 36/ 18 234 965 692 152.2 A2 0 2 25.92 0 2 21.60 18/ 36 36/ 18 566 2,338 1,209 180.0 A3 12 2.5 35.00 12 2.5 29.44 18/ 36 36/ 18 796 8,427 2,667 230.0 A4 30 2.5 35.33 30 2.5 29.09 18/ 36 36/ 18 1,305 13,814 3,414 259.8 B1 14 1.5 13.50 30 1.5 13.60 18/ 45 36/ 20 248 1,474 754 166.8 B2 0 2 24.48 27.3 2 18.00 18/ 45 36/ 20 462 4,898 1,556 216.0 B3 12 2.5 35.00 29", "8 F3 28 2.5 22.50 20 2 27.96 18/ 36 18/ 54 695 7,937 2,572 254.8 F4 26 3 27.00 4 2.5 34.73 18/ 36 18/ 54 1,613 18,455 4,375 300.4 pair, i.e., for members 2 and 4\u2032, the results are helix angle 26.1\u00b0, module 1.25 mm, and face width 13.95 mm. Likewise, the optimal designs for the 24 different spindle gearboxes studied are given for both configurations (Tables 2 and 3). Note that by comparing the results of these two spindle configurations one observes that the kinetic energy of the designs based on Fig. 2b is always greater than that of the designs based on Fig. 2a. Also, the moment of inertia, the volume, and the total diameter of the Fig. 2b based designs are also almost always greater than those of the designs based on Fig. 2a. Nonetheless, it is important to bear in mind that for the greatest reduction ratio, i.e., 5:1, the moment of inertia is always greater in the designs of Fig. 2a, and the volume and the total diameter are also greater in two of these designs. Table 4 summarizes the comparison between the optimal designs of these two configurations. In particular, for each speed ratio, Table 4 gives the ratios between the averages of the kinetic energies (KE(b/a)), moments of inertia (J(b/a)), volumes (Vol(b/a)), and diameters ( (b/a)) of the designs based on Fig. 2a and b, respectively. Analyzing the information of Table 4, it is important to note that even though the kinetic energy is always greater in the designs of Fig. 2b, the two spindle gearbox designs are really not so different mechanically, as one observes from the ratios between their moments of inertia (J(b/a)), volumes (Vol(b/a)), and total diameters ( (b/a)) of the two optimal designs. The reason that the ratio between the kinetic energies is higher than the other ratios is that for a given speed ratio, the planets of the gearbox design of Fig. 2b have higher rotation speeds. Figure 3 shows a comparison between planet speeds and input speeds for the two optimal spindle gearbox configurations. With these results, one can now evaluate the best alternative for a specific spindle gearbox design. The first factor to analyze is the speed ratio, since certain values of this factor involve greater differences between the two configurations. Indeed, one sees in Table 4 that the speed ratios of 3.5:1 and 4.75:1 have a high value of KE(b/a), especially in the case of the 3.5:1 ratio. In this case, too, the ratios J(b/a), Vol(b/a), and (b/a) are high. For these designs, therefore, the most suitable configuration is that of Fig. 2a. On the contrary, the 5:1 speed ratio has the smallest KE(b/a) ratio, and even the ratios J(b/a), Vol(b/a), and (b/a) are less than unity. In these cases, therefore, the most favourable design is that based on Fig. 2b, with the added advantage of its lower cost. In sum, the results show that the final decision on the optimal spindle gearbox configuration depends on its specific characteristics (maximum input speed, nominal output speed, and speed ratio) and on the cost of the configuration, since not using a ring gear makes the designs based on Fig. 2b less expensive. Hence, in general, when the ratios KE(b/a), J(b/a), Vol(b/a), and (b/a) are not very high, the appropriate spindle gearbox design will be that of Fig. 2b, whereas if those ratios are high, then the appropriate design will be that of Fig. 2a. Finally, we calculated the overall efficiencies of all the proposed spindle gearbox designs for different ordinary efficiencies [10] in order to verify that they were optimal. This is a necessary step in PGT design since they can present power recirculation, and this phenomenon is notorious for severely reducing the efficiency [5]. The results are summarized in Table 5. To conclude this work, we performed several experiments. In the first experiment we compared two different spindle gearboxes of different manufacturers, one based on the configuration of Fig. 2a and the other on the configuration of Fig. 2b. The characteristics of the two spindle gearboxes (given by manufacturers) were: 3:1, 630 Nm, 6,000 rpm, and 1,980 kg mm2 for the spindle based on Fig. 2a; and 3:1, 620 Nm, 6,000 rpm, and 3,250 kg mm2 for that based on Fig. 2b. The kinetic energy of each spindle gearbox for the maximum input speed (6,000 rpm) was determined. We obtained a kinetic energy of 79 J for the design based on Fig. 2a and 696 J for the design based on Fig. 2b. This means that the commercially available spindle gearboxes (design A2) used in the experiment have greater kinetic energies than that of the spindle gearbox optimized for minimum kinetic energy (see Tables 2 and 3). In particular, they are 16% greater for the Fig. 2a design and 23% greater for the Fig. 2b design. In other works, changing the configuration design of these commercial spindle gearboxes to that of given in Tables 2 and 3, while maintaining the bearing types, bearing location, spindle shaft dimensions, etc., a design with less kinetic energy can be obtained, in particular the minimum kinetic energy design (designs given in Tables 2 and 3). Another test was to measure the vibrations in each spindle gearbox for different machining conditions. For this purpose, an accelerometer was placed in each spindle gearbox, and the signals from the accelerometers were processed and logged via a data acquisition card connected directly to a PC. Then, the RMS value of the recorded vibration signals was determined. Subsequently, the means (RMS a\u00f0 \u00de and RMS b\u00f0 \u00de) of the RMS values for each spindle gearbox were calculated. The value of the ratio (RMS b=a\u00f0 \u00de) was found to be 1.112. In other words, the vibrations were 11.2% greater in the design based on the configuration of Fig. 2b. Finally, we conducted another experiment where we designed two spindle gearboxes that were manufactured by a company specializing in the fabrication and assembly of mechanical transmissions. The specific design chosen was D2, and the configuration that of Fig. 2b. One gearbox was optimized by minimizing the volume and the other by minimizing the kinetic energy. The design corresponding to the minimum kinetic energy is given in Table 3 (D2). The characteristics of the minimum volume design were: 807 J, 5,930 kg mm2, and 1,380\u00d710\u22123 mm3. The ratio between the kinetic energy of the minimum volume design and the minimum kinetic energy design at their maximum speed (8,000 rpm) is 1.15. With these two transmissions, another test to measure the vibrations was conducted", " The level A is for \u201cnew machines\u201d, the level B is for \u201cunlimited long-term operation allowable\u201d, level C is for \u201cshort term operation allowable\u201d and level D when the \u201cvibrations cause damage\u201d. Previously to this determination, the machine must be classified in one of the four groups established by the norm depending on the type of installation and the power of the machine, since the range for each vibration level depends on this classification. Of the two commercial spindle drive gearboxes, one was classified in the highest values of the level A (the design based on Fig. 2a) and the other one in the lowest values of the level B (the design based on Fig. 2b). The two gearboxes designed by us, were classified in the level A. This method is also used in [21] to determine the condition of spindle drives analyzing and classifying the vibrations obtained with these ISO-Norms. This paper has presented the methodological framework for determining an optimal spindle gearbox design. The method was applied by designing 24 different industrial spindle gearboxes used in industry. Experiments demonstrated that the proposed method is indeed appropriate for this task", " The following summarized conclusions can be drawn from the results: \u2013 The constructional solution of the planetary gear train used in the design of a spindle gearbox and its kinetic energy affect the functionality of spindle gearboxes, hence the design of these planetary gear trains must be optimized. \u2013 The final decision on the optimal spindle gearbox configuration will depend on its specific characteristics (maximum input speed, nominal output speed, and speed ratio) and on the configuration cost. \u2013 A general rule for this decision is that: if for an specific spindle gearbox design the ratios KE(b/a), J(b/a), Vol(b/a), and (b/a) are not very high (compare with the information given in Tables 2, 3, and 4), the appropriate spindle gearbox design is that of Fig. 2b, whereas if they are high, the appropriate design is that of Fig. 2a. In the authors\u2019 opinion, these results could be of great interest for manufacturers and engineers involved with the marketing and design of spindle drive gearboxes. Acknowledgements The authors wish to express their gratitude to Redex-Andantex Inc. for their collaboration and interest in this project, as well as P. Rebolledo for his valuable help. The financial support of this work by the Plan Nacional de I+ D of the Ministerio de Ciencia y Tecnologia of the Government of Spain is gratefully acknowledged" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000481_28.993169-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000481_28.993169-Figure5-1.png", "caption": "Fig. 5. Lamination of a round-stator PM motor.", "texts": [ " This has negative influence on steady-state performance of the motor because a wider air gap decreases the flux density and rated power of the motor. PM MOTOR Another way to build a small single-phase PM machine is to take a round stator, as is the case in most other machines. A round-stator motor can be built with two phase windings, which eliminates the need for a position sensor for starting purposes. In this section, the performance of a round-stator single-phase PM motor, the stator lamination of which is shown in Fig. 5, is calculated and compared with measured data. In order to allow comparison with a U-core motor, the round-stator motor is built around the same rotor as the U-core motor. This means that the round-stator motor analyzed in this section was not optimized. The performance of an optimized round-stator motor is discussed in Section V of this paper. The equivalent circuit of a round-stator PM motor is shown in Fig. 6, and its vector diagram in Fig. 7. Since the stator winding resistance is not negligible compared to its synchronous reactance, as is the case in larger machines, the voltage drop on the resistance has to be taken into account in the analysis of this type of machine" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001732_05698190490504244-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001732_05698190490504244-Figure2-1.png", "caption": "Fig. 2\u2014Bearing geometry and surface profile.", "texts": [ " The influences of the surface roughness parameter and roughness orientations such as transverse, isotropic, and longitudinal roughness patterns on the static and dynamic performance characteristics of an orifice-compensated hole-entry hybrid journal bearing system are studied, including thermal effects. The results presented in this article are expected to be quite useful to bearing designers. The Dowson generalized Reynolds equation governing the flow of lubricant with variable viscosity in the clearance space between two smooth surfaces can be modified as follows. Applying no-slip boundary conditions at the two rough surfaces (Fig. 2(b)), the local velocity components uL and vL can be expressed as (Ramesh et al. (9)) uL = \u2202pL \u2202x [\u222b z 0 z \u00b5 dz \u2212 F1 F0 \u222b z 0 dz \u00b5 ] + U F0 \u222b z 0 dz \u00b5 [1a] vL = \u2202pL \u2202y [\u222b z 0 z \u00b5 dz \u2212 F1 F0 \u222b z 0 dz \u00b5 ] [1b] where F0 = \u222b hL 0 (1/\u00b5)dz and F1 = \u222b hL 0 (z/\u00b5) dz, pL is the local fluid-film pressure, and hL is the local fluid-film thickness. The local lubricant flow per unit width in the x and y directions can be obtained by integrating the respective velocity components across the local fluid-film thickness and are expressed as qx = UhL \u2212 \u2202pL \u2202x F2 \u2212 U F1 F0 [1c] qy = \u2212 \u2202pL \u2202y F2 [1d] where F2 = \u222b hL 0 ( z2 \u00b5 \u2212 z \u00b5 F1 F0 ) dz Using the nondimensional parameters listed in the nomenclature, the preceding equations can be expressed in nondimensional form as q\u0304x = \u2212h\u03043 LF\u03042 \u2202 p\u0304L \u2202\u03b1 + ( 1 \u2212 F\u03041 F\u03040 ) h\u0304L [1e] q\u0304y = \u2212h\u03043 LF\u03042 \u2202 p\u0304L \u2202\u03b2 [1f] where F\u03040 = \u222b 1 0 dz\u0304 \u00b5\u0304 F\u03041 = \u222b 1 0 z\u0304 \u00b5\u0304 dz\u0304 F\u03042 = \u222b 1 0 z\u0304 \u00b5\u0304 ( z\u0304 \u2212 F\u03041 F\u03040 ) dz\u0304 are the cross-film viscosity integrals", " [3b]) when one rough surface moves over the other, and this parameter has particular values under the following cases (Patir and Cheng (12)): For stationary roughness (i.e., a rough bearing and smooth journal), V\u0304r j = 0.0. For two-sided roughness (i.e., both bearing and journal surfaces have identical roughness distribution, but with different standard deviations), V\u0304r j = 0.5. For moving roughness (i.e., a smooth bearing and rough journal), V\u0304r j = 1.0. The geometry and coordinate system of a hole-entry journal bearing system with a rough surface profile is shown in Fig. 2. Assuming a Gaussian distribution of surface heights, the nondimensional form of the average fluid-film thickness h\u0304T , which is equal to the expected or mean value of the local fluid-film thickness (h\u0304L = h\u0304 + \u03b4\u0304), is expressed as h\u0304T = E{h\u0304L} = \u222b +\u221e \u2212\u221e (h\u0304 + \u03b4\u0304)\u03c8(\u03b4\u0304)d\u03b4\u0304 [4] For the fully lubricated (i.e., for h\u0304 \u2265 3) and partially lubricated (i.e., for h\u0304 < 3) regions, the expression for average fluid-film thickness (h\u0304T) is expressed as (Nagaraju, et al. (7)) h\u0304T = h\u0304 for h\u0304 \u2265 3 h\u0304 2 [ 1 + erf ( h\u0304\u221a 2 )] + 1 \u221a 2\u03c0 e\u2212( h\u0304)2/2 for h\u0304 < 3 [5] where h\u0304 is the nominal fluid-film thickness (i", " (8)) as Q\u0304R = C\u0304S2 (1 \u2212 p\u0304c)1/2 [7] The boundary conditions used for the solution of the lubricant flow field are described as follows: 1. Nodes situated on the external boundary of the bearing have zero pressure; p\u0304|\u03b2=\u00b51.0 = 0.0. 2. At the trailing edge of the positive region, p\u0304 = \u2202 p\u0304 \u2202\u03b1 = 0.0. Fluid-Film Velocity Components For the thermal analysis of a roughened journal bearing system, the flows between two rough surfaces can be modeled by an equivalent flow model, which is defined as two smooth surfaces separated by a clearance equal to the average gap (h\u0304T) as shown in Fig. 2(c) (Shi and Wang (10)). Based on the equivalence of flows through the average fluid-film thickness and through the local fluid-film thickness, a group of new pressure flow factors (\u03c6\u2032 x, \u03c6 \u2032 y) and shear flow factor (\u03c6\u2032 s) can be derived as (Shi and Wang (10)) \u03c6\u2032 x = h\u03043 h\u03043 T \u03c6x \u03c6\u2032 y = h\u03043 h\u03043 T \u03c6y \u03c6\u2032 s = \u03c6s [8] The mean or expected velocity components can be obtained by modifying the Poiseuille and Couette terms in the expression of local velocity components using the new flow factors and are expressed in nondimensional form as u\u0304 = h\u03042 T\u03c6\u2032 x \u2202 p\u0304 \u2202\u03b1 [\u222b z\u0304 0 z\u0304 \u00b5\u0304 dz\u0304 \u2212 F\u03041 F\u03040 \u222b z\u0304 0 dz\u0304 \u00b5\u0304 ] + F\u03040 \u222b z\u0304 0 dz\u0304 \u00b5\u0304 + \u03c6\u2032 s h\u0304T F\u03040 \u222b z\u0304 0 dz\u0304 \u00b5\u0304 [9a] v\u0304 = h\u03042 T\u03c6\u2032 y \u2202 p\u0304 \u2202\u03b2 [\u222b z\u0304 0 z\u0304 \u00b5\u0304 dz\u0304 \u2212 F\u03041 F\u03040 \u222b z\u0304 0 dz\u0304 \u00b5\u0304 ] [9b] The fluid-film velocity component across the fluid film is obtained from the continuity equation (Ferron, et al" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure5.16-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure5.16-1.png", "caption": "Fig. 5.16. 2D measurement machine", "texts": [ " Preventive methods are to ensure all equipment is rigidly secured and supported, and to use sufficient fans to allow adequate air circulation. Common to all works on geometric error compensation and more is a model of the machine errors, which is either implicitly or explicitly used in the com- 5.7 Overall Error Model 145 pensator. The geometrical machine model is designed to compensate for the systematic part of the geometric errors in the machine based on a rigid-body assumption. Consider a 2D meaurement machine as shown in Figure 5.16. Three independent co-ordinate systems, as shown in Figure 5.16, are used in the model with respect to the table (O, X, Y ), the bridge (O1, X1, Y1), and the X-carriage (O2, X2, Y2) respectively. It is assumed, as initial conditions, that all three origins coincide and the axes of all three systems are properly aligned. Thus, when the bridge moves a nominal distance Y, the actual position of the bridge origin O1, with respect to the table system, is given by the vector \u2212\u2212\u2192 OO1 = [ \u03b4x(y) y + \u03b4y(y) ] . (5.1) At the same time, the bridge co-ordinate system rotates with respect to the table system due to the angular error motion" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002028_tasc.2004.830935-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002028_tasc.2004.830935-Figure2-1.png", "caption": "Fig. 2. Plunger analysis model (Unit : (mm)).", "texts": [ " Here, , which represents the mutual inductance between coil 1 and 2; and are self-inductance of coil 1 and 2, respectively. In this case, the magnetic force is expressed as: (15) These above state equations have been solved using the Runge-Kutta method. When the Rung-Kutta method is applied, the inductance and its derivatives are interpolated by cubic spline. To exhibit the validity of the proposed method for solving electromagnetic system, we tested two dynamic electro-magnetic systems, which were activated by the electrical sources. Fig. 2 shows the plunger analysis model, which is moving along the z-direction. The spring and damper was connected to the moving bar. The spring constant was 1000 N/m; the damping coefficient was 5 Ns/m; the mass was 0.1 kg; and the number of turns was 1000. When the current was applied, the state equations of (6) and (7) were used. On the contrary, when voltage was applied, the state equations of (8), (9), and (10) were used. The input current was A, and the input voltage was V. In both cases, the frequency was 10 Hz" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001595_asru.2003.1318446-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001595_asru.2003.1318446-Figure6-1.png", "caption": "Fig. 6. Feature of each gesture", "texts": [ "4(a)) is extracted by skin color and hair color information(in Fig.4(b)). Furthermore, the neck region is eliminated by introducing the ratio of width and height of head region(in Fig4(c)). Opticalflows of the all pixels in the extracted head region are treated as values representing a head movement. As in Fig.5, a head region is divided into 4 regions. The average of optical-flows in each region is a feature to recognize the head gesture. Therefore, total dimension of a feature vector is 8. It is expected to capture the feature of each head gesture, as in Fig.6. In order to recognize the gesture, we introduce Nterbi algorithm in left to right HMM(Hidden Markov Model). In this study, in order to recognize head gestures during a spoken dialogue, spotting is required. 2 models, stillness model and garbage model, are introduced for spotting. Stillness model represents stopping of a head and garbage model represents other movements of a head than the three gestures. 4.4. Experiment and result The recorded data for the experiment consist of the natural dialogues described in Section 4" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002807_iros.2007.4399285-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002807_iros.2007.4399285-Figure4-1.png", "caption": "Fig. 4. Approximate model (1-particle)", "texts": [ " In this research, we limit the ZMP modification value to 40 mm along x axis and 30 mm along y axis. The limitation number was determined through basic experiments. ( ) m m m zmp p w v w m m m m vzmp pzmp zmp zmp x K x K x x x x x Limit \u2206 = \u2206 + \u2206 = + \u2206 \u2206 \u2264 (5) D. Landing Point Variation Computation When the waist trajectory does not converge with only reference ZMP variation, the divergence can be inhibited by changing a ZMP trajectory and a foot-landing point. To compute the landing point variation, we use a one particle model for the waist as shown in Fig. 4. Then, the mass of the legs are assumed to be 0. The moment balance around a varied reference ZMP can be expressed as follows: ( )( ) ( ) 0 m m m w w vzmp w q m m m w w vzmp z m z z x x m x x g \u2212 + \u2212 \u2212 = (6) The deviation from the preset trajectory of the waist is m wx\u2206 and the changing value of the ZMP is m zmpx\u2206 . Then, we obtain the differential equation on the deviation. ( ) ( ) 0 m m m w w vzmp w m m m w w vzmp z m z z x m x x g \u2212 \u2206 \u2212 \u2206 \u2212 \u2206 = (7) The solution on (7) is described as follow: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 ( ) ( ) 2 2 ( ) ( ) 2 2 , , , p pm At At w p p pm At At w m mz w t tm m w vzmp m m w t t p zmp t t A X R X A X R X x e e R A A A X R X A X R X x e e gA X x z z X x R x \u2212 \u2212 = = = \u2212 + \u2212 \u2212 \u2206 = + + \u2212 + \u2212 \u2212 \u2206 = \u2212 = = \u2206 \u2212 = \u2206 = \u2206 (8) Equations (8) express deviations m wx\u2206 and m wx\u2206 past t sec after a certain time when deviations 0X and 0X are given as initial values" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003806_icelmach.2010.5608274-Figure13-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003806_icelmach.2010.5608274-Figure13-1.png", "caption": "Fig. 13. Magnitude of the twenty-fourth harmonic of magnetic flux density", "texts": [], "surrounding_texts": [ "The four-pole energy-saving small induction motor with core made from the non-oriented silicon steel M600-50A was examined. The supply voltage was 230 V for the frequency 50 Hz. Stator windings were delta connected. The number of series turns of stator windings was 368. The external diameter of the stator core was 120 mm, the internal diameter is 70.5 mm, and stator core lengths is 102 mm." ] }, { "image_filename": "designv11_32_0000167_1.1636771-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000167_1.1636771-Figure1-1.png", "caption": "Fig. 1 A torsional dynamic model of the spur gear pair", "texts": [ " The effect of the error in the estimated fundamental gear mesh frequency is analyzed and compared to two types of LMS-based adaptive controllers. Finally a series of numerical examples are performed to demonstrate the salient features of the proposed controller. For the spur gear pair considered here, the torsional mesh dynamics are modeled using a concept proposed by Tuplin @13#, which has been widely used by many gear researchers @14\u201316#. The model consists of an infinitesimal gear mesh spring-damper element that is positioned in series with the gear transmission error excitation eg(t) as shown in Fig. 1. The pinion and gear are modeled as two lumped mass moment of inertias. The system model possesses two degrees-of-freedom and naturally produces two analytical modes. One is a rigid body gear pair rotation mode since the system is semi-definite, while the other is an out-ofphase gear pair torsion mode. The model can be further reduced to a definite single-degree-of-freedom system @15# by retaining only the latter flexible mode. The resultant equation of motion is: mx\u03081cmx\u03071km~ t !x5km~ t !eg~ t " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002002_t-ed.1977.18852-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002002_t-ed.1977.18852-Figure7-1.png", "caption": "Fig. 7. Class I11 B-on-W systems. (a) Type 111. (b) Type IIIa.", "texts": [ " The Type IIc system [22] shown in Fig. 6(c) is, in some sense, the classical schlieren system. The schlieren lens S images the input bars into the output slots. Another DEWEY PROJECTION SYSTEMS FOR LIGHT VALVES 925 (cl \u2018Type IIc Fig. 6. Class I1 multiple-stop W-on-B systems. (a) Type IIa. (b) Type IIb. (c) Type TIC. function of S is to act as a field lens in order to minimize the diameter of P. A perfect field lens would image C into P, but this is not possible in this case. C. Class 111 Systems In Class I11 systems, as shown in Fig. 7, the source L (or the image of a source) is placed at the focus of a condenser or schlieren lens S. This illuminates the LV with a \u201ccollimated\u201d beam, and allows the LV to be some distance away from both S and P. As will be seen later, this is important for reflective LV\u2019s where the system must be folded. Since L is at the focus of S , this is a telecentric system and the illumination aperture is Dlx, where x is the focal length of S. In order that the area of uniform illumination be a significant portion of the clear area of S and P , the illumination aperture must be small", " In fact, for all Class I and Class I1 systems shown, the LV is either too close to the condenser [Figs. 1,4(a)], or it is too close to the first element of the projection lens, or to the field lens [Figs. 4(b), (c), 5, and 61. There are no examples of a reflective Class I1 system: it would require a projection-lens diameter much larger than the LV. There is one example, however, of a reflective Type I system that will be described in the next section. In a Class 111 system with relatively small-aperture illumination, as shown in Fig. 7, the LV may be located a t some distance from both S and P. Folding the system about the LV will still put the illumination and projection systems on top of each other, but there are several solutions to this problem. One is to make one lens do both jobs, as will be seen later. Another is to use a 50/50 beamsplitter at 45\u2019 in order to fold the illumination axis sideways. The major problem with this arrangement is that the optical efficiency is only 25 percent of the equivalent transmissive system. Another way to keep the illumination and projection systems separate is to fold the system at an angle. One way of doing this is to take Fig. 7(a) [or 7(b)], tilt the LV at an angle to the axis, and then fold about the LV. The resulting system, which will be similar to Fig. 9 (with P normal to the projection direction), is often erroneously referred to as \u201coff-axis projection,\u201d and is frequently illustrated in discussions of reflective LV\u2019s [3], [B], [lo]. The problem with this arrangement is that the LV is at an angle (20\u201d or more) to the projection axis. The image will also be at an oblique angle to the axis and will suffer from \u201ckeystone\u201d distortion", " I system [18] is that the size of the projection lens is mi:lnimized, and its limiting aperture is a t (or inside) the 1e:lla. The disadvantage is that the condenser must have twice It is of interest to note that the prism in Fig. 10 is not used to equalize the optical path length between the LV and the lens (it would be inverted if it were). The fact that a plane wave leaving normal to the LV would be refracted along the \u201coptic axis\u2019\u2019 of the figure is of little consequence when attempting to image through the prism. G. On-Axis Reflex System [71, [91, [12] Referring to Fig. 7, if identical lenses are used for S and P (or P l ) , and if they are arranged to be equidistant from the LV, then folding the system about the LV will put the light source L on top of the stop and S on top of P (or P l ) . In this manner, a single lens performs both as a telecentric schlieren lens and as the projection lens. For a W-on-B system, this arrangement can be made to work by replacing the opaque center stop by a small 45\u201d mirror. The light can then be brought in from the side, as in Fig. 11, and since the mirror is imaged onto itself by the lens and the reflective LV, no light reaches the screen when the LV is not written [ 111. In Fig. 11 the small mirror has been placed slightly off-axis so that light specularly reflected by the LV misses the mirror and reaches the screen. Light from written areas of the LV is prevented from reaching the screen in this B-on-W arrangement by an aperture. For a reflective B-on-W system, the arrangement of Fig. 11, or the equivalent of Fig. 7(b) (i.e., with an additional projection lens element beyond the stop), is probably the best choice. For a W-on-B system, however, there is a problem with this arrangement that is hard to correct. The DEWEY: PROJECTION SYSTEMS FOR LIGHT VALVES 927 illuminating beam diverges from the 45\u201d mirror and is partially reflected by the lens surfaces. This reflected beam diverges around the stop and appears on the screen as a luminous \u201cdonut,\u201d the center being shadowed by the stop. Antireflection coatings on the lenses can reduce its intensity but not below a noticeable level", " The magnitude of this effect will, in most cases, be insignificant or, a t worst, tolerable. For a W-on-B reflective system, the best choice is to eliminate the lens P1 altogether, as is done in the Eidophor system (see the next section). If, however, the LV cannot be made concave, one of the off-axis systems will be preferable. H. The Eidophor System [ll, [261 A schematic of the Eidophor projection system is shown in Fig. 12. The light source L is actually the relayed image of a Xenon arc [l]. This system is essentially a multistop version. of the Type IIIa system shown in Fig. 7(b). The lenses S and P1 are replaced by the concave reflective LV which images the mirror bars into themselves. The lens C and field lens F in Fig. 12 form an image of the arc on the mirror bars which corresponds to the light source L in Fig. 7(b). The system uses diffractive schlieren effects to obtain a W-on-B image. Being the most successful of all LV\u2019s, little more need be said. IV. IMAGE OVERLAY In many applications it is necessary to overlay dynamic information on a relatively static, high-resolution image of a map, insurance form, etc. The simplest way to create this image is with a slide projector, and if the overlay image is W-on-B (or color on black), which is added to the slide To Screen I d l + \\ + L V \\ Axis Fig. 12. Reflective Type IIIa W-on-B system (Eidophor)", " Thus greater optical efficiency will be gained with a smaller source, a larger LV, and a projection lens of larger aperture (faster) and shorter focal length (wide-angle). In fact, these conditions are true for all projection systems, although the exact geometrical relationship is different in each case. In Class 11, where the source is imaged onto the LV, an elliptical reflector is commonly used as the condenser. If the source magnification is large enough, the light can be collected over an angle of more than 90\u2019 with an efficiency of greater than 50 percent. In Class 111, the situation can be explained with reference to Fig. 7(a). The effective illumination aperture is D/x and the usable light aperture is E/x, where E is the diameter of the LV. The optimal illumination aperture will be determined by the characteristics of the LV, and the diameter of the LV will be related to that of the lens. As an example, assume that P is a standard 88-mm, f/3.5 lens and that we wish to work at flll . Then the diameter of the stop is 8 mm and E is about 88/3.5-8 or 17 mm. If we choose an 8-mm incandescent source, then the source magnification is one, and x is 88 mm" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000989_s0022-460x(03)00744-2-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000989_s0022-460x(03)00744-2-Figure1-1.png", "caption": "Fig. 1. A single-link flexible manipulator.", "texts": [ " Instead, the integrated average value of the imposed disturbance is used over a certain sampling period to avoid noise and chattering phenomena. After formulating the governing equation of a single-link flexible arm, a sliding mode controller with disturbance estimator is designed. The controller is then experimentally implemented and vibration control performances of the flexible arm subjected to sinusoidal torque disturbances are presented in time domain. Consider the horizontal motion of a single-link flexible manipulator as shown in Fig. 1. The uniform beam of total length l and width b is attached to the rotating hub that has a moment of inertia Ih: The axis ou0 is the fixed reference line and ou is the tangential line to the beam\u2019s neutral axis at the hub. T\u00f0t\u00de is the input torque and w0\u00f0u; t\u00de the elastic deflection of the link. Upon assuming Euler\u2013Bernoulli beam theory, small elastic deflections, small angular velocities and neglecting axial deflections, the system model can be obtained in the state space as follows [2,6]: \u2019x\u00f0t\u00de \u00bc Ax\u00f0t\u00de \u00fe BT\u00f0t\u00de; y\u00f0t\u00de \u00bc Cx\u00f0t\u00de; \u00f01\u00de where x\u00f0t\u00de \u00bc \u00bdq0\u00f0t\u00de \u2019q0\u00f0t\u00de q1\u00f0t\u00de \u2019q1\u00f0t\u00de " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001495_0954405041897185-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001495_0954405041897185-Figure2-1.png", "caption": "Fig. 2 Finite element model of the segment of an internal gear machined with a gear-type tool. The main tool parameters are z0 \u00bc 28, a0 \u00bc 0:5mm and s0 \u00bc 4:32mm. The main gear parameters are mn \u00bc 2:75mm, n \u00bc 208, \u00bc 08, s1 \u00bc 4:265mm and z1 \u00bc 73", "texts": [ " This approach assumes that, in each considered case, the load is equally distributed along the tooth line and deflections and their distributions of stresses in the transverse sections of the tooth and gear are the same. Axial symmetry of the gear allows the finite element model to be reduced to a representative segment of gear, as far as the distribution of stress in the loaded tooth and in its surrounding is concerned. Therefore, not the whole gears need to be modelled, but certain segments of them, containing for example three, four, five or more teeth. In this case, the load is applied to the central tooth of the gear segment and boundary conditions are applied to external teeth of the segment (Fig. 2). A spur gear tooth loaded with in-plane forces (concentrated and/or distributed) orthogonal to the gear axis can be analysed as a plane stress model, representing a unit-length slice of gear in its transverse section. In this model, a two-dimensional stress state occurs. Considering the z axis normal to the transverse section of a gear, it can be concluded that all components of the stress vector equal zero, except normal components of the stress vector txx and tyy, and the shear stress txy, which are uniformly distributed across the tooth thickness" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000956_3.19783-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000956_3.19783-Figure2-1.png", "caption": "Fig. 2 Domain of maneuverability for the aerodynamic force.", "texts": [ " The domain of flight1 may be further restricted by the line of maximum dynamic pressure (15)kp and the line of maximum Mach number obtained by solving the equation d K/d/ = 0 with T=rmax so that Optimal Thrust Control For the thrust control, we consider Pv, called the switching function. To maximize//, if Py>0, Py<0, f o r t e [ t l t t 2 ] f= variable boost arc coast arc sustained arc (18) The last case of sustained arc is the singular thrust arc along which the thrust is at an intermediate level. The optimal trajectory is a combination of boost arc (B arc), coast arc (C arc), and sustained arc (S arc). Optimal Aerodynamic Control The aerodynamic control consists of and n, i.e., /. Figure 2 shows the domain of maneuverability described by the terminus of a. This domain of maneuverability is a surface of revolution \u00a3 about the x2 axis. It is bounded by constraint Eq. (12) in the case where is unbounded; it is bounded by constraint Eqs. (13) and (14) in the case where is bounded. The domain of maneuverability is a parabolic drag polar on the plane formed by the x axis and the 7. axis; In order to obtain the optimal aerodynamic control, H is expressed in another form as FcoS7 /cos0 +" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003347_imtc.2007.379200-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003347_imtc.2007.379200-Figure4-1.png", "caption": "Fig. 4. FPGA-based vehicle.", "texts": [ " The GUI is formed by five horizontal LEDs which represent, from left to right, the most significant bits that are converted into a decimal value. A remote user sets the LED values by a mouse click: a light coloured turned-on led button means a programmed \"1\", a darker turned-off led button means \"0\". The binary sequence in Fig. 3 is \"01011\" and the corresponding decimal value \"11\" is shown on the on-board display, monitored by the web-cam. The second and third experiments implemented for the remote laboratory are automation applications: the former (Fig.4) drives a two-wheel vehicle based on M\\AX7000S chip, the latter (Fig.5) controls movements and actions of a robotic arm prototype (Lynxmotion Lynx5 Satellite Arm without electronics) [16]. The hardware realizing the two-wheel prototype consists of the UPIX board, two servos Futaba S3003, a 7.2 Volt battery and an infrared sensor. The control algorithm, written in VHDL for the M\\AX7000S FPGA, allows the remote students to drive the robot in all of the four perpendicular directions (ahead, behind, left and right)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003206_jst.28-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003206_jst.28-Figure1-1.png", "caption": "Figure 1. Newtonian model of ball impact [6]. ui, impact angle. nxi, impact horizontal velocity. nyi, impact vertical velocity. oi, impact back spin. F, friction force. R, reaction force. uo, rebounded angle. vxo, rebound horizontal velocity. nyo, rebound vertical velocity. oo, rebound back spin.", "texts": [ " Literature review shows that theoretical sports ball models have been generally classified into two main categories: (i) mathematical models; and (ii) numerical (mostly finite element [FE]) models. Mathematical models have been quite popular, and because of their convenient features, such as simplicity and economic performance, they are still being used. In order to successfully develop a cricket ball model, it is important to understand the impact mechanism. In a fundamental study by Daish [6], he examined a theoretical case of a rigid sphere impacting a rigid surface as shown in Figure 1. Daish [6] analyzed a rigid ball approaching a rigid surface at an angle of yi with velocity components of vxi and vyi, as well as back spin of oi. A friction force (F) and a reaction force (R) were imposed during impact with the rigid surface. After the collision, the ball rebounded at an angle of yo, but remained within the same plane. The rebound velocity components are vxo and vyo. The spin rate is taken as positive, oo. Daish [6] presented two scenarios based on the amount of frictional force" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001499_s0022-0728(81)80187-8-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001499_s0022-0728(81)80187-8-Figure1-1.png", "caption": "Fig. 1. Optically transparent thin-layer electrochemical cells with indicator electrodes. (A) Cell with Pt resinate indicator electrode, exploded view. (B) Cell with Pt resinate indicator electrode, side view. (C) Cell with Pt wire indicator electrode, side view.", "texts": [ " An important consideration in the selection of an appropriate mediatortitrant is proximity of its formal reduction potential U \u00b0' to that of the biocomponent . When performing the spectropotentiostat ic experiment, it is assumed that the potential of the thin solution layer is coupled to that of the electrode by the mediator-titrant. Consequently, it is important to know the potential range over which a mediator-titrant is capable of controlling solution potential. This paper examines the potential ranges for some typical mediatortitrants. Figure 1 depicts the two thin-layer cells which were used for this investigation. The cells were basically of the glass microscope slide-minigrid variety [3] with the following modifications. Prior to assembling cell A (Fig. 1A), a strip of platinum--gold resinate (Liquid Bright Pt. No. 1; Englehardt Inc., E. Newark, NY) was painted on one microscope slide in the form of a strip going across the face of the slide where it would be directly opposite the middle of the minigrid (Fig. 1B). The resinate was extended up the side of the slide and around to the opposite face to provide electrical contact. The slide was dried at 125\u00b0C for 10 min and then placed in an annealing oven where it was ~ired at 650\u00b0C for 10 min, allowing the Pt--Au to bond to the glass. The resinate served as a potent iometric indicator electrode in the thin-layer cell. Two layers of 2-mil pressure-sensitive fluorofilm DF-1200 Teflon tape (Dilectrix Corp., Farmingdale, NY) spacers were placed along the periphery of the microscope slide with the resinate strip. A triply deposited, 120 lines per inch gold minigrid (Buckbee Mears Co., St. Paul, MN) was used as the working electrode. The extra depositions of gold gave the minigrid rigidity so that it would lie fiat against the face of the microscopesl ide opposite the indicator electrode and not short against the indicator electrode. Some measurements were made with a cell in which the potentiometric indicator electrode consisted of a piece of Pt wire sealed into a Plexiglas slide, as shown in Fig. 1C. In the investigation of mediator-titrants which proved to be oxygen sensitive, a previously described anaerobic cell was used [5]. A Pt--Au resinate strip and a triply deposited gold minigrid were used as the indicator and working electrodes respectively. A Princeton Applied Research Model 173 potentiostat in conjunction with a Model 175 Universal Programmer was used for applying potentials to the cell and for obtaining cyclic voltammograms. The applied potentials were measured with a Digitec 261C digital voltmeter", "e, b Me thy l v io logen - - 6 9 0 2 - A n t h r a q u i n o n e su l fonic acid - - 4 7 0 2 , 5 - D i h y d r o x y - p - b e n z o q u i n o n e c - - 3 7 0 Ga l locyan ine - - 2 1 0 1 , 2 - N a p h t h o q u i n o n e c - -90 1 ,2 -Naph thoqu inone -4 - su l fon i c acid - -25 2 , 6 - D i c h l o r o p h e n o l i n d o p h e n o l - -15 N ,N,N ' ,N ' -Te t r ame thy l -p - p h e n y l e n e d i a m i n e 4 0 , 3 1 0 d Po tass ium fer r icyanide 190 P o r p h y r e x i d e 480 1 - -750 to - -630 2 - - 5 1 0 to - - 4 0 0 2 - - 3 7 0 to - - 3 0 0 2 - -270 to - -100 2 - -90 to 0 2 - -60 to 10 2 - -50 to 75 1, 1 40 to 410 1 130 to 300 1 340 to 580 a D e t e r m i n e d f r o m th in- layer cyclic v o l t a m m o g r a m . b Range over which Vindicato r is w i th in 5 m V of Vapplie d. c A n a e r o b i c cell. d Two waves: LO' = 40, revers ible; Up, a = 310, irreversible. The potential range over which a particular mediator-ti trant could effectively poise the solution potential was determined by means of the thin-layer cells shown in Fig. 1. The gold minigrid electrode was used to control the solution potential; the deposited platinum strip or the platinum wire was used as an indicating electrode to measure potentiometrically the solution potential on the opposite side of the thin-layer cell. Figure 3 shows results for 2-anthraquinonesulfonic acid where the potential of the indicating electrode (Vindicator) - 0 . 5 4 - 0 . 5 0 - 0 . 4 6 - 0 . 4 2 ~ ~ \u2022 . - 0 . 3 8 /\"/appI(VvsSCE') ' ~ 1 is plot ted versus the potential applied to the gold minigrid (Uapplied)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003382_scored.2007.4451443-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003382_scored.2007.4451443-Figure2-1.png", "caption": "Fig. 2. The total forces acting on the AMB rotor.", "texts": [ " 1 illustrates the five degree-of-freedom (DOF) vertical magnetic bearing in which the vertical axis (z-axis) is assumed to be decoupled from the system and hence controlled separately. The top part of the rotor of the system in Fig. 1 is controlled actively by the magnetic bearing, labeled as AMB, in which the coil currents are the inputs. The bottom part of the rotor however is levitated to the center of the system by using two sets of permanent magnets labeled as PMB. The rotation of rotor around the z-axis is supplied by external driving mechanism and considered a time-varying parameter. Fig. 2 illustrates the free-body diagram of the rotor which shows the total forces produced by the AMB and PMB of the system. Based on the principle of flight dynamics [11], the equations of motion of the rotor-magnetic bearing system is as follows: )cos(2 tlmffxm unxxg bu \u03c9\u03c9++= bu xbxuzar fLfLJJ \u2212+\u2212= \u03b1\u03c9\u03b2 )sin(2 tlmffym unyyg bu \u03c9\u03c9++= bu ybyuzar fLfLJJ +\u2212= \u03b2\u03c9\u03b1 The terms )cos(2 tlmun \u03c9\u03c9 and )sin(2 tlmun \u03c9\u03c9 are the imbalances due the difference between rotor geometric center and mass center. These imbalances cause the whirling motion and the magnitude is proportional to the rotor rotational speed, \u03c9" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000514_3-540-45118-8_49-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000514_3-540-45118-8_49-Figure1-1.png", "caption": "Figure 1. The PUMA 560 at zero position, by Craig\u2019s modified DH parameter [6]", "texts": [ " These singularities can happen individually, or as a combination of two of even three at the same time. Mathematically, singularity occurs when the determinant of the Jacobian matrix approaches zero, i.e.: Det(J) = 0 or Det(JJT = 0) for manipulators with non-square Jacobians [11]. For PUMA 560 with 6 DOF, the Jacobian is a square 6 x 6 matrix, which can be partitioned into: J = [ J11 J12 J21 J22 ] (5) By defining the control point to be at the wrist, we will obtain a Jacobian matrix with J12 = 03x3. With the frame assignment shown in Figure 1, and modified DH parameters according to Craig\u2019s [6] (See Table 1), the determinant of PUMA is shown as: Det(J) = Det(Jd) = Det(J11)Det(J22); Det(J11) = \u2212a2(d4C3 \u2212 a3S3)(d4S23 + a2C2 + a3C23); Det(J22) = \u2212S5; (6) (Cheng et al[4]) where a2 = 0.4318(m), a3 = \u22120.0203(m), d2 = 0.2435(m), d3 = \u22120.0934(m), d4 = 0.4331(m). When the determinant equals zero, Equation 6 represents the elbow, head, and wrist singularities respectively. When singularity occurs, there is a row(s) in the Jacobian - when it is transformed onto the correct frame - that contains only zeros", " 4J = (a2C2 + d4S23)S4 + C23(\u2212(d2 + d3)C4 + a3S4) C4(d4 \u2212 a2S23) d4C4 0 0 0 (a2C2C4 + d4C4S23 + C23(a3C4 + (d2 + d3)S4) \u2212(d4 + a2S3)S4 \u2212d4S4 0 0 0 \u2212(d2 + d3)S23 \u2212a3 \u2212 a2C3 \u2212a3 0 0 0 \u2212C4S23 S4 S4 0 0 S5 S23S4 C4 C4 0 1 0 C23 0 0 1 0 C5 (8) When (\u03d15 = 0), a row of zero only appears at the last three elements of the fourth row of 4J : 4 J22 = [ 0 0 0 0 1 0 1 0 1 ] (9) This means that it is still possible to rotate around the X-axis of Frame{4} in wrist singularity, but it is produced by the first three joints, which would also change the position of the end effector (i.e. not possible in 6 DOF). Therefore, the first row of 4J22, (or the fourth row of 4J) is the degenerate direction, representing the rotation around X-axis of Frame{4} (see Figure 1 and 4). Collapsing the Jacobian is then done by eliminating the fourth row of 4J . Elbow singularity is shown by projecting the Jacobian and the task space forces onto Frame{B} which is not one of the frames in our DH assignment (see Figure 2 for the frame assignment, and Equation (10) for the resulting Jacobian). At this configuration, the singular direction is found to fall along the line connecting the wrist point to the origin of base frame. BJ [1][1] = (d2+d3)S2(d4C3\u2212a3S3) (a2+a3C3+d4S3)D BJ [1][2] = (d4C3\u2212a3S3)(a2+a3C3+d4S3) 2D a2 2+d2 2+2d2d3+d2 3+2a2a3C3+a2 3C2 3+2a2d4S3+d2 4S2 3+a3d4Sin[2q3] BJ [1][3] = d4C3\u2212a3S3 D BJ [2][1] = (d2 + d3)S2; BJ [2][2] = a2 + a3C3 + d4S3 BJ [2][3] = a3C3 + d4S3 BJ [3][1] = C2(a 2 2+d2 2+2d2d3+d2 3+a2a3C3+a2d4S3)+(a2+a3C3+d4S3)(a3C23+d4S23) (a2+a3C3+d4S3)D BJ [3][2] = (d2+d3)(d4C3\u2212a3S3) (a2+a3C3+d4S3)D ; BJ [3][3] = (d2+d3)(d4C3\u2212a3S3) (a2+a3C3+d4S3)D where: D = \u221a 1 + (d2 + d3)2 (a2 + a3C3 + d4S3)2 (10) Frame{B} is obtained by rotating Frame{2} by angle \u03b2, which is defined as: \u03b2 = Tan \u22121 [ d2 + d3 a2 + a3C3 + d4S3 ] (11) From (6), it is shown that \u2212a2(d4C3 \u2212 a3S3) = 0 at elbow singularity" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001740_1.1135224-FigureI-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001740_1.1135224-FigureI-1.png", "caption": "FIG. I. Schematic cross-sectional view of the pressure vessel with the closure.", "texts": [], "surrounding_texts": [ "Simple closure for high pressures and low temperatures W. Goedegebuure, J. A. Schouten, and N. J. Trappeniers Citation: Review of Scientific Instruments 48, 1213 (1977); doi: 10.1063/1.1135224 View online: http://dx.doi.org/10.1063/1.1135224 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/48/9?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Highpressure, lowtemperature, demountable, compact, and simple seal Rev. Sci. Instrum. 60, 3562 (1989); 10.1063/1.1140513 Simple lowtemperature press for diamondanvil high pressure cells Rev. Sci. Instrum. 52, 1103 (1981); 10.1063/1.1136717 Iodine at high pressures and low temperatures J. Chem. Phys. 72, 2936 (1980); 10.1063/1.439493 Low capacitance electrical feedthrough and simple, reuseable closure seal for hydrostatic pressures to 7 kilobar and temperatures to 200 \u00b0C: application to NMR Rev. Sci. Instrum. 45, 111 (1974); 10.1063/1.1686420 Simple Low Temperature Closure and Electrical Leadthrough for High Pressure Gas Systems Rev. Sci. Instrum. 39, 270 (1968); 10.1063/1.1683344\nThis 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:\n129.174.21.5 On: Mon, 22 Dec 2014 07:41:33", "much thicker (200-300 nm) niobium superconductor. Other normal metals which may be satisfactory for the proximity layer are platinum and rhodium. The solid moving switch contacts were made of Babbitt, a soft easily machined material, rather than gold-coated niobium, since contacts made between two hard super conductors have lower critical currents because of smaller contact area. 2\nA four-pole, four-position prototype superconducting switch that has been constructed and tested is illustrated in Fig. 1. The switch has been mUltiply cycled to liquid helium temperatures, has undergone several hundred switching operations, and has been stored in air at room temperature for over three months without any indica tions of degradation. (One set of multilayer film con tacts was stored more than a year at room temperature before testing.) The critical currents of the switch con tacts were measured in all four positions to be greater than 100 mA, the maximum output of the current source usually used for testing. However, in one test with a different current source, individual contacts were ob-\nserved to have critical currents greater than I A, and all carried 0.5 A.4 The compactness of the planar switch geometry is particularly useful in low-tempera ture environments where space is usually limited. The extension of this design to switches with more poles and contacts is a simple and straightforward procedure.\nWe wish to thank J. Toots for sputtering the niobium and gold thin-film contacts, and C. K. Summers for machining the switch parts.\n* Supported in part by the Calibration Coordination Group of the Department of Defense. t Currently with the Heat Division. 1 G. W. A. Dummer, Materials for Conductive and Resistive\nFunctions (Hayden, New York, 1970), Chap. II, pp. 156-175. 2 J. D. Siegwarth and D. B. Sullivan, Rev. Sci. Instrum. 43, 153\n(1972). 3 H. W. Meissner, U.S. Patent No. 3,096,421 (1963). 4 The maximum supercurrent each contact will carry is temperature\ndependent; values quoted in the text were measured at T = 2 K, the temperature of operation for our application. The smallest critical current at T = 4.2 K was 52 rnA, but most contacts would carry 100 rnA, provided the switch had been operated a few times after cooldown to ensure contact self-cleaning.\nSimple closure for high pressures and low temperatures* W. Goedegebuure, J. A. Schouten, and N. J. Trappeniers\nVan der Waals-Laboratorium, Universiteit van Amsterdam. Amsterdam. The Netherlands\n(Received 4 March 1977; in final form, 19 April 1977)\nA new seal is described which can be used at pressures up to 15 kilobar.\nAn important experimental problem in high-pressure re search, in the traditional hydrostatic region up to 15 kilo bar, is the design of suitable closures for pressure vessels and the connection of tubing. The most successful con structions make use of the principle of unsupported area. The purpose of this note is to describe a new seal, based on this principle, which has the important advantages of universal applicability over a wide range of pressure (0-15 kilobar) and temperature (5-400 K). Moreover, it can be used both for liquids and gases and it requires only a minimum of space owing to the simplicity of its construction.\nAs shown in Fig. 1, the edges at the inside of the two parts of the vessel to be sealed are beveled at an angle of 45\u00b0. The seal itself consists of a circular cylindrical ring made of steel or beryllium-copper, machined with great care so as to fit exactly into the inside diam eter of the vessel. By pressurizing the vessel with oil the ring is forced into the small cavity machined between the two parts to be joined and a slight ridge is formed on the outside which brings about the closing.\nIn practice it has proved advantageous to perform the initial deformation of the sealing rings in a separate vessel which has the same height as the rings. Usually\n1213 Rev. Sci. Instrum., Vol. 48, No.9, September 1977\nthe initial fit of the ring into this vessel is sufficiently close that little or no leak occurs when pressurizing for the first time. If the fit is insufficient, especially for larger sizes, the initial sealing can be achieved by using a rubber O-ring at the bottom and the top of the vessel.\nFigure 2 shows the closure in more detail. The metal\nNotes 1213\nThis 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:\n129.174.21.5 On: Mon, 22 Dec 2014 07:41:33", "ring is pressed by the hydrostatic pressure against the narrow edge b, while part of b and an area with height d are unsupported. The dimensions of d and b have to be chosen carefully in order to prevent the ring from yielding.\nIn this laboratory, during the last few years, seals made of steel and Be-Cu of internal diameter varying from 0.4 to 25 mm have been used successfully up to 12 kilobar, while an internal diameter of 55 mm has been used up to 3 kilobar. The thickness of the ring varied from 0.15 to 0.6 and the height from 2.5 to 8 mm, while the projected height c (Fig. 2) ranged from 0.1 to 0.7 mm. The hardness of the seal is always somewhat higher than that of the pressure vessel. When the ring is formed the distance d is about 0.2 mm. Tightening the closure a little bit makes the seal vacuum tight. ]n those cases where the apparatus has a limited space and the height of the ring is much reduced, the seal tends to deform. It is therefore advisable to preform the closure by using an auxiliary piece which fits exactly inside the ring and by applying the working pressure to the vessel.\nThe seal has been used mainly in the temperature region 90-300 K and gas pressures up to 10 kilobar. It is interesting to note, however, that some experi ments have been carried out also at liquid helium tem perature and pressures up to 3 kilobar with very good results.\n236th publication of the Vander Waals fund.\nComment on the equivalent noise bandwidth approximation* Peter Kittel\nDepartment of Physics, University of Oregon, Eugene, Oregon 97403\n(Received 2 May 1977; in final form, 16 May 1977)\nThere is an ambiguity when the equivalent noise bandwidth (ENBW) is used to calculate the response to noise of an ac voltmeter. This difficulty can be overcome by a more complete definition of the ENBW.\nThe equivalent noise bandwidth (ENBW) of a network is usually defined in terms of the magnitude of the transfer function,l\n!:J.f = [' IG(fWGo- 2 df, (I)\nwhere !:J.f is the ENBW, G(f) is the voltage gain (i.e., transfer function), and Go is the gain at some reference frequency. This reference frequency is usually chosen to be the center frequency of the pass band or to be the frequency where G(f) is maximum.2 Clearly the choice of the reference frequency, and hence of Go, will affect the value of !:J.f. Therefore !:J.f is undefined to the extent that we are free to choose Go. This inde finability does not normally cause any difficulties since the useful quantity is Go\n2!:J.f.2 Equation (1) can be re written to show this product explicitly:\nGo 2!:J.f = fX I G(fW df.\n()\n(2)\nSince the right-hand side of Eq. (2) involves quantities that are fixed properties of the network, Go\n2!:J.f is a constant.\n1214 Rev. Sci. Instrum., Vol. 48, No.9, September 1977\nHowever, a difficulty does arise when the ENBW is used to calculate the response of a nonlinear device such as an ac voltmeter. When an ac voltmeter is used to measure bandwidth-limited white noise, the output of the meter is seen to fluctuate about a mean value. We are interested in relating these fluctuations to the ENBW of the signal.\nFor simplicity, we will consider the following situa tion. An initial voltage signal (V;) that is white and has a power spectrum of unity (d( Vn = df) is passed through a network whose transfer function is G(f). The resulting signal (V) will have a power spectrum of d (V2; = 1 G(f) 12 df. This signal is then detected by a mean square meter that incorporates a simple RC filter. The output of the meter will be Vo = (V2; + v. where v is the fluctuating part of the output. If we let a be the relative mean square fluctuation. then\na = (p2 > ( V2 > -2 .\nThis is often written as a function of !:J.f.2\na = (2T!:J.f)-I,\n(3)\n(4)\nwhere T = (RC)-l and where it has been assumed that\nNotes 1214\nThis 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:\n129.174.21.5 On: Mon, 22 Dec 2014 07:41:33" ] }, { "image_filename": "designv11_32_0003850_gt2009-60186-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003850_gt2009-60186-Figure2-1.png", "caption": "Figure 2. Test rig in the static load configuration", "texts": [ "025 N m) \u2022 Bearing load capacity (\u00b14 N) \u2022 Shaft rotational speed (\u00b15 rpm) \u2022 Bearing temperatures (\u00b12 \u25e6C) Table 1 presents the test rig performance specifications. Test rig rotational speed is limited by the drive turbine\u2019s greasepacked ball bearings; oil-mist lubrication of these bearings would raise the rotational speed limit to 80 krpm. The bearing load-deflection behaviour was assessed using the static loading system, in order to gain some insight into the nominal bearing stiffness. The static loading system, illustrated in Figure 2, uses a pneumatic cylinder, platen, and aerostatic load application bearing, to apply a pure vertical load to the bearing under test. This applied load mimics the static weight of a rotor. 3 loaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/01/2016 Term Static loads between 0\u22121200N (in increments of 100N) were applied to the bearing and its positional change was measured. The four proximity probes in each principal direction allow us to resolve the motion of the bearing\u2019s geometric centre" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002716_0041-2678(72)90033-4-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002716_0041-2678(72)90033-4-Figure4-1.png", "caption": "Fig 4 Fi lm thickness, h f o r z = 0 for a given speed, u = 8 cm/s and di f ferent loads, 14/. Viscosity, r /= 1.3 PI n : W= 0.75 N , v : W = 1.1 N,t-I : W= 1.5 N , 0 : W = 3 . 0 N, o : W = 4 . 6 N , A ; W = 7 . 8 N , o : W = 1 0 . S N", "texts": [], "surrounding_texts": [ "speeds against a fixed transparent plate and in which either a constant or a variable load could be applied. Film shape was measured by interferometry, traction and load by strain gauge dynamometers.\nThe electrodynamic, mechanical and optical parts of the apparatus will now be described.\nThe electrodynamic system Among the many methods which can provide both constant and and variable loads an electrodynamic system was chosen in which the load application point can vary slightly with no modification in load.\nAn inductive coil creates a constant radial magnetic field in a circular gap. According to Laplace's law, a force W = k i (t) where k is a constant, is generated in a movable coil fed by a variable current i (t) perpendicular to the magnetic field lines. The applied load can vary between 1 to 103N.\nThe frame which is made out of an alloy with a saturation value of 1.5 Wb/m z is shaped so as to guarantee radial field lines with small edge effects. The magnetic field is generated by a fixed coil which for 1.5 Wb/m 2 has the following characteristics: 30 000 Ampdre-turns; 450 V; and 4.4 A. Field strength can be varied by acting on the direct current fed to the fixed coil.\nA current whose intensity varies according to the desired load variation is fed to the moving coil. A constant load of 10aN with a 1.5 Wb/m z magnetic field is obtained for 1200 Ampdre-turns, 37 V and 1.75 A. This system is thus able to yield a constant intensity signal which can be\nFi9 2 Mechanical mounting of the test specimens\nmodulated by a low frequency signal given by an 1.f. generator.\nThe mechanical system The ball is driven at constant speed through a gear box by a d.c. motor. Contact sliding speeds between 4 mm/s and 4 m/s are possible. The specimen geometry is controlled optically and its surface is polished with diamond past to remove all asperities higher than 0.01/am. Maximum measured eccentricity is less than 3/am and thus limits the parasitic effect introduced by inertial forces. Fig 2 gives a detailed view of the mechanical assembly and shows that test specimens can be interchanged.\nThe load is transmitted vertically to the plane specimen through a frame mounted on two vertical supports instrumented to measure the applied load. The supports are sufficiently thin to accommodate a small horizontal deformation in the direction of the traction force. This deformation is opposed by a strain gauge dynamometer which measures traction. The system is such that both measurements can be performed simultaneously and independently.\nSupport dimensions and dynamometer rigidity can be adjusted to the load and traction considered and the precision desired. Longitudinal elasticity of the beam introduces an upper limit in the applied load frequency. An elementary one degree of freedom vibration analysis shows that the system can be described by the relation: mj) + @ + ky = W(t) where my is the inertia force of the mobile assembly, c)~ the damping force generated by the magnetic field, ky the elastic beam contribution and I~(t) the variable applied load. This analysis gives 300 Hertz as the upper limit of the system.\nAll parts of the apparatus head were machined within a 1/am tolerance. Thus oil films whose thickness varies between 0.1 to 2/am can be followed without any parasitic effects. The lowest applied load is 0.2 N and the lowest traction measured is 0.01 N. For a given set of beams and related instruments used in this experimental programme:\nSliding speed was varied between 0.01 and 2 m/s and measured within 1% Load was varied between 0.2 and 80 N and defined within 0.05 N at the lower end Oil inlet temperature varied between 20 and 30\u00b0C and was defined within 0.5\u00b0C by placing a 0.25 mm thermocouple at 0.5 cm from the contact centre. The lower part of the ball was immersed in oil which was\ndragged into the contact. Oil film thickness at entry was roughly 1 mm for an oil viscosity of I P1.\nThe optical system Film thickness between the transparent plate and reflecting ball was determined by optical interferometry. The principle of the method is well described elsewhere 4'1\u00b0-~2 . A large difference in refractive index between the transparent plane and the oil film is required. This led us to choose a glass with a large index (n = 1.9). The glass was polished within 0.01/am, its lower face coated with a thin chromium film (100 A), the upper face with an anti-reflecting coating. The glass plate is fixed to a sub-frame fastened to the moving assembly. The sub-frame can turn around a vertical axis eccentric from the point contact. Thus one single glass plate can offer many contact surfaces. The refractive index of the oil varies with pressure and temperature and must thus be known accross the entire pressure field to determine the oil film thickness, h. We will suppose that the oil is\n112 TRIBOLOGY June 1972", "isotropic and that its specific refraction R, which is given by the expression:\nn2 - 1 1 R s - n 2 + 1 p\nstays constant for a given wavelength. This allows us to obtain the variation of n with p and thus with temperature 0 and the pressure, p as relation p = p (p,0) can be determined experimentally. However, up to 50 daN/mm 2 and under isothermal conditions the variation ofp only modifies the relative index n - n o / n o by 10%. Correction will therefore only be applied when the pressure exceeds 30 daN/mm 2 and will be based on a Hertzian elliptical pressure distribution.\nIn steady state, the Newton rings are obtained with a still camera. In unsteady state when the film thickness varies with time 13 a high speed camera or stroboscopic means for cyclic changes, are needed.\nA mercury vapour lamp, and a low voltage tungsten lamp were used respectively as monochromatic and white lights. For monochromatic light X = 546 -+ 12 nm and for an oil of refractive index, n = 1.50 the distance between two con-\nsecutive black rings corresponds to a difference of film thickness of 0.182/am. Thus curves of equal film thickness can be established for 0.091 -+ 0.003/am. For white light, the relation between film thickness and colour can be obtained by calibration using two surfaces of precise and known geometry. Difference of 0.02/am in film thickness can be measured. This method which was first introduced by Cameron and Gohar 4 and later taken up by Foord and a114 is particularly useful for small film thicknesses. As the definition of colour is subjective, calibration and actual test must be performed by the same person.\nExperimental results Data obtained in pure sliding under light and medium loads will be compared to our theoretical results calculated for rigid point contacts under isoviscous and variable viscosity conditions 1'8. The transition first between these conditions and then to elastohydrodynamic conditions will be observed. Finally evidence concerning starvation effects will be presented.\nReproductibility is satisfactory even though thermal conditions are very difficult to control. Differences in measured film thickness between two tests run under identical conditions are less than 10%.\nResults will be given only for one oil whose characteristics are detailed in Table 1.", "G : W = 4 . 6 N , A : W = 7 . 8 N , o : W = I O . 8 N\nTheory ; u = 11 cm/s, - - - equiviscous, - - p iezoviscous Exper iment ; u = 11 cm/s, v : h y d r o d y n a m i c , \u2022 : elastoh y d r o d y n a m i c\nSimul taneous measurements The study parameters are the linear speed, u along ox, the applied load along oy, the traction force, f measured along ox on the plane and the film thickness h = h (x,z) which will be characterized by the film thickness at contact centre, ho.\nContact shape. Fig 3 shows the change of contact geometry as the load increases. In (a) and (b) the surfaces are not\ndeformed, Newton rings are circular. Deformation starts in (c) and increases in (d), (e) and (f). Figs 4 and 5 give graphs showing contact shape in the plane of symmetry (z = 0) and in the transverse plane (x = 0), for the same speed but at different loads. These deformations which occur in both plate and sphere are larger by a factor of seven in the glass plate than in the ball.\nOther measurments. Simultaneous measurements of load W, traction,f, and sliding speed, u and film thickness, ho were performed. Results are shown in Figs 6-10:\nTheory ; W = 3.0 N, - - - equiviscous, - - p iezoviscous Exper imen t ; [] : W = 1.5 N, 0 : W = 3.0 N, [:] : W = 10.8 N\n(> n : h y d r o d y n a m i c , \u2022 \u2022 I : e l as tohyd rodynamic\nTheory ; u = 11 cm/s, - - - equiv iscous hyd rodynam ic , - - p iezoviscous hyd rodynam ic , - -x - Cameron and G ohar e las tohyd rodynamic Exper iment ; ? : u = 11 cm/s v : h y d r o d y n a m i c , \u2022 : e las tohyd rodynamic\n114 T R I B O L O G Y June 1972" ] }, { "image_filename": "designv11_32_0003732_iros.2010.5651753-FigureII-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003732_iros.2010.5651753-FigureII-1.png", "caption": "Fig. II. Design of gripper for removing Jenga block", "texts": [], "surrounding_texts": [ "A, Equipment According to the strategy above, we have devel oped a manipulation system to removing Jenga blocks. Yaskawa MOTOMAN-UPJ, a 6-d.o.f. manipulator with 6- axis force/torque sensor at its wrist is used. As an end effector, an air-gripper with jaws shown above is attached. This manipulator is a small one, so it cannot approach to back side of block tower. So we introduce a rotary table which is moved by human operator. Robot program orders to human operator which face should be in front of the robot. The whole system is as shown in Fig. 15. This system cannot re-grasp a block and then cannot put removed block on the top of the tower. So, human operator represent to put the removed block on the top. After that, human operator input the place with keyboard. When the system and a human player play competition, the robot cannot find which block the human player removed and where he/she puts it on. So, human operator also input the removed block and set place with keyboard. To avoid collision between a manipulator and a table, some blocks (red, black etc.) are piled on the rotary table. They are fixed to the rotary table not to break during manipulation. When the robot grasps a block, its position and posture must be known. But, block pose may have some errors. At that time, human operator helps its small modification to close position of the block. B. Advance measurement of friction We should set coefficient of static friction in kinematics model. We did advance measuring experiment of friction force before Jenga block manipulation. Here, blocks are made from wood, there may be difference according to direction. So, we tested both of width direction and depth direction. Farther, coefficient could be changed according to temperature and humidity, We should measure just before manipulation. On the target block, we put blocks one layer (3 blocks) to 16 layers for each step. To two direction, we measured 18 times for every pattern. Mass of one layer is measured as 38.5[g]. From this measurement, we obtain ILwdir=0.211 and ILddir=0.216 as coefficient of friction to width and depth direction respectively. So we consider there is no difference depend on block direction. Then, in this time, we set coefficient of friction as 0.213 for experiment. C. Threshold for avoidance to break In our strategy, we decide whether a robot removes a block or not according to difference between ideal model and actual force. So, we must set a certain threshold for abandonment. Here, we use the manipulator with a 6-axis force/torque sensor, which measures reaction force during removing block. From several arbitrary formed block tower, the ma nipulator removes a block in several position. We compare these results with ideal model force. The comparison result is shown in Fig. 16. Green circles mean successful removing and red triangles mean failures. From the results, we can find that when actual force is smaller than the modeled value, almost all removing are successfully achieved. If the actual force becomes larger than the modeled value, it may succeed or it may fail to remove. From this, we set the threshold for changing candidate block as the same as modeled value. During operation, if the force sensor measures larger force than modeled value, the robot gives up the first candidate block and changes to the second one, the third one, and so on. If there is no block which acting force is smaller than the threshold, the robot elevate the threshold slightly and return to the first candidate again. VI. EXPERIMENT RESULT A. Removing by robot With the equipment, we did some experiments. First one IS removing only by robot manipulator. In the previous research of Wang[3], they evaluate their system by number of successfully removed blocks by removing only by a robot. So, we also count the number of removed blocks before tower breaking or failure of operation. Putting a block on the top of the tower after removing is done by human operator according to robot order. If there is no blocks on the top layer, a block should be put at the center. In other case, the robot orders random position from both side. The result of 20 trials is shown in Fig. 17. B. Competition with human player The second experiment is competition by robot manipula tor and a human player. As same as the first experiment, games are continued until breaking tower or failure of operation. Where human player removes and where he puts the block on are entered with keyboard. With this input, the robot recognize current situation of block tower. The result of 16 trials is shown in Fig. 18. In all of these 16 trials, the game is finished by robot fail ure. But, when we did not record the experiment operation, the robot won to human player with removing 13 blocks. VII. DISCUSSION In research of Wang[3]et aI., 8 blocks in 9 layers are candidate of removing. In their experiment with 20 trials, maximum number of removed block is 5 and average is 2.7. It may not be fit to compare this result and our result because of different approaches (vision based and concentration to force), but our result seems to be good for the task. In particular, it is very regrettable that we did not record, but it is very impressive that the robot won to human player. From these results, we consider, it is a good approach for some dexterous manipulation methods to make kinematics models and to modify with actual force which is observed. But, we have to pay attention to one point. From the result graphs, there are some failures at very few number of blocks like as 0 or 1. It is not happened to human players. Almost all cases of failure is by moving upper blocks together as shown in Fig. 7. We have to check precisely kinematics model. But, it may be hard to recognize whether upper blocks moves together or not after it starts to move. The reacting force may not be different so much. So it may be hard to sense only by force sensors. In the future, we should use vision sensor, range sensor etc. And we should develop modification strategy of kinematics model parameters; when the robot measures a certain force at a certain place, acting force in the whole block tower may be modified with the information. VIII. CONCLUSION In this paper, we have develop Jenga kinematics model. We showed kinematics model of stable Jenga tower and another kinematics model during removing block. Using these kinematics models, robot manipulator chooses the most safe block to remove. But since there exist differ ence of acting force between ideal model and actual Jenga tower, the robot judges the acting force against ideal one whether the block can be removed or not. When it is judged not to remove, the robot changes to next candidate to remove. According this force based manipulation strategy, the robot has achieved to remove more than twelve blocks form Jenga block tower. During competition with human, the robot can remove a block after more than twenty blocks are removed. It is a good approach for some dexterous manipulation methods to make kinematics models and to modify with actual force which is observed. After this research, we will try other applications. There are several tasks which requires human dexterity like as force sensing, fine motion, etc. For example, parts assembly with very precise insertion with very small gap between peg and hole, metal-carving with very precise impact force, and so on." ] }, { "image_filename": "designv11_32_0001158_icsmc.1998.726649-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001158_icsmc.1998.726649-Figure4-1.png", "caption": "Figure 4 Transition between two equilibrium points.", "texts": [], "surrounding_texts": [ "head F Robot in equilibrium. The masses a.re placed to position the center of gravity above the contact.\n- the regulation with state feedback, - all the steps needed to move the robot from one singular point to another. We control the robot around one point and then we move from one point to another nearest point.\n4.1 Linearization with one contact\nThe set of equations (2) are linearized around a given singular points (qO,QO,uO). For little variation (64, 64, 6u) around the considered point. We obtained:\nWhere : - O, represents the null matrix (dim m n ) . - I, represents identity matrix (dim nxn).\n6 U\n(5 )\nThis can be written again under the well known first order linear differential form :\n(10) x = AcdeX + B,d, c/\nWith the dynamics written in (2) and the partial derivatives through the different variables computed at the point (XO,uO), we can obtain the coefficients of equation (10) :\n0, Is - %de=[ 3 1 Evolution matrix 6x6.\n- v = du = (sr, sr, lT Vector of the two\ntorques around u0.\nThe Kalman controllability criterion is used to check the controllability of the equilibrium and compute the matrix A& and B,de and the controllability matrix. If the rank of this matrix is equal to the order of the system, all the system and all the variables are controllable (Kalman criterion).\nWe have not computed all the singular points but only the main points, robot upright, robot at right angles and the position presented on Figure 2 . In each case, the Kalman's criterion is verified, that means all these configurations are controllable and we can linearly stabilize the system.\n4.2 Regulation with state feedback\nOn the first order linear differential equation we compute the control V=U-L*X to make a state feedback and to obtain the equivalent system :\nWe can build the corresponding control scheme modelling the equilibrium and the robustness of the system (Figure 3 ).\nThe system has initially null eigenvalues and the state feedback allows to place the poles anywhere. Feedback", "matrix L is computed in order to place the poles of the equivalent evolution matrix - Bcde * L). The poles must have real negative parts and we choose for the next experiments the values -3, -3.3, -3.9, -4.2 and 4 , 6 . The system is servo-controlled only around the resting point considered because all the feedback has been made with linearization around this point.\n1\n4.3 Transition with state feedback\n- ............ i ............................ i .............. j ..............\nNow, we know how to control the position of the robot around an equilibrium point, so, to move from initial point (X0,uo) to a final point (Xf,uf), we can generate a \u201ctrajectory\u201d of singular points between the initial and final ones, and for each transition point we use the state feedback regulation, thus we linearize around each point and we compute the feedback matrix L in each case.\n-0.5\n@M-.&+.45. , .... 4 I\nBut to be able to move from one equilibrium point to another, the sytem must stabilize on the point faster than we change the current equilibrium point to the following one.\nThus, with this pseudo-compensation scheme, we are able to follow a trajectory of equilibrium points, but without changing the number of contact.\n4.4 Experiments on balance\nThe disturbance are introduced through a noise input and an error on the initial conditions vector. The error made on the initial condition correspond to an error made on the equilibrium position at the beginning of the test. The behavior of the non linear system (2 ) is equal to the linearized one (10). The system is controlled around the point where the control is efficient.\nWe study the position as shown on Figure 2 (the free foot mass and the head mass compensate the mass of the hip).\nIt is important to note that we balance a quasi double inverted pendulum, without actuators at ground contact point but this double pendulum is counterbalanced with the mass of the free leg.\nFor numerical application the robot has: - the same length for legs and trunk : - different punctual masses : l=lh=OSm\nmt=0.5kg for the head mh=lSkg at hip m=0.5kg for each foot.\nWe simulate the behavior of the biped for two different initial positions near one solution of equilibrium chosen at : 00=-0.41rd, qlo=0.57rd, q20=0.82rd (Figure 2 ).\n- 0ini=-0.45 The robot recovers its stability (Figure 5 a-b-c) - 0ini-4.381rd The robot fall backward and can never be straighten up\n(Figure 5 a-b-c).\nfig 5 -a: Pitch angle of the head 1.51 1\n\u2018 0 1 2 3 4 5 Time (s)\nfig 5-b: Position of the joint on contact 1.61\n0.4 I 0 1 z 3 4 5\nTime (s)", "5. Prototype\nWe show on each drawing the results obtained with the two different initiad conditions : 8ini=-0.45( 1) and e i n i 4 . 3 8 l r d (2) instead of eO=-O.41rd.\nIn the first caste (Bini=-0.45), the robot stays in equilibrium. Disturbances are well managed with little movements of the free leg (Figure 5 -c). In this case this special double inverted pendulum remains stable.\nIn the second case (@ini=-0.381), the robot can not be servo-controlled to the desired steady point in presence of large disturbance. It leaves the linearization domain.\nA domain exists to have a correct control, this domain corresponds to the domain of validity of the linearization. That is why in the first test ( 1 ) the robot stay around the desired point. The feedback are well computed and the robot stay stable (Figure 5 a-b-c) due to little movement and disturbance.\nHere, we only study the controllability of the biped and we did not define any trajectories to follow. The system is controllable but that not means we can follow a trajectory, moreover we are lirmted to the domain of validity of this control scheme.\nWe must test the transition with state feedback to move the robot from one equilibrium to another. Of course, to walk (or run) this approach is not sufficient but must provide an interesting case to be studied with prototype.\nWe have build a prototype to evaluate our model and moreover our control law. Figure 6 presents a photo of our prototype.\nThe structure is artificially constrained, with a large foot on contact, to stay in a plan to be similar to the model we have defined. The two actuators are electrical DC-motors (24 Volts, 75 Watts) with a speed reducer for each leg. To be as close as possible to the model, we have used carbon pipe for the segments: trunk and legs, and thus masses are located mainly at the feet, the hip (motor and speed reducer) and head (we can load down it). Simple encoders will provide the necessary coordinates q I , q2, and to provide 8, we use a real time correlator.\nThis correlator is made of a camera, an input output card with a processor (transputer T80.5) and a FPGA (Altera IOK100). The signal produces by the camera is digitalized on 8 bits (256 gray scales). The FPGA use these datas to correlate the digitalized image with four different tags. It provides at each image (24 images per second) the positions of four tags (positionned on the extremity and along the trunk) using a correlation mask of 29 pixels per 9 pixels, to obtaine the correlated online image 300 per 300 pixels." ] }, { "image_filename": "designv11_32_0002361_jps.2600621115-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002361_jps.2600621115-Figure7-1.png", "caption": "Figure 7-Placement of polyelhvlene clamps 10 elintitlare sliortirig.", "texts": [ " The wicks were placed with the dialysis membranes in contact with either end of the elcctrophoregram and not extending onto the platen beyond the foam rubber pads. The upper polyethylene insulating sheet was placed in position, and the apparatus was closed and pressurized to 5 psig. Two pieces of polyethylene tubing [1.27-cm. ( 0 . 5 4 . ) 0.d. X 0.16- cm. (0.069-in.) wall X 5.08-cm. (2-in.) length], slit lengthwise, were placed as clamps over the sides of the polyethylene insulating sheets snd extended slightly beyond the aluminum angles (Fig. 7) on the high tension end of the apparatus. The high tension is the anode with the power supply used3. Previous work showed that almost all electrical shorts occur at this end of the apparatus and that most of them result from the deposition of moisture between the insulating sheets; when the moisture reaches the edge of the sheet, a spark jumps to * Shnndon modcl 2550. Savant model 11V-5000-TC. Neslab model HX-75. 5ASTM No. 7-140-105. 17.78 X 57.15 cm. (7 X 22.5 in.), 105-p porosity. Kressilk Products, Inc" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001468_elan.200302908-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001468_elan.200302908-Figure2-1.png", "caption": "Fig. 2. Schematic diagram of the flow system.", "texts": [ " The AndCare sensors include a traditional threeelectrode configuration, which comprises a disk-shaped working (4-mm diameter), counter and silver pseudoreference electrodes printed on polycarbonate substrates (4.5 1.5 cm). Working and counter electrodes were made using heat curing carbon composite inks. An insulating layer was printed over the electrode system, leaving uncovered a working electrode area of 7 5 mm and the electric contacts. A ring-shaped layer further printed around the working area constituted the electrochemical cell and voltammetric measurements were carried out by casting a 40- L drop of the corresponding solution in this area. Figure 2 shows schematically the FIA system employed. The 12 cylinder Perimax Spetec peristaltic pump (Spetec GmbH, Germany) allows the 1.0 M H2SO4 stream to flow through the system. Desired solutions are injected by means of a six-port rotary valve, Model 1106 (Omnifit Ltd., UK) equipped with a 100- L loop. Detector consists of homemade wall-jet flow cell (two methacrylate blocks fixed together with four strews) where the SPCEs were placed. One of the two pieces of methacrylate has inlet and outlet flow channels forming an angle of 30 " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000621_rob.4620070104-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000621_rob.4620070104-Figure4-1.png", "caption": "Figure 4. Illustration of center of mass of composite rigid body. mi: Center of mass link i . CM,: Center of mass of composite system composed of link i through link n.", "texts": [ " Furthermore, using intrinsic equations allows one to choose the optimal coordinate frame(s) for their projection by analyzing the vectors and the tensors involved in the equations. The projection scheme of the fourth section shows an example in which a greater efficiency has been achieved by using different coordinate frames for projection of the intrinsic equations. However, this optimal choice of the coordinate frames could not be easily known in advance. The computation of the composite rigid-body algorithm is performed in two steps as (Fig. 4): 78 Journal of Robotic Systems - 1990 Step 1 For i = n , n - 1 , . . . , 1 M i = M ; + l + mi i& = i ~ ~ + ~ ( ' + l & + ~ - Mi+l i+lD;+l i+ lZj \\+ l + ' + l J i - mi;+ lbii+lLj,)iR: I 1 + 1 'Fi = Zo x MfCi with Zo = 'zi = [0 0 11' aii = Zo . 'ni If joint i is revolute aii = Zo . i f i If joint i is sliding Step 2 F o r j = i - l , i - 2 , . . . , 1 aij = Zo - inj If joint j is revolute aij = Zo 'fi If joint j is sliding (4414) The research described in this paper was performed at the Jet Propulsion Laboratory, California Institute of Technology, under the contract with the National Aeronautics and Space Administration (NASA)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003739_gt2009-59285-Figure12-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003739_gt2009-59285-Figure12-1.png", "caption": "Figure 12: Adding shims between upper and lower bearing halves to increase vertical clearance", "texts": [ " The rotor and bearing properties for Setup #2 are shown in Table 1 with all other bearing properties the same as Setup #1. Despite the modifications to the rotor and bearings in the test rig Setup #2, the system was still very stable beyond 100+ krpm, the maximum speed tested. In order to test the effectiveness of dampers behind the pad, the bearings were purposely made unstable by increasing the clearance in the vertical direction via placing shims between the upper and lower halves of the bearings (Figure 12). Then, dampers were used behind the pad to enhance the Copyright \u00a9 2009 by ASME rl=/data/conferences/gt2009/70651/ on 03/21/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Dow stability. The damping material used was a 3M\u2122 110P05 viscoelastic damping polymer. The damper was used in its original packing, which is a laminate between layers of paper backing and plastic film, and was cut to fit in the wire-EDM gap (approximately 13 mm wide). Stiffness of the damper was estimated to be approximately 2-3 610 N/m based on comparisons of the pad radial natural frequency with/without the damper installed" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001839_tia.1979.4503695-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001839_tia.1979.4503695-Figure4-1.png", "caption": "Fig. 4. Inductances measurements.", "texts": [ " Granting the following: Xsd = Lsd Id Xsq = Lsq * Iq, (2) we have the habitual formulation, but with L,d and L,q dependent upon Isd and Iq: Lsd Lsd(Isd, Isq ) Lsq =Lsq(Isq, ISd). (3) Measurements Measurements will exist in the experimental determination of curves for L8d and L8q with respect to Isd and Isq In order not to involve the rotor winding, the flow is determined by integrating the voltage at the terminals of the stator windings, which are connected to a resistor when the current varies from +Io to -Io. The principle of measurement is shown in Fig. 4. The machine is wye connected, and the flux is measured at the terminals S2 and S3 of two windings for a direct current Io throughout windings 2 and 3, whilst an independent direct current I, passes through the third winding. The rotor is positioned either on the axis of the windings with current Io or in the axis in the quadrature to determine Lsd and Lsq, respectively, (see (4)). The relations between the amplitudes of direct currents Io, I, and Isd Isq are easily determined by using a d, q transformation: 0 =900 'sq = 2I /3 Isd = 2Io/-3 (4a)Lsd = X23/(2Q1) and 0 =00 Isq = 2Io/V Isd = 2I1/3 Lsq = X23/(2Io)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003104_335101-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003104_335101-Figure2-1.png", "caption": "Figure 2. (a) The idealized bookshelf SmA alignment when the director n, represented by the short bold lines, coincides with the layer normal a and \u03b80 = \u03b8p = \u03b40 = 0. The sample is confined between boundary plates located at z = 0 and d . (b) The boundary conditions for the director and layer normal are dictated by a competition between elastic effects in the bulk and the preferred director alignment \u03b8p at the boundary. For weak anchoring, the value of \u03b8 on the boundary, denoted by \u03b80, will generally differ from \u03b8p. The smectic layer tilt at the boundary is \u03b40 and is determined from classical natural boundary conditions. (c) Definitions of the orientation angles \u03b8 and \u03b4 for the director n and smectic layer normal a. The preferred director orientation on the boundary, np, makes an angle \u03b8p, determined by physical alignment processes.", "texts": [ " This supplements the work of Stewart [10] where strong anchoring of the director and a supposed fixed smectic layer alignment at the boundaries were assumed in some preliminary studies of equilibrium configurations of SmA. The two key features of this present paper are, firstly, the consideration of equilibrium solutions for the director and smectic layers when n no longer necessarily coincides with a and, secondly, a comparison between the results for strong and weak anchoring of the director. In all cases, natural boundary conditions are imposed upon the smectic layer alignment. We consider a sample of \u2018bookshelf\u2019 aligned SmA liquid crystal confined between boundary plates as shown in figure 2 below. The mathematical model, governing equilibrium equations and boundary conditions are discussed in section 2, together with elementary models for the bulk and surface energy densities. The special case of strong anchoring of the director with natural boundary conditions for the smectic layer tilt is discussed in section 3 while solutions for weak anchoring are investigated in section 4. A discussion of the results is given in section 5. Equilibrium configurations for bounded samples of SmA will be considered and the equilibrium equations for n and a will be obtained by minimizing the associated energy consisting of bulk and surface contributions", " In this formulation, the surface energy is minimized when n is parallel to np. The total energy per unit volume is W = \u222b w d + \u222b S ws dS, (2.3) where is the sample volume and S is its surface. We shall examine what is commonly called the \u2018bookshelf\u2019 alignment of SmA. In a perfectly aligned sample of bookshelf SmA the director is parallel to the smectic layer normal and the planar smectic layers themselves are arranged in a bookshelf formation perpendicular to parallel planar boundaries, as shown in figure 2(a). Such an idealized alignment is only possible when np = n = a, which is generally not the case. It will be assumed that the director n and the smectic layer normal a are uniform in the x and y directions so that their respective orientation angles \u03b8 and \u03b4, measured with respect to the x-axis as shown in figure 2(c), are functions of z only, i.e. \u03b8 = \u03b8(z) and \u03b4 = \u03b4(z). Note that the boundary orientation angle \u03b8p of the preferred director alignment np is fixed at the boundary. The anticipated director and smectic layer alignment in a bookshelf-type geometry across a sample of depth d in the z-direction is shown schematically in figure 2(b). The director n and the layer representation may then assume the forms [10] n = (cos \u03b8(z), 0, sin \u03b8(z)), (2.4) (x, z) = x + \u222b z z0 tan \u03b4(t) dt, (2.5) where z0 is an arbitrary constant. It follows immediately that \u2207 = (1, 0, tan \u03b4(z)), |\u2207 | = sec \u03b4(z) (2.6) a = \u2207 |\u2207 | = (cos \u03b4(z), 0, sin \u03b4(z)), (2.7) n \u00b7 a = cos(\u03b8(z) \u2212 \u03b4(z)). (2.8) It will be supposed that \u03b8 and \u03b4 will only take values strictly lying between \u2212\u03c0/2 and \u03c0/2. From the expected symmetry of the problem, we look for solutions of the form \u03b8(z) = \u2212\u03b8(d \u2212 z), 0 z d, (2.9) \u03b4(z) = \u2212\u03b4(d \u2212 z), 0 z d, (2.10) \u03b8 \u2032(0) = \u03b8 \u2032(d), \u03b4\u2032(0) = \u03b4\u2032(d), (2.11) where a prime denotes the differentiation with respect to z. The boundary conditions will then lead to \u03b8(0) = \u03b80, \u03b4(0) = \u03b40, \u03b8(d) = \u2212\u03b80, \u03b4(d) = \u2212\u03b40, (2.12) for constant angles \u03b80 and \u03b40 that have to be determined from the minimization of the total energy when a given preferred orientation np for the director at the boundary is prescribed (see figure 2). These constant angles at the boundaries will be determined as part of the solution process and, despite being influenced by all the material parameters, they will be governed primarily by the magnitude of the weak anchoring strength \u03c40\u03c9 and the preferred director orientation angle \u03b8p at the boundaries. In general, \u03b80 = \u03b8p for weak anchoring whereas \u03b80 = \u03b8p under any strong anchoring assumptions. The bulk energy density (2.1) becomes w = 1 2 K n 1 (\u03b8 \u2032)2 cos2 \u03b8 + 1 2 K a 1 (\u03b4\u2032)2 cos2 \u03b4 + 1 2 B0[sec \u03b4 + cos(\u03b8 \u2212 \u03b4) \u2212 2]2 + 1 2 B1 sin2(\u03b8 \u2212 \u03b4)", " The surface pretilt \u03b80 of the director was fixed while the natural boundary value \u03b40 for the surface tilt of the smectic layers was calculated numerically; its dependence on the dimensionless parameters \u03ba and B was displayed in figure 4. Comparisons with earlier theoretical results [10] for prescribed \u03b40 were also made, in addition to comparisons with the experimental work contained in [1, 19, 20]. Strong anchoring in smectics with a variable director tilt relative to the smectic layer normal has also been discussed by McKay and Leslie [21] and McKay [22], who also discussed a geometrical set-up similar to that in figure 2(b) above. Despite some differences in the nonlinear smectic energy density used, the mathematical approach for strong anchoring employed in [21, 22] is similar in style to that presented here. The influence of weak anchoring was determined in section 4 and solutions were obtained numerically to produce the results in figures 5\u20137. Although the boundary layer effects were similar to those discussed above for strong anchoring, there were great differences in the determination, and values, of \u03b80 and \u03b40 at the boundaries" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002253_00207177408932797-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002253_00207177408932797-Figure5-1.png", "caption": "Figure 5 (a) Root-locus as function of C1 for method 1.", "texts": [ " G;(s) denotes the resulting filter action of the error filter and the 8VG in order to compute eU ), j =O(I)n. In the ideal case when no error filter is used G;(s) =s;. In (19 a) {k =P(k+lln + yuok, k =O(I)n - I Ol=bo (:t~ V2= V1+z'rRz (21) D ow nl oa de d by [ ] at 0 8: 09 2 4 D ec em be r 20 14 984 A", " D ow nl oa de d by [ ] at 0 8: 09 2 4 D ec em be r 20 14 !I88 A. J. Udink ten Gate and N. D. L. Verstoep .5. J. Deterministic signals If noise is not present in the 1\\lRAC system, or when its influence can be neglected, there is no need to filter thc error signal. In Fig. 3 (a) the TAE criteria are shown as functions of the speed of adapta tion lX, when only the gain is adapted by adjusting kn . It can be' seen that method I will give oscillatory responses for large values of lX. This is caused by the ADF's as can be seen in Fig. 5 (a) which gives the root-locus plot of the characteristic eqn. (I H) where OJ represents the resulting filter action of the ADF's. In Figs. 5 (b) and 5 (c) the root-locus of methods II and III are given, illustrating the better convergence properties of these methods because of the introduction of additional zeros in eqn. (I H), for convenience here Wd, = J0.5 and Wd, = 11.0. Also, Fig. 3 (a) shows that method IV does not give an improvement compared to III. Therefore, method IV was not included in a further com parison" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000514_3-540-45118-8_49-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000514_3-540-45118-8_49-Figure2-1.png", "caption": "Figure 2. PUMA, from top view, shows the degenerate direction at elbow singularity, expressed in Frame{B}, which is derived from rotating Frame{2} by angle \u03b2", "texts": [ " 4J = (a2C2 + d4S23)S4 + C23(\u2212(d2 + d3)C4 + a3S4) C4(d4 \u2212 a2S23) d4C4 0 0 0 (a2C2C4 + d4C4S23 + C23(a3C4 + (d2 + d3)S4) \u2212(d4 + a2S3)S4 \u2212d4S4 0 0 0 \u2212(d2 + d3)S23 \u2212a3 \u2212 a2C3 \u2212a3 0 0 0 \u2212C4S23 S4 S4 0 0 S5 S23S4 C4 C4 0 1 0 C23 0 0 1 0 C5 (8) When (\u03d15 = 0), a row of zero only appears at the last three elements of the fourth row of 4J : 4 J22 = [ 0 0 0 0 1 0 1 0 1 ] (9) This means that it is still possible to rotate around the X-axis of Frame{4} in wrist singularity, but it is produced by the first three joints, which would also change the position of the end effector (i.e. not possible in 6 DOF). Therefore, the first row of 4J22, (or the fourth row of 4J) is the degenerate direction, representing the rotation around X-axis of Frame{4} (see Figure 1 and 4). Collapsing the Jacobian is then done by eliminating the fourth row of 4J . Elbow singularity is shown by projecting the Jacobian and the task space forces onto Frame{B} which is not one of the frames in our DH assignment (see Figure 2 for the frame assignment, and Equation (10) for the resulting Jacobian). At this configuration, the singular direction is found to fall along the line connecting the wrist point to the origin of base frame. BJ [1][1] = (d2+d3)S2(d4C3\u2212a3S3) (a2+a3C3+d4S3)D BJ [1][2] = (d4C3\u2212a3S3)(a2+a3C3+d4S3) 2D a2 2+d2 2+2d2d3+d2 3+2a2a3C3+a2 3C2 3+2a2d4S3+d2 4S2 3+a3d4Sin[2q3] BJ [1][3] = d4C3\u2212a3S3 D BJ [2][1] = (d2 + d3)S2; BJ [2][2] = a2 + a3C3 + d4S3 BJ [2][3] = a3C3 + d4S3 BJ [3][1] = C2(a 2 2+d2 2+2d2d3+d2 3+a2a3C3+a2d4S3)+(a2+a3C3+d4S3)(a3C23+d4S23) (a2+a3C3+d4S3)D BJ [3][2] = (d2+d3)(d4C3\u2212a3S3) (a2+a3C3+d4S3)D ; BJ [3][3] = (d2+d3)(d4C3\u2212a3S3) (a2+a3C3+d4S3)D where: D = \u221a 1 + (d2 + d3)2 (a2 + a3C3 + d4S3)2 (10) Frame{B} is obtained by rotating Frame{2} by angle \u03b2, which is defined as: \u03b2 = Tan \u22121 [ d2 + d3 a2 + a3C3 + d4S3 ] (11) From (6), it is shown that \u2212a2(d4C3 \u2212 a3S3) = 0 at elbow singularity. Therefore, the first row of BJ11 is a zero row (BJ [1][1] =B J [1][2] =B J [1][3] = 0). This shows that the degenerate direction lies along the X-axis of Frame{B} (see Figure 2). Equation 10 only shows the elements BJ from the top left quadrant, because the top right quadrant is a zero matrix. The idea of removing the degenerate component is done by removing the row(s) of the Jacobian matrix and elements of the task space force F (see Equation (2)) that represent the degenerate direction(s) of motion. To do so, the Jacobian matrix and force vector need to be expressed in the frame in which one of the axes represents the direction of singularity (degenerate direction). Force vector in task space is obtained from the control law to represent the virtual force that \u2019pulls\u2019 the end effector to the desired position and orientation (see Equations (2), (3))", " It is shown that in most cases, the error generated is not larger than that found in non-singular motion, except for some trade off shown in the cases of desired trajectory lying along non-feasible path, where exactness of orientation tracking was sacrificed to make the motion feasible. Type 1 Singularity, or in the case of PUMA, the elbow lock, is one where null space torque would generate motion in the singular direction. This means, for the case of PUMA, null space motion of joint 3 would generate motion in the singular direction (see Figure 2 for singular direction). Comparing the tracking error (position and orientation) of the manipulator moving out of elbow singularity into the degenerate direction with that of non-singular motion, no significant increase in position and orientation error is observed. (Compare Figure A7 and A8 to Figure A1 and A2). A common type 2 singularity in PUMA is when the wrist joint is straightened (\u03d15 = 0 ). The non-feasible path is when it contains the component of degenerate direction, i.e. it requires the end-effector to turn around the X-axis of Frame{4}, or if the desired trajectory lies on the YZ plane of Frame{4}" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003297_j.rcim.2008.07.002-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003297_j.rcim.2008.07.002-Figure1-1.png", "caption": "Fig. 1. Spherical gear.", "texts": [ " The theoretical feasibility of this kind of gear is proven by the analysis of the profile, contact ratios and undercut. It makes the process of manufacturing easier than before, improving the manufacturing precision and simplifying the manufacturing process. This paper introduces the theory and manufacturing method of concave tooth profile, that is spherical cone gearing. The analysis and calculations on the convex tooth profile engaging with the concave cone tooth is also proved. & 2008 Elsevier Ltd. All rights reserved. The spherical gear is the key component of the robot\u2019s wrist. As shown in Fig. 1, by using the spherical crowns of two different spherical centers as a joint curved surface, and their spherical center as a rotational center, the spherical gearing can be formed on two spherical surfaces with convex teeth and concave teeth engaging each other. Theoretical analysis shows [1\u20133] that the concave tooth profile of a spherical gear can be the rotation of the involutes surface. The curved surface of convex tooth profiles are formed according to concave tooth profiles through the envelopes of dual parameters", " According to our calculations, every pair of convex teeth and concave teeth engages an area f \u00bc 0.2236-0.1029 rad. Since this area is larger than 15, the gearing can act continuously. The convex tooth surface is a curved rotational surface. The sectional profile of the axle is shown in Fig. 2. According to Eq. (3), thus umax \u00bc 17:7909 According to Eq. (24), on the undercutting limited point, thus uc \u00bc 17:7042 Since uc4umax, there is no undercutting. Spherical gearing is the key part of a robot\u2019s wrist. As shown in Fig. 1, the two balls are the pitched surfaces; the centers of the balls are the revolving centers. On the two spherical surfaces, there are concave and convex teeth, respectively, which can engage so as to mesh meshing with each other. So that the spherical gear transmission is realized. The theoretical analysis [1] proves that the concave tooth of the spherical gear can be the rotational involutes, which is the surface formed in the process of double parameters of involution. But both the concave and convex teeth are hard to generate" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000918_bf00140121-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000918_bf00140121-Figure1-1.png", "caption": "Fig. 1, (c) a<4 I, h>O", "texts": [ " We are given three charged particles with mass: one is positive and moves on a symmetry axis, its total effect being equivalent to that of a charge + a ; the others move symmetrically with respect to the axis and are negative with the same charges and masses, their total effect being equivalent to particles of charge -1 . The potential is obtained by changing the sign in one term of the celestial mechanics isosceles 3-body potential [10], to account for a repulsive force: U(x, y) = - (2x) -1 + 2a/4\"~x2+ y2; x > 0, y ~ R , (3) Looking at the equipotential curves in configuration space, we have to consider three cases which correspond to how big a > 0 is with respect to ). This is shown in Figure 1, where some equipotential curves U- -cons tan t are drawn, making clear the lines U = 0 and the (possibly empty) regions U > 0 and U < 0. The tv0ical U + h >/0 regions are shaded and the bounded one corresponds to h < 0. In any case, we have homothetic solutions projecting along the x-axis. They satisfy the equation ~2/2 = ~ ( a -\u00bc) /x + h, which is the energy relation of a one-dimensional Kepler problem if a > \u00bc, a repulsive one if a < ~, and a uniform speed motion if ot = 1. These solutions are called collinear because the particles remain along the axis. Since the so-called Hill regions U + h >1 0 represent the allowed positions for fixed h, Figure 1 shows that collisions of the three bodies or x = y = 0, can occur only when a I> ~ to overcome the repulsion of the - 1 charges, and they actually occur asymptotically inside the sector U >/0 defined by l Yl ~< x/(4ct) 2 - 1 x. There are no other approaches to the y-axis, since that would correspond to binary collisions of the - 1 charges, which rather repel each other. The mass matrix is A = diag(2, 2a/(2 + a)) so that r 2 = 2x 2 + 2ay2/(2 + a). The blow up transformation at the origin (of type I) is written as q = rQ, p = r-1/2P" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003997_1.4002089-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003997_1.4002089-Figure1-1.png", "caption": "Fig. 1 Two-axle IRW truck", "texts": [ "asme.org/pdfacc wisdom of IRW that hunting instability is completely removed in IRW. Oscillatory motion of IRW obtained using the multibody dynamics simulations are reported in the literature 8 as well, while the stability and the vibration characteristics of IRW truck are not thoroughly discussed in these literatures. It is, therefore, the objective of this investigation that the dynamic characteristics of a two-axle IRW truck, which has been widely used in the middle truck of LRV, as shown in Fig. 1, are investigated. In particular, the hunting stability, vibration characteristics, and the curving performances of the two-axle IRW truck are discussed. To this end, the linear stability analysis of a two-axle IRW truck is first performed, and the vibration characteristics of IRW truck are investigated with the model that considers the independent wheel rotations. The results are compared with those obtained using the multibody dynamics IRW model developed using the velocity transformation method" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001933_05698190590948232-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001933_05698190590948232-Figure6-1.png", "caption": "Fig. 6\u2014Structure drawing of the latest combined single seal with floating bushing seal: 1, rotating seat; 2, primary ring; 3, sleeve; 4, 0-ring secondary seal; 5, spring; 6, retainer; and 7, floating bushing.", "texts": [ " Since the seal went into operation in 1996, the unit has been operating normally and reliably, nearly without leakage, for more than 7 years. Example 2 The ammonia refrigeration gas compressor is the key equipment of an ammonia synthesis plant. The main parameters of the centrifugal compressor used in a certain fertilizer plant are given as follows. The sealed gas media is ammonia gas, suction pressure 0.31 MPaA, discharge pressure 1.45 MPaA, rotating speed 10,295 r/min, and seal size 116 mm. As shown in Fig. 6, noncontacting, zero-leakage single seals with single-row spiral grooves, combined with a floating bushing seal, were used. The principle of the supporting system is shown in Fig. 16, in which a conventional outside circulation system is adopted. Since the seal went into operation in 1999, the unit has been operating normally and reliably, nearly without leakage, for more than 3 years. The experimental investigations about oil-film-lubricated mechanical face seals with spiral grooves are performed" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001606_j.1471-4159.1982.tb07973.x-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001606_j.1471-4159.1982.tb07973.x-Figure1-1.png", "caption": "FIG. 1B. Double-reciprocal plot of 1251-a-BT binding to membranes from rat diaphragm in the absence (0) and presence (0) of 10 pM AAsCh and 20 pM AAsCh (A). Inset depicts the slope as a function of inhibitor (AAsCh) concentration.", "texts": [ "1 d) were generated using longitudinal muscle strips as described by Kilbinger and Wessler (1980). Exposure to agonist was for 1 min at 6-min intervals. Kinetic constants (Ki) and ED,,JlC,, values were determined graphically. AAsCh was a muscarinic cholinergic ligand in the central and peripheral nervous system. It displaced radioactively labeled with high specific activity muscarinic antagonist 4-NMPB bound to rnuscarinic receptors in the rat cerebral cortex. The inhibition of the [3H]4-NMPB binding was competitive, as indicated by the doublereciprocal plot in Fig. 1A. The Ki value was 10 p M . Comparison of binding of ACh and AAsCh to muscarinic receptors from the cerebral cortex shows that they were equally potent as inhibitors of [3H]4-NMPB binding (Table 1) . In myenteric neurons AAsCh (10 p M ) was a presynaptic muscarinic agonist and depressed the electrically evoked secretion of ['HH]ACh in the presence of eserine (10 p M ) by 15 t 2% (n = 3; p < 0.001). The secretory response was depressed by endogenous ACh after additional eserine (10 p M ) (cf. Alberts et al., 1982), and addi- y 2 0 pM AAsCh 04 0 0.5 1 1.5 '/mM] h N M P B FIG. 1A. Double-reciprocal plot of [3H]4-NMPB binding to membranes from rat cerebral cortex in the absence (0) and presence (0) of 5 pM AAsCh, 10 pM AAsCH (A), and 20 pM AAsCh (A). Inset depicts the slope as a function of inhibitor (AAsCh) concentration. J . Nriirochrrn.. V o l . 3Y. No. 3, 1982 ACETYLARSENOCHOLINE: A CHOLINERGIC AGONIST tion of exogenous ACh (10 pM) did not further depress the evoked secretion of ['HH]ACh. At the peripheral muscarinic postsynaptic rcceptor of the guinea pig ileum longitudinal muscle, the efticiency of AAsCh was only 1% of that of ACh in evoking the contractile response (Table I)", " Another possibility is that the apparent discrepancy in the potency of the two compounds in the periphery but not in the CNS reflects the fact that only binding data are available \u20acor muscarinic receptors in the CNS, whereas the data from the ileum include the efficiency of the step coupling of the binding of agonist to the receptor with the contraction. It is possible that the binding properties of ACh and AAsCh are similar but that the subsequent coupling step differs when AAsCh or ACh is bound to the receptor. Competi t ion s tudies with 1251-a-BT, a nicot inic antagonist, at receptors from rat medulla-pons and diaphragm indicate that AAsCh also was a nicotinic ligand (Fig. 1B). Experiments with choline acetyltransferase indicate that this enzyme can utilize arsenocholine as a substrate: we were able to identify AAsCh in incubation mixture consisting of the enzyme, acetyl-CoA, and arsenocholine; in addition we found that the K , value was 240 mM (Table 1). The investigation was initiated when the presence of AAsCh was indicated in shrimp (Norin and Christakopoulos, 1982). By use of ligand binding studies, we have confirmed the results of Roepke and Welch (1936), showing that AAsCh is a cholinergic ligand acting at both muscarinic and nicotinic receptors, but that it is less potent at 873 peripheral muscarinic receptors than ACh" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001144_978-3-642-83410-3_7-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001144_978-3-642-83410-3_7-Figure5-1.png", "caption": "Fig. 5. PVF2-based sensorized fingertip", "texts": [ " The tactile sensor we have designed is based on the technology of the ferroelectric polymer PVF2, and is capable of extracting, when appropriate motor acts are commanded to the supporting articulated finger, information about the explored object. The sensor, intended to mimick, at least functionally, even if not morphologically, the human finger pad skin, includes two sensing layers (a deep, \"dermal\" layer and a superficial, \"epidermal\" layer separated by a compliant rubber layer (Dario et al. 1984). The dermal layer is primarily sensitive to the local, contact-induced normal stress. It has relatively high spatial resolution (128 circular sensing sites, diameter 1.5 mm, center to center spacing 2.5 mm, as depicted in Fig. 5), and it is capable of providing a quasi-static response to force signals. Thus, the role of the dermal sensing elements can be conceptually associated to that of the slowly adapting (SA) receptors of the human skin, which are sensitive to the tiny spatial features of the indenting object (Phillips and Johnson 1982). The epidermal layer includes only a few sensing sites (7 circular elements, diameter 1.5 mm, center to center spacing 2.5 mm) concentrated in a small area (the tactile \"fovea\") of the fingertip and particularly sensitive, like the quickly adapting (QA) skin receptors, to dynamic contact stimuli" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003854_icinfa.2010.5512359-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003854_icinfa.2010.5512359-Figure8-1.png", "caption": "Fig. 8. Temperature field of the bearing", "texts": [ "87 K/W. It occupies 2.54% of the total thermal resistance. It means that the thermal resistances computed by using the heat network model and the finite element method are quite close. It shows that our simplified heat network model is feasible. Based on the finite element sub-model of the bearing, friction heat of the bearing, and the temperature of the innerring and the outer ring of the bearing presented in the previous sections, the finite element analysis for the No. 1 bearing was performed. Fig. 8 shows the finite element result of the temperature field for the bearing. It is obvious that the temperature gradient of the contact surface between the ball and the inner and outer ring is higher. The reason is that the thermal conductivity of the grease is smaller than that of the steel. Accordingly, the heat mainly transfers from the inner ring to the outer ring across the rolling ball. Fig. 9 shows the heat flow distribution of the bearing. Note that the heat flow in bearing is non-uniform. The density of heat flow rate on the interface between the rolling ball and the inner and outer rings is very large" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure5.7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure5.7-1.png", "caption": "Fig. 5.7. Angular measurement", "texts": [ " This angular displacement may vary with the linear travel distance of the moving part. The primary causes of an angular deviation include the physical guide imperfections and possibly cogging related effects. The optics and accessories used for the angular measurement are rather similar to those used for linear measurements. A breakdown of these devices and accessories is given in Figure A.2. The set-up for pitch and yaw measurements are given respectively in Figure A.3 and Figure A.4. A closed-up view of the traverse path of the laser beams is given in Figure 5.7 which illustrate that the angular measurement is comprised of two linear measurements at a precisely known separation. Roll measurement is addressed separately in the next section as this measurement will typically require a level-sensitive device to be used. The objective of a straightness measurement is to determine whether the moving part is moving along a straight path. The main source for a straightness 5.3 Overview of Laser Calibration 137 error is the straightness profile of the guiding mechanisms which guide the motion of the moving part" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003249_1.2821385-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003249_1.2821385-Figure6-1.png", "caption": "Fig. 6 and the first case in Fig. 18, the end segments added to the envelopes directly give the boundary, whereas in the latter two cases in Fig. 18 more involved trimming operations are necessary.", "texts": [ " 5 c are artifacts of numerical computations, which could result if the concerned instantaneous center lies near the locations with relatively high curvature on its locus. However, the steps of loop decomposition and the tests for internal singularity trim off such spurious features from the boundaries. 5.4 Special Situations. The swept area or workspace is always a bounded area, and hence the boundary curves are simple and closed, irrespective of the nature of the generating and sweep curves. Thus, when envelopes are open, then the boundary will contain finite portions of the sweeping curves along with the envelopes for closing the bounded areas Fig. 6 . This happens when the underlying manipulator admits only a restricted range of the input parameters. The boundary of the swept area would contain Transactions of the ASME x?url=/data/journals/jmdedb/27868/ on 01/29/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use fi c c t p m c s w t r t o c t t m a l F r o F n l F s J Downloaded Fr nite portions of the sweeping curves also when the sweep motion eases to be smooth enough, e.g., when the locus of instantaneous enters contains cusps or sharp kinks Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003096_1774674.1774705-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003096_1774674.1774705-Figure3-1.png", "caption": "Figure 3. Concentric circular remote sensing survey and parameters.", "texts": [ " Measurements along a line-of-sight between t he r over-mounted ac tive i nstrument a nd the fi xed component acc ount f or 2 -D coverage o f t errain be low the line-of-sight. Such measurement techniques are used on Earth with l aser-based s pectrometers t o pr obe f or a nd de tect ga s emissions during environmental s ite s urveys [ 11], a nd they are being developed for the same on Mars [10]. A n accumulation of such l inear m easurements from di screte ra dial l ocations and distances achieves survey region coverage. The following four parameters are used to configure a concentric circular t rajectory c overing a gi ven survey re gion ( Fig. 3) : innermost c ircle r adius, 1; ra dial distance, c, b etween circumferences of c onsecutive circles; a rc l ength, s, b etween consecutive m -nodes on a circle; a nd pos itive i nteger, n, designating the nth or outermost circle including the survey region. The algorithm assumes that the rover is already within the survey region and that the fixed component is w ithin l ine-of-sight from the r over [ 5]. I f i t i s not , t hen no m easurement i s m ade. The survey completes when the nth circular trajectory is followed" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-FigureA.8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-FigureA.8-1.png", "caption": "Fig. A.8. Squareness measurements - first axis (horizontal plane)", "texts": [ " A CMM with a probe that moves vertically and mounted on a bridge which moves horizontally is another example. The main cause of a squareness deviation is probably the constraints during the manufacture or assembly of the machine to fix two axes exactly perpendicular to each other. The squareness measurement will be useful to allow the small angular difference to be measured and compensated for. The optics required for squareness measurements are given in Figure A.7. The main procedure for squareness measurement on a horizontal plane is to carry out a measurement along the first axis as shown in Figure A.8 using an optical square, and subsequently to carry out a measurement along the second axis according to the set-up in Figure A.9. The second axis measurement is simply a horizontal straightness measurement along the axis on which the reflector was earlier mounted during the first measurement. Figure 5.9 illustrates the concept of obtaining the squareness error from the two straightness measurements. 5.5 Accuracy Assessment 139 The procedure to execute a squareness measurement in the vertical plane is similar to that of the horizontal plane, except for additional requirements in terms of optics" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000457_978-3-642-55848-1-Figure10.12-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000457_978-3-642-55848-1-Figure10.12-1.png", "caption": "Fig. 10.12. A beam in planar motion. (a) An element of the beam, (b) The co-ordinates", "texts": [ " In spite of its simplicity, it is quite useful for solving various practical problems in flexible body dynamics. We will use it to solve problems of packaging systems vibration testing in Sect. 10.5; and of Coriolis mass-flow me- 10.4 Bond Graph Model of a Beam 411 ters in Sect. 10.6. Another bond graph approach to Euler-Bernoulli beams is de scribed in [5]. We begin by analysing an element of a beam that moves in a plane with respect to a body frame Oxz, which for this analysis is assumed to be fixed in a base frame (Fig. 10.12a). Fig. 1O.12b shows an element of the beam oflength L with an attached element frame Oex\"ze. It will be assumed that the undeformed beam ele ment is straight, having a uniform cross section and parallel to the body frame. Displacement of the element with respect to the body frame is described by two vertical displacements of its ends-w1 and w2-and two end slopes, 91 and 92. A beam element can be represented by a BFE component with two ports, corre sponding to the left and the right ends of the element (Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003397_tmag.2008.918920-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003397_tmag.2008.918920-Figure7-1.png", "caption": "Fig. 7. Top: The three rotors used with the stator frame. Bottom: Position of the stator coil.", "texts": [ " In this section, four magnet geometries are illustrated: \u2022 Rectangular-1 layer\u2014radial magnetization; \u2022 Pyramidal-2 layers\u2014radial magnetization; \u2022 T-shape-2 layers\u2014radial magnetization; \u2022 Halbach-2 layers\u2014radial and tangential magnetizations. For each configuration, the space harmonics of the remanent flux densities and are illustrated, with the theoretical EMF waveform calculated with (19), (20), and (21). For each configuration, a rotor and stator were built and the EMF waveform was measured with an oscilloscope across 1 coil made of five turns, as shown in Fig. 7 (bottom). Fig. 7 illustrates the electrical machine and the rotors used in the experiments. In Fig. 7 (top), three rotors are illustrated. The four configurations could not be shown on the same picture because only three rotors were used. The T configuration was prepared with the rightmost rotor in the picture, where additional magnets were glued with a larger width than those already fixed, at the center of each pole to obtain the T. The parameters of each configuration are given in Table I. Fig. 7 (bottom) shows where the stator coil is positioned. We note that it is directly on the stator laminations and its axial length (2.0 cm) is shorter than the laminations axial length to minimize end effects. Here, PMs The experimental EMF waveforms are illustrated in Figs. 8(c), 9(c), 10(c), and Fig. 11(c) and compared with the theoretical waveforms on the same figure. For a rectangular magnet shape with radial magnetization, Fig. 8 shows the magnet configuration, the spectral content of the remanent flux density in the radial direction , and the experimental and theoretical EMF waveforms" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003909_2013.38735-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003909_2013.38735-Figure1-1.png", "caption": "FIG. 1 Schematic diagram of basic simulation approach.", "texts": [ " The general ap proach used to describe the continuous drying process was to divide the proc ess into many small processes and simu late them by consecutively calculating the changes that occur during short in crements of time. The basic simulation approach used was to calculate the drying performed on a thin layer of grain and then combine many thin lay ers to form the grain bed. Thin Layer Grain Drying Briefly, the drying of a thin layer of grain was simulated by considering the changes that occur in the corn and the drying air as shown in Fig. 1. Drying air (T deg F, H lb (water/lb dry air) is passed through a thin layer of corn (M percent moisture, G deg F temperature) for a drying time interval At. During this interval AM percent moisture is evaporated from the corn into the air increasing its absolute hu midity to f f + AH lb water/ lb dry air. During drying the temperature of the drying air is decreased (AT deg F) in proportion to the temperature increase of the corn (AG deg F) and the evap orative cooling accompanying the mois ture evaporation" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003337_apex.2007.357701-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003337_apex.2007.357701-Figure1-1.png", "caption": "Fig. 1. Frequency Spectra ofPWM Inverter Output Voltage", "texts": [ " When the current detection timing is delayed, the difference between the detected currents at tops and bottoms of the carrier waves has DC offset. The relationship between the DC offset and the estimated position error is linear. II. POLE POSITION ESTIMATION WITH ONLY DC LINK CURRENT MEASUREMENT AND THREE PHASE TRIANGULAR CARRIER WAVIE The proposed method uses the three phase triangular carrier waves for PWM inverter, so that the three phase triangular carrier waves have high frequency components that the single phase triangular carrier wave don't have. The high frequency components give the information of the pole position. Fig. 1 shows the frequency spectra of the output voltages of the PWM inverter. Figs. 1(a) and 1(b) are the ones for the single phase triangular carrier wave and for the three phase triangular carrier waves, respectively. The former spectrum cancels the carrier frequency components each other. While, the latter spectrum mainly includes the carrier frequency components at the low modulation index region. So, these carrier frequency components enable measurement of motor inductance. An IPMSM is described by the following equation in the a-,l stationary reference frame", " So the effect of the current detecting timing delay is investigated by calculation of the timing delay equations. When the current detection timing is delayed, the difference between the detected currents at tops and bottoms of carrier waves has DC offset. The relationship between the DC offset and the estimated position errors is linear. If the current detection timing is delayed, the u-phase current cannot be detected at Oht=O and cht =ir So, Eq. (6) becomes Eq. (11). The angles ctj,t2 are the points moved a little from c,t=0, c,t = T, respectively as shown in Fig. 1 1. Eqs. (12) and (13) are obtained about the phase v and w with the same procedures as the phase u. The pole position is calculated by Eqs. (9) and (10). Using Eqs. (9) - (13), 70.0 60.0 50.0 -d 40.0 a) 30.0D- 20.0 10.0 the pole positions are calculated with the timing delay from -5 gs to 5 gs. The ratings and parameters in calculation's model of the IPMSM are shown in TABLE I. The three phase triangular carrier waves were used. The carrier frequency was 5.0 kHz. Fig. 12 and Fig. 13 show the calculation results of the estimated pole position with 5 gs and -5gs delay, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000196_0094-114x(87)90080-2-FigureI-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000196_0094-114x(87)90080-2-FigureI-1.png", "caption": "Fig. I. Position error of a four-bar coupler curve due to errors in file link lengths.", "texts": [ " These cognate linkages, however, may have different sensitivity to the errors in their link lengths. The position errors of two cognate linkages, having identical errors in their link lengths, are compared. This will lead to the better choice between the cognate linkages when mechanical error is inevitable. This i$ true, of course, only if all the cognate linkages considered can be used in practice. In an actual situation, a particular cognate linkage may not be useful from several considerations like space requirement or movability etc. Figure I shows the actual four-bar linkage as O~A'C'B'O~, where O~ and O~ are the fixed hinges and A 'B 'C ' is the coupler with C' as the tracing point. This linkage is assumed to have some error in all the linkage lengths. The ideal linkage, i.e. the one without any error has one of its fixed hinges (O2) at O~ and 86 G. B. CHATTE~EE and A. K. MALLIK the fixed link along O~O~. For the same crank angle @~, the tracing point of the ideal linkage is at C. The mechanical error in the coupler curve, for the crank angle @,, is represented by the vector CC'" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002215_1.2387164-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002215_1.2387164-Figure1-1.png", "caption": "FIG. 1. Geometry of the system taken from Ref. 18 .", "texts": [ " We mention at this point that in a truly hydrodynamic description, in which all the effects under consideration are of much larger wavelengths than the inherent lengths of the system, the cholesteric phase is properly characterized by the direction of orientation of the helical axis p\u0302 r instead of the director field see Ref. 17 . This representation was also used in Ref. 14, where rotatoelectricity was discussed for the first time. However, we will refer to systems of cholesteric pitch larger than the thickness of the sample, and because of that we choose the local nematiclike description of the cholesteric phase using a director field n\u0302 r . If we further select the z\u0302 axis of our coordinate system to be parallel to the cholesteric helical axis as it is the case in the geometry depicted in Fig. 1, the ground state conformation n\u03020 r of the director field is given by n\u03020 r = nox z noy z noz = cos q0z sin q0z 0 . 1 Here, q0 denotes the wave number of the rotation of the cholesteric helix and is equal to /L, 2L being the cholesteric pitch see Fig. 1 . As n\u03020 cannot distinguish head or tail and consequently is even under parity, q0 must be a pseudoscalar. Variations of the director field from its ground state conformation are expressed by n r = n\u0302 r \u2212 n\u03020 r = cos q0z + r cos nz r sin q0z + r cos nz r sin nz r \u2212 cos q0z sin q0z 0 \u2212 noy z r nox z r nz r . 2 Here, nz r describes a local tilt of the director out of the planes perpendicular to the helical axis, whereas r denotes local variations of the phase of the helicoidal director orientation and thus local rotations of the director around the helical axis", " We can see that in the regime of small external electric field amplitudes, to which we restrict ourselves in this paper, the dielectric term does not enter the governing equations of the system, because only terms linear in Ei i=x ,y ,z are taken into account. As we mentioned at the end of the last section we want to investigate a situation in which E=Ez\u0302 is parallel to the cholesteric helical axis. The cholesteric SCLSCE can, for this purpose, be assumed to be confined between two parallel plates with a distance d, located at z=0 and z=d, as illustrated in Fig. 1. For simplicity we consider the plates to be infinitely extended in x\u0302 and y\u0302 direction. If we impose no boundary conditions onto the system, the simplest solution to the problem is a spatially homogeneous one. Equations A1 \u2013 A5 show that in this case the variable decouples from the other ones. As, however, Eq. A5 is the only equation in which the external electric field E=Ez\u0302 enters, the field E acts exclusively on the phase angle . We therefore can set all the other variables equal to zero, without loss of generality, ux = uy = uz = nz = 0", " A control experiment with a nematic SCLSCE q0=0 is expected to give no effect, since rotatoelectricity is a novel phenomenon only associated with SCLSCEs with macroscopic handedness. Furthermore, as can be inferred from Eqs. 18 \u2013 25 , measurements of samples with different sample thicknesses d should allow an estimate of the ratio R /D1. This is the ratio of the rotatoelectric material parameter to the material parameter that governs the contribution to the energy density of the system resulting only from relative rotations. It is very important to address the question whether the reaction of a cholesteric SCLSCE in the geometry of Fig. 1 to an external electric field with strong anchoring boundary conditions occurs laterally homogeneously or whether spatial modulations in the lateral directions might complicate the experimental observation of rotatoelectricity. Therefore we want to compare our situation with that of an external electric field E=Ez\u0302 of larger magnitude. Then the dielectric term becomes important and leads to an additional contribution \u2212 aE2nz in Eq. A4 . We studied this situation for a 0 in Ref. 18, where we neglected the rotatoelectric term, the terms with the coefficients i i=1,2 , and partly the flexoelectric terms as effects linear in E. The geometry we investigated was the one depicted in Fig. 1, in which a cholesteric SCLSCE is confined between two parallel plates infinitely extended in x\u0302 and y\u0302 directions, located at z=0 and z=d. However, as boundary conditions we imposed zux=0= zuy no tangential mechanical shear stresses and uz=0 as well as n\u0302 x\u0302 strong anchoring at the plate surfaces at z=0 and z =d. As a result, for this configuration we found an electric threshold field, at which either an undulatory instability with undulations at least in one of the lateral directions x\u0302 and y\u0302 arises or only a z-dependent instability without lateral spatial modulations sets in. For our purposes it is important to note that in the bigger part of the parameter range we inspected, the laterally homogeneous instability was energetically favored. In particular, this was the case in all the situations of D2 0 we inspected and when the elastic constant c1 was large. These facts support our assumption that a major group of cholesteric SCLSCEs in the geometry sketched in Fig. 1 should react to the external electric field by a laterally homogeneous solution, which makes us confident that the effect of rotatoelectricity can be observed in an experiment. In the case of a 0 we do not expect an instability arising from the dielectric term at all, because the ground state orientation of the director in the planes perpendicular to the helical axis is stabilized. Such a stabilization of the director adds to the rotation of the director around the helical axis within these planes due to rotatoelectricity" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003662_s12239-009-0025-1-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003662_s12239-009-0025-1-Figure4-1.png", "caption": "Figure 4. Predictive error vector at t+\u03b4t.", "texts": [ " (7) where The feed-forward vectors defined in Equation (8) are nonlinear terms separated from the tracking error functions. These tracking error functions are then derived in Equation (9), which are designable linear state functions. (8) (9) 4.2. Feedback Control Vector The feedback control vectors can be expressed in the form of a matrix, as shown in Equation (10). The state variables are extracted from the conditions of the controlled vehicle and the reference vehicle. where (10) Two vectors shown in Figure 4 affect the predictive error in the subsequent time step. The first vector, e r , is the distance vector indicating the movement of the reference vehicle, which can be simply calculated from the reference vehicle input and the current error state variable using Equation (3). The second vector, \u03b4e, indicates the movement of a controlled vehicle to reduce error. The predictive error distance vector \u03b5 at time t+\u03b4t can be expressed as the sum of e r and \u2212\u03b4e, as shown in Equation (11). e\u00b7= e\u00b7 x e\u00b7 y e\u00b7\u03c8 = cose\u03c8 0 sine\u03c8 0 0 1 \u03c5ref \u03c8\u00b7 ref cos\u2013 \u03b2 ey sin\u2013 \u03b2 ex 0 1\u2013 \u03c5 \u03c8\u00b7 \u03c8\u00b7 = sin\u03b2 lr --------- \u03c5\u239d \u23a0 \u239b \u239e e\u00b7 x=\u03c5ref cose\u03c8\u22c5 \u03c5\u2013 cos\u03b2\u22c5 ey+ sin\u03b2 lr ---------\u22c5 \u03c5 e\u00b7 y=\u03c5ref sine\u03c8\u22c5 \u03c5\u2013 sin\u03b2\u22c5 \u2212ex sin\u03b2 lr ---------\u22c5 \u03c5 x y x y x y e\u00b7 x=\u03c5ref cose\u03c8\u22c5 \u2212x+ ey lr --- y e\u00b7 y=\u03c5ref sine\u03c8\u22c5 \u2212 1+ ex lr ---\u239d \u23a0 \u239b \u239e y\u239d \u23a0 \u239c \u239f \u239c \u239f \u239c \u239f \u239b \u239e x y e\u00b7 x=\u03c5ref cose\u03c8\u22c5 \u2212xf \u2212xb+ ey lr --- yf+ ey lr --- yb e\u00b7 y =\u03c5ref sine\u03c8\u22c5 \u2212\u03bayf \u2212 \u03bayb\u239d \u23a0 \u239c \u239f \u239b \u239e x=xf +xb, y=yf+yb, \u03ba= 1 ex lr ---+\u239d \u23a0 \u239b \u239e xf =\u03c5ref cose\u03c8\u22c5 yf= \u03c5ref sine\u03c8\u22c5 \u03ba ------------------------\u239d \u23a0 \u239c \u239f \u239b \u239e e\u00b7 x e\u00b7 y = xb\u2013 + ey lr --- yf + ey lr --- yb \u03bayb\u2013\u239d \u23a0 \u239c \u239f \u239b \u239e e=A e( )+B e( )ub A= ey lr --- yf 0 , B= 1\u2013 ey lr --- 0 \u03ba\u2013 , ub= xb yb By defining the time step t+\u03b4t as the (k+1)th status, the predictive error vector at time t+\u03b4t can be expressed as (11) where k denotes the current step" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000393_6.2002-3794-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000393_6.2002-3794-Figure2-1.png", "caption": "Figure 2. Bristle Geometry.", "texts": [], "surrounding_texts": [ "American Institute of Aeronautics and Astronautics 1\nThe hysteresis loop that brush seals produce when they are stiffness checked has proved hard to evaluate using simple beam theory.\nThe development of a Finite Element Analysis model of a brush seal pack is tracked through from simple beam element models through to complex multi layer non-linear models. The simple beam element models show a good match to simple beam theory but not such a good match to test data. The more complex models exhibit a good match to the test data but an increased stiffness when compared to simple beam theory. The increased stiffness is due mainly to bristle-bristle interaction.\nTest data is shown on seal blow down and pressure driven stiffening that will be used to further evaluate the model of the brush seal pack\nNomenclature\nd Wire diameter (inches) L Free wire length (inches) E Young\u2019s modulus (psi) \u03b8 Bristle angle (degrees) \u00b5 Coefficient of Friction\nWire_Tip_Area Tip area of single bristle Stiffness Theoretical stiffness of a single\nbristle during a 0.001\u201d radial offset (lbs)\nBTP Theoretical Bristle Tip Pressure of a single bristle during a 0.001\u201d radial offset. (psi)\nIntroduction\nCross has been producing brush seals since the 1970\u2019s for the Aerospace Industry and was instrumental in their introduction to the Power Generation Industry in the 1990\u2019s. Cross brush seals continue to be applied to a wide range of industrial and aerospace applications, with particularly strong growth in industrial applications. We continue to offer a high quality product with a consistent bristle pack that is designed for each specific application, as shown in Figure 1.\nThis paper describes the typical hysteresis loop produced when stiffness checking a brush seal and then goes on to reproduce these characteristics by using a Finite Element Analysis model of the bristle pack. This paper describes the initial stages of development of the Finite Element Analysis model from simple single beam element models, through to non-linear multi layer multi bristle 3D models with bristle to bristle and bristle to back plate contact. All models have contact elements at the tips of the bristles; comparisons are drawn to simple beam theory and to test data. Some coefficients of friction are experimentally determined and then used in one of the models.\nFurther test data is also shown that will be used to validate the model as it evolves. This test data shows some typical blow down characteristics and pressure stiffening effects of brush seals.\nCopyright \u00a9 2002 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.", "American Institute of Aeronautics and Astronautics\nSimple Beam Theory\nSimple beam theory has been used for many years to characterise the contact forces exerted by brush seals under idealized conditions. Flower1 presented the following equations in 1990. These equations have been in use since then by many people.\n\u03b8 \u03c0 cos4 __ 2d AreaTipWire = (1)\n\u03b823\n4\nsin6790L\nEd Stiffness = (2)\n\u03b8 \u03b8 23 2 sin5333 cos L Ed BTP = (3)\nBoth of equations (2) and (3) express load or pressure as a result of a 0.001\u201d radial deflection of a single bristle.\nNote how the bristle angle is struck from the bore of the seal, this is the only place on the seal that you can always see the bristles and thus measure the angle. The difference between the angle at the bore and measured at the outside diameter can be considerable on small diameter seals.\nSome people tend to get confused between the Bristle Tip Pressure (BTP) and the stiffness. The BTP is a good way of comparing seals with differing wire sizes.\nStiffness Measurement\nAs we presented in 20012 we have looked at stiffness checking brush seals since 1984. Figure 3 shows our adaptation of a standard tensile test machine, this allows for a flexible machine that can be used on round and segment seals.\nThe typical hysteresis curve obtained from a test is shown in Figure 4. The test is performed by bringing a shoe, shaped to the curvature of the bristle bore, into contact with the bristles and then displacing it a further 0.040\u201d and then retracting it slowly.\nIt is clear from the hysteresis curve above that friction is an important factor in the stiffness of a brush seal. The loop in the experimental data leads to two different seal stiffness values, one high value taken as the bristles compress and one low value as the bristles recover. In order to reduce the end errors we use two different lengths of shoe and the stiffness calculated by subtracting the data from the shorter one from the longer one.", "American Institute of Aeronautics and Astronautics\nFrom our initial finite element data that we presented in 2001 it was clear that friction is a major influence on the brush seal. We reviewed the published data by Aksit3 and Aksit and Tichy4 and decided that we should approach the problem in the following 4 stages.\nStage 1 Single bristle beam element problem. Stage 2 Ten Bristle single layer beam element problem. Stage 3 Five bristle 3D single layer 27 node element problem. Stage 4 twenty-five bristle 3D 5 layer 27 node element\nproblem.\nIn all cases contact would be introduced between the bristle tip and the shoe with friction varying from 0 up to 0.4. For each stage 5 different bristle cases were run, these all had the same theoretical stiffness but differing angles and free lengths as shown in Table 1. All bristles were 0.0056\u201d in diameter and a Youngs Modulus of 30E6 psi was used for all calculations.\nStages 2, 3 and 4 would also have contact between the bristles and the back plate and between adjacent bristles. All models were run so as to compress the bristles 0.050\u201d and then release them, typically this was accomplished with 10 equal compression steps and then 10 equal steps to release them. We continued to use the commercial FEA package Adina for all this work. Adina is very good at solving contact problems and is used to solve many metal forming problems in industry. All problems were solved on a single processor P.C. with 394Mb of RAM.\nThis model was constructed using 20 2d beam elements, with contact at the bristle tips. This model proved very fast to run, typically solving 20 steps in less than 1 second. A view of the model is shown in Figure 5.\nResults from this model are summarized in Figure 6 by comparing the data at 0.010\u201d deflection with the simple beam theory calculation.\nNote how with no friction present the FEA data is very close to the beam theory, however as friction is introduced this has a much greater effect on the lower bristle angles.\nThis simple model was encouraging in the close match to the simple beam bending theory and opened our eyes to the effect bristle angle can have on the hysteresis.\nBased on the encouraging data from the single bristle model we put together a parametric 10 bristle model using beam elements. Again 20 elements were used per bristle and contact was introduced between the bristle tips and the shoe and between adjacent bristles. This was achieved by using offset contact surfaces. The model is shown in Figure 7 Comparisons with the simple beam theory are made in Figure 8. Clearly this is similar to the single beam model except that there is some additional stiffening of the pack caused by the bristle to bristle interaction." ] }, { "image_filename": "designv11_32_0001580_acc.2004.1384048-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001580_acc.2004.1384048-Figure2-1.png", "caption": "Fig. 2. The feasible set P(t ,z) Fig. 3. The feasible set P(t , z ) at at timet = t , . time t = t 2 .", "texts": [ " Similar to the SDRE controller, the actual control is a projection of u,(t, z) = [uc, U d ] to the space defined by the input constraints (7) as follows uo = sat(u,,g,D) U 1 = sat(ud,g,u). (16) IV. CONSTRAINED NONLINEAR TRACKING CONTROL FOR UAVS In this section, we introduce hvo other nonlinear tracking controllers which explicitly account for input constraints. A. Tracking Controller Based on the Geometric Center of the Feasible Set Define the feasible control set as F(t , z ) = {uEUzlLf~V+Lg,vu I -W(z)} , where W(z) is given by Eq. (9). Note that the fact that V is a constrained CLF for system (8) guarantees that F(t, z) is nonempty for any t and z. Fig. 2 and 3 show the feasible set at time t = tl and t = t 2 respectively. The line denoted by L,,Vu+Lf,V+W = 0 separates the 2-D control space into two halves, where the right half in Fig. 2 and the left half in Fig. 3 represent the unconstrained stabilizing controls satisfying V 5 -W(z) at time tl and t z respectively. The rectangle area denotes the time-varying input constraints (7). The shaded area represents the stabilizing controls which also satisfy input constraints (7), that is, the feasible set F( t ,x ) . In Fig. 2 and 3, U, represents the geometric center of the feasible set. Obviously, such controls will stay in the feasible set at each time. As a comparison, we also plot the vector -X(L,,V)T in both figures, where X > 0. Note that this vector is orthogonal to the line L,, Vu + Lfl V + W = 0. It can be verified that the control based on Sontag's formula in Section IIIB can be represented as uZls(t,x) = -X(t,z)(L,,V)T, where X(t,r) is a nonnegative scalar function of t and x. Therefore, the control based on Sontag's formula lies along the vector -X(L,,V)T but may have a different magnitude. In Fig. 2, we can see that the control based on Sontag's formula may or may not stay in the feasible set depending on its magnitude. However, a proper scale of the control can always bring it back to the feasible set. With the input constraints (7), the actual control will be a projection of u,(t,z) to the rectangle region. As shown in Fig. 2, a projection of u8(t ,x), denoted as up, is either inside the feasible set or on the boundq' of the feasible set depending on its magnitude. In either case, the projected control based on Sontag's formula guarantees stability even if there are input constraints. In Fig. 3, we can see that the control based on Sontag's formula cannot stay within the feasible set even with some scaling due to its direction. In this case, a projection of us(t, x) is not guaranteed to stay within the feasible set. However, it is straightfoward to see that vu,( t ,x) , where U > 1, is still a stabilizing control in the case of U E R\"" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002338_j.jmatprotec.2006.03.081-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002338_j.jmatprotec.2006.03.081-Figure4-1.png", "caption": "Fig. 4. Boundary curve among af", "texts": [ " To reconstruct the original surface it is necessary, in first lace, to interpolate internal points with the information of oints entirely located in the undamaged area of the surface ffected by cavitation. According to Zeid [6] this interpolaion can be accomplished using the Coons\u2019 equation of bi-cubic urface. i u ent of the points. With the information of points located in the undamaged and lso the points interpolated in the central area, an estimation f the original surface of the type uniform bi-cubic B-spline i,j(u, v) is generated, according to Qiulin [7]. This surface, as hown in Fig. 4, is formed by a group of (k \u2212 2)x(l \u2212 2) patches n the directions u and v, respectively. The surface damaged by cavitation si,j(o, w) is obtained sing all points acquired from the undamaged and damaged fected and unaffected area. 234 N.G. Bonacorso et al. / Journal of Materials Processing Technology 179 (2006) 231\u2013238 es (a) a s i d b b g o a w b e a o w a t i i d e e n i r 2 p d F t o j a t d c o t d i t a 3 3 w t f S r d reas. Its equation is also described as an uniform bi-cubic Bpline. The points that compose the trajectory of all weld beads are nitially located on the damaged surface si,j(o, w) along of the irection w" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001495_0954405041897185-Figure14-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001495_0954405041897185-Figure14-1.png", "caption": "Fig. 14 Variation in the parameters of the critical section of an internal gear with the tool regrinding rate of a gear-", "texts": [ " 13) as well as some parameters of the machined gear, namely rcf1, the radius of the tooth active profile at the tooth root, and rf1, the root radius of the gear, and the parameters of the critical section become different. Relations between these parameters concerning external gears have been described in detail in references [11], [16] and [20]. In this work, internal gears are investigated. The properties of the considered internal gears are computed and analysed using the method described in section 3 and using the FEM. An exemplary graph which shows the influence of the parameter u associated with sharpening of gear-shaper cutter on parameters of internal gears machined with such tool is given in Fig. 14. In the described case it is assumed that the tool regrinding rate is defined by the following conditions: u \u00bc u0 \u00bc 10 and u \u00bc u00 \u00bc 10. Section I\u2013I (Fig. 14) corresponds to a new cutter (u \u00bc 10). Section II\u2013II corresponds to the same cutter but in the almost wornout state, i.e. to the cutter which has reached its regrinding limit (u \u00bc 10). Such a tool can still be used but cannot be used any longer after the next sharpening. From Fig. 14 it follows that successive cycles consisting of gear generation of several gears and the following of sharpening of the gear-shaper cutter lead to enlarging type tool: I\u2013I, section of the new tool (before the first sharpening); O\u2013O, initial section (u \u00bc 0); II\u2013II, section of the tool after the last sharpening. The parameters are calculated according to the method given in reference [11] B04403 # IMechE 2004 Proc. Instn Mech. Engrs Vol. 218 Part B: J. Engineering Manufacture at NORTH CAROLINA STATE UNIV on May 9, 2015pib" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000623_0021-9673(90)85155-o-FigureI-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000623_0021-9673(90)85155-o-FigureI-1.png", "caption": "Fig. I. High-pressure electrochemical cell with a platinum microdisc electrode.", "texts": [], "surrounding_texts": [ "Operat ion o f an electrochemical detector in a flowing stream of supercritical media places strict requirements on both the electrode system and the cell. The electrochemical cell must be placed before fluid decompression in order to make measurements while the mobile phase is in the supercritical state. This means that under conventional SFC operat ing conditions the detector must withstand pressures up to 5000 p.s.i. The current response of amperometr ic detectors employing conventional electrodes in laminar flow streams is propor t ional to 1/3 power o f the flow-rate [8]. In liquid chromatographic systems where analyses are conducted under conditions of constant flow, this does not present a problem. However in SFC, pressure or density are controlled as opposed to flow; this results in varying flow-rates throughout the chromatographic run. This precludes the use of conventional-sized electrodes in SFC detectors. The small diffusion layer at an microelectrode is predominantly within the stagnant layer next to the electrode surface which eliminates current flow-rate dependencies. Voltammetric data obtained with a two-electrode system in resistive media cannot be directly compared to that obtained in conventional solutions with a threeelectrode system. For this reason initial cell characterizations were carried out using ferrocene since (i) this redox couple has been widely used in the characterization of electrochemical systems, thus providing means for comparison and (ii) ferrocene is soluble in supercritical carbon dioxide [9]. Cyclic voltammograms of ferrocene in acetonitrile and supporting electrolyte were carried out using the 10-pro platinum working electrode in a conventional three-electrode mode. A sigmoidal-shaped cyclic voltammogram with a half-wave potential of 0.42 V was obtained. This established the performance of the electrode under normal operating conditions. The platinum working electrode was then incorporated into the flow cell, the flow cell was then filled with the same ferrocen~acetonitri le-supporting eletrolyte mixture and a cyclic voltammogram carried out under static conditions using a two-electrode mode, where the cell body is used as a quasi-reference electrode. This established the performance of the working electrode in the cell operating in the two-electrode mode. The cyclic voltammogram has retained its characteristic sigmoidal shape but the half-wave potential has shifted negatively by 140 mV. This is due to the lack of a true reference electrode. The electrode performance was then evaluated under more realistic operating conditions though still in the static mode. A solution of ferrocene-acetonitrile-supporting electrolyte (50 pl) was placed in the cell, the system then sealed and pressurised with carbon dioxide from a syringe pump to 2000 p.s.i, at 40\u00b0C. Cyclic voltammograms were recorded with the cell inverted such that measurements were obtained in the supercritical fluid as opposed to in undissolved acetonitrile supporting electrolyte mixture. Again the sigmoidal shape of the cyclic voltammogram is maintained but the half-wave potential shifted more negatively by about 220 mV (Fig. 2), again due to the lack of a true reference electrode. This established the performance of the detector using carbon dioxide-acetonitrile-supporting electrolyte mixtures under supercritical but static conditions. The next evaluation was to establish its performance in a flowing stream under normal operating conditions. Due to interference from injection solvents and turbulence generated by the injection process itself it was necessary to develop a chromatographic procedure so that the ferrocene could be separated from these void volume effects. Separations were achieved on a reversed-phase column at 40\u00b0C using a variety of mobile phases from simple carbon dioxide to mixtures of carbon dioxid~acetonitr i le-tetrabutylammonium tetrafluoroborate. An ultraviolet absorbance detector was positioned before the electrochemical detector, to monitor the retention time of the ferrocene. Ferrocene-acetonitrile solutions were then injected onto the column and the detector response monitored under a variety of operating conditions. No faradaic response was obtained from the electrochemical detector at applied potentials up to 1.2 V with simple carbon dioxide mobile phases. Acetonitrile I 10 nA / ~ , ~ 0.O7 V +o15 olo -oL5 POTENTIAL (Volts) Fig. 2. Cyclic voltammogram for 5.0 mM solution of ferrocene in acetonitrile with 0.1 M tetrabutylammonium tetrafluoroborate. Working electrode: platinum microelectrode. Scan rate: I00 mV/s. Electrochemical cell, stainless-steel quasi-reference electrode, pressurized at 2000 p.s.i, with CO2 at 40C. modifier was then added to the carbon dioxide up to 1.6 mole% at 0.4-mole% intervals. Again no faradaic response was detected at applied potentials ranging from 0.0 to 1.2 V. Te t r abu ty lammonium tetraf luoroborate (TBATFB) at 0.05 mole% was then added to the acetonitrile-modified supercritical carbon dioxide and a faradaic response was observed from the electrochemical detector. Fig. 3 represents a chromatogram obtained for a 10-/xg on-column injection o f ferrocene in acetonitrile using a 1.6 mole% acetonitrile and 0.05 mole% T B A T F B modified supercritical carbon dioxide mobile phase under isobaric condit ions at 2200 p.s.i, and 40\u00b0C. The addit ion of the electrolyte has either increased the conductivi ty o f the mobile phase or, as predicted by Niehaus et al. [10], the electrolyte has formed a conduct ing layer on the electrode surfaces. The latter is unlikely as in silu format ion of a conduct ing layer would tend to give irrepreducible current responses, at least initially, and this was not observed. The high solubility o f T B A T F B in acetonitrile and the low concentrat ion o f the electrolyte in the mobile phase also precludes the precipitation o f the salt at the electrode surface. Formal redox potential tables or potentials obtained from cyclic vo l tammograms obtained under static condit ions are insufficient for determining the optimal operat ing potential for detecting the same species in a flowing stream. This is due to the increased iR drop in these systems. The op t imum operat ing potential for the detection at 0.8 V. For chromatographic conditions refer to text. of ferrocene was established by injecting 10/~g of ferrocene on column and measuring the current response at applied potentials between 0.0 and 1.1 V. The reduced capacitative currents at microelectrodes lead to rapid equilibration after changes in the applied potential. Unlike liquid chromatographic systems, chromatograms were recorded within 15 rain of a change in applied potential. A hydrodynamic vol tammogram plotted for ferrocene in this system shows an optimal applied potential of 0.9 V (Fig. 4). Beyond this potential there is a drop in the current response that may be due to increased iR drop which produces a reduction in the effective applied potential. The relative standard deviation calculated for three replicate injections at each applied potential is less than 5% indicating good reproducibility for this electrochemical detection system. Although it is necessary to add an electrolyte to the mobile phase for detection, anticipated problems of precipitation of the tetraalkylammonium salt at the restrictor were not encountered. The results reported above have shown the feasibility of developing an electrochemical detection strategy for SFC. According to two recent reports [11,12], vol tammetry in supercritical carbon dioxide is possible only with a thin film of conducting phase, either in the form of an ion-exchange polymer or a molten salt layer, on both the surfaces of the working and quasi-reference electrodes. We have demonstrated that this conducting phase is not necessary and that electroactive species can be detected at a bare platinum microdisc working electrode of an SFC electrochemical detection system." ] }, { "image_filename": "designv11_32_0001141_icec.1998.699495-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001141_icec.1998.699495-Figure2-1.png", "caption": "Fig. 2. Construction of a ath in 2-dimensions. Given the start and the goal points the knot I oint tree (Fig. l (b)) is constructed using the binary tree of Figure l (a) . The knot points are generated using a modified Gram-Schmidt ori hogonalieation process.", "texts": [ " Given the start the construction of the order traversal of the This construction protess points in a binary trele point is appended as t1.e the goal point is appended most node of the bintry knot points and a Adi, puted using a modified process as detailed in quence of knot points of the knot point tree. by Figure l(b) is ~ 0 0 Figure l(a). Each Ad; uniquely del)-dimensional space defined by the of two D-dimensional knot points. space defined by the perpendicular points is a line, in 3-dimensions, it is a ildi represents an intermediate knot and goal points, Figure 2 shows path using Adi's given by the prebinary tree shown in Figure l(a). provides the intermediate knot as shown Figure l(b). The start left child of the leftmost node and as the right child of the righttree of knot points. Given two the intermediate knot point is comGram-Schmidt orthogonalization our previous work [8; lo]. The se.s obtained by an in-order traversal The sequen.ce of knot points defined (S,Ib4,P3,P5,P2,P6,P1,P8,P9,P7,G). of the node by a small amount. Once a feasible path is found by the evolutionary process, the operator probabilities are adjusted such that, the probability of selecting this operator for mutation is higher" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001217_tasc.2003.813065-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001217_tasc.2003.813065-Figure3-1.png", "caption": "Fig. 3. Type-1 PM and type-2 PM rotor.", "texts": [ " The iron plates\u2019 role is to enhance the magnetic field. The outer and inner radii are 23.0 mm and 17.0 mm. The heights of PM\u2019s and iron plates are 12.0 mm and 2.0 mm, respectively. In this study, we made experiments using two types of PM rotors. One is the PM rotor without the insulating thin films, another is the advanced PM rotor with the insulating thin films. Their dimensions are the same, but the latter\u2019s two PM\u2019s consist of 2 mm thick PM plates and very thin insulating films as shown in Fig. 3. Here we named the former the type-1 PM rotor, and the latter the type-2 PM rotor. It is expected that the eddy current in the type-2 PM rotor is forcibly intercepted by the insulator films comparing with the type-1. As a result, the rotation speed degradation due to cause-C will be suppressed if the type-2 PM rotor is used. 1) The pressure in the vacuum vessel is kept under 3.0 Pa. 2) The AMB levitated the PM rotor. 3) The relative position of the PM rotor and the HTSC stator is set at the initial position " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002710_iet-epa:20060301-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002710_iet-epa:20060301-Figure1-1.png", "caption": "Fig. 1 Estimation of rotor angle", "texts": [ " For example, if the estimation is used during the commissioning of the drive not all the parameters would be known before then. The intention is to derive expressions in which the minimum number of motor parameters are needed. Whichever of these two methods is used, the rotor angle is obtained by determining an estimate for the load anglebd s and calculating the rotor angle estimate bu r with bu r \u00bc bu s bd s (1) wherebu s is the angle of the stator flux linkage estimate bc s s in the stator coordinates. A similar approach is also used in [9]. With the definitions of Fig.1 the quadrature axis flux linkage csqis written as csq \u00bc Lsqisq (2) , jc s j sin ds \u00bc Lsqjisj sin (ds \u00fe g) (3) Utilising sin(ds \u00fe g) \u00bc sin ds cos g\u00fe cos ds sin g gives (jc s j Lsqjisj cosg) sin ds \u00bc Lsqjisj sin g cos ds (4) The load angle estimatebd s is then obtained by replacing the true load angle ds with the estimated bd s, and the true stator flux linkage c s with the estimated stator flux linkage bc s tanbds \u00bc Lsqjisj sin g jbc s j Lsqjisj cos g (5) The trigonometric functions sin g and cos g are avoided since bc s is \u00bc jbc s jjisj cos g (6) bc s is \u00bc jbc s jjisj sin g (7) g is the angle between the stator current and the stator flux linkage vectors 300 The tangent of the load angle estimate is then tanbds \u00bc Lsqcs is jbc s j2 Lsq bc s is (8) It should be noted that when per-unit values are used, the torque estimate is bte \u00bc bc s is and the equation of the load angle estimate can be expressed as tanbds \u00bc Lsq bte jbc s j2 Lsq bc s is (9) An optional method of determining the load angle can be formulated from the definition of the direct-axis flux linkage equation csd \u00bc Lsdisd \u00fe cPM , jc s j cos ds \u00bc Lsdjisj cos (ds \u00fe g)\u00fe cPM (10) By substituting cos (ds \u00fe g) \u00bc cos ds cos g sin ds sin g, the following form can be obtained jc s j cos ds \u00bc Lsdjisj[ cos ds cos g sin ds sin g] \u00fe cPM (11) Equation (11) can be reformulated as follows (jc s j Lsdjisj cos g)cos ds \u00fe Lsdjisj sin g sin ds cPM \u00bc 0 , jc s j Lsd c s is jc s j " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure7.13-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure7.13-1.png", "caption": "Fig. 7.13. Coupling of triangular plane-structure to tetrahedron space-structure with six members", "texts": [], "surrounding_texts": [ "Thus far, the approach to obtain the tetrahedron space-structure from the triangle plane-structure, the pyramid from the tetrahedron, and the box from the tetrahedron has been illustrated. The next aspect of the design is to combine some of these structures. The structures can be treated as being coupled together as rigid bodies, and a rigid body in space has six degrees of freedom, i.e., the structure is capable of translations in the x, y and z directions, and rotation about the x, y and z axes. Therefore, six members are needed providing six reactive forces to exactly constrain the structure in space. Figure 7.11 shows a typical gantry configuration, which is used extensively in many coordinate-measuring machines (CMM). However, one of the members is bearing a bending load, which has been shown earlier to be very detrimental 7.1 Mechanical Design to Minimise Vibration 205 to the stiffness of the structure. There are alternative structure configurations as shown in Figures 7.12 and 7.13, although some redesign maybe needed if such a configuration is utilized. If the ground is perceived as another rigid body in which the spacestructure is to be coupled, then the design of the supports for a space-structure is similar to those of coupling two space-structures together, i.e., six reactive forces are needed to exactly constrain the space-structure. Some ways to arrange the six supporting members constraining a space-structure are suggested in Figure 7.14. Examples of physical supports offering one, two or three reactive forces are shown in Figure 7.15. This method of design, known as kinematical design, requires the use of point contact at the interfaces. Unfortunately, this method has some disadvantages, namely: \u2022 Load carrying limitation \u2022 Stiffness may be too low for application 206 7 Vibration Monitoring and Control \u2022 Low damping There are, however, ways to overcome the disadvantages which are via the semi-kinematical approach. This approach is a modification of the kinematical approach, and it targets to overcome the limitations of pure kinematical design. The direct way is to replace all point contact with a small area, as shown in Figure 7.16. Doing so decreases the contact stress, but increases the stiffness and load carrying capacity. However, the area contact should be kept to a reasonably small area. This section has only illustrated some fundamental concepts in designing rigid and statically determinate machine structures. Interested readers may refer to (Blanding, 1999) for more details on designing machine using the exact constraints principles. 7.2 Adaptive Notch Filter 207" ] }, { "image_filename": "designv11_32_0001047_12.478510-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001047_12.478510-Figure7-1.png", "caption": "Figure 7. Prediction of third measurement.", "texts": [ " This leads to a large uncertainty in the predicted slant range.) In addition, there are lines from the center of the ellipse to the mean estimated launch point and to the actual observation (whose uncertainty is too small to show up here). The updated launch point estimate is shown in Fig. 5. The prediction for the third observation is shown in Fig. 6, and the prediction for the fourth observation is added Proc. SPIE Vol. 4728 269 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 05/19/2015 Terms of Use: http://spiedl.org/terms in Fig. 7. Its elevation from the launch point is intermediate between the first two predictions. The uncertainty in predicted slant range has not improved much. The estimated launch point after three updates is shown in Fig. 8. The estimate has a bias in crossrange. Let dll = [L\u0302\u03bb\u0302]T \u2212 [L\u03bb]T be the error in the estimated launch position, and Pll be the corresponding part of the estimated covariance. If the filter\u2019s estimated covariance were accurate, then the normalized distance D2 = dTP\u22121 ll d (57) would be chi-square distributed with two degrees of freedom" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000257_s1474-6670(17)37858-8-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000257_s1474-6670(17)37858-8-Figure2-1.png", "caption": "Fig. 2 Schematic of the Rotary Inverted Pendulum", "texts": [ " In this paper, we described two experiments adapted for online Internet laboratory. The apparatus used is a rotary inverted pendulum and the two experiments are (1) parameter estimation of the inverted pendulum and (2) design of a swing up and balancing controller. The objective of the laboratory experiments is to supplement the control systems courses covering the topics of parameter estimation and controller design. 2. THEORY Fig. 1 shows a rotary ann version of the inverted pendulum system used in this project. The schematic is represented in Fig. 2. The inverted pendulum system consists of two sections, namely the rotating ann and the pendulum. A dynamic model for the pendulum system can be expressed as (KRI, 1999): Jo +~.4. + n\u00a512 sin a ~1J1 CO'i)I~] + ~1J1 coe[) .J.. +~l; e G I ~ +1~I;esin28 -~1JJesirf)+1~I~asin2BI~]+ -1~I;asin28 C; a (1) [ ~gtsir6 ] =[ ~ } where u is the control input to the system. The measurements available are the ann speed of rotation, a , and the pendulum position, e . To design a linear controller to balance the pendulum in the upright position, the following linearised model can be used: To swing up the pendulum from the pendent to the upright position, we use the energy method (Astrom and Furata, 1996) which gives the control law u = sat(kE )sign(/3 cos f3 ) (3) where \u2022 2 E = LJl + mlgfl cos f3 - mlgfl, is 2 the total energy of the system, k is the tuning parameter and sat is the saturation function saturated at the limits of the control signal u" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001782_j.microc.2004.11.002-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001782_j.microc.2004.11.002-Figure1-1.png", "caption": "Fig. 1. Schematic diagram of the flow-injection biamperometric detection system. (P) peristaltic pump, (V) valve, (S) sample, (C) carrier solution, (D) biamperometric detector, (A) sample inlet, (F) sample outlet, (E) platinum wire electrode, (B) KMnO4 solution inlet, (T) salt bridge.", "texts": [ "05 mol l 1 H2SO4 solution. All reagents used were of analytical grade unless specified otherwise. Twice distilled water was used throughout the experiments. A CHI660 electrochemical workstation (CH Instruments, USA) equipped with a personal computer was used to impose the potential difference and to record the resulting current. Additionally, it was used to perform the cyclic voltammeter experiments. The schematic diagram of the homemade biamperometric detector, which was constructed from a Teflon rod, was shown as Fig. 1. The two electrode rooms in the detector were separated by means of a salt bridge. The internal volume of each room was estimated to be 20 Al (1.2 cm length, 0.7 mm i.d.). The platinum wire electrodes (1.1 cm length, A 0.5 mm) were pretreated electrochemically by alternating polarization between +1.55 and 0.2 V in 0.05 mol l 1 H2SO4 solution after soaked with concentrated nitric acid for 5 min and rinsed with water prior to every measurement. A potential difference DE was imposed between two platinum wire electrodes of the biamperometric detector by connecting both the auxiliary electrode and the reference electrode led to one side of the detector and the working electrode led to the other side" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001542_zamm.200310138-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001542_zamm.200310138-Figure1-1.png", "caption": "Fig. 1 Squeeze film geometry. Enlarged pictures in circles indicate the unidirectional roughness pattern iny-direction (longitudinal roughness).", "texts": [ "in c\u00a9 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 826 N. B. Naduvinamani et al.: On the squeeze effect of lubricants between plates have considered the upper solid surface to be rough and lower porous surface to be smooth. Following Christensen\u2019s stochastic theory for rough surfaces, a modified Reynolds type equation is derived for unidirectional roughness structure. An eigen-type of expressions are obtained for the mean squeeze film pressure, mean load carrying capacity and the squeeze film time. Fig. 1 shows a schematic diagram of the squeeze film geometry under consideration. In the present paper, a squeezing flow of couplestress fluid between two rectangular plates is considered. The upper rectangular plate having surface roughness is approaching towards lower isotropic porous rectangular plate. In addition to the usual assumptions of hydrodynamic lubrication, we assume that the fluid is incompressible, and body forces and body couples are absent. Under these assumptions, the equations of motion derived by Stokes [15] takes the form \u2202u \u2202x + \u2202v \u2202y + \u2202w \u2202z = 0, (1) \u00b5 \u22022u \u2202z2 \u2212 \u03b7 \u22024u \u2202z4 = \u2202p \u2202x , (2) \u00b5 \u22022v \u2202z2 \u2212 \u03b7 \u22024v \u2202z4 = \u2202p \u2202y , (3) 0 = \u2202p \u2202z , (4) where u, v and w are the fluid velocity components along x, y and z directions respectively in the film region and p is the pressure in the film region" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure7.7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure7.7-1.png", "caption": "Fig. 7.7. a\u2013e Various configurations", "texts": [ "1, that the stiffness of a bar is much better in axial loading as compared to bending loading. For a value of d=0.05 m, and L=1.2 m, the ratio of kt/kb is 192. That is, a bar is 192 times stiffer when loaded axially as compared to bending. Therefore, when designing a rigid and stiff structure, the members must be loaded in tension or compression, never in bending. At times, re-designing the way an external load is applied onto a structure can greatly improve the stiffness of the structure. Various configurations are shown in Figure 7.7, while the comparison of stiffness is 7.1 Mechanical Design to Minimise Vibration 201 shown in Table 7.2. As a general rule to observe, the loading point should be located at the joints. Next, space-structures or three-dimensional structures will be considered. These are structures that are of interest in most applications. In a very general sense, space-structures can be perceived as a combination of many plane-structures, arranged in a manner that all the planes are not coplanar. Therefore, for a space-structure to be rigid, every plane-structure that makes up the space-structure must be rigid in its own right" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001177_roman.1996.568855-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001177_roman.1996.568855-Figure1-1.png", "caption": "Fig. 1. The mobile robot kinematics model.", "texts": [ " Several approaches have been proposed in the literature to stabilize mobile robot [lo-121. However to the authors knowledge, the problem of a communication delay in the mobile robot has not been discussed elsewhere. The mobile robot is seen as system with message queue controlled through a multiplex communication link, The queues are setup both at the sensor and the actuator. 2.1 The Kinematics Model In this section we describe the mobile robot model we are concerned with. The mobile robot is shown in figure 1 and consists of :cart with two driving wheels. The state of mobile robot are the position of the wheel axis center (x,y) and 8 is the cart orientation with respect to the x axis. The distance between the point (x,y) and each of the wheel locations is c,. (see figure 1) The vectors V I and v2 are the tangent velocities of each wheel at its center of rotation. The kinematics model of the cart is given by: i = cose(v, + v2) 2 j = sin B(vl + v2) / 2 e = - v2) / 2cr (6 ) I letting vc = - v 1 + v 2 undm=- v1 - v2 the system (6) 2 % becomes, x = cos&, y = sin&, o = w (7) The tangent velocity U! = v, and the angular velocity u2 = w can be regarded as the inputs to the system. Notice that the system (7) can be written as: k = A(X)U where T x = [ x y 81 u=[ul U * l T -312- The underlying discrete time model is obtaine from the Taylor expansion: I Taking g= 1, one get approximation crete time Euler Yk+l = Y k + h s i n @ k u l ( k ) (10) Qk+l = Qk +hu2(k) This approximation is valid provided that, the blems: The timing of signals in our control shown in figure 3", " Lemma 2: Assume that there is no queues at the actuator and sensor nodes, then the mobile robot control let: hence, U 1 ( k ) = U 2 ( k ) = - and, -2(xk cos e k + Yk sin 8 k ) kl +h -28k (19) k2 + h (20) Hence v k decreases and both 6$ andx, goes to zero, while yk is bounded, the system is then stable. 00 1 1 2 V V = - - k12 hu: ( k ) - y k22 hu; ( k ) system is stable provided that Now we can state the following result. -2(xk cosek +Yk s h @ k ) kl +h Lemma 3: U1 ( k ) = u2(k)=-20k (I2) Consider the control system of figure 1 and assume that the length of the actuator queues are respectivelyj and i then the closed loop system is stable if k2 +h no where k, and k2 are positive parameters. which is positive defined, let V V = vk+l - v k , our system is stable if VVk is negative. one has L + - [ y k 1 +hul sinek12 +-[ek 1 +hu2] 2 2 2 Consider the following Lyapunov functions which is positive defined, let V V = vk+l - v k , our system is stable if v v , is negative. one has -314- u2(k- i ) (h2 +2) 2 ( k - i)[2hek-, +id U 2 ( k - 2)1 and the result directly 4 Conclusion his paper we have studied the closed loop ility of mobile robot in the esence of sensor and actuator network delays" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003881_3.4598-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003881_3.4598-Figure1-1.png", "caption": "Fig. 1 Control angles.", "texts": [ " Letting (X^X^X^) and (X^X5,Xo) be the velocity and position components, respectively, in the (X4,X5,X6)-coordinate system, the equations of motion are dXi/dr = -yR~3X4 + 12 cost/i cost/2 dXz/dr = -yR~*X5 + 12 cost/i sin[72 dX5/dr = X2 where #2 = Xf + X5 2 + X6 2 and 12 = ftc/(l - /3r) on the interval 0 < r < r\\. For the units chosen in the problem, time is days, position is in a.u., velocity is in a.u./day, mass is in vehicle mass, with r = 0 - (12:00 noon May 9, 1971) ft = 0.00108 vehicle mass/day c = 0.0453649854 a.u./day 7 - 0.000296007536 a.u. 3/day2 The control angles are shown in Fig. 1. The initial conditions at r = 0 are XiCO) = -0.0003455906 Z2(0) = -0.0171986836 Z3(0) = 0.0 Z4(0) = -0.9998 Z5(0) = 0.02009 Z6(0) - 0.0 The terminal conditions are Xi(ri) \u2014 Fz-(n) = 0, i = 1,2, . . . , 6 with Yi = dYi+2/dn, i = 1,2,3. The position of Mars at time r is given by Y4(r) = kuDi + kuD2 75(r) = A^D! + &22\u00a3>2 Y6(r) = fcsiDi + &32A where = \u2014 sinco 2 = (cosco) (cosi) = (cosco) (sini) Kii = COSCO fei = (cosi) (sinco) A;3i = (sini) (sinco) Di = a(cosE \u2014 e) co = 5.8541335, the argument of perihelion of Mars at r = 0" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003188_j.mechmachtheory.2007.07.001-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003188_j.mechmachtheory.2007.07.001-Figure7-1.png", "caption": "Fig. 7. Sketch for generating the enveloping surfaces by indirect method.", "texts": [ " According to the properties of intermediate conjugation, the initial position of the surface R(3) with respect to Z(3)-axis can be arbitrarily employed. The following is a special case of intermediate conjugation for normal-circular-arc surfaces. Here, the center P is perfectly in Z(3)-axis, the rotation of the spherical surface R(3) around Z(3)-axis becomes a redundant motion, and then the intermediate screw motion degenerates into a translation along Z(3)-axis and the meshing line C(0) will be collinear with Z(3)-axis, as shown in Fig. 7(a). Here datum surfaces R\u00f01\u00dep and R\u00f02\u00dep are two hyperboloids of one sheet, generated by rotating Z(3)-axis around Z(1) and Z(2), respectively, and the directrixes C\u00f01\u00dep ;C\u00f02\u00dep become two spiral curves with a constant lead, which are attached to respective datum surfaces. It follows from Section 2.3 that the envelope to a one-parameter family of planes must be a developable surface. When a plane R(3) is chosen as the generating surface, the resulting surfaces R(1) and R(2), enveloped by the plane R(3), must be a pair of conjugate developable surfaces, and the common contact-line of R\u00f01\u00de;R\u00f02\u00de and R(3) is the straight generator", " However, the intermediate motion in this case is a screw motion, and then it brings the complexity of the machine setting and the difficulty of manufacture. According to the properties of intermediate conjugation, we can resolve these problems by employing properly the initial position of the plane R(3) with respect to Z(3)-axis. The following is two cases for this kind of conjugation: (1) the generating surface R(3) is parallel with Z(3)-axis, thus its translational motion along Z(3)-axis becomes a redundant motion, the intermediate screw motion degenerates into a rotation about Z(3)-axis, as shown in Fig. 7(b). The planes R(3) and R\u00f03 \u00de denote left and right generating surfaces, and are parallel with Z(3)-axis. When R(3) and R\u00f03 \u00de rotate about Z(3)-axis, the resulting surfaces, enveloped by them with respect to Z(1) and Z(2), are left and right tooth surfaces, and they form two pairs of conjugate developable surfaces;(2) the generating surface R(3) is orthogonal to Z(3)-axis, thus its rotation about Z(3)-axis becomes a redundant motion, the intermediate screw motion degenerates into a translation. When R(3) rotates about Z(3)-axis, the enveloped surfaces with respect to Z(1)-axis and Z(2)-axis are a pair of conjugate helical involutes" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000140_s0025579300015230-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000140_s0025579300015230-Figure2-1.png", "caption": "Figure 2. Rotlet streamline patterns in the plane y = 0 for representative c-values. (a) 1 \u2022 (b) c ,3.", "texts": [ " The second separation point P2 starts at the pole d = 0 where the positive z-axis intersects the sphere and with increasing c moves steadily towards the point 8 = \\tr in the azimuthal plane

3. The stagnation points are S, and S2> S, being a saddle point, and the points of SOME STOKES FLOWS EXTERIOR TO A SPHERICAL BOUNDARY 241 flow separation are Pi, i\" = l , . . . , 4 . Figure 2(b) exhibits a detached vortex surrounding the stagnation point S2 (not marked). For c = 3 this point has just reached the surface of the sphere r = 1 at 6 = n, the separation points P,, P3 having coincided there. Further the separation and reattachment streamlines from P1 and P3 are now incident with the separatrix through 5, . In order to compute the force and couple experienced by the sphere r = 1 in the flow field of the rotlet, the stress tensor T arising from the velocity field (2) must be evaluated at r = 1", ") is grateful to the Natural Science and Engineering Research Council of Canada and Professor K.B. Ranger for a grant which enabled him to visit the University of Toronto, where some of the work reported here was completed. The work of the second author formed part of a dissertation submitted to the University of Surrey in partial fulfilment of the requirements for the award of the B.Sc. degree in mathematics. We thank Mr. Marc Chamberland of the University of Waterloo, Ontario, Canada, whose numerical investigations helped in the construction of Fig. 2, and also a referee for supplying useful references. References 1. M. E. O'Neill. Small particles in viscous media. Science Progress, 67 (1981), 149-184. 2. W. Hackborn, M. E. O'Neill and K. B. Ranger. The structure of an asymmetric Stokes flow. Q. J. Mech. appl. Math., 39 (1986), 1-14. 246 SOME STOKES FLOWS EXTERIOR TO A SPHERICAL BOUNDARY 3. R. Shail. A note on some asymmetric Stokes flows within a sphere. Q. J. Mech. appl. Math., 40 (1987), 223-233. 4. C. W. Oseen. Hydrodynamik (Adademische Verlagsgesellschaft M" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001714_02678290500161363-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001714_02678290500161363-Figure5-1.png", "caption": "Figure 5. The geometry of the SAXS measurement for the free-standing smectic elastomer films.", "texts": [ " A certain problem is the sensitivity of the available X-ray set-up, when the very small signal from the film is recorded. In previous work, the temperature dependence of the smectic layer spacing of the given material was studied using small angle Xray scattering [8]. The measurements were performed on elastomer balloons, but in the balloon experiments it was impossible to measure the influence of strain on the smectic layer spacing. In the balloon geometry, strains of only a few percent could be achieved [8]. In this work, the compression of smectic layers has been studied in planar free-standing films. Figure 5 shows the experimental geometry for the SAXS diffraction measurements. Measurements were performed at two different temperatures, T 5 90 and 120uC, corresponding to the SmC* and SmA phases, respectively. The values of the smectic layer spacing obtained for the relaxed film at given temperatures are in a good agreement with those measured in the elastomer balloons [8]. Figure 6 shows SAXS data for the smectic elastomer film at zero deformation in the SmA phase. The intensity distribution for the non-stretched film has three peaks" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003762_09544054jem1913-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003762_09544054jem1913-Figure7-1.png", "caption": "Fig. 7 Calculation of the absolute area for a contour", "texts": [ " This matrix has two pair points of P1, P2 and P5, P6, but the XPr is not between any of indices x of consecutive pair points (P1, P2) and (P5, P6). This shows that contour A is not inside contour D. This method is done for all of the layer\u2019s contours. For a contour in the layer, if the number of its parent is odd, this means that the contour is internal. Otherwise the contour is external. To estimate total travel length of the laser, the ESTIMATOR algorithm applies the area of contours. Although the area of simple contours can be computed by the usual formulae, the method presented in Fig. 7 can be used for every convex and non-convex contours. For a sample contour, minimum indices y of its CM is obtained and then a horizontal line (HL) is drawn as y = ymin (Fig. 7). For each two consecutive points of the CM, a line is drawn perpendicular to the HL to make a quadrilateral. For the two consecutive points, if index x of point Pi+1 is more than x index of point Pi , the area of the quadrilateral is considered positive. Otherwise, the area is negative. It is obvious that if XPi+1 = XPi , the area is zero. The absolute sum of areas of all quadrilaterals is equal to area of the contour. The absolute areas for all of the layer\u2019s contours are computed. The area for an internal contour is considered negative and for an external contour is considered positive" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000364_robot.1988.12028-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000364_robot.1988.12028-Figure6-1.png", "caption": "Figure 6: Quantities for Vertex Liftability Regions.", "texts": [ " regi and B4 meet at the cross-over point, t2c, which is the only point on the edge which is an element of the translation region. Physically, if inequality (9) is satisfied, then the resultant of the finger contact forces opposes gravity. Therefore, as the hand squeezes more and more tightly, the weight of the object is overcome, so it must rise. The second contact point need not occur on an edge of the polygon. It may occur on the kth vertex, in which case the contact angle, y 2 . is free to vary between the inward normals of edges k and k-1 (see Figure 6), which in turn allows the moment arm, t2, to vary according to Substituting equation (11) into equations (4) and (5) allows us to determine the liftability regions of a vertex. Figure 7 shows the edge of the second finger against the vertex in the jamming region, J. Tilting the finger clockwise or counter-clockwise eventually changes the contact to region B4 or B3 respectively. Thus for a vertex, we see that the liftability regions are defined as partitions of the range of possible contact ang le s " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003271_12.733905-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003271_12.733905-Figure2-1.png", "caption": "Figure 2: FBG sensor gage length (1 cm) and corresponding gear tooth coverage", "texts": [ " The testing for this effort was conducted at the University of Maryland, Alfred Gessow Rotorcraft Center on a Transmission Test Rig. The gearing assembly was mounted within the test rig as shown in Figure 1. There was enough space between the two mounting plates (top mounting plate not shown in Figure 1), for an optical fiber to be bonded onto the surface of the ring gear and not be damaged within the assembly in the transmission test rig. The typical gage length for a FBG sensor is 1 cm. As is shown in Figure 2, this translates into just over 1.5 gear tooth distance. Therefore, the FBG response should provide an average measurement for the planetary gear mesh at the location of the FBG sensor. Proc. of SPIE Vol. 6758 675808-2 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 10/10/2013 Terms of Use: http://spiedl.org/terms change, the cantilever beam returns to the start position and this angular location can be clearly identified, as shown in Figure 4. Figure 3: 1/rev FBG sensor installed on transmission rig Ring Gear 1 cm gage length Proc" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003271_12.733905-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003271_12.733905-Figure1-1.png", "caption": "Figure 1: Image of transmission gear", "texts": [ "he health of internal stages of a planetary helicopter transmission has historically been difficult to diagnose due to the complex geometry of the planetary gearbox and the inability to directly monitor the rotating gears. An example of a planetary stage, as used in a helicopter transmission, is shown in Figure 1. The planetary stage consists of three main gear levels. The central gear is referred to as the sun gear and the three gears that rotate about the sun gear are called the planetary gears. The planetary gears are connected to a carrier plate, not shown, which provides the output to the system. The planetary gears ride within the stationary ring gear. Typically for damage detection purposes, a small number of accelerometers are mounted externally to the gearbox housing to record the vibration signals", " A key advantage of using fiber optic sensors for this project was the ability to multiplex many sensors onto the ring gear. Hence fiber Bragg Grating (FBG) sensors were chosen. During this research effort, Micron Optics Inc. instrumentation systems were used to monitor a 14 FBG sensor array that was mounted to the outer surface of the ring gear at sampling rates up to 1 kHz. The testing for this effort was conducted at the University of Maryland, Alfred Gessow Rotorcraft Center on a Transmission Test Rig. The gearing assembly was mounted within the test rig as shown in Figure 1. There was enough space between the two mounting plates (top mounting plate not shown in Figure 1), for an optical fiber to be bonded onto the surface of the ring gear and not be damaged within the assembly in the transmission test rig. The typical gage length for a FBG sensor is 1 cm. As is shown in Figure 2, this translates into just over 1.5 gear tooth distance. Therefore, the FBG response should provide an average measurement for the planetary gear mesh at the location of the FBG sensor. Proc. of SPIE Vol. 6758 675808-2 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 10/10/2013 Terms of Use: http://spiedl", " In this graph, four sequential FBG responses are shown. Although the plot is relatively busy, the passing of a planet gear can be seen for each of the four sensors with the planet passing the first FBG sensor, and then the next. After passing the fourth FBG, the second planet passes the first FBG sensor and repeats. The response from each of the FBGs is similar but it can be noticed that some sensors do respond higher than others. At this time, it is believed that geometric differences in the ring gear (e.g. mounting bolt locations, as shown in Figure 1) are creating these differences. For instance, a mounting bolt hole located between the teeth and the FBG sensor would clearly alter the strain experienced by the sensor. The data captured during these tests was acquired with the Micron Optics sm130 interrogation system at a sampling rate of 1 kHz. Proc. of SPIE Vol. 6758 675808-5 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 10/10/2013 Terms of Use: http://spiedl.org/terms The plot shown in Figure 7 displays the wavelength response for all 14 FBG sensors during one of the transmission rig tests" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000243_095441002321029035-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000243_095441002321029035-Figure7-1.png", "caption": "Fig. 7 Hertzian elliptic contact", "texts": [], "surrounding_texts": [ "The forms used are those given by the Hertzian theory for a contact between two cylinders on a length supposed to be in\u00aenite (see F ig. 6). The maximum stress in compression (also called Hertzian pressure) is sC \u02c6 pHertz \u02c6 2 p p KD CE r MPa \u20261\u2020 where KD \u02c6 equivalent diameter (mm) CE \u02c6 inverse of the equivalent module (MPa\u00a11) p \u02c6 applied pressure for unitary width (N= mm) with KD \u02c6 2r1r2 r1 \u2021 r2 \u20262\u2020 CE \u02c6 1 \u00a1 n2 1 E1 \u2021 1 \u00a1 n2 2 E2 \u20263\u2020 p \u02c6 F=L \u20264\u2020 where, for i \u02c6 1, 2, ri \u02c6 pitch radius of cylinder i (mm) Ei \u02c6 elasticity module (MPa) ni \u02c6 Poisson coefficient F \u02c6 applied load (N) L \u02c6 contact length (mm)" ] }, { "image_filename": "designv11_32_0000641_1527-2648(200103)3:3<111::aid-adem111>3.0.co;2-z-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000641_1527-2648(200103)3:3<111::aid-adem111>3.0.co;2-z-Figure4-1.png", "caption": "Fig. 4. The new cooling concept for rotor and housing surfaces.", "texts": [ "[6] For higher temperatures it is necessary to combine the ferritic steels with a suitable cooling system. Therefore new cooling concepts, based on effusion cooling, for rotor- and housing surfaces have to be developed in this research program. The innovative idea is to protect the turbine rotor and casing parts by applying an open-pored heat shield on the rotor surface. This heat shield is based on a patented sandwich material called \u00aagrid sheet\u00aa with perforated cover sheets and a hollow interlayer containing cavities that allow a cooling medium to flow through (Figure 4).[7] FE A TU R E A R TI C LE 112 ADVANCED ENGINEERING MATERIALS 2001, 3, No. 3 A preliminary investigation dealt with the analysis of suitable hollow structures. The structure had to fulfil a lot of requirements: a plain outer surface, calculable cavities, excellent formability, and good welding properties. All these can be fulfilled by neither a purely homogeneous nor a purely inhomogeneous material. Only the combination of both property profiles meets all the requirements. Therefore sandwich materials combining plane sheet metals on top and bottom and a hollow interlayer material are presently thought to be the best choice", " This process also has the advantages of good accessibility and the possibility of exact regulation of heat input. First tests with laser-beam welded base materials show the feasibility of this process, but there is a significant hardness increase because of the structural transformation, which can be critical and has to be further investigated (Figure 10). FE A TU R E A R TI C LE 114 ADVANCED ENGINEERING MATERIALS 2001, 3, No. 3 The hollow structure has to be tested on a steam turbine rotor with a diameter of 800 mm. Figure 4 shows how the sandwich structure should be applied in the turbine casing or on the rotor surface. The limits of the forming process imply that the ring can not be manufactured in one piece. Therefore, quarter-ring segments of the sandwich material were formed in an axial bending process to obtain the required radius (Figure 11). The main problem of the bending process is the elastic spring-back of the sandwich material after stress removal. The elastic recovery depends on mechanical properties of the material and the geometry (especially the thickness) of the structure" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003773_s11668-009-9268-4-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003773_s11668-009-9268-4-Figure1-1.png", "caption": "Fig. 1 Schematic diagram and photographs of the failed component with fractured surfaces", "texts": [ " Dye Penetrate Inspection (DPI) of the assembly was carried out to find evidence of cracking but no crack (s) or crack-like indications were detected. The gear was reinstalled in the assembly, and after two days of service abnormal sounds were heard, emerging from the W. Muhammad (&) N. Ejaz S. A. Rizvi Metallurgy Division, Rawalpindi, Pakistan e-mail: valimuhammad@yahoo.com gear box. Operation was suspended again for inspection, and the pinion shaft of the gearbox was found broken. Visual and Stereomicroscopic Examination The schematic diagram of the pinion gear shaft is shown in Fig. 1. The pinion gear shaft after failure is also shown in Fig. 1 along with the inner races of the roller bearings \u2018A\u2019 and \u2018B\u2019 (in the subsequent text these will be termed inner race \u2018A\u2019 and inner race \u2018B\u2019). The fracture was just on one side of the inner race \u2018A\u2019. Press marks from the rollers were also observed on the inner race \u2018A\u2019, Fig. 2. On the fractured surface, features like river marks were observed near one end and in the central region. The river markings were generally diverging from a point, Fig. 3. A number of progression marks were visible near one edge, Fig. 4. Multiple ratchet marks were also observed on one edge, Fig. 5. A small shear lip was also observed on one of the surfaces. The fractured surfaces were also smeared at some locations. High-temperature color bands were present on fractured surface. These bands were due to heat tinting probably resulting from friction on the fracture surfaces prior to and after final failure. Dark bands were observed on the shaft on \u2018motor side\u2019 of the fractured surface, Fig. 1. The inner race \u2018A\u2019 was separated from the shaft. The shaft surface below the race was found to be severely damaged. Features such as deep scoring and tracking were observed, Fig. 6. Similar features were found on the mating surface of the inner race, Fig. 7. A cross section of the inner race of the roller bearing is shown in Fig. 7b, and some material was observed adhered to the inner surface. Longitudinal and transverse cracks were observed in the region of gear shaft under the inner race \u2018A\u2019, Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000673_1.1478075-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000673_1.1478075-Figure4-1.png", "caption": "Fig. 4 Cross section of test stator: back-pressure annulus", "texts": [ " has four unknowns and only two equations, two independent orthogonal dynamic loads are applied to yield the four necessary equations to solve for the impedance. The two independent excitations are obtained by alternately exciting the stator in each orthogonal direction ~x and y!. In addition to providing the excitation necessary to measure the dynamic impedance of the test seals, the shakers are also used to maintain the static position of the stator at a given eccentricity with respect to the rotor. Six high-sensitivity inductance-type proximity transducers, located in each back-pressure annulus shown in Fig. 4., record the relative motion of the stator with respect to the rotor for each axis of excitation. These proximity probes are used to determine both the static position and dynamic motion of the stator relative to the rotor. Accelerometers and load cells are used to measure stator acceleration and reaction forces. The dynamic measurements obtained from the proximity transducers, the load cells, and the accelerometers are used to determine frequency-dependent direct D( jV) and cross-coupled E( jV) impedances of the test seals" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001439_12.584626-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001439_12.584626-Figure2-1.png", "caption": "Fig. 2. Alternative schemes for immobilization and positioning of embryos into arrays.", "texts": [ " This approach requires techniques for immobilization and positioning of embryos in well ordered 2-D arrays, allowing for parallel manipulation or analysis. A schematic drawing of a concept for a high-throughout injection system is shown in Fig. 1. As described above a critical part of the injection scheme is to position the embryos in well-ordered arrays so that they can be injected in parallel by a matching array of micromachined injectors. Alternative techniques for immobilization and positioning of embryos into arrays are shown in Fig 2. A simple and versatile method for capturing embryos is to apply an under pressure to a chip structured with micromachined cavities and holes. See Fig. 2a). This technique is utilized by Tixier-Mita et al. [3] in a microsystem for parallel gene transfection into cells. In this system electrodes for electroporation are integrated into the cavities. Dielectrophoresis [7] is a well known method for moving capturing, manipulation, and separation of bacteria and cells. When an uncharged particle, such as a cell, is placed in a non-uniform electric field a net electrical force is exerted on the particle as a result of polarization (Fig. 2 b). This dielectrophoretic force is dependant on the cell size and shape, and on the magnitude and non-uniformity of the applied electric field. The polarity of the force is determined by the conductivity and permittivities of the cells and the suspending medium. Dielectrophoretic techniques are widely used for characterization, separation, and manipulation of cells and micro-organisms [8]. Demonstration of arrays of embryos realized by this method is to our knowledge, however, not published. 68 Proc. of SPIE Vol. 5641 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 05/19/2015 Terms of Use: http://spiedl.org/terms As part of the DARPA [Bio:Micro:Info] program (MDA972-00-1-0032) the author and groups at Stanford University have developed a technique for immobilization and positioning of Drosophila embryos in 2-D arrays based on fluidic micro assembly on silicon chips (Fig. 2c) [9]. An array of hydrophobic immobilization sites were established by formation of self-assembled monolayers selectively on patterned gold pads. The oxidized silicon substrate was kept hydrophilic. The samples were subsequently covered with a film of polychlorotrifluoro-ethylene based oil. Samples completely covered with oil were immersed in water, leaving oil only at the hydrophobic sites. Finally Drosophila embryos were dispensed onto the surface keeping the sample submerged in water. As a result embryos were immobilized only at the oil-covered pads forming a well ordered 2-D array" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000798_app.1989.070370809-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000798_app.1989.070370809-Figure4-1.png", "caption": "Fig. 4. Cyelic voltammogram of (PPY-Br,)-l (-) and (PPY-Br2)-4 (. . . . ) samples in 0.5-M aqueous NaBr at M mV/min.", "texts": [ " The thermal decomposition mechanism of PPY-I, complex has been postulated to be the decomposition of I; to 13 and 12,18 as in the case of I,-doped polya~etylene.'~ The decomposition mechanisms for PPY-Br, and PPY-Cl, complexes are not clear a t present but are expected to differ from that of PPY-I, because of the presence of covalent as well as ionic halide in the former cases. 2178 NEOH, KANG, AND TAN Electrochemical Characterization The cyclic voltammograms of (PPY-Br,)-1 and (PPY-Br2)-4 are given in Figure 4. These voltammograms were obtained in 0.5-M aqueous NaBr at a sweep rate of 10 mV/min. The two major differences between the two voltammograms are the shift in the redox potential of the (PPY-Br2)-4 sample to a more positive value than that for (PPY-Br,)-1 and the poor resolution of the oxidation peak of the former sample. Audebert and Bidang have shown that chemically and electrochemically synthesized polyhalopyrroles have more positive redox potentials than that of PPY. Since a large fraction of the Br, in the (PPY-Br,)-4 sample may have been covalently bonded to the f i position of the pyrrole ring, the shifting of the redox potential toward a more positive value and the resulting poorer resolution in the voltammogram may be due to the combined redox effects of PPY as well as polybromopyrrole" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002957_s1004-4132(08)60088-2-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002957_s1004-4132(08)60088-2-Figure1-1.png", "caption": "Fig. 1 The figure of missile\u2019s and targets\u2019 motion", "texts": [ " There are three advantages in the proposed guidance law here: firstly, only the missile-target line-of-sight angle and the angular velocity are needed to measure online; secondly, the distance between missiles and targets as well as the relative velocity between them adopted in the guidance law are substituted by estimated values, and the estimation errors as well as the target\u2019s velocity and maneuver acceleration are treated as bounded disturbance; lastly, the above disturbance can be resisted suc- cessfully if the parameters of the guidance law are appropriately chosen. Figure 1 shows the motion of missiles and surface targets. In Fig.1, M , T , and MT denote missiles, targets, and the missile-target line of sight respectively. r is the distance between missiles and targets, q\u03b8 is the obliquity of MT , and q\u03c6 is the azimuth of MT . vt denotes the velocity of targets and \u03c6t is the azimuth of vt. The obliquity of vt is zero since it is supposed that the target is moving on the ground level all the time. vm denotes the velocity of missiles, and the obliquity and azimuth of vm are denoted by \u03b8m and \u03c6m, respectively. The definition of \u03b8m and \u03c6m is similar to the definitions of q\u03b8 and q\u03c6. Th rectangular coordinate of missiles is denoted by (xm, ym, zm)T and the rectangular coordinate of targets is denoted by (xt, 0, zt) T; then the motion equations of missiles and targets are as follows \u23a7\u23aa\u23aa\u23a8 \u23aa\u23aa\u23a9 x\u0307m = vm cos \u03b8m cos\u03c6m y\u0307m = vm sin \u03b8m z\u0307m = \u2212vm cos \u03b8m sin\u03c6m (1) \u23a7\u23aa\u23aa\u23a8 \u23aa\u23aa\u23a9 x\u0307t = vt cos\u03c6t y\u0307t = 0 z\u0307t = \u2212vt sin \u03c6t (2) The equations of missile-target relative motion can be deduced by considering Eqs. (1) and (2) according to Fig. 1 r\u0307 =\u2212vm[cos \u03b8m cos q\u03b8 cos (q\u03c6 \u2212 \u03c6m)+ sin \u03b8m sin q\u03b8] + vt cos q\u03b8 cos (q\u03c6 \u2212 \u03c6t) (3) rq\u0307\u03b8 =vm[cos \u03b8m sin q\u03b8 cos (q\u03c6 \u2212 \u03c6m)\u2212 sin \u03b8m cos q\u03b8] \u2212 vt sin q\u03b8 cos (q\u03c6 \u2212 \u03c6t) (4) rq\u0307\u03c6 cos q\u03b8 = vm cos \u03b8m sin (q\u03c6 \u2212 \u03c6m)\u2212 vt sin (q\u03c6 \u2212 \u03c6t) (5) The dynamical equations of the center of the missile\u2019s mass are [4] \u23a7\u23a8 \u23a9 vm\u03b8\u0307m = \u2212g cos \u03b8m + u1 vm\u03c6\u0307m cos \u03b8m = \u2212u2 (6) where, u1 and u2 denote the force imposed on the missile along the Y axis and the Z axis of the flight path coordinate system. The motion of missiles and targets has been described adequately by equations[1\u22126]" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000457_978-3-642-55848-1-Figure9.37-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000457_978-3-642-55848-1-Figure9.37-1.png", "caption": "Fig. 9.37. Base and body frames", "texts": [ "7 Hz with an amplitude of 38.6 rad/s. There are also amplitude peaks on both sides of the resonant fre quency, which are displaced by twice the fundamental frequency, i.e. 57.4 Hz. This is termed the secondary resonance and is the result of non-linear inter coupling in the engine's reciprocating mechanism [17]. The spectrum diagrams, as well as the characteristic frequencies, agree well with the experimental results re ported in [17]. To describe motion of a body in space we use two fundamental coordinate frames (Fig. 9.37) - a base frame Oxyz and a body frame Cx'y'z moving with it, as we did in Sec. 9.2. There can be a number of bodies and, hence, a number of body frames that are used for their description. On the other hand, there is a single base (iner tial) frame. In robotics it is often convenient to introduce other frames, as well [9]. All of the frames are 3D Cartesian coordinate frames. We assume that the position of a body frame with respect to the base is defined by a position vector rc of the origin C of the body frame" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002158_ias.2005.1518846-FigureA-2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002158_ias.2005.1518846-FigureA-2-1.png", "caption": "Fig. A-2: Motor # 3", "texts": [ " Marques Cardoso, \u201cAnalysis of SRM drives behaviour under the occurrence of power converter faults\u201d, 2003 IEEE Intern. Symp. on Industrial Electronics, ISIE '03., Vol. 2 , pp. 821-825, June 2003. Three motors were used for the analysis and the tests: Motor # 1: 4 phase; 8/6; rated torque: 2.0 Nm; base speed: 2,500 rpm; 42V. Motor # 2: 3 phase; 12/8; rated torque: 1.0 Nm; base speed: 3,000 rpm; 42 V (Fig. A-1). Motor # 3: 4 phase; 8/6; rated torque: 0.8 Nm; base speed: 2,500 rpm; 12V; 8 turns per pole (Fig. A-2). IAS 2005 2740 0-7803-9208-6/05/$20.00 \u00a9 2005 IEEE" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001740_1.1135224-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001740_1.1135224-Figure2-1.png", "caption": "FIG. 2. Detail of the closure.", "texts": [ " In practice it has proved advantageous to perform the initial deformation of the sealing rings in a separate vessel which has the same height as the rings. Usually 1213 Rev. Sci. Instrum., Vol. 48, No.9, September 1977 the initial fit of the ring into this vessel is sufficiently close that little or no leak occurs when pressurizing for the first time. If the fit is insufficient, especially for larger sizes, the initial sealing can be achieved by using a rubber O-ring at the bottom and the top of the vessel. Figure 2 shows the closure in more detail. The metal Notes 1213 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: 129.174.21.5 On: Mon, 22 Dec 2014 07:41:33 ring is pressed by the hydrostatic pressure against the narrow edge b, while part of b and an area with height d are unsupported. The dimensions of d and b have to be chosen carefully in order to prevent the ring from yielding. In this laboratory, during the last few years, seals made of steel and Be-Cu of internal diameter varying from 0.4 to 25 mm have been used successfully up to 12 kilobar, while an internal diameter of 55 mm has been used up to 3 kilobar. The thickness of the ring varied from 0.15 to 0.6 and the height from 2.5 to 8 mm, while the projected height c (Fig. 2) ranged from 0.1 to 0.7 mm. The hardness of the seal is always somewhat higher than that of the pressure vessel. When the ring is formed the distance d is about 0.2 mm. Tightening the closure a little bit makes the seal vacuum tight. ]n those cases where the apparatus has a limited space and the height of the ring is much reduced, the seal tends to deform. It is therefore advisable to preform the closure by using an auxiliary piece which fits exactly inside the ring and by applying the working pressure to the vessel" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003843_1.3617038-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003843_1.3617038-Figure6-1.png", "caption": "Fig. 6 Bearing geometry", "texts": [ "r3 are given by the relation dT >=s ^ KsTls - = n ( n - x*r) Y , dx X3 \u2014 X3s \u2022 r = S E - r = l X-3 \u2014 X3r XS \u2014 X33 = 0 (33) Since r = s E -X3 \u2014 x$r Wj \u2014 .1*3 j (34) it results that the position of these points of maximum and minimum are dependent on xi and they are not in a plane normal to the bearing axis, excepting the case of a symmetrical variation of the temperature with respect to the median section. In this case, condition (33) is fulfilled implicitly for x3 = (62 \u2014 bi) /2 , that is to say, in the plane of symmetry of the bearing. Usually, b-2 = bh so that the plane Oxix* is in the middle of the bearing (Fig. 6) and the solution can be performed b y using the functions T,{x 1) = ( T ) \u201e _ \u00b1 W 2 and TMtc) = (T ) I S _o . B y the help of relation (31), one finds T = rM - (TV - T.) 4. b(35) T h e parabolic variation obtained in this way closely resembles the experimental one (Fig. 5). Although solutions (31) do not satisfy equation (7), they constitute generally an acceptable approximation. The Dist r ibut ion of Temperatures in the Unloaded Fi lm ( t t < e < 2TT) For the divergent zone, one can write dp dx, = 0 dp_ bx-3 Pb ~ Pa dp (Pb ^ Pa); = bx3 (Pb = Pa) (36) Journal of Lubr icat ion Technology O C T O B E R 1 9 6 7 / 4 8 7 Downloaded From: http://tribology" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001182_robot.2002.1014767-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001182_robot.2002.1014767-Figure4-1.png", "caption": "Figure 4 The working of the procedure AntipodalConvex-March when e(s,) c 0 an e(%) < 0.", "texts": [ "1 Endpoint Antipodal Angles with the Same Sign The marching strategy will rely on the following result. Proposition 2 When S and 7 are convex, the vector r (s) rotates counterclockwise as s increases from sa to S b . Proof ating the vector T yields We need only show that x T < 0. Differenti- - = --(a@) - a ( s ) ) = T(t) dr d ds ds Since K ( s ) , K ( ~ ) > 0, we have 1 + # > 0. Hence is in the direction of T(t). Meanwhile, from condition (v) that r(s) N ( s ) > 0 it follows that T(s ) x T ( S ) > 0 and 0 Figure 4 illustrates the working of an iterative method when 8(s,) < 0 and < 0. The iteration starts with s and t at SO = S b and t o = t b , respectively. From Proposition 2, as s moves towards sa, the vector T ( S ) rotates clockwise. At the ith iteration step move s from si to si+l at which the normal is parallel to si). If no such point si+l exists, stop. Otherwise, move t from ti to ti+l where N(ti+l) + N(si+l ) = 0. The iteration continues until ~ ( t ) x T ( S ) < 0. Therefore x T ( S ) < 0. si and ti converge to a pair of antipodal points, as in Figure 5(a), or they reach sa and t,, in which case no antipodal points exist as in Figure 4. When 8(s,) > 0 and (?(sa) > 0, the march starts at sa and t , and moves towards 8 b and t b , respectively, in the same manner. The method has been implemented in the procedure Ant i poda 1 -Convex- March . Below we establish the correctness of the procedure when @(sa) < 0 and 8 ( S b ) < 0. Lemma 3 In the case e(&) < 0 and e(&,) < 0 of theprocedure Antipodal-Convex-March, si > si+1 and every s E [si+l, s i ) satisfies 8(s) < 0 for all i 2 0. Proof We use induction. That O(s0) = @ ( S a ) < 0 follows directly from the initial condition" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003167_gt2008-50257-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003167_gt2008-50257-Figure3-1.png", "caption": "FIG. 3 INFLOW CASING FOR SWIRL GENERATION", "texts": [ " 2 the test rig is shown with its BSS sealing configuration. The rotor with a diameter of 180 mm is driven by a speed regulated direct current motor with a rotational speed up to 12000 rpm. The test rig is supplied with compressed air. The maximum pressure difference between the first and the last sealing tooth is up to 900 kPa. The seal assembly has an axial length of about 60 mm from prechamber to outlet; the seal chamber height between rotor and chamber walls is 6 mm. The preswirl is generated in the inflow casing (Fig. 3) and its magnitude can be adjusted in the range between 100 and 300 m/s in the prechamber. Incoming compressed air travels in the collecting duct before it enters the prechambers of both flows of the rig through the bypass channel; each flow has its own bypass channels on either side. The flow through the tangential bypass channels creates a preswirl in the prechambers. From each prechamber the air is divided into two parts. One part leaves the test rig through the sealing configuration, the other part travels towards the center of the rig, where the flow from both sides is sucked off through the outflow tubes" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003762_09544054jem1913-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003762_09544054jem1913-Figure6-1.png", "caption": "Fig. 6 Relations between contour A and the other contours", "texts": [ " It can also be applied to calculate build time with the adaptive slicing method. In this algorithm, the time to build the contours is computed in a similar way to what has been presented for the EXACT algorithm (Fig. 3) while bout hatching the layers, the algorithm uses a new procedure. First, it is essential to determine the relations between the layer\u2019s contours (distinguishing external and internal contours). Second, the hatching method is carried out by computing the area of the contours to calculate hatching time. Figure 6 helps in understanding the relations among contours. Random point Pr is chosen on the contour, Ai . Among all points of the contour B, every two consecutive JEM1913 Proc. IMechE Vol. 224 Part B: J. Engineering Manufacture at YORK UNIV on November 7, 2012pib.sagepub.comDownloaded from points in which the index y of random point Ai is between indices y of these consecutive points are selected and stored in the relative matrix. This matrix is sorted based on amount of indices x of the points. If the relative matrix is zero, this means that two contours are external. Otherwise, if index x of a random point in contour A is between a pair of points in the relative matrix in contour B, this shows that the contour A is inside the contour B. If not, contour A is outside contour B. To distinguish the relations among contour A and other contours in Fig. 6, a random point Pr is selected on contour A. About contour C relative to contour A, the relative matrix is void, because contour C does not have any contact with the horizontal line. This means that contour A is outside the contour C. In contour B, the relative matrix is equal to [P3, P4] and XP3 < XPr < XP4. This shows that contour A is inside contour B. It can be said that contour B is parent of contour A. The relative matrix for contour D relative to contour A is [P1, P2, P5, P6]. This matrix has two pair points of P1, P2 and P5, P6, but the XPr is not between any of indices x of consecutive pair points (P1, P2) and (P5, P6)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001279_icsmc.1997.638103-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001279_icsmc.1997.638103-Figure5-1.png", "caption": "Fig. 5 Satellite model", "texts": [ " The results contained in Fig. 4 include a fast response delivered by the PD controller with k and kd equal to 1.0 and 1.5. The slow yet overshoot - free response is assured by the PD controller with k=1.0 and kd=21. The response of the hierarchical system is also included. Pitch control (see Fig. 6) is decoupled from yaw and roll control. The pitch control law is given in (9). 3. APPLICATION Fuzzy hierarchical control has been used in an experiments for an attitude contoller for a small satellite (see Fig. 5 ) with the following characteristics: earth-pointing 3-axis stabilized geostationary orbit double-gimbled, momentum-wheel ACS 500 - 800 km altitude -15 orbits per day (574 km alt) total mass = 123 kg (100 kg payload) 4. CONCLUSION. The hierarchical control structures in which the fuzzy controllers are situated at the higher level have been studied in depth. Through the two levels of control one can clearly distinguish between a strategic and a tactic form of control objectives and control knowledge" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003434_6.2008-4505-Figure15-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003434_6.2008-4505-Figure15-1.png", "caption": "Figure 15 Comparison of measurement and theory for 4.37\" OD seal with L/R = 0.351 and 0.223.", "texts": [ " In order to be able to compare data between the different seal configurations and account for the size differences data was normalized to flow factor was used. Where Flow Factor is defined as: American Institute of Aeronautics and Astronautics 092407 6 [ ]uPDTm / . Overall, the importance of and reason for conducting these tests was to determine the impact of radial path length on the leakage since total radial space is often limited. III. Test Results Based on the data analysis and comparison to the theoretical model (Equation 1), theory and experiment correlate quite well, especially for the seals with L/R ratios of 0.327 and 0.223 as seen in Figure 15, Figure 16 and Figure 17. When comparing the correlation of the 3.88\u201d full radial length pad data to analysis, the discrepancy becomes large when differential pressure is high. It should be understood that the primary cause for this discrepancy is that the gap between pads is much greater for the 3.88-inch diameter seal than for the 4.37 inch diameter seal. For example, the gap on the 3.88-inch seal is 10\u00b0 between each pad, whereas for the 4.37-inch diameter seal, the pad gap is only 6\u00b0 or a 40% reduction" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002613_tpas.1971.293054-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002613_tpas.1971.293054-Figure6-1.png", "caption": "Fig. 6. Doubly-Fed Machine Phasor Diagrams a) Time Phasor Diagram", "texts": [ " This is the function of the position sensor, which is mechanically coupled to the rotor and must rotate with fixed relationships between its instantaneous output voltages and the rotor position. The model is based on the assumption that a fixed space angle (6) exists between stator MMF and rotor MMF regardless of the speed of the motor. This assumption is met when starting, (since direct current exists) and also at low speeds. Experimental observation of the phaseback waveforms indicates that the assumption is also reasonable at higher speeds. -Since three current sensors were needed (one per phase) and Fig. 6 shows the time phasor and space phasor relationships in some matching of characteristics was required, three separate battery- the doubly-fed machie. The analysis begins with the assumption of a resistor combinations were used as part of the experimental system so value for line current at a reference phase angle of zero degreesf and as to permit individual null controls. the selection of a torque angle 6 and an operating speed. A known space angle, 8, (determined by transducer setting) exists between stator and rotor MMF's", " Cycloconverter Input Voltage = 400 Hz, 200 V, 3 phase, Curve 1, 6 = 1500, Shunt Resistance = 200S2 (wye); Curve 2, 6 = 120\u00b0, Shunt Resistance = oo; Curve 3, 6 = 900, Shunt Resistance = 200Q2 (wye). 10.0 12.5 b) Space Phasor Diagram at t = 0, ia = maximum 15.0r 12.5[- I.._ -C) w 0. co o 10.0 E cr Z 7.5 D u 5.0 2.5 0 I I TEXP -. - TCALC IIEXP AI- I 529 F IEEE TRANSACTIONS ON POWER APPARATUS AND SYSTEMS, MARCH/APRIL 1971 equal to that of the turns ratio, rotor-referred value of Es, that is, the magnitude of Es times Nr/Ns. To calculate its phase angle, consider that the resultant stator referred current Ip lags stator current by an angle Ss (Fig. 6b) and leads thet referred rotor current Ir by an angle Br, Since a 90\u00b0 shift exists between MMF and EMF, stator internal voltage will be at an angle of 900\u00b08s, while rotor internal voltage will be at 90\u00b0-Sr, The total (line to neutral) internally generated voltage, Ej 't, is the phasor sum of Es and Er, Adding this to the resistive and leakage reactance voltage drops in the stator and rotor windings yields the motor input voltage, supplied from the cycloconverter. This calculated voltage can be compared with the fundamental rms input voltage, and iterations performed on the assumed input current to solve the equations", " K7C6536; 3 phase, 5 hp, 60 Hz, 1750 r/min, stator voltage I I0/220V, stator current 27.2/13.6A, rotor voltage 13V, rotor current 21 A. When connected for 11OV operation, the machine has the following per phase 60 Hz equivalent circuit parameters: stator winding impedance rotor winding impedance magnetizing impedance 0.080+jO. 198Q2 0.104+jO.198fl 0.39+j6.6092 Sample Calculations Known data 8 = 120,= 50\u00b0 , VQ-ccv 20OV, 400 Hz Experimental data n = 540 r/min, X = 56.5 rad/s, I = 9.OA, T = 6.32 N-i Calculations (refer to Fig. 6) Iline = .85 x 9.0 = 7.65L/. A (fundamental rms) I> I='line + (Iline Nr/Ns) 1/6 lo, = 7.65/-590A Es = Ij(co/wo)X= 7.5/31\u00b0V Sr = S-8s= 610 Er Eint = IESI (Nr/Ns)/900-6r 57.6/290 V = Er+Es = 15.1/300_V T = Eint I line cos OE1 (nq/2co) = (15.1) (7.65) (.87) (2 X 3 X 56.5) T = 5.3N-m REFERENCES 1. V. D. Albertson, \"Analysis and Stabilization of the Doubly-Fed Wound Rotor Polyphase Machine,\" Ph.D Thesis, University of Wisconsin, 1962. 2. J. H. Gifford, \"A Double Synchronous Speed Induction Machine,\" M" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002457_cdc.2005.1582362-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002457_cdc.2005.1582362-Figure4-1.png", "caption": "Fig. 4. The interpretation of Lemma 2 form a geometric view point.", "texts": [ " In the right side of the above equation, note that terms depending \u03d5 are only A and A is the inner product between \u03b1o and R\u03d5\u2206\u03b1\u2032 o. Therefore, the term A is minimized with respect to \u03d5 when the angle made by \u03b1o and R\u03d5\u2206\u03b1\u2032 o is \u03c0, i.e. \u03d5 satisfies (16). Consider the interpretation of Lemma 2 from a geometric view point. From (4) and (5), the incremental distance \u2206\u03b7\u0303 is rewritten as \u2206\u03b7\u0303 = [ R\u03d5\u2206\u03b1\u2032 o \u2206\u03c8 ] = \u23a1 \u23a3 \u2016\u2206\u03b1\u2032 o\u2016 ( R\u03d5 \u2206\u03b1\u2032 o \u2016\u2206\u03b1\u2032 o\u2016 ) \u2206\u03c8 \u23a4 \u23a6 . (17) This structure of (17) is illustrated in the left hand of Fig. 4. In the left figure, P represents the point of \u03b7\u0303 = [ \u03b1T o \u03c8 ]T = [ uo vo \u03c8 ]T in the three-dimensional space of \u03b7\u0303 and the shaded area represents the reachable area of the closed path on the plane (\u2016\u2206\u03b1\u2032 o\u2016,\u2206\u03c8) at P with the origin. We call this area \u2126. Observing the structure of (17) leads to the fact that the reachable area of \u2206\u03b7\u0303 is obtained by rotating the area \u2126 through \u03d5 about \u2206\u03c8axis. Therefore, the geometric interpretation of (16) is that \u03d5 is determined such that \u2016\u2206\u03b1\u2032 o\u2016- axis coincides \u2212 \u03b1o \u2016\u03b1o\u2016 as seen in the right figure of Fig. 4. By using \u03d5 satisfying (16), the determination problem of (\u03b81, \u03b82, \u03d5) for the convergence of \u2016\u03b7\u0303 + \u2206\u03b7\u0303\u2016 is reduced to that of (\u03b81, \u03b82) since \u2016\u2206\u03b1\u2032 o\u2016 and \u2206\u03c8 are functions of \u03b81 and \u03b82. Figure 5 shows the concept for \u03b7\u0303 to converge to the target point by using the reachable area \u2126. The areas surrounded by dashed lines are the reachable areas \u2126 at each iteration. As in Fig. 5, \u03b7\u0303 can converges to the target point by shifting to points on the reachable areas \u2126 iteratively. To do so, precise analysis of the reachable area \u2126 is necessary", " 12, the kth circle represents the position (\u2016\u2206\u03b1\u2032 o[k]\u2016,\u2206\u03c8[k]) by the kth closed path and the areas shaped as the lunes are the reachable areas \u2126. Figure 13 shows the trajectory of \u03b1f , where the closed paths are generated with time interval 2[sec] and the heavy lines show the values of the boundaries of the rolling motion \u03b8r. In Fig. 11, \u03b1o and \u03c8 have converged on the target point simultaneously by five number of the iterations. Furthermore, there exist the circles \u25e6 on the dashed line from the initial point to the target point. This corresponds to the fact that the direction of the shift of \u03b1o is determined by \u03d5 such that (16) (See Fig. 4). In Fig. 12, the points of k = 1, 2, 3 to which the control variable shifts are the end points of the reachable areas \u2126 at each iteration. Next, those of k = 4, 5 are adjusted such that the control variable converges to the target point. These transitions show the effectiveness of the algorithm. In Fig. 13, it is evident for uf and vf of \u03b1f = [ uf vf ]T to involve in the range between \u2212\u03b8r and \u03b8r, where \u03b8r \u2248 1.56. In this paper, we discussed control of contact coordinates for a contact point between a sphere and a plane with pure rolling contact by using iterative trapezoidal closed paths on the sphere with contstrained rolling motion" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001232_tasc.2003.813042-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001232_tasc.2003.813042-Figure2-1.png", "caption": "Fig. 2. Circuit for pull-out test.", "texts": [ "00 \u00a9 2003 IEEE A hysteresis motor using bulk superconductors in the rotor generates a torque that increases with a cubic of a armature current in steady operation when the armature current is small enough [1]. This characteristic is caused by the magnetic hysteresis characteristics of superconductors. But characteristics of the motor change if the speed of the motor changes, because bulk superconductor have frequency-dependent characteristics. We performed pull-out tests to examine the characteristics of this motor in the overload operation. Fig. 2 shows the circuit that was used in this experiment. A DC motor was used as a load and generates a reverse toque against the superconducting motor. The voltage of the bulk superconducting motor was kept constant when the armature current reaches a set value. The frequency of the armature current was set at 30 Hz and the synchronous speed is 900 rpm. The superconducting motor started first without load, and then the load was increased until the motor stopped. Fig. 3 shows the dependence of torque characteristics of the motor on slip when the initial set value of the armature current was between 7" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000913_s00542-003-0323-x-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000913_s00542-003-0323-x-Figure1-1.png", "caption": "Fig. 1. Schematic diagram of a 2.5-inch HDD", "texts": [ " 3, we discuss the process in which seeking noise is generated. In Sect. 4, we present the procedure for SRS analysis and propose the SRS-based design method for reducing the seeking noise. In Sect. 5, the seeking current is shaped for reducing the seeking noise and the effect of the current shaping is evaluated. The validity of the SRS-based design method is verified experimentally. 2 Head-positioning servo system 2.1 Head positioning mechanism and its model A schematic diagram of a 2.5-inch form factor HDD is shown in Fig. 1. Two disks are stacked on the spindle motor shaft and rotate at 4200 rpm. On the surface of the disk, more than 10,000 data tracks are magnetically recorded. The head is supported by a suspension and a carriage. An actuator, called the voice coil motor (VCM), actuates the carriage and moves the head to the desired track. The mechanical parts are the head, the disk, the spindle motor, the VCM, the suspension, and the carriage. The spindle motor and the VCM are mounted on a base frame. On the back of the head-disk assembly mechanism (HDA) is a circuit board on which a microprocessor or a digital signal processor (DSP) is mounted" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002073_s00366-005-0008-4-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002073_s00366-005-0008-4-Figure2-1.png", "caption": "Fig. 2 Graphical representation of mechanical drawing primitives", "texts": [ " Furthermore, rather than displaying the plots on the computer screen, they can be saved to files of different formats, such as a postscript file, PNG, and GIF. The users are also able to simulate the motion of the various linkages and cam-follower systems available in the Ch Mechanism Toolkit. Each mechanism class contains an animation() function to perform this task. This member function utilizes the QuickAnimationTM software module to generate the desired animation. Figure 1 shows the drawing primitives available in QuickAnimationTM. These basic primitives are used to create the mechanical drawing primitives shown in Fig. 2, which are used for generating linkage animations. Member function animation() utilizes these primitives to draw the linkages for each frame of animation. Similar to the plotting features of the toolkit, the animation data may also be saved to a file, with extension .qnm. Using the animation data, the QuickAnimationTM software module can perform animation at a later time. Object-oriented programming refers to the use of C++ style classes, which consist of a set of variables and functions. The attributes and operations for a class are usually referred to as data members and member functions, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003144_13506501jet447-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003144_13506501jet447-Figure1-1.png", "caption": "Fig. 1 Principles of a twin-disc test device", "texts": [ " The objective of the work was to evaluate, and develop further, a method to determine the limiting shear stress and actual viscosity properties of lubricants using a traction model based on an elliptical EHL contact and traction curves, measured at a wide range of temperatures and pressures using twin-disc test devices. Measurements were made with mineral and polyalphaolefin (PAO) base oils, which are generally used in industrial gears. The measured lubricant parameters can be used as input values in gear-contact power-loss calculations in future work. Traction tests were performed using a previously developed high-pressure twin-disc test device, which is presented in more detail in references [22] and [23]. The principle used for the test device and the coordinate system is shown in Fig. 1. In the test device, each disc is driven by separate electric motors with adjustable rotation speeds, resulting in a continuous variable sliding velocity. Loading and rotation speeds can be varied on-line with automated computer control. Measured signals from the twin-disc test device include bulk disc temperature, mean contact resistance, and traction moment in addition to load and shaft rotation speeds. The bulk disc temperature is measured 3 mm below the surface with a thermocouple, and the signal is transmitted from the axle using a telemetry device" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002599_05698197108983235-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002599_05698197108983235-Figure1-1.png", "caption": "Fig. 1-Relationship between frictional force and normal force for various sliding speeds.", "texts": [ " This was inconsistent with experimentally measured temperatures and they proposed that the physical properties should be taken a t the temperature of the material just below the asperities, now called the subsurface temperature, Bs, This was assumed equal to the equilibrium temperature recorded by the thermocouple when nominally terminating at the surface. The same assumption is made in the work presented in this paper. EXPERIMENTAL RESULTS Mean values of frictional force from tests in which mild wear conditions were obtained are plotted against normal force in Fig. 1 . Where periodic breakdowns of the oxidised surface layer (2) occurred the value of frictional force during ~ubsequent mild wear was used. There is a linear relationship between F a n d N for a constant sliding speed. If N is held constant then F decreases with increasing sliding speed. In Fig. 2 Os has been plotted against p along iso-U lines, changes in Os and p being effected solely by varying N. A discontinuity is apparent in each curve at a Bs value of about 210 C irrespective of speed. At lower temperatures changes in either N o r U cause significant changes in p whilst above 2 10 C, p appears to be near-independent of N and only slightly dependent on U, remaining in the range 0" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001183_cdc.1989.70628-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001183_cdc.1989.70628-Figure5-1.png", "caption": "Fig. 5 Trajectories With Cdllision", "texts": [ " For simplicity, the torque constraints are assumed to be Idzrl/dtzl 5 l (mz/s) , IdZPl/dtZI 5 3, ld2rz/dtZI 5 The outputs of PLANNER are plotted in Figs. 2 and 3. RI was delayed by 0.81 sec. and the resulting total finish time was 2.86 sec. To see how the two robots avoid collision more clearly, their movements along the optimal collision-free trajectories are plotted in Fig. 4 and their movements along the minimum time trajectories obtained in Step 1 of Algorithm 1 (i.e., without delaying RI) are plotted in Fig. 5. Note that a collision occurred in the latter case. Clearly, both assumptions of the theorem are satisfied for this example. Thus, from the optimality of Algorithm 1, the trajectories obtained will ensure that two robots reach their ending positions along the preassumed paths in minimum time. However, because of the path-velocity decomposition used in the algorithm, the trajectories may not be overall optimal. For example, the total finish time was reduced to 2.77 seconds when we chose the preassumed paths to be rl = 1 + SI, PI = (1 - 2s1)*/2 and r2 = 1 + sz * sZ, pz = (2sz - 1)7r/2, 0 5 si 5 1 ,0 5 sz I 1" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-FigureA.6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-FigureA.6-1.png", "caption": "Fig. A.6. Set-up for X-axis and Y-axis straightness measurements", "texts": [ " The objective of a straightness measurement is to determine whether the moving part is moving along a straight path. The main source for a straightness 5.3 Overview of Laser Calibration 137 error is the straightness profile of the guiding mechanisms which guide the motion of the moving part. The optics required for straightness measurement is given in Figure A.5. The straightness profile can be divided into two components: namely the horizontal and vertical straightness. The schematic of the set-up to carry out these measurements is given in Figure A.6. Figure 5.8 illustrates the two light paths of travel within the interferometer. The mirror axis serves as an optical straight edge to provide a reference for the straightness meaurements. Straightness and squareness measurements are usually done concurrently, since a squareness measurement consists of two straightness measurements carried out perpendicularly to each other. These measurements allow the user to determine whether two machine axes are oriented perpendicularly to each other. A milling machine with a horizontal spindle and a bed which moves perpendicularly to the spindle is an example of a machine with two perpendicular axes" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002792_0009-8981(73)90467-1-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002792_0009-8981(73)90467-1-Figure3-1.png", "caption": "Fig. 3. Effect of neu t ra l s u b s t a n c e s on observed ca lc ium ion ac t iv i ty . E .m. f . ( test so lu t ion- re fer - ence solution) p lo t t ed aga ins t concen t r a t i on of t e s t ma te r i a l in reference so lu t ion (CaC12, o .ooi mole / l ; NaC1, o.I 5 mole / l ; p H 5-5)- Me thod as for Fig. i .", "texts": [ " Closely similar curves were obtained using methylamine, piperidine, ethanolamine, tris(hydroxymethyl)aminomethane, triethanolamine and morpholine. Pyridine, 2-pieoline, 2,4,6-collidine and lutidine (2:4/2:5--rat io of isomers unknown) formed a distinct group differing from the other bases in that they caused an apparent increase in the calcium ion activity. Imidazole (glyoxaline) was unique in that it behaved like pyridine at low concentrations, but like the first group of bases at higher concentrations. Fig. 3 shows some representative results of experiments carried out at pH 5.5. Benzene, benzaldehyde, benzyl alcohol, aniline, phenol, methanol, ethanol, n-propanol, n-butanol and amyl alcohol (mixed isomers) were examined and all found to cause an apparent fall in the calcium ion activity in the range of concentration lO .4 to IO 1 mole/1. Ethane diol and glycerol had the same effect in tile range lO -1 to I mole/l, but urea and glucose had the opposite effect in the concentration range IO--~ to r mole/1" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001714_02678290500161363-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001714_02678290500161363-Figure2-1.png", "caption": "Figure 2. Schematic diagram of the film preparation set-up.", "texts": [ " As a result, the material forms a 3D network, and the coupling between the orientation of the mesogens and the polymer network is strong in comparison with socalled intralayer crosslinked elastomers, in which crosslinks are formed preferentially within the siloxane sublayers [7]. The phase sequence in the non-crosslinked material is SmX 65uC SmC* 95\u201396uC SmA 125uC I. Samples for the X-ray measurements were prepared by irradiation of free-standing films of the photo-crosslinkable polymer (in the SmA phase) using a 250 W Panacol-Elosol UV point source UV-P 280. The geometry used for film preparation is shown in figure 2. During UV crosslinking, two side edges of the free standing film are shielded from UV exposure with an opaque mask [1]. After crosslinking, the sample consists of an elastomer strip in the middle and two liquid parts at both sides of this strip; these liquid edges can be easily removed. This method allows us to obtain freestanding films fixed at two opposite edges [1, 6]. The UV irradiation time was 2 h; it was performed in two D ow nl oa de d by [ L ou gh bo ro ug h U ni ve rs ity ] at 0 9: 33 1 0 D ec em be r 20 14 steps" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000028_auto.2000.48.4.157-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000028_auto.2000.48.4.157-Figure8-1.png", "caption": "Figure 8: Diagram of the experimental setup.", "texts": [ " In the framework of a competitive game, in which the robot seeks to score goals on an opponent while simultaneously protecting its own goal, air hockey requires not only rapid response but also highly accurate estimation of the puck trajectory given a (usually) sparse data set. Using the visually estimated motion of the puck, the robot must plan and execute trajectories of the circular mallet (attached to the tip of the last link of the manipulator) such that the outgoing puck velocity after impact matches some desired pro le. Our system is shown below in Figure 8. Our hy- brid control strategy is based on the fundamental tenet that control should be determined by the reliability of sensor data. This means that the supervisor should choose a conservative control strategy when con dence in the sensor data is low and an agressive control strategy when con dence in the 316 Brought to you by | provisional account Unauthenticated Download Date | 6/25/15 4:44 PM sensor data is high. Con dence is determined statistically from the sensory data. The supervisory control strategy is shown in Figure 10" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002754_j.mechrescom.2007.01.001-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002754_j.mechrescom.2007.01.001-Figure1-1.png", "caption": "Fig. 1. Two forces F1 and F2 acting on an elastic body.", "texts": [ " Briefly, consider two forces F1 and F2, acting at points 1 and 2, respectively, of a properly supported, linearly elastic body of arbitrary shape, and let u12 be the displacement 0093-6413/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechrescom.2007.01.001 * Corresponding author. Tel.: +49 421 218 2255; fax: +49 421 218 7478. E-mail addresses: g.herrmann@dplanet.ch (G. Herrmann), rkienzler@uni-bremen.de (R. Kienzler). z Readers will be very sad to learn of the mournful death of Prof. Dr. Dr. h.c. George Herrmann on January 7, 2007. at point 1 due to the force F2 and u21 be the displacement at point 2 due to the force F1 (Fig. 1). A reciprocity theorem states F1 u12 \u00bc F2 u21; \u00f01\u00de where the dot indicates a scalar product between the two vectors. In Barber (1992); this form of the theorem is ascribed to Maxwell and in Marguerre, 1962; to Betti. If the component of u12 in the direction of the force F1 and produced by the force F2 is labelled here uP 12 and the component of u21 in the direction of F2 and produced by F1 is called uP 12, we arrive at a scalar form of (1) as F 1uP 12 \u00bc F 2uP 21: \u00f02\u00de with F1 and F2 being the magnitude of F1 and F2, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000457_978-3-642-55848-1-Figure9.17-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000457_978-3-642-55848-1-Figure9.17-1.png", "caption": "Fig. 9.17. The Andrews' squeezer mechanism (Schiehlen [3], used with permission)", "texts": [ " Some inter esting points are given in Table 9.3. The data obtained by simulation agree fairly well with the exact data obtained from the geometry of the problem 344 9 Multibody Dynamics We now apply the method developed in Sec. 9.2 to the well-known Andrews' squeezer mechanism problem. This problem has been promoted as a test of nu merical codes [3,13,14]. We take the formulation of the problem as given in [3, 14] and compare the simulation results obtained by the BondSim program to the solution given in [14]. The mechanism (Fig. 9.17) consists of seven bodies that can move in a plane. The bodies are interconnected by revolute joints and also to the base. The arm K1 rotates about the fixed joint at 0 under the action ofthe driving torque Md and this pushes, via body K2, the central revolute joint where three bodies-K3, K4 and K6-are connected. Bodies K4 and K6 are further connected via bodies K5 and K7 to another revolute joint A that is fixed to the base. The third body, K3, can rotate about the fixed revolute joint at B. The end 0 of body K3 is connected to a spring that simulates the squeezer effect", " To develop a simulation model using BondSim, we create a project called An drews Squeezer Mechanism. All of the bodies-Kl to K7--will be represented by the standard plane body motion component model of Sec. 9.2.1. To create component models of the bodies, the component Body from the library is copied into the document seven times. The components are then moved to positions that approximately correspond to their positions in the mechanism (Fig. 9.18). The 9.3 Andrews' Squeezer Mechanism 345 component names Body are then changed to the names used in Fig. 9.17, K 1 to K7. The weights of the bodies are not included in the component models. The revolute joints are created by copying the standard revolute component model Joint from the library. The names of the joints that are fixed to the mecha nism base are changed to the names used in Fig. 9.17, i.e. A, Band O. For the oth ers the default names Joint are retained. To simplifY the model, there is no sepa- 346 9 Multibody Dynamics rate base component, as in the last example (Fig. 9.12). Its effect is included di rectly in the A, Band 0 components. Table 9.5. Mechanical parameters Kl K2 K3 K4 K5 K6 K7 Mass [kg] 0.04325 0.00365 0.02373 0.00706 0.0705 0.00706 0.05498 Inertia [kg\u00b7m2] 2.l94e-6 4.4lOe-7 5.255e-6 5.667e-7 1.16ge-5 5.667e-7 1.912e-5 Other It was assumed that there is no friction in the joints", " The power then branches out on one side to two paths--one through bodies K4 and K5, and one through K6 and K7 -to the joint A, and then to the base. On the other side, it flows through the body K3 and then branches through joint B to the base and to the spring. This clearly shows that the power generated by the source is used to move the bodies and to squeeze the spring that is, after all, the purpose of the mechanism. There are many signals between the components and we ex plain them next. The body coordinate frames in the original Schiehlen scheme of Fig. 9.17 ex actly correspond to the coordinate frames used in the formulation of the body bond graph model in Sec. 9.2.1. We use as a base frame, the co-ordinate frame Oxy of Fig. 9.17. We can look at this as the frame of the base to which the mecha nism is jointed by the revolute joints A, 0 and B. The angles specified in the scheme, however, are not the absolute, but are relative to the body frames of the connected bodies. Thus angle (3 of body K1 is relative to the base frame, but the 348 9 Multibody Dynamics angle e of the next body K2 is given with respect to the previous body K1 frame, etc. These angles are used as generalized coordinates of the mechanism in [13, 14]. To compare the results we introduce a vector of generalized coordinates de fined as in [13] (9.29) By inspection of Fig. 9.17, it is easy to find the relationships between these coor dinates and the body rotation angles. The generalized coordinates of bodies K1, K3, K5 and K7 correspond to body rotation angles. Hence q1 = 4>1 , q3 = 4>3 ' q5 = 4>5 ' q7 = 4>7 For the others, these are relative rotation angles q2 = 4>2 -4>1 } q4 = 4>4 - 4>5 q6 = 4>6 - 4>7 (9.30) (9.31 ) These last relationships are represented by summators inside the joint components. This is the reason why the signals from some bodies in Fig. 9.18 are fed back to their common revolute joints", " The output from the summator is taken out of the joint and connected to the display component (the bottom right component in Fig. 9.18). For the others, the outputs from the bodies are fed directly to the display component. We now return to the problem of modelling the spring. The spring is attached between point D of the body and point C of the base. We assume that the attach ments are such that the spring extends and contracts without bending. The coordi nates of the attachment point D in the base frame are given by (Fig. 9.17) xd = xb + sc\u00b7 sin4> + sd\u00b7 cos4>} yd = yb - sc . cos 4> + sd . sin 4> (9.32) Angle 4> in these equations is the rotation angle of body K3. In this way the coor dinates of point D can be evaluated inside component K3 as shown in Fig. 9.21. This is achieved by component D, which consists of two functions that implement 9.3 Andrews' Squeezer Mechanism 349 Eq. (9.32). Information on the coordinates is available at the top-right control output port. At point 0 there is a force acting on the spring, which is represented by two components in the base coordinate frame (Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002823_ls.47-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002823_ls.47-Figure1-1.png", "caption": "Figure 1. Journal bearing scheme.", "texts": [ "1002/ls The journal speeds are given as U R V h t = = \u2202 \u2202 \u03c9 (14) The governing model for the hydrodynamic lubrication pressure in the shaft-bearing wedge is a dimensionless modifi ed form of equation (12): \u2202 \u2202 ( ) \u2202 \u2202 + \u2202 \u2202 ( ) \u2202 \u2202 = \u2202 \u2202 + \u2202 \u2202\u03b8 \u03c4 \u03b8 \u03c4 \u03b8 g h p z g h p z h h t ; ; 2 (15) g h h h h ; tan\u03c4 \u03c4 \u03c4 \u03c4 ( ) = \u2212 \u2212 3 212 2 2 h (16) In equations (15) and (16), these dimensionless variables have been introduced: p R C p p p p h h C C z z R ref ref = = \u2212 = = + = =6 1 2 0\u00b5\u03c9 \u03b5 \u03b8 \u03c4cos (17) Short Couple Stress-bearing Model With reference to the geometry of the short journal bearing (Figure 1), equation (15) appears as follows: \u2202 \u2202 \u2212 \u2212 \u2202 \u2202 = \u2202 \u2202 \u2212( ) + z h h h p z h3 212 2 2 1 2 2\u03c4 \u03c4 \u03c4 \u03b8 \u03d5 \u03b5tan cosh \u03b8 (18) Imposing void values of pressure to the edges of the bearing, by integrating equation (18) gives p z L D z h h \u03b8 \u03b5 \u03d5 \u03b8 \u03b5 \u03b8 \u03c4 \u03c4 , sin cos ta ( ) = \u2212 \u2212( ) \u2212 \u2212 \u2212 1 2 1 2 2 12 2 2 2 3 2 nh h 2\u03c4 (19) Copyright \u00a9 2007 John Wiley & Sons, Ltd. Lubrication Science 2007; 19: 247\u2013267 DOI: 10.1002/ls For each value of \u03b8 out from the interval (\u03b1,\u03b1 + \u03c0), it is assumed p(\u03b8,z) = 0, where \u03b1 is the angle that results from \u03b5 \u03b1 \u03b5 \u03d5 \u03b1 \u03b5 \u03b1 \u03b5 \u03d5 \u03b1 cos sin cos cos + \u2212( ) = \u2212 \u2212( ) \u2265 1 2 0 1 2 0 (20) The dimensionless oil fi lm force components are obtained by integrating the pressure over the fi lm domain: f f W F F p z z L D z L D r t r t + , = = ( ) \u2212\u222b\u222b =\u2212 =1 \u03c3 \u03b8 \u03b8 \u03b8\u03b1 \u03b1 \u03c0 / / cos sin d dz\u03b8 (21) in which \u03c3 is the modifi ed Sommerfeld number: \u03c3 \u00b5\u03c9= RL W L D R C 2 2 (22) Fluid Film Force The oil fi lm forces can be calculated in approximate way as f I Ir = \u2212 \u2212 +\u03b5 \u03d5 \u03b5( )1 2 23 2 (23) f I It = \u2212 \u2212\u03b5 \u03d5 \u03b5( )1 2 21 3 (24) with I h d I h d I h d1 2 3 2 2 3 3 3 = = = + + + \u222b \u222b \u222bsin cos sin cos\u03b8 \u03b8 \u03b8 \u03b8 \u03b8 \u03b8 \u03b8 \u03b1 \u03b1 \u03c0 \u03b1 \u03b1 \u03c0 \u03b1 \u03b1 \u03c0 (25) h( , ; ) cos\u03b8 \u03b5 \u03c4 \u03b5 \u03b8 \u03c4\u03b5= + \u22121 (26) Numerical calculations show that equation (26) gives good results within the normal operating conditions of a short couple stress bearing" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000304_epjap:2000113-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000304_epjap:2000113-Figure1-1.png", "caption": "Fig. 1. Specimen configuration.", "texts": [ ") thin films on polycarbonate substrates has been investigated and characterised by atomic force microscope (AFM) [11] using an experimental apparatus allowing the in situ observation of the specimen during compression. Elastic energy calculations have been carried out to model the interaction of straight-sided wrinkles observed during the compressive tests. a e-mail: Cleymand@lmp.univ-poitiers.fr 304 L S.S. thin films were deposited on polycarbonate substrates at room temperature using an argon ion beam sputtering technique operating in a vacuum chamber. The sample configuration is presented in Figure 1. The choice of substrate was made depending on its elastic behaviour over a large range of strain and its dimensions are nominally 2.5 \u00d7 2.5 \u00d7 5 mm3. Before deposition, the polycarbonate substrates were cleaned in a neutral solution for 48 hours followed by annealing at 120 \u25e6C under an Ar atmosphere to decrease the humidity content. The faces destined to be compressed were then mechanically polished by standard metallographic procedure. The sputtering system has been described in detail in reference [12]" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002707_j.tsf.2007.07.138-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002707_j.tsf.2007.07.138-Figure2-1.png", "caption": "Fig. 2. Experimental set-up: PANI film has been grown in situ on gold (Au) electrode sputtered on PET support. After conversion of PANI film to base form, the tungsten (W) sphere was placed on the PANI-base film as top electrode.", "texts": [ " The breakdown channel is represented by an opening of the 10\u201320 \u03bcm diameter in the film. Once localized, it is well discernible in the optical microscope but may be difficult to find after the transport of the samples. That is why the future breakdown area was marked at first by the gold electrode of 1 mm width, which is well seen under the PANI film. PANI film has been grown on a comb of 1 mm gold-sputtered electrodes deposited on 100 \u03bcm poly-(ethylene terephthalate) (PET) foil (used for copier transparencies) (Fig. 2). A tungsten sphere of 2-mm diameter was placed on the polymer film opposite the gold electrode. Constant pressure was applied to the sphere, and the electrode and contact area were surrounded with silicone oil to prevent discharges. Oil was later washed off with cyclohexane before attempting the spectroscopic characterization of the samples. The linearly increasing direct voltage of various polarities was applied to the samples, dU/dt\u22480.15 V s\u22121. The voltagesU+ andU \u2212 correspond, respectively, to the breakdown voltages at positive and negative polarity of the tungsten electrode with respect to a gold base" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001251_icit.2002.1189888-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001251_icit.2002.1189888-Figure8-1.png", "caption": "Figure 8: Symmetrical Clothoid", "texts": [ " (14) k C k rz = - 2 (19) After a summit of the v-shape, S(xi, A), and orientation, Of, are located, path on which WL is able to move can be The symmetrical clothoid, 0-S will be defined. A section between S and Z will he filled with a line segment, where (7) (8) demonstrated as follows: (9) r2 ( I I) 3. Symmetrical clothoid parameter determinations r , = +x; 2 sin[ 5 - Of?] xi, = rl(I+cosO:) (12) As we see from the previous section, V-shape path partially consists of 2 symmetrical clothoids. The characteristics of 1 y: = rlsine; symmetrical clothoid can be illustrated in Figure 8. We detine such a symmetrical clothoid curve C that has following properties: 3) After a summit of the v-shape, s(~;, A), and orientation, Of. are located, path on which WL is able to move can be 189 IEEE ICIT'02, Bangkok, THAILAND 1. At (xo. yo), and (xe, ye ) , curvature c o f C is zero 2. At the middle of (x, y,) i.e. equidistance point from (xo, yo) and from (xe, ye) along C, whose distance is denoted as sm, the symmetncal clothoid C has maximum curvature c,. 3. Curvature c along C from (xo, yo) to (xm, y", " According to the properties of the symmetrical clothoid, parameters of curvature at s, c(s), O(s) of orientation of WL at s, and WL position, (x(k, s), y(k, s)) at s with li, are derived as follows: ;(0 5 s i s m ) 2 2sm) c(s) = -ks + ks, ;(s, 5 s (21) (22) i\" = l c ( s ) d s , x(k, s) = cos[c(s)]ds, (23) y ( k , s) = [sin[c(s)]ds. 0 (24) We can easily derive following properties: Let us consider k first. We can see that k is a function of be, e,) or (xe, %), assuming if -n/2 5 0, < a/2. Considering Figure 8, xe andy, are denoted as: .re = r + rcosO, (27) ye = rsine,. (28) From the properties ofx(k, s) andy(k, s), However, (x,, y , ) is simultaneously denoted as: x, = Y , = Ye Therefore, we can obtain following equations: cos[- 4 - 3 2 +kT,s+-]}ds k.', (33) 2 2 sin!- -ks2 +ks,s+ - ] }ds ks! (34) 2 2 In the mathematical formulation, k and s m could be derived ifwe could solve the simultaneous equations (33) and (34), which is very difficult to be solved analytically. Therefore, we will solve k and s, by numerical way" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003623_9780470567319.ch5-Figure5.20-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003623_9780470567319.ch5-Figure5.20-1.png", "caption": "Figure 5.20 Abbott sensor showing size relative to U.S. dime. Copyright 2008 Abbott. Used with permission.", "texts": [ " The blood glucose meter is built into the receiver, so the calibration is done automatically when a blood glucose measurement is made. After 5 days the user is instructed to remove and dispose of the sensor support mount. The transmitter is reusable and contains replaceable batteries. The transmitter and mount are water resistant and can be worn during showers. The receiver is not water resistant because the receiver contains the open port for insertion of a blood glucose test strip. The tip of the sensor is inserted at an angle of approximately 90 to the skin to a depth of about 5mm (Figure 5.20). The sensor contains electrodes that are patterned by screen printing. The electrode system functions as a three-electrode system with a working electrode, counter electrode, and a silver/silver chloride reference electrode. The working electrode contains glucose oxidase bound to a polymer that contains mediator molecules also bound to the polymer (Figure 5.2). Glucose oxidase reacts with the glucose and the reduced enzyme reacts with the mediator in the polymer. The reduced mediator reacts with other mediator sites in the polymer until eventually a reduced mediator near the metal surface of the electrode is oxidized by the metal surface poised at a low potential, 0" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002134_1.5060506-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002134_1.5060506-Figure3-1.png", "caption": "Figure 3. Adaptive slicing.", "texts": [ " For small values of layer thickness the overhang angle a can be approximated by cos pt s \u03b1 = \u2206 (3) Using Eq. 1 and Eq. 3 the required number of clad tracks can be written as 1 cos z \u03b1 = (4) Fig. 2 shows the required number of clad tracks for a fixed layer thickness in z-direction as a function of the overhang angle a. A particular case is horizontal slicing of a horizontal structure (a=90\u00b0) which results in a infinity number of clad tracks inside a layer. Thus the slicing direction and thickness must be adapted to the geometry of the part contour, as shown in Fig. 3. In the following example the part contour is defined by a B\u00e9zier curve [2] with the control points b0(p0,q0), b1(p1,q1), and b2(p2,q2). The quadric B\u00e9zier curve can be written as [ ]2 2 0 1 2( ) (1 ) 2(1 ) , 0,1C t t b t t b t b for t= \u2212 + \u2212 + \u2208 (5) and can be expressed in the parametric form (x(t),y(t)) where Page 311 Laser Materials Processing Conference ICALEO\u00ae 2005 Congress Proceedings 2 2 0 1 2( ) (1 ) 2(1 ) ,x t t p t t p t p a= \u2212 + \u2212 + nd 2 (6) 2 2 0 1( ) (1 ) 2(1 )y t t q t t q t q= \u2212 + \u2212 + Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001144_978-3-642-83410-3_7-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001144_978-3-642-83410-3_7-Figure4-1.png", "caption": "Fig. 4. Tendon actuated 4 d.o.f. sensorized finger", "texts": [ " In particular the fundamental importance of a system approach to the design of a sophisticated tactile sensing system will be pointed out. 4.1 Anthropomorphic robot finger The finger we have designed and fabricated has an anthropomorphic configuration, and is composed of four rigid links connected by joints providing a total of four degrees of freedom. two-degree-of-freedom articulation of the proximal phalanx of the hinge The human fingers is reproduced by two separate joints with perpendicular axes. The finger is presently mounted on a rigid fixture, as shown in Fig. 4, that qui te severely limits its exploratory capabilities. The intention is to eventually connect it to a mul ti-degree-of-freedom manipulator making it capable of following complex object surfaces. Despite this limitation, finger dexterity is sufficient to investigate fundamental problems associated with the simple tactile exploration procedures we intend to replicate. Each articulation is driven via plastic coated stainless steel tendons, routed through flexible and incompressible sheaths, and actuated by remotely located dc servomotors" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001190_robot.1992.219930-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001190_robot.1992.219930-Figure1-1.png", "caption": "Figure 1: Two Manipulators Grasping a Pair of Pliers", "texts": [ " In general, the dynamics of the two manipulators grasping an object can be combined as H ( q ) i + (C(P, 4) + B)4 + G(P) + F(4) = T + where 9 = [ ;;I, and Equation (17) may now be used with this formulation to solve for X with equations (21 -(28 and the constraint equations, (8), being use d h in t e calculation. In this model, the forces of constraint, i.e., the vector A, are precisely the desired interactive forces. As an example, consider the case of handling a pair of pliers illustrated in Figure 1. The object has a single joint with a single degree-of-freedom and is free to rotate about the joint axis, which is assumed to be parallel with the normal axes of the two end-effectors. Thus an orientation constraint will not exist about this axis. Zheng and Luh [12] have developed the constraint equations for this case. They consist of three position and two orientation constraint equations. The position constraint equations are given by where Xp(ql) and X,(q,) are the end-effector positions and Rt(q1) and R$(qr) are the end-effector orientation matrices of the left and right manipulators, respectively, and 11 and 1, are the distances from the left manipulator end-effector and right manipulator endeffector to the pliers joint, respectively" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001197_iros.1998.724648-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001197_iros.1998.724648-Figure4-1.png", "caption": "Figure 4: Example 1", "texts": [ " 6.3 Examples of OPTPT From IK, we can reformulate the OPTPT by considering a criteria that is only function of q,f. We have chosen (recall: qg = (0, o,o) ) : and the constraint q,f E Sp(xf) writes: (xi - a2 cos zf - 2\u2019)\u2019 + (xi - a2 sin 2; - yf)\u2019 = a12 the configuration of the arm being uniquely defined by IK for a given q,f. This criteria is calculated for the previous three local planners and the minimizing problem solved in these three cases. Finally, the best solution is chosen. Example 1: (Fig. 4) We consider the following example: qo = ( O , O , O , F, 5 ) and xf = (4,5.36, %). The final configuration is then gf = (3.04,3.46,0.25,0.83, -0.04) and the local planner is the barycentric one. Different criteria may have physical meaning and it is always difficult to propose a [\u2018natural\u201d criteria for this problem. Another optimization process that proved useful is the following: first, determine (xf , y f ) by minimizing (yf)\u2019 for q,f E Si. Then, determine 19\u2019 solving the scalar optimization problem: Roughly speaking, this optimization process tends to minimize the projection of q,f along the direction normal to the nonholonomic distribution [7] in the initial configuration" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002297_bf02482627-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002297_bf02482627-Figure2-1.png", "caption": "Fig. 2. Gas bubble in rotating liquid, coordinate system", "texts": [ " sin (Qt + ~) + k~; (3) The initial conditions are = o R(o) R(o) \\ Ing. Arch. Bd. 45, H. 5]6 (1976) In these equations, tile virtual mass of the bubble is denoted by M (---- m 0 + n m ) , the mass of the bubble (in the computations assumed to be negligible) by too, the mass of the displaced liquid by m, the virtual mass coefficient by ~, the acceleration due to gravi ty by g, and the time by t. A dot denotes differentiation with respect to time. The direction of gravi ty is parallel to the vertical and perpendicular to the spin axis (Fig. 2); its magnitude is not necessarily restricted to the terrestrial value. The physical origin of the forces involved (inertia, gravity, friction drag, centrifugal- and Coriolis terms) is easily recognized. In the absence of gravi ty the last but one terms on the right hand sides of (2, 3) have to be omitted. Since the flow velocities are assumed to be small, the drag (kR, kr is proportional to the flow velocity and acts in a direction opposite of tha t velocity, hence k R = - - K R , k~ = - - K R c ~ , K = const ( > o) " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000882_0301-679x(87)90073-9-FigureI-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000882_0301-679x(87)90073-9-FigureI-1.png", "caption": "Fig I Bearing nomenclature and wetted film extent", "texts": [], "surrounding_texts": [ "Effect of loading direction on the performance of a twin-axial groove cylindrical-bore bearing\nD.T. Gethin* and M.K.I. El Deihi*\nAn analysis based on the finite-element method is presented for the incompressible hydrodynamic lubrication of a cylindrical-bore bearing subjected to different loading directions. The model accounts fully for the extent of the lubricant film in both load-carrying and ruptured parts of the bearing. A number of loading directions are considered, and the results when computed show that load-carrying ability, hydrodynamic flow and attitude angle all depend significantly on loading direction.\nKeywords: cylindrical-bore bearings, loading direction, lubricant film, bearL~g performance\nMany practical situations exist in which the direction of loading on a journal bearing varies during its operation. A typical example is a gearbox where the direction of loading is the vector sum of the shaft weight and a force component generated by the combination of torque transmission and gearbox design layout. Clearly during operation it may be expected that the torque transmitted may vary, and this will be reflected in a variation of loading direction on the\nsupport bearings.\nA journal bearing fed by two axial grooves has wide practical application due to its good load-carrying capacity 1 and ability to operate where reversal of shaft rotation occurs. These bearings are usually arranged so that the grooves are positioned orthogonal to the predominant load direction since this gives optimum load-carrying ability. For\nNotation\nC Cd D H\nh\nL Lo Ls N P\nat\naz R\nRe\nradial clearance diametral clearance journal diameter power loss\nr -\ndimensionless power loss =] uNT-LD 2\nbearing length film length at inlet to region 1 film length at location's' (see Fig 2) rotational speed rev/s load capacity\ndimensionless pressure\ndimensionless load capacity\nI p.f Cd dimensionless feed pressure\nside leakage\ndimensionless side leakage\njournal radius\nnominal film Reynolds number = P ~\nU h ho hs P pf\nqo\nqs\nX , Z\n0 , ~\n~2\nC\n#z\nPX~ VZ\nP\nsliding speed local film thickness film thickness at inlet to region 1 film thickness at section's' (see Fig 2) film pressure lubricant feed pressure streamwise flow rate per unit width at inlet to region 1\nstreamwise flow rate per unit width at section's' (see Fig 2) coordinate directions (see Fig 2) angular positions (see Fig 1) attitude angle (see Fig 1) angular location (see Fig 1) eccentricity ratio molecular viscosity molecular viscosity in the z direction kinematic viscosity kinematic viscosity in the x, z direction lubricant density rotational speed (tad/s)\nThe remaining symbols are defined where they are introduced in the text.\n*Department of Mechanical Engineering, University College of Swansea, Singleton Park, Swansea SA2 8PP, UK.\nTRIBOLOGY international 0301-679X/87/040179-07 $03.00 \u00a9 Butterworth & Co (Publishers) Ltd 179", "gearbox applications however, it is clear that these bearing types will operate under off-design conditions, particularly where reversal of shaft rotation occurs. Little is known about the performance of a twin-axial groove bearing that runs under such conditions. It may be anticipated that if the bearing is loaded into the groove, its load-carrying ability will be diminished, but the effect on hydrodynamic lubricant flow rate and power loss is not so obvious. Indeed under conditions of light loading, it may be advantageous to load into the groove, since this reduces the likelihood of bearing instability 2 , as for a given load, the journal will run more eccentrically. The objective of the work described here was to investigate theoretically the steady-state performance of a twin-axial groove bearing operating under such conditions.\nPrevious work The Reynolds equation 3 is fundamental to the analysis of hydrodynamic journal-bearing behaviour. This may be solved using either the well known finite-difference technique or the finite-element methods as explained by Huebner\". For straightforward calculation of fully flooded hydrodynamic lubrication, the finite-difference approach may be more suitable since the film may be subdivided into a regular rectangular grid. However, where irregular boundaries occur, the finite-element method has distinct advantages since the mesh may be mapped to fit the boundary.\nIn hydrodynamic lubrication, irregular film boundaries occur either where the lubricant film reforms in pressurefed bearings that incorporate a groove feed arrangement s or where starvation occurs in circumferentially-grooved types when low-lubricant feed pressures are used 6 . In Reference 5, Dowson et al illustrate the effect of modelling film reformation for both high- and low-feed pressures. Their analysis shows that the use of higher feed pressures results in the bearing having a higher toad-carrying capacity and running at a much increased attitude angle. Some aspects of their analysis was confirmed by experimental observation as described in Reference 7. In Reference 6, Dowson et al give a detailed description of a model to simulate the steady state and dynamic behaviour of a circumferentially-grooved bearing. The finite-difference approach was used in this work, and considerable numerical ingenuity was required to approximate closely the extent of the lubricant film. Their analysis also illustrates the trends in bearing performance associated with increasing lubricant supply pressure. The extent of the lubricant film also has considerable implication on rotor-bearing stability as explained in Reference 8. In this paper, a rotor-bearing stability model was developed and prediction compared with experimental observation. Even with the approximate model for the film, theoretical and experimental trends were in agreement.\nWhere twin-axial groove bearings operate steadily under offdesign conditions (i.e. when the load line is not orthogonal to the grooves), it is expected that important load-carrying parts of the bearing will operate with an incomplete film. This can be explained most clearly with reference to Fig 1 which illustrates some of the geometric nomenclature to be used in this paper and a schematic representation of the wetted surface in the bearing. From this, it can be seen that the grooves are accounted for by including their circunrferential extent in the geometry. Regions 1 and 2 are the load-bearing areas of the film, while regions 3 and 4 comprise the cavitated zone, which (from a consideration\nof flow continuity) wets a part of the bearing surface only. It can also be deduced that only part of region 1 is wetted by lubricant, and therefore this area of the load-carrying film may be considered to be incomplete.\nAn approximate model of the bearing may be constructed by considering the film to be flooded fully throughout and to extend from the maximum film thickness to the rupture point (just past hmin). The effect of grooving may be embodied by prescribing lubricant feed pressure at the appropriate location in the film as demonstrated by Huebner 4. Apart from the work described in Reference 5, as far as the present authors are aware this is the only approximate method of treating the effect of oil grooves that has been presented in the literature to date. For a more accurate analysis, careful consideration of film extent needs to be included. This is expected to influence hydrodynamic leakage significantly and load-carrying ability under some circumstances. Such a model may be based on the work described in Reference 9, in which the authors describe a finite-element model to synthesize lubricant-starvation effects. In contrast with the finite-difference approach explained in Reference 6, the adoption of the finite-element approach enables the mesh to be distorted according to flow continuity requirements to determine the extent of the wetted film in the loaded part of the bearing.\nA final point that needs consideration is that when bearings operate at high rotational speeds, it is now widely accepted that there is a departure from laminar flow in the film. Under isothermal conditions, evidence of this is present in experimental data obtained from water-lubricated bearings 1\u00b0 being characterized by an upturn in the torque-speed characteristic. Methods of incorporating this effect into the prediction of bearing performance have been presented in the literature n-13, probably tile nrost widely adopted being\n180 August 1987 Vol 20 No 4", "that described in Reference 11. Its incorporation will be described together with the development of the numerical model in the following section.\nTheoretical background and numerical model\nTheoretical basis\nIn building a numerical model, it is useful to consider first the basic hydrodynamic equations. For an aligned journalbearing system operating steadily at high speed using an incompressible lubricant, the Reynolds equation may be written\n~p 8 8p dh - - - - + - - = 6 p U - - (I) ~ x vx ~z v z dx\nand for turbulent lubrication, according to Reference 11\nux = v(1.0 + 0.000375 ReT 1\"\u00b0~) (2a)\nuz = v(1.0 + 0.000175 ReT 1\"~) (2b)\nwhere the film Reynolds number is given by\nUh Re T = Ref = - - (3)\nP\nHowever, when flow is transitional (neither wholly laminar nor turbulent), the film Reynolds number may be given by\n(Ref -Recl ). Ref Rer = (4) (Rec2 - Reel )\nwhere according to the experimental evidence cited in Reference 10, Rec2 = 2Reel and Recl is given by Taylor's criterion, i.e.\nReel = 41.2 ~ (5)\nFor any hydrodynamic film, equation (1), (when subject to the appropriate boundary conditions and the constraints imposed by equations (2) to (5)), may be solved iteratively to yield the pressure field in the film. From this, the usual bearing parameters of load, attitude angle, power loss and hydrodynamic leakage may be determined. In the loaded part of the film, (regions 1 and 2) power loss is given by\nH = wR f sz [ \u00a5 l~U h 8P 1 -- +- -- d~2 (6)\nh 2 8x\nRegion 1\nwhile for the cavitated film (regions 3 and 4) it is given by\nt/U H = wR f s~ \u00a5 -- d~2 (7)\nh\nwhich may be integrated numerically accounting for the prevailing flow conditions (laminar or turbulent) and the extent of the wetted film. In equations (6) and (7), the dimensionless Couette shear stress (T) is given as described in Reference 12.\n= 1 + 0.0012 ReT \u00b0'94\nwhere Re T is defined as in equation 4. Similarly, side leakage from the film may be computed from the integral along the bearing edge, i.e.\nh 3 ap\nQz = f r 12/lz ~z 0F (8)\nNumerical model\nThe performance of a bearing running at high speed under steady load may be predicted using equation (i) subject to the conditions prescribed by equations (2) to (5), To do so by the finite-element method requires the discretization of the load-carrying film and prescription of appropriate boundary conditions.\nWith reference to Fig 1, it can be seen that there are two load-carrying regions (1 and 2), and a finite-element mesh may be mapped onto these as shown in Fig 2, which illustrates half the bearing width only. For region 1, it can be seen that the mesh is distorted to account for the incompleteness of the film. The axial extent of this part of the film may be obtained from flow continuity considerations, i.e. at any section's' (see Fig 2).\nfY2Ls f~Lo qs ds = qo dx (9) 0 0\nwhere the flow per unit width may be obtained from combined Couette and Poiseulle flow, i.e.\nUh h 3 8p q = -- - (10)\n2 12pvx 8x\nand Lo is determined from the volumetric flow supplied at groove 2 and the fact that flow may be assumed to be purely Couette in region 4.\nRegion 2 -- = i ;-= 9;\nX Section's'\n> . o , 0 0 L\nFig 2 Element diseretization for the load-carrying film\nTR IBOLOGY international 181" ] }, { "image_filename": "designv11_32_0002168_3-540-29461-9_104-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002168_3-540-29461-9_104-Figure6-1.png", "caption": "Fig. 6. The joint of the vacuum suckers", "texts": [ " Because the glass walls of the Shanghai Science and Technology Museum have no window frames, there are supporting wheels near the vacuum suckers in the X and Y directions, which have been added to the mechanical construction to increase the stiffness. In order to move from one column of glass to another in the right-left direction, a specially designed ankle joint gives a passive turning motion to the suckers. This joint is located between the connecting piece which joins the vacuum suckers with the Y cylinder and the plank beneath it to which 4 vacuum-suckers are attached (shown in Fig. 6). In order to meet the requirements of the lightweight and dexterous movement mechanism, considerable stress is laid on weight reduction. All mechanical parts are designed specifically and mainly manufactured in aluminum. Figure 7 shows some examples of the mechanical planks. A PLC is used for the robot control system (shown in Fig. 8), which can directly count the pulse signals from the encoder and directly drive the solenoid valves, relays and vacuum ejectors. FX2N-4AD which is added to the system can identify the ultrasonic sensor signals and other analog sensors" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000001_s0389-4304(01)00108-4-Figure12-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000001_s0389-4304(01)00108-4-Figure12-1.png", "caption": "Fig. 12. Timing chain layout model.", "texts": [ " (1) Effect of main oil hole pressure We investigated the effect of main oil hole pressure on the torque in each part. Fig. 11 shows the result. Marks \u2018\u2018I\u2019\u2019 in the chart indicate the range of measurement dispersion (number of measurements N \u00bc 6). As the main oil hole pressure increased, the torque in guide L, positioned on the chain tension reducing side, increased at a rate greater than for guide R, positioned on the chain tensioning side. This is because of difference in the constant (see Eqs. (9) and (10)) determined by the guide layout angle, shown in Fig. 12. Due to this difference, increase in the chain pressing force against guide L, resulting from increase in the main oil hole pressure, is 2.1 times the increase in the pressing force against guide R. Pressing force of guide L: F1 F1 \u00bc 1:5 \u00f0P S \u00fe Fk\u00de: \u00f09\u00de where 1.5 is a constant decided by layout angle of guide L. Pressing force of guide R: F2 F2 \u00bc 0:7 \u00f0P S \u00fe Fk\u00de \u00fe 0:5 Tr=r: \u00f010\u00de where 0.7 is a constant decided by layout angle of guide R. (2) Effect of camshaft torque Next we investigated the effect of camshaft torque on the torque in each part" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002269_j.engfracmech.2006.04.002-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002269_j.engfracmech.2006.04.002-Figure2-1.png", "caption": "Fig. 2. Representation of the geometry for the studied hypoid gear: (a) pinion mating with the gear member; (b) zoom of the mating teeth.", "texts": [ " In order to compute the pressure distribution over the tooth flanks, it is necessary to develop the gear contact analysis. As prescribed by the theory of gearing [22], this aim can be accomplished in a reliable way only if the geometry of the mating surfaces is very accurately described; this is true especially when complex tooth shape, as the one object of this study, are handled. In this paper, an articulate algorithm based on the numerical simulation of the gear cutting process [18] allowed to compute very precisely the mathematical representation of hypoid gear tooth surfaces. Fig. 2 shows the representation of the pinion meshing with the driven gear member which has been obtained for the studied hypoid gear drive by means of the mentioned mathematical model. Then, these gear tooth surfaces have been provided as input for an advanced contact solver which combines a semi-analytical surface integral theory (for solving the contact problem) and the traditional finite element method (for computation of gross deflections associated with tooth bending) [19,20]. This approach makes possible to carry out very accurate contact analysis and stress calculation employing a relative coarse mesh; in particular, unlike the usual solvers based only on the Finite Element Method, a locally refined mesh around the contact region is not required" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002558_978-3-540-71364-7_29-Figure28.3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002558_978-3-540-71364-7_29-Figure28.3-1.png", "caption": "Fig. 28.3. Arm angle \u03b8 definition", "texts": [ "1) where p = [px py pz]T is the position vector of the end effector and Q = [\u03b5T \u03b7]T is the unit quaternion representing the orientation of the end effector in which \u03b7 and \u03b5 denote scalar and vector part. Using unit quaternions to represent orientation errors allows global parametrization of orientation not suffering from representation singularities [13]. The arm angle \u03b8 proposed in [11, 12] represents the orientation of the arm plane determined by the centers of the shoulder s, elbow e, and wrist w, see Fig. 28.3. It is a kinematic function of the joint angle vector q, which gives a measure of the following physical mobility: if we hold the shoulder s, the wrist w, and the end-effector t in fixed positions, the elbow e is still free to swivel about the axis from the shoulder s to wrist w. The arm angle on the circle can be defined by an interior angle between the planes se0w and sew. The reference position e0 of elbow is chosen such that e0 is on the plane which is spanned by s, w and the other shoulder position s\u2032 of the dual arm manipulator so that \u03b8 is equal to zero when e = e0" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003880_j.tcs.2010.03.006-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003880_j.tcs.2010.03.006-Figure2-1.png", "caption": "Fig. 2. The body-fixed reference frame of Kobot is depicted. It is fixed to the center of the robot. The x-axis of the body-fixed reference frame coincides with the rotation axis of the wheels. The forward velocity (u) is along the y-axis of the body-fixed reference frame. The angular velocity of the robot is denoted with \u03c9. The velocities of the right and left motors are denoted as vR and vL , respectively. The current heading of the robot, \u03b8 , is the angle between the y-axis of the body-fixed reference frame and the sensed north direction (ns). l is the distance between the wheels. Source: The image is taken from [22].", "texts": [ " No detection is denoted by ok = 0. The compass and the wireless communication module of the robots are used to create a directional heading sensing system, called the virtual heading sensor (VHS), which lets the robots sense the relative headings of their neighbors. At each control step, which is approximately 110 ms, a robot measures its own heading (\u03b8 ) and then broadcasts it to the robots within the communication range. The heading measurement is done in a clockwise direction with respect to the sensed north, as shown in Fig. 2. The neighbors whose heading values are received in a control step are called VHS neighbors. In [22], the number of maximum VHS neighbors was reported to be 20 through simulations conducted using Prowler [24], an event-driven probabilistic wireless network simulator. The heading value (\u03b8rj) received from the jth VHS neighbor is converted to the body-fixed reference frame of the robot using1 1 The heading of the robot, \u03b8 , is the angle between the sensed north and the y-axis of its body-fixed reference frame in a clockwise direction; see Fig. 2. \u03c0 2 is added to \u03b8 \u2212 \u03b8rj to obtain the heading of the jth neighbor in the body-fixed reference frame. \u03b8j = \u03b8 \u2212 \u03b8rj + \u03c0 2 where \u03b8j is the heading of the jth VHS neighbor with respect to the body-fixed reference frame of the robot. It is important to point out that the VHS does not assume the sensing of absolute north and hence does not rely on the sensing of a global coordinate frame. Instead, the only assumption that the VHS makes is that the sensed north remains approximately the same among the robots that are communicating among themselves", " Using the received headings of the VHS neighbors, the heading alignment vector (Eh) is calculated as Eh = \u2211 j\u2208NR ei\u03b8j \u2016 \u2211 j\u2208NR ei\u03b8j\u2016 whereNR denotes the set of VHS neighborswhen the communication range of VHS is set to R. The heading of the jth neighbor in the body-fixed reference frame is denoted by \u03b8j. The proximal control behavior aims to maintain the cohesion of the flock while avoiding the obstacles. Using the data obtained from the IRSS, the normalized proximal control vector, Ep, is calculated as Ep = 1 8 8\u2211 k=1 fkei\u03c6k where k refers to the sensor placed at angle of \u03c6k = \u03c0 4 kwith the x-axis of the body-fixed reference frame (Fig. 2). The virtual force applied by the kth sensor to the robot is represented by fk and calculated as fk = { \u2212 (ok\u2212odes)2 C if ok \u2265 odes (ok\u2212odes)2 C otherwise where C is a scaling constant, ok indicates the detection level for the kth sensor, namely the distance from the object, and odes is the desired detection level that is taken as 3 for robots, and 0 for obstacles. The homing behavior aims to align the robot with the desired homing direction, \u03b8d, given in a clockwise direction with respect to the sensed north", " The original flocking behavior (corresponding to the case where \u03b3 is set to 0) that was proposed in [22] would make the flock wander aimlessly within an environment, avoiding obstacles in its path, with no preferred direction. In this sense, the movement of the flock resembles that of a single robot running Braitenberg\u2019s obstacle avoidance behaviors [25]. The forward (u) and angular (\u03c9) velocities are calculated using the desired heading vector (Ea). The forward (u) velocity is calculated as u = { (Ea \u00b7 Eac) umax if Ea \u00b7 Eac \u2265 0 0 otherwise (1) where Eac is the current heading vector of the robot coincident with the y-axis of the body-fixed reference frame (see Fig. 2). The dot product of the desired (Ea) and current heading (Eac) vectors in Eq. (1) is used to modulate the forward velocity of the robot. When the robot is moving in the desired direction the dot product results in 1 and the robot attains its maximum forward velocity (umax). If the robot deviates from the desired direction, the dot product and hence u decreases and converges to 0 when the angle between the two vectors gets closer to 90\u25e6. If the angle exceeds 90\u25e6 then the dot product is negative. In this case, u is set to 0 causing the robot to rotate in place. The angular velocity (\u03c9) of the robot is controlled by a proportional controller using the angular difference between the desired and current heading vectors: \u03c9 = (6 Eac \u2212 6 Ea)Kp where Kp is the proportional gain of the controller. The rotational speeds of the right and left motors (Fig. 2) are eventually calculated as follows: NR = ( u\u2212 \u03c9 2 l ) 60 2\u03c0r NL = ( u+ \u03c9 2 l ) 60 2\u03c0r where NR and NL are the rotational speeds (rotations per minute) of the right and left motors respectively, l is the distance between thewheels of the robot (meters), u is the forward velocity (meters per second) and\u03c9 is the angular velocity (radians per second). The flocking behavior, described in the previous section, has a number of parameters, namely the weight of proximal control (\u03b2), the weight of goal direction (\u03b3 ), the proportional gain for angular velocity (Kp), the maximum forward speed (umax), and the desired detection level (odes)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003119_demped.2007.4393112-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003119_demped.2007.4393112-Figure1-1.png", "caption": "Fig. 1- Block diagram ofthe systemunder investigation. same pulsation. Unfortunately the angular displacements are also", "texts": [ " X and A41 at pulsation , and angular displacement ad and oc These procedures, even if approximate, allow not only a thorough it holds: physical comprehension of the machine behavior but they also r[(Id +AI cos(aot +ad )) (I + AI cos(at +o) (4) evidence the main machine parameters that influence the d O q\u00b0Mq frequency components amplitude [12,14]. Due to the current components the torque presents a periodical oscillation: Ifm. IdANDIqOBSERVER-RECONSTRUCTION OF T +AT (t) = r +AId COS[toht+ad I +AI cos[aqt+aji ELECTROMAGNETIC TORQUE AND CURRENT e e d _ q qj = 3pMrs, Id, Iq, +ATem (t) Figure 1 shows the block diagran of the system under Neglecting +A\u00b0 (t) investigation. Field current id and torque current in rotor flux Neglet t secon or th u q ~~~component at pulsation a0h iS: reference frame are computed by means of an observer. The outputs ofthe observer are the rotor flux amplitude and angle while A= 3pMr J(IJqAldcOsad + IdAicosa)2 + (Jq Aid sin ad + IdAJq sina)2 (5) its inputs are the rotor speed and the stator voltages and currents. Its amplitude referred to the mean torque value is: Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001260_cdc.1998.757991-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001260_cdc.1998.757991-Figure1-1.png", "caption": "Figure 1: The general n-trailer system.", "texts": [], "surrounding_texts": [ "Suppose we have a generalized n-trailer system with rn (rn 5 n) of the trailers not directly attached at the center of the previous axle but at a positive distance Mi from this point. It is convenient to use the following notation: we call 121,. . . ]n,, nj < nj+l, nm < n the indices of the axles having kingpin hitching (Mnj # 0). We can group together the axles between two consecutive off-axle hitches: {0 ,1 , . . . , nl} , . . . , {nj-1 + 1,. . . , r a j } , . . . ] {n, + 1,. . . ,n} . The kinematic model for the general n-trailer problem is: vn,+i tan(On,+i-l - OnJ+i) Ln,+i enj+i = %,+i = Vn,+i-l cos(&,+i-i - &,+i) j E (1 ,..., m + l } , i E { 2 , 3 , . . . , nj+l-nj} , and nm+i = n. CallingP1 = 00-81, we can take as steering input: A and as translational input the velocity of the last trailer rescaled by COS&, (as in [4], it is the generator of the whole multi-input chain). Assuming that we do not have two consecutive off-axles hitches, for a generic axle n j + i we have: where To complete the state space model of the general ntrailer system, we take the Cartesian coordinates of the midpoint of the last axle: xn = v yn = vtanB, The basic idea is that the n-trailer system with m offhitching joints can be converted into an n + m-trailer system with m + 1 steering wheels. These m virtual steering wheels are passive, in the sense that their steering angles are (uniquely) determined via feedback by the configuration and by the dynamics of the system. Proposition 1 Consider the 2-trailer off-hitching connection between the trailers n j and n j + 1. This subsystem is equivalent to a standard 3-trailer system with a steering wheel in the middle (Fig. 2). If e-,, is the orientation angle of the steering wheel and its steering angle is defined as yj = BYj - B n j + l , then it must A be: Mnj . y j = enj - enj+l + arctan (--enj) vnj The proof can be obtained from geometric considerations, see Fig. 2. The j-th virtual input can be considerd as: where the right side of the equation constitutes the nonlinear state feedback that decides the steering angle of the j-th passive steering wheel linking two consecutive groups of axles." ] }, { "image_filename": "designv11_32_0002048_acc.2003.1243371-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002048_acc.2003.1243371-Figure1-1.png", "caption": "Figure 1: The walking toy", "texts": [ " Section 3 presents a flatness based tracking controller and devotes close attention to the problem of trajectory planning which simultaneously ensures zero velocity landing of the swing leg and satisfaction of the physical constraints. In that section, we explain how to use the proposed solution to the single step trajectory tracking to achieve continuous walking with homogeneous, or non-homogeneous, step velocity features. Section 4 is devoted to present the simulation and computer animation results. The last section is devoted to the conclusions and suggestions for further work in this area. 2 The Walking Toy dynamics Consider the walking toy, shown in Figure 1, consisting of two legs of identical mass Ml, and of length L, connected to an inertia wheel (hub) of mass M, through a set of two rotating motors providing the necessary torque to move the legs. We distinguish the leg in-theair as the \u201cswing leg\u201d and the leg pivoting on the flor as the \u201cstance leg\u201d. The two legs are attached to the center axis of the rotating hub. We refer to such axis as the \u201chip\u201d of the machine. The mathematical model of the system is given by the following set of differential equations (see [Si) Jog0 = mgLsin(cp0) - 71 = 7 1 - 7 2 201 a Proceedings of the American Control Conference Denver, Colorado June 4-6, 2003 where JO is the inertia of the stance leg and the hub with respect to the pivot point in the floor, J1 and J2 represent, respectively, the rotational inertia of the hub and the swing leg about the \u201chip\u201d axis of the machine" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003627_ecc.2009.7075000-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003627_ecc.2009.7075000-Figure1-1.png", "caption": "Fig. 1. (a) Quadrotor prototype of GIPSA-Lab, (b) Quadrotor configuration: the inertial frame N(xn,yn,zn) and the body-fixed frame B(xb,yb,zb)", "texts": [ " The attitude dynamics for a rigid body is described by I f \u0307\u03c9 = \u2212 \u03c9 \u00d7 (I f \u03c9)+\u0393 (5) where I f \u2208 R 3\u00d73 is the symmetric positive definite constant inertial matrix of the rigid body expressed in the B frame, \u00d7 is the cross product and \u0393 \u2208 R 3 is the vector of control torques. Note that these torques also depend on the environmental disturbance torques (aerodynamic, gravity gradient, etc.). The quadrotor is a small aerial vehicle controlled by the rotational speed of four blades, driven by four electric motors, mounted at the four ends of a simple cross frame. On this platform (see Fig.1, (a)), given that the front and rear motors rotate counter-clockwise while the other two rotate clockwise, gyroscopic effects and aerodynamic torques tend to cancel in trimmed flight. The collective input (or throttle input) is the sum of the thrusts of each rotor ( f1 + f2 + f3 + f4). The pitch movement (\u03b8 ) is obtained by increasing (reducing) the speed of the rear motor while reducing (increasing) the speed of the front motor. The roll movement (\u03c6 ) is obtained similarly using the lateral motors. The yaw movement (\u03c8) is obtained by increasing (decreasing) the speed of the front and rear motors while decreasing (increasing) the speed of the lateral motors. This can be done while keeping the total thrust constant. The inertial frame N(xn,yn,zn) and the body-fixed frame B(xb,yb,zb) (Fig.1 (b)) are used to model the system dynamics. The quadrotor model can be expressed in terms of quater- S. Lesecq et al.: Quadrotor Attitude Estimation with Data Losses WeA11.3 nions with p\u0307 = v, v\u0307 = gN \u2212 1 m CT (q) T (6) q\u0307 = 1 2 \u039e(q) \u03c9 (7) I f \u0307\u03c9 = \u2212 \u03c9 \u00d7 I f \u03c9 \u2212\u0393G +\u0393 (8) m denotes the mass of the quadrotor, g is the vector of the gravity acceleration. p = (x,y,z)T represents the position of the origin of frame B with respect to frame N, v = (vx,vy,vz) T is the linear velocity of the origin of frame B expressed in frame N", " Actually, equations in (37)-(38)-(39) can be formulated using matrix C\u0304k = TkCk, Tk = M\u22121 k , especially Pk+1/k+1 = Pk+1/k \u2212Pk+1/kC\u0304 T k+1 (40) \u00d7 [ C\u0304k+1Pk+1/kC\u0304 T k+1 +Rk+1 ]\u22121 C\u0304k+1Pk+1/k K\u0304k+1 = Kk+1Tk+1 (41) 2) Results: The Extended Kalman filter for attitude estimation in the presence of packet losses has been implemented within the quadrotor simulator developed under the Matlab/Simulink platform. The control law is similar to the one proposed in [5]. Several experiments have been conducted. Various data loss rate for different scenarios of the lost measurements have been studied. Note that the loss of rate gyro measurements is not considered here because the attitude dynamics of the quadrotor are not well known. The first experiment reported in the present paper considers 10% of loss on the measurement accx acquired on the xb axis (see Fig. 1). Note that the attitude is given in the rollpitch-yaw representation for the sake of clarity. The initial attitude is (\u221225,\u221230,\u221210)(deg) and the reference one is (5,4,3)(deg). The attitude estimation filter is initialized with (\u221210,5,\u221223)(deg). The convergence spped is very fast, thus the attitude initialization can be seen on Fig. 2 where the real (top) and estimated (bottom) attitudes are depicted. Fig. 3 gives the attitude error and the data loss indicator: 0 means that the measurement accx is present for the estimation while 1 stands for \u201daccx has not been received\u201d" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001186_s00216-003-2022-y-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001186_s00216-003-2022-y-Figure2-1.png", "caption": "Fig. 2 H3PO4 0.1 M media, pH 2.2, \u03bd=100 mV s\u20131 with constant stirring. 1 ta=12 min, accumulation and oxidation in phenol 10 mg L\u20131; 2 ta=12 min, accumulation in phenol 10 mg L\u20131 and oxidation in phenol-free electrolyte; 3 ta=0 min, oxidation in phenol 10 mg L\u20131", "texts": [ " At the same time, peak intensity corresponding to phenol oxidation decreases each cycle, and finally disappears. The number of cycles until phenol disappears is a function of both concentration and accumulation time. When phenol is put under the electrochemical recovery process detailed in the previous paragraphs, these redox pairs disappear and the initial residual current is restored. As it has been shown, phenol measurements are obtained after compound accumulation on the electrode surface. In order to verify a possible phenol adsorption on electrode surface, tests shown in Fig. 2 were performed, using a 10 mg L\u20131 phenol solution in 0.1 M phosphoric acid media at pH 2.2, between 800 mV and 1,200 mV at 100 mV s\u20131. As it can be seen in Fig. 2, the compound is spontaneously adsorbed on the electrode, contributing to an important peak intensity increment. This increment is a function of the accumulation time. Fig. 3 shows peak intensity behaviour as a function of accumulation time (ta) for different concentration values (0.6, 10.0 and 14.0 mg L\u20131). As can be seen, three parallel functions are obtained, which do not converge for each different concentration. In the other side, after a 30-min accumulation time, surface saturation has not taken place; however, for a given concentration, no important variation is observed after 15 min" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002067_(asce)1052-3928(2005)131:1(41)-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002067_(asce)1052-3928(2005)131:1(41)-Figure4-1.png", "caption": "Fig. 4. Aluminum single-degree-of-freedom inverted pendulum model", "texts": [ " In the following sections, details of the Webshaker Web site are discussed and experience in using this Web site for education is presented. The Webshaker Web site (Fig. 1) allows students to conduct a shaking table test on simple structural models. A unidirectional shaking table capable of generating lateral motion simulates the effects of moving ground during an earthquake. Simple structural models (Figs. 2\u20134), typical of those used in dynamics and earthquake engineering experiments (Chopra 1995; Filiatrault 1998), include a single-degree-of-freedom (SDOF) system (Fig. 4) and a two-story shear frame (Fig. 2). These models (which represent single-story and two-story buildings) are attached to the shake table (Fig. 4), with instrumentation installed to measure floor displacements and accelerations (Fig. 5). ERING EDUCATION AND PRACTICE \u00a9 ASCE / JANUARY 2005 / 41 Students use standard Internet browsers to view the test setup, conduct the visually observed experiment, and execute the associated computational simulations. Through the Web site (Fig. 6), users can see the model (using Windows MediaPlayer or similar standard video steaming application) and select the type and amplitude of base shaking signal. Harmonic oscillatory signals or an 42 / JOURNAL OF PROFESSIONAL ISSUES IN ENGINEERING EDUCATIO earthquake-like motion (constructed by scaling selected acceleration records from historic events, such as the 1994 Northridge earthquake) can be employed as base excitation (Figs" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000269_cdc.1994.411206-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000269_cdc.1994.411206-Figure1-1.png", "caption": "Fig. 1 The inverted pendulum system", "texts": [ " The purpose of this paper is as follows: Taking the inverted pendulum as an example of nonlinear systems which are not exactly linearizable, we design a nonlinear controller for the system based on the approximate linearization. In the controller design, we take the higher order terms into account when we construct the new coordinate for the a p proximate linearization. Then, we evaluate its effectiveness by experiments. 2. Description of the PIant (A) Model of the Dendulum system We consider the TIT type inverted pendulum system [5] shown in Fig.1. The dynamics of this system is described by &J + I, sin\u2019 e + mL\u2019) + 2i&1,, sin e cos e -ZjmlL cos e + B\u2019mU sin e = U - D,,,$ (I) 81, - $mU cos e - PI,, sin e cos e - mgl sin e = -D,B ( 2 ) where I,, := I + ml\u2019 and U is the input torque to the motor, 8 , m, 21, and I are the rotation angle, the mass, the length and the moment of inertia of the pendulum, respectively. Similarly, q5 2L, and J are the rotation angle, the length, and the moment of inertia of the arm. D. and D, are viscous friction terms, and g denotes the gravity acceleration" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002073_s00366-005-0008-4-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002073_s00366-005-0008-4-Figure3-1.png", "caption": "Fig. 3 Fourbar linkage", "texts": [ " For example, all classes of the Ch Mechanism Toolkit contain member functions for calculating the angular positions, velocities, and accelerations of individual link members for a given mechanism configuration. Furthermore, if a coupler is attached to one of the links, kinematic analysis can be performed on the coupler point as well. 3.1 Data members As described earlier, the private data members of a Ch Mechanism toolkit class consists of parameters that defines a unique configuration of a planar linkage. For example, consider the fourbar linkage shown in Fig. 3. Link lengths r1, r2, r3, and r4, and phase angle h1 for link 1 are some parameters that can be used to define a fourbar linkage. These values are used to perform various analysis on the fourbar linkage, such as calculating the angular position, velocity, and acceleration of the individual links. Table 1 is the list of private data members for class CFourbar. Note that the variable names are prefixed by m_ to indicate that they are private members. Among the list of data members are m_rp and m_beta, which can be used to specify a coupler, if one is attached to the fourbar", " Once this is done, member functions for specifying and analyzing the fourbar can be called. To correctly perform the analysis, however, all the necessary setup function(s) should be called prior to the analysis function(s). Otherwise, the results from the analysis may be incorrect. Default values for specifying a fourbar linkage are used in the calculations if the user does not specify them. In this section, three examples are presented to illustrate features and applications of the Ch Mechanism Toolkit. 5.1 Example 1 Problem statement: The link lengths of a fourbar linkage in Fig. 3 are given as follows: r1=12 cm, r2=4 cm, r3=12 cm, and r4=7 cm. The phase angle for the ground link is h1=10 . The coupler point P is defined int angularAccel() Angular acceleration analysis int angularPos() Angular position analysis int angularVel() Angular velocity analysis int animation() Simulate motion of fourbar void couplerCurve() Calculate coordinates of coupler curve double complex coupler PointAccel() Calculate coupler point acceleration void couplerPointPos() Calculate coupler point position double complex couplerPointVel() Calculate coupler point velocity int displayPosition() Display a configuration of fourbar linkage int displayPositions() Display multiple configurations of fourbar linkage int getAngle() Calculate a joint angle int getJointLimits() Calculate joint limits for input and output links int grashof() Determine the type of fourbar linkage void forceTorque() Calculate joint forces and output torque void plotCouplerCurve() Plot coupler curve void plotTransAngles() Plot transmission angles int printJointLimits() Print joint limits for input and output links int synthesis() Synthesis for fourbar linkage void transAngle() Calculate a transmission angle void transAngles() Calculate transmission angles void uscUnit() Specify SI or US customary unit int angularAccels() Angular acceleration analysis int angularPoss() Angular position analysis int angularVels() Angular velocity analysis int forceTorques() Calculate joint forces and output torques void plotAngularAccels() Plot angular acceleration void plotAngularPoss() Plot angular position void plotAngularVels() Plot angular velocity void plotForceTorques() Plot joint forces and output torques by the distance r_p=5 cm and constant angle b=20 ", " The desired results are then obtained through function calls to angularPos(), couplerPointPos(), plotCouplerCurve(), and displayPosition(). Figures 5 and 6 from Program 1 are the configuration and coupler curve for the first branch of the fourbar linkage, respectively. Figures 7 and 8 are the configuration and coupler curve for the second branch of the fourbar linkage, respectively. The numerical results of Program 1 are given below. 5.2 Example 2 Problem statement: The link lengths of a fourbar linkage in Fig. 3 are given as follows: r1=12 cm, r2=4 cm, r3=12 cm, and r4=7 cm. The phase angle for the ground link is h1=10 , and the constant angular velocity of the input link is x2=5 rad/sec. Plot the angular positions, velocities, and accelerations of links 3 and 4 with respect to time for the first branch. Using the plotting features of the Ch Mechanism Toolkit, this problem is solved by Program 2. After links r1 to r4 and phase angle h1 have been set, member function setAngularVel() is called to specify the constant angular velocity x2" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002277_robio.2006.340146-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002277_robio.2006.340146-Figure1-1.png", "caption": "Fig. 1. General Model of a Single Arm Space Robot", "texts": [ " The paper is organized as follows: In section two, we derive the equations used to plan the path. Then, the problem of the non-holonomic path planning is discussed in section three. And the problem is solved based on genetic algorithm in section four. In Section five, the computer simulation study and results are showed. Section six is the discussion and conclusion of the work. II. EQUATIONS OF MOTION A. Space Robotic System Some research achievements on space robot dynamic and control were collected by Y. S. Xu and T. Kanade [7]. Fig.1 shows a general model of a space robot system with a single manipulator arm, which is regarded as a n+1 serial link system connected with n degree of freedom active joints. Bo denotes the satellite main body, Bi (i = 1, ..., n) denotes the ith link of the manipulator, and Ji is the joint which connects Bi-, and Bi. Some symbols and variables are defined as follows: 1I the inertia frame; LE: the frame of the end-effector; 1-4244-0571-8/06/$20.00 C)2006 IEEE 1471 Zi(i 0, ..., n): the frame of Bi; Ci(i O, " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000223_20.996232-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000223_20.996232-Figure2-1.png", "caption": "Fig. 2. The operators P and S and the function H.", "texts": [ " In particular, if is sufficiently large with respect to the frequency of the input signal, i.e., (6) the rate-dependent addendum in (4) can be omitted and the EC exhibits a quasi-static behavior with respect to input variation. Under this condition, the quasi-static relationship between the input voltage and the voltages at the nodes of the EC can be analytically determined for , provided that the voltage across the capacitor is known at , i.e., (7) (8) (9) The function and the operators and are shown in Fig. 2 and set up the basic hysteresis operators employed by the model for scalar static hysteresis. Under quasi-static conditions, the operators and and the function depend only on the threshold voltages and . The operator equals a generalized play hysteron, and the operator equals a generalized stop hysteron [4]. The function is a sigmoidal function and can be viewed as the limit case of the operators and [4]. Finally, the area enclosed by the operators and is proportional to the energy dissipated in the elementary cell during a hysteresis loop and results (10) By relaxing the condition of the quasi-static response of the EC, i" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002949_ecc.2007.7068815-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002949_ecc.2007.7068815-Figure1-1.png", "caption": "Fig. 1. The PVTOL aircraft(front view)", "texts": [ " In section IV, the proposed controller is compared through simulation to the Teel\u2019s nested saturations control. Experimental results are shown in Section V, and conclusion is given in Section VI. The mathematical model to describe the dynamics of a PVTOL aircraft is given by [9] x\u0308 = \u2212 sin(\u03b8)u1 + \u03b5 cos(\u03b8)u2 y\u0308 = cos(\u03b8)u1 + \u03b5 sin(\u03b8)u2 \u2212 1 \u03b8\u0308 = u2 (1) where x is the horizontal displacement, y is the vertical displacement and \u03b8 is the angle the PVTOL makes with the horizontal line. u1 is the collective input and u2 is the couple as shown in Figure 1. The parameter \u03b5 is a small coefficient which characterizes the coupling between the rolling moment and the lateral acceleration of the aircraft. The term \u22121 is the normalized gravitational acceleration. We will consider a simplified model of the PVTOL aircraft system, i.e. with \u03b5 = 0. Indeed, we have neglected 3486ISBN 978-3-9524173-8-6 the coupling between the rolling moment and the lateral acceleration of the aircraft. This choice is due to the fact that the coefficient \u03b5 is very small \u03b5 << 1 and not always well-known" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002890_j.1432-1033.1972.tb01682.x-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002890_j.1432-1033.1972.tb01682.x-Figure1-1.png", "caption": "Fig. 1. Effect of tRNA on the initial rate of ATP-PPi exchange catalyzed by the isoleueyl-tRNA synthetase of B. stearothermophilus. The standard ATP-PPI exchange reaction mixture was as described under Methods except that varying total tRNA concentrations were added. The exchange rate is expressed in nmol [32P]ATP formed at 40 \u201cC. 0, without tRNA; A , with 0.042 mg/ml tRNA from B. stearothermophilus; X, with 0.208 mg/ml periodate-oxidised tRNA from E. coli; 0 , with 0.613 mg/ml tRNA from B. stearothermophilus", "texts": [ " The bound tRNAIle is eluted afterwards with 1 ml of 0.05 M Tris-HC1 buffer pH 8.0. Protection against thermal inactivation was measured by heating the isoleucyl-tRNA synthetase under the conditions specified for each experiment and withdrawing samples at stated times; these are diluted, cooled and assayed for the residual enzymatic activity a t 40 \u201cC. The presence of total tRNA enhanced up to 3- to 5-fold the rate of ATP-PPi exchange catalyzed by the purified isoleucyl-tRNA synthetase from B. stearothermophilus (Fig.1). This effect depends on the concentration of tRNA and is equally marked with periodate-oxidized tRNA ; it is therefore independent of the acylation of the tRNA. Experiments with fractions containing different proportions of tRNAIle show that the stimulation of the ATP-PPi exchange is proportional to the isoleucine-accepting capacity of the samples (Table 1). The \u201cstimulation constant\u201d ( K ) is defined as the tRNA concentration a t which the ATP-PPi-exchange increase in the presence of tRNA reaches half its maximum value; it can be estimated by plotting the reciprocal of the rate increase (v - vo) against the reciprocal of the tRNA concentration" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000655_0954407011528194-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000655_0954407011528194-Figure2-1.png", "caption": "Fig. 2 Double-wrap band geometry", "texts": [ " However, the most commonly used model in engagement torque analyses and automatic 2 EXPERIMENTAL SET-UPtransmission shift prediction is based on a simple algebraic relationship between the band brake applied force and the band engagement torque [1 ]. Without The band brake system consists of a band, drum and servo assembly. Figure 1 shows a picture of the bandaccounting for the eVects of oil lm dynamics, the predictability of such a static model is limited within a and the drum used in this model validation study. This type of band is commonly referred to as a double-wrapcertain operating condition. This paper describes experimental validation of the band since it wraps around the drum surface twice as depicted in Fig. 2. As shown in Fig. 2a, when the systemdynamic band engagement model developed by Fujii et al. [2 ]. The model is based on rst principles, including is assembled, one end of the band is anchored to a test stand housing. In an actual automotive system, the bandthe physics of the squeeze lm, asperity deformation, porous oil diVusion, heat transfer and loading pressure is anchored to a stationary component, usually the transmission case. The other end is connected to a servodistribution caused by a self-energizing mechanism. The model is implemented as a stand-alone computer pro- assembly. Figure 2b illustrates how the band wraps the drum twice. Figure 2c shows the geometry of the double-gram to simulate the band engagement behaviour on an inertia absorption type band engagement test stand. wrap band when it is stretched out. The double-wrap band can be divided into two segments as shown in theSimulation results show a good agreement with experimental torque pro les over a wide range of operating gure. The speci cations of the band and drum system are listed in Table 1. Friction material characteristics areconditions. The model provides an analytical interpretation of widely varying engagement behaviour resulting speci ed on the basis of information from a friction material manufacturer (A", " The drum is connected to an electric the drum with a speci ed pressure level. This action gen-motor and an inertial ywheel as shown in Fig. 3. erates both viscous and dry engagement torque at theAutomatic transmission oil lubricates the band\u2013drum interface with a speci ed owrate. The oil rst ows band\u2013drum interface. The engagement torque tends to D05900 \u00a9 IMechE 2001 Proc Instn Mech Engrs Vol 215 Part D at UNIV CALIFORNIA SANTA BARBARA on June 29, 2015pid.sagepub.comDownloaded from twist the entire test housing through the anchored end band. As shown in Fig. 2c, the double-wrap band can of the band and is measured using a torque sensor. The be divided into two segments. Segment II consists of engagement completes when the slip speed between the two identical strips. The area where segment I meets band and the drum surfaces becomes zero. Figure 4 segment II is often called the bridge. This bridge area is shows the actual servo pressure pro le from the experi- short and occupies only 2.5 per cent of the overall band ment. This pressure pro le is applied to collect all the length" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002467_jmes_jour_1975_017_038_02-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002467_jmes_jour_1975_017_038_02-Figure6-1.png", "caption": "Fig. 6. Rough hydrostatic bearing", "texts": [ " From this we see that this function increases for m = 0 and decreases for m = 3 as o increases. Thus we infer from equation (21) that the flow flux, at a given inlet mean pressure E(Pi), increases for m = 3 and decreases for m = 0 with increase of o. But if E(Q) is assumed constant, then the mean pressure E(P) decreases for m = 3 and increases for m = 0 as o increases. Similarly, for a given mean flow flux, the load capacity decreases for m = 3 and increases for m = 0. 3.4 Hydrostatic bearing Consider now a rough hydrostatic bearing with constant nominal film thickness as shown in Fig. 6. Assuming that the variance of the film-thickness is constant, we have from equation (8) the equation determining the pressure in this case as follows: Intcgrating equation (20) and using the definition of tlow flux, we have 7tr E(N\") d 6~ E(H\" ~ ') 3r E(Q) = - - - E ( P ) . . ' Solving equation (21) and using boundary conditions E ( P ) = E(Pi) at r = ri and E(P) = 0 at r = re, we have the following expressions for pressures : We have also studied the characteristic of this bearing by representing the roughness as a series of cosine functions (Appendix 2) for o/h + 1", " Similarly from the function g; we have for m = 0, Ai = 0 (i # 0) for all i, Journal Mechanical Engineering Science @IMechE 1975 Vol 17 No 5 1975 at University of Birmingham on June 4, 2015jms.sagepub.comDownloaded from 1 -![I +4, +o4(0) . . o2 - h ha (36) . . . . which increases as o increases. From equation (35), for rn = 3, Ai = 0 ( i # 3) for all i, we have (37) which decreases as (z increases. From equation (35), ( i ) for m = 0, A , = 1, Ai = 0 (i # 0, 1) for all i, and (ii) for m = 3, A , = 1, A, = 0 (i # 1, 3) for all i, we have which increases as o increases. APPENDIX 2 SINUSOIDAL APPROACH FOR HYDROSTATIC BEARING For a hydrostatic bearing (see Fig. 6), the equation determining the pressure is given by 6rlQ - d P dr nrH3 . . . . . . . . . (39) which, on integration and using the boundary conditions P = 0 at r = re and P = Pi at r = ri, gives and (40) . . . Equation (40) determines the pressure while (41) gives the flow flux in the bearing. The load capacity is given by W = nP,r? + J:; 27crP dr which, after using equation (40), simplifies to the following: ' (42) Similarly the equation for frictional torque can be written as re r3 T z 2 ~ y Q -dr " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure7.24-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure7.24-1.png", "caption": "Fig. 7.24. Test platform: the shaker table", "texts": [ " Also, the frequency range of the input should be chosen so that it has most of its energy in the frequency bands that are important for the system. Where input signals cannot be applied to the system in the open-loop, the set-point signal will serve as the input for the closed-loop system, since it may not be possible to directly access the system under closed-loop control. Careful considerations of the mentioned issues will ensure that significant information can be obtained from the machine. A shaker table as shown in Figure 7.24 is used as the test platform for the experiments presented here. The shaker table can be used to simulate machine vibrations and evaluate the performance of active mass dampers. This table is driven by a high torque direct drive motor. The maximum linear travel of the table is \u00b12 cm. The shaker table is controlled via a DSP module implemented on a standalone mode, using the Texas Instruments\u2019 DSP emulator board (TMS320C24x model). The vibration analysis and monitoring program is coded in C24x assembly language" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000624_s0022-5193(89)80100-6-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000624_s0022-5193(89)80100-6-Figure2-1.png", "caption": "FIG. 2. A model Spirillum cell.", "texts": [ ", 1980), helical filaments (Johnson & Brokaw 1979; Higdon, 1979c) and flow patterns generated by sessile micro-organisms (Higdon, 1979b). In this paper we briefly explain the mathematical model and use it to solve for the cell velocity, to determine the force distribution on the cell and to examine the effect of various structures in locomotion. We consider a model unipolar S. volutans cell where the flagellar bundle is represented as being a cylindrical rod length l', radius b' held at angle X to the body axis (see Fig. 2). The cell body is modelled as a cylinder, radius b, length 21, which is twisted into a helix of amplitude h with wavelength a. We construct a set of axes with the origin on the axis of the cell body helix and the xl-direction along this body axis, with the positive direction away from the flagellar bundle as in Fig. 2. In this frame of reference the equations of the centreline A M O D E L F O R S W I M M I N G U N I P O L A R S P I R I L L A 203 of the cell body are $ xl - (1 + h2k2) 1/2 x 2 = h c o s Ks (1) xs = h sin Ks where s is the arc length along the centreline of the body with - l - s - l, k = 2~r/A is the wavenumber measured along the body axis and K = k(l+h2k2) I/2 is the wavenumber measured along the body centreline. The body helix is right-handed when the co-ordinate axes are a right-handed set and left-handed when the axes are chosen as a left-handed set" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003806_icelmach.2010.5608274-Figure15-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003806_icelmach.2010.5608274-Figure15-1.png", "caption": "Fig. 15. Magnitude of the first harmonic of magnetic flux density.", "texts": [], "surrounding_texts": [ "The four-pole energy-saving small induction motor with core made from the non-oriented silicon steel M600-50A was examined. The supply voltage was 230 V for the frequency 50 Hz. Stator windings were delta connected. The number of series turns of stator windings was 368. The external diameter of the stator core was 120 mm, the internal diameter is 70.5 mm, and stator core lengths is 102 mm." ] }, { "image_filename": "designv11_32_0002053_fuzz.2003.1209399-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002053_fuzz.2003.1209399-Figure4-1.png", "caption": "Fig. 4 Phase plane of PD controllers", "texts": [ " Properties of Conventional Linear PD Controller We recall that the PD control law is described by u(t) = K p e ( f ) + K,e ( t ) (3) where Kp and K,+ are the proportional and derivative gains of the controller, respectively, and e(!, is the error signal defined by e( t ) = r ( f ) - y ( t ) , with r(t) being the reference signal and y(t) the system output. We will analysis the properties of PD controller on the phase plane. Eq. (3) can he written as If we let U = 0, U > 0, and U < 0, we can draw three lines on the phase plane as shown in Fig. 4, where H denotes the distance between a line U = 0 and lines U # 0. U H=Jm ( 5 ) Based on the Figure 4, we can outline the properties of PD controller as follows: (i) There is the \u201czero line\u201d on which the controller output is equal to zero. (ii) The output is positive (negative) in upper (lower) part of the zero line. (iii) The magnitude of output is linearly proportional to the distance H from the zero line. 41 5 The IEEE International Conference on Fuzzy Systems Next we give a standard procedure to design fuzzy PD controller: (i) fuzzification, (ii) fuzzy logic rule base, and (iii) defuzzification" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000364_robot.1988.12028-Figure12-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000364_robot.1988.12028-Figure12-1.png", "caption": "Figure 12: Liftability Windows for Two-Point Grasp.", "texts": [ " The region, 11, is the remaining set of curve segments, again excluding the segment between the support contacts (see Figure 11). Second, the lines of action of the forces, f3, f4, and mg, are divided into seven liftability windows by the line of action of f l . at the points 413. 414, and q ig . The J windows are closed half lines beginning at their respective q points, while the Q and P windows are open half lines. The remaining point, q l g . is the only element of the most important window, the translat ion window, TW (see Figure 12). Third, the regions J , B3, B4, and T are defined by considering the possible contact normals of the points in region 11. Each point whose normal intersects 4 3 and P3 or J3 belongs to the liftability region B3 or J, respectively. Similarly, if the normal intersects Q4 and P4 or 54, the point belongs to B4 or J, respectively. Any point whose normal passes through TW and P3 or 53 belongs to T or J respectively. Figure 13 shows the liftability regions for the object. Notice that for the two-point initial grasp considered, T is only one orientation of contact against the vertex and thus is unusable" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003701_ijtc2010-41063-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003701_ijtc2010-41063-Figure5-1.png", "caption": "Fig. 5. Temperature in water film (CFD commercial code)", "texts": [ " The impact of high pressure Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use 2 Copyright \u00a9 2010 by ASME and temperature on viscosity is surprising and significant (Fig.3.)[5]. In a typical water film, pressure is usually lower than 2 MPa so that effect does not have to be taken into consideration. For calculations, the EHL model was used (Fig. 4.). The isothermal model was proper for these calculations because of low increase of lubricant (water) temperature (Fig.5.). Temperature rising in fluid film was lower than two degrees. All calculations were conducted for stern tube bearing with length to diameter ratio of two (L/D=2). The lubrication grooves were located in the upper bush part so they had no significant impact on the hydrodynamic field. The shaft diameter was 100 mm, similar to those on a small cargo ship or fishing vessel. The diameter clearance was 0.3mm as often recommended for this shaft diameter by bush manufacturers. Calculations were conducted for stiff composite material with the 4500MPa module of elasticity" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001205_robot.1996.506877-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001205_robot.1996.506877-Figure1-1.png", "caption": "Figure 1: A schematic of a 2R planar rigid robot.", "texts": [ " The organization of the paper is as follows: we first develop the dynamical system to be studied and list a few analytical results, then describe the numerical study done, then follow up with a discussion of the results and finally present our conclusion 2 Dynamic Equations of a 2R Robot The dynamics of a 2R, rigid, planar manipulator can be modeled as in[2] : where, 0 ( t ) is the 2 x 1 vector of joint angles, M(B) is the mass matrix, C(8, e ) is the 2 x 1 vector of Coriolis and centrifugal torques, and r is the vector of joint torques. Equation (1) can be represented in state space form as x1 = x 2 = x3 = x4 = where, the state variables are the joint variables 01, 02 and their derivatives, and In the above equations, mi, l i , Ii and ri are the mass, length, inertia and location of the center of gravity of link i respectively. Figure 1 shows a sketch of the 2R robot under consideration. 3 Feedback Control of a 2R Robot We consider the following two well known control laws[2], namely, (i) Proportional Derivative (PD) Control and (ii) Model Based Control. For the PD controller, the torque at the joint i is calculated as where, o d , ( t ) is the desired periodic trajectory to be tracked in joint space, ICp, and K,, are the positive proportional and derivative gains. It can be shown that, in the absence of gravity, the PD control law achieves asymptotic tracking of the desired joint positions [lo, 111", " The above systems are much more complicated compared to the systems studied in chaos literature which are usually of dimensions less than four, and usually with nonlinearities which facilitate some analytical study. One way to study these systems is by a digital computer. In the next section, we present the details of the numerical study done for the above systems. 4 Numerical Study To perform a numerical study on the two nonlinear, non-autonomous, ordinary differential equations, representing feedback control of a planar 2R robot, we have chosen the Denavit-Hartenberg and inertial parameters of the first two links of the CMU DD Arm II[13]. Figure 1 shows a sketch of the 2R robot with all its parameters. As mentioned before, we are interested in global behavior when the controller gains are varied. In general there would be 4 controller gains - IC, and K, for each of the two joints. To make the search space smaller we have assumed that the gains are same for both joints. The state equations were integrated numerically by a variable step, variable order, predictor corrector Adams algorithm[l4]. In order to ensure that the numerical plots were not an artifact of the numerical integration scheme, the results were verified with Runge-Kutta 5-6[15] integration routine" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000299_robot.2001.932795-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000299_robot.2001.932795-Figure1-1.png", "caption": "Figure 1. Staircase effect in (a) thick, and (b) thin layer thickness model", "texts": [ " In general, current manufacturing process uses traditional slicing methods which slice the model in uniform layer thickness. Therefore, the user must make a choice between part accuracy (thin slices) and build speed (thick slices). Theoretically, the part built by rapid prototyping machine should be equivalent to the 3D CAD model, if layer thickness can be built ihin enough. But in actual, most commercial rapid prototyping systems use uniform slicing procedures with a fixed layer thickness to build parts. Therefore, as shown in Figure 1, staircase effect is significant when the system builds the part in thick thickness, and long fabrication time is necessary for thin thickness to reduce the staircase effect. In this research, an adaptive slicing method was developed to decrease fabrication time without drastically reducing the model accuracy. 2. Previous Works The basic concept behind adaptive slicing is to slice the CAD model into contours by using diverse thickness within acceptable thickness range [t,,,, , t,,, 1, according to characteristics of the CAD model", " CASE 2: As shown in Figure 9, the model is designed to have the same contour Circumference at any horizontal levels. The slicing algorithm can determine the layer thickness according to A(;, when the difference in circumference between adjacent contours is close to zero. Similar to CASE I , we slice this model by using uniform and adaptive slicing methods, and definition of maximum and minimum thickness is also the same as the setting of CASE 1. The uniform and adaptive slicing results are shown in Figure 10 and Figure 1 I , respectively. The simulated results are described in Table 1 which shows the layer numbers comparison by using uniform and proposed adaptive slicing method in CASE 1 and CASE 2. From the experimental results, we can conclude that the proposed adaptive slicing can reduce almost 50 percent number of layers than uniform slicing method without reducing the model accuracy. B. Design and Implementation of Experimental Prototype for The Layered Manufacturing System In order to demonstrate that the proposed approach to adaptive slicing is more efficient than uniform thickness slicing methods, we can implement this algorithm on an LCD panel display based rapid prototyping system which we developed" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000227_s0142-1123(00)00049-9-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000227_s0142-1123(00)00049-9-Figure7-1.png", "caption": "Fig. 7. Different situations of crack opening when minimum load is applied: (a) crack completely open, (b) crack partially open, (c) crack completely closed.", "texts": [ " During a loading cycle, when the maximum load is applied, the crack is generally completely open and the effective stress intensity factor is: K max eff 5K max a 1Kr (9) The K max a values were calculated by multiplying the previously defined b factors by the nominal stress, snom. The Kr pattern (see Fig. 6) was found using the weight function defined for the gear tooth and the residual stresses, sr, experimentally measured on the carburized gears. When the minimum load is applied, three different situations can be considered, as shown in Fig. 7, where the crack is completely open (a), partially closed (b) and completely closed (c) [26]. For every case, it is necessary to define different values for the minimum effective stress intensity factor: case (a): K min eff 5K min a 1Kr (10) Reff5 K min eff K max eff (11) case (b): The minimum effective stress intensity factor depends on the crack geometry and an iterative technique is necessary for the calculation case (c): K min eff 50 Reff50 When the crack is partially closed, as in case (b) in Fig. 7, the effective stress intensity factor, K min eff , is evaluated on the open crack face: K min eff 5E a xc s(x)W(x,a)dx (12) where W(x,a) is the weight function used for the gear tooth and xc is the distance between the crack tip and the point at which the crack faces come into contact. The xc value is found by an iterative procedure, which begins by establishing a value of xc. The crack tip opening displacements, CTOD, and the contact stresses on the crack faces are calculated: the exact value of xc is obtained when the CTOD values, under the minimum load, are greater than 0 in the open crack zone, and when the contact stresses are lower than or equal to 0 in the closed crack zone" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002102_zpch.1977.105.5_6.225-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002102_zpch.1977.105.5_6.225-Figure6-1.png", "caption": "Fig. 6. Cross section between four cylinders", "texts": [ " For a rectangular capillary, h= 2(\u00b0 + fr>3;cose (i6)abgAg v ' where a and b are the lengths of each side. Finally, examples of the capillary rise between parallel cylinders will be considered. When identical circular cylinders are arranged in a hexagonal lattice with distance 2d, as shown in Fig. 5, the hydraulic radius for the open space is : Rfi = v'3 li a. A!2_ Jl R \\ 2 R. (17) Brought to you by | New York University Bobst Library Technical Services Authenticated Download Date | 9/8/15 6:34 PM The Gauss Equation in Capillarity 231 Referring to Fig.6, a similar calculation yields, for the square lattice: 2 L , d VR I!. (18) Substitutions of Eqs. (17) and (18) into Eq. (8) will give the capillary rise equations for the respective systems. The results of these computations are shown in Figs. 7 and 8 together with their results obtained by Princen [8] for 0 = 0 only. As shown in Eqs. (13) and (14), the heights of capillary rise for triangular and square capillaries are also different from those calculated by Princen*. However, it is interesting to note that Princen's calcula- * It should be noted here that the height of capillary rise in Princen's calculation is the height to the lowest point of the meniscus, while the heights calculated by Eqs" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001582_0954406042369071-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001582_0954406042369071-Figure7-1.png", "caption": "Fig. 7 Machining the rotor using the designed milling cutter", "texts": [ " This proves that there is no interference while machining the arc\u2013cycloidal helical rotor with the designed milling cutter. Based on the above analysis and design, the milling cutter has been produced and used for machining the arc\u2013cycloidal helical rotor with three lobes. The verification process of checking the cutter design and the process of using the designed cutter to machine the helical rotor are illustrated in Fig. 6. Using the developed milling cutter from the previous analysis, the machining process is illustrated in Fig. 7. In the machining process, the rotor material has been chosen as an olefin, a hydrocarbon of the ethylene series, for rapidly machining to examine quickly the analysis and design of the milling cutter and any machining interference. This was machined [15] in a Hitachi SeikiML universal milling machine. Figure 8 gives the machined arc\u2013cycloidal helical rotor. The cross-section of the machined helical rotor has been measured and compared with that of a theoretically designed rotor. The concave and convex arcs radius at the cross-section of the machined helical rotor is 22" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure7.9-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure7.9-1.png", "caption": "Fig. 7.9. Pyramid-structure derived from tetrahedron-structure", "texts": [], "surrounding_texts": [ "Next, space-structures or three-dimensional structures will be considered. These are structures that are of interest in most applications. In a very general sense, space-structures can be perceived as a combination of many plane-structures, arranged in a manner that all the planes are not coplanar. Therefore, for a space-structure to be rigid, every plane-structure that makes up the space-structure must be rigid in its own right. This is one reason to have a good understanding of plane structural rigidity. Since machine structures are stationary, the sum of the forces and moments acting on it must be zero; which is in accordance with Newton\u2019s second law. Mathematically, this implies \u2211 F = 0, (7.5) \u2211 M = 0, (7.6) where F and M are three-dimensional force and moment vectors, respectively. The sign conventions as depicted in Figure 7.1 will be used. As before, each structural configuration can be tested to verify if the planestructure satisfies the equation 3j = m + 6, (7.7) where j denotes the number of joints and m denotes the number of members; then, there are three possible cases, namely 7.1 Mechanical Design to Minimise Vibration 203 2. If 3j > m + 6, then the structure is unstable 3. If 3j < m + 6, then the structure is statically indeterminate In the plane-structure, the triangle is the basic shape, which is rigid and statically determinate. In a space-structure, the basic form for rigidity and statically determinant is the tetrahedron, which is depicted in Figure 7.8. Adding a new non-coplanar joint to the three existing joints of a triangular plane-structure derives the tetrahedron-structure. This new joint is connected to the existing joints with three new members. By following this procedure, rigid and statically determinate space-structure can be derived. Other space-structures are shown in Figures 7.9 and 7.10. It is also noteworthy that the members are connected with ball-joints. 1. If 3j = m + 6, then the structure is statically determinate" ] }, { "image_filename": "designv11_32_0002815_j.mechmachtheory.2007.01.005-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002815_j.mechmachtheory.2007.01.005-Figure1-1.png", "caption": "Fig. 1. The motion of an RR dyad.", "texts": [ " However, we should be cautious in employing linear algebra in the operations of finite screw systems because linear properties of screw systems in finite kinematics are not the same as those of screw systems in instantaneous kinematics (referred to as infinitesimal screw systems) and statics. In this section, we illustrate the concept by the analysis of an RR dyad. Since there is a dual relationship between statics and instantaneous kinematics [19], we will focus on finite and instantaneous kinematic analyses only. Fig. 1 shows the schematic drawing of an RR dyad. The instantaneous twist, T13, of link 3 with respective to link 1 is obtained by: T13 \u00bc x13 bS13 \u00bc x12 bS12 \u00fe x23 bS23 \u00f01\u00de where bS12 and bS23 denote the unit screws of the two revolute joints, and x12 and x23 are the corresponding relative angular velocities. The twist T13 is about screw bS13, and the amplitude of the twist is x13. All possible screws are said to form a screw system of the 2nd order, which contains 11 screws. On the other hand, the finite twist Tf 13, of link 1 with respective to link 3, with the finite rotations h12 and h23 of the R joints, is represented [10] by: Tf 13 \u00bc 2 tan h13 2 bS13 \u00bc 2 1 tan h12 2 tan h23 2 \u00f0bs12 bs23\u00de tan h12 2 bS12 \u00fe tan h23 2 bS23 \u00fe tan h12 2 tan h23 2 Sc \u00f02\u00de where bs12 and bs23 are the direction cosine vectors of bS12 and bS23, respectively, and Sc is the screw product of bS12 and bS23. As shown in Fig. 1, the axis of Sc is the common perpendicular of the axes of bS12 and bS23. According to Eq. (2), bS13 belongs to a screw system of the 3rd order, which contains12 screws. Note that here the pitch of screws is defined as the ratio of one-half the translation to the tangent of one-half the rotation [6]. Note that for the above two-degree-of-freedom system, the screw system associated with its infinitesimal kinematics is of the second order, while that associated with its finite kinematics is of the third order. In fact if finite displacement screws of a body constitute a screw system, the number of degrees of freedom of the motion of the body is one less than the order of the screw system. For the example shown in Fig. 1, it is obvious that, for infinitesimal kinematics, all possible twists of T13 form a vector subspace, of which bS12 and bS23 are a set of basis vectors. By varying the angular velocities x12 and x23, we obtain12 twists of T13; however, there are only11 different screws of bS13 because the resultant screw bS13 depends upon only the ratio of the angular velocities x12 and x23. For each bS13, there are11 possible amplitudes of T13. Comparing to the definitions of vector subspaces, T13 belongs to a vector subspace of V6, and the dimension of the vector subspace is 2" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000457_978-3-642-55848-1-Figure6.54-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000457_978-3-642-55848-1-Figure6.54-1.png", "caption": "Fig. 6.54. A ball bouncing on a table at rest", "texts": [ " This is represented by the capacitive element C and the resistive R elements, which in conjunction with the third effort junction, describes the second equation in Eqs. (6.31) and (6.32). 210 6 Mechanical Systems The switch element Sw changes the condition represented by the third equations depending upon the body relative displacement evaluated by the integrator. The constitutive relation of the switch is simply yr > O? F: vr = 0 (6.37) We now analyse the motion of a ball, which is dropped from a height h onto a ta ble that is at rest (Fig. 6.54). The ball drops under the action of gravity, hits the ta ble and bounces back. It continues to bounce until it eventually reaches rest. We treat the ball as a particle moving in a vertical direction under the action of gravity. The model of the system consists of three components Ball, Ground and Contact (Fig. 6.55). The Ball is represented in the usual way by an inertial element representing the ball inertia in the vertical direction and a source effort describing 6.4 Bouncing Ball Problems 211 its weight connected to a common effort junction" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure2.4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure2.4-1.png", "caption": "Fig. 2.4. Construction of partially-rotating actuator", "texts": [ " For example, when an electric voltage is applied between the outer and inner diameter of a thin-walled tube, the tube contracts axially and radially. A variety of chemical and materials processing applications use ceramic tubes. Ceramic tubes are also used to fabricate electrical parts for high voltage or power applications such as insulators, igniters or heating elements. 2.1 Piezoelectric Actuators 13 The design employs a piezoelectric cylinder from LPZT(lithium-lead-zirconiumtitanate) ceramic with radial polarization. The sketch of the design is presented in Figure 2.4, in which a piezoelectric cylinder (2) is mounted on a rigid base (1). The movement at the free end of the piezoelectric cylinder is transmitted to a friction pad (3). A spring (4) provides a normal force against the friction pad to generate friction force. A stopper (5) and a rod (6) serve to act as the axis of rotation. The actuator is designed based on the indirect mode of actuation, therefore reducing the effect of hysteresis in the actuator output. The outer surface of the piezoelectric cylinder is divided into several sections" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003648_iccas.2010.5669710-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003648_iccas.2010.5669710-Figure3-1.png", "caption": "Fig. 3 Test Model of Unmanned Vehicle.", "texts": [ " When the vehicle receives the RF (Radio Frequency) signal, transmitters are synchronized with receivers. RF Transmitters transmit signal in regular the intervals of 0.4sec, and the system calculate TOF(Time of Flight), and then, the distance between transmitters and receivers can be measured.. Using 2 receivers the absolute position based on 3 dimensional space(X,Y,Z) and angle of direction\u03b8 can be measured. Fig. 2. shows way of measuring position (X,Y,Z ) and angle of direction \u03b8 using PUS . and Fig. 3. shows the test model. Getting information about where the vehicle is moving to is important as well as getting to know the position of it. As you see on Fig. 4 the vehicle is equipped with 2 Ultra sonic receiver to get information of angle of direction as well as of position of the vehicle. After the position of the vehicle is decided, an angle of direction of the vehicle can be calculated by below equation (2.6) 1tan ( )front rear front rear y y x x \u03b8 \u2212 \u2212 = \u2212 (2.6) Herein, \u03b8 is angle between X axis and the direction the vehicle is forwarded to", "8) Letting sampling period t\u0394 and discretizing the continuous time model, k\u03a6 can be obtained as below 1 0 1k t\u0394\u239b \u239e \u03a6 = \u239c \u239f \u239d \u23a0 (2.9) 0 ( ) ( ) t T T kQ Q d \u03b4 \u03c4 \u03c4 \u03c4= \u03a6 \u0393 \u0393 \u03a6\u222b 3 2 2 W Wt t W t W t \u239b \u239e\u0394 \u0394\u239c \u239f = \u239c \u239f \u239c \u239f\u0394 \u0394\u239c \u239f \u239d \u23a0 (2.10) Getting data as azimuth angle from PUS The measurement equation can be obtained as below [ ] ( ) ( )H k x k\u03b8 = [ ]1 0kH = (2.11) Using Kalman filter with data from the above state space model and the measurement equation, optimal angle of direction can be obtained minimizing covariance as an gap between the reference and data from Gyro and PUS. On Fig 3.1, The circle(small circle) through all the points scattered on the coordinate plane is given reference route. And the other circle(large circle) is path followed by the vehicle. We can see the vehicle traced given path smoothly. Fig 3.2 shows a variation of the vehicle\u2019s angle using Kalman filter while it moves around in given path . Stable steering characteristic in circular movement can be seen. Having 180 degree at the point of departure the angle of vehicle\u2019s direction increases from 180 to 360 (0), and to 180 degree. Fig 3.3 shows angular gap between given reference and vehicle heading direction. It fluctuates approximately between -10 and 30 degrees of angle. Fig 3.4 shows distance gap between given reference and vehicle\u2019s position. It ranges within 220mm. Fig.3.1 Position Estimation at Vehicle speed 0.38(m/s). Fig.3.2. Vehicle angle using Kalman filter. 1000 2000 3000 4000 5000 6000 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 X position (mm) Y p os iti on ( m m ) 0 5 10 15 20 25 30 35 40 45 50 0 50 100 150 200 250 300 350 Time(sec) V eh ic le A ng le (d eg ) IMU USAT Kalman Filter 978-89-93215-02-1 98560/10/$15 \u00a9ICROS 1127 4. CONCLUSION The localization of mobile robot is an important part of control problem. PUS is useful device as a positioning detection system. But, To have better performance while the vehicle trace a given path as an reference" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000918_bf00140121-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000918_bf00140121-Figure5-1.png", "caption": "Fig. 5.", "texts": [ " We now study a slightly more complicated problem, with the Henon Heiles potential U(x, y) = - a ( x y 2 - x3/3), again homogeneous of degree 3. Hamilton's equations in this case are = Pl, y = P2, 151 = (x 2 - y2)a, ~ = -2axy . The only equilibrium point is the origin in the phase space, located in the zero energy level. The topology is simpler, since there are no singular sets as in the problem above. The equipotential curves are the y-axis, the lines y = \u00b1x/x/-3 and hyperbolic-like curves in the six regions in between. The Hill regions U + h >/0 for the three possible cases are shown in Figure 5 where there are six central configurations corresponding to the vertices of the hyperbolas. We make Q = (X, Y) = (x 2 + y2)-W2(x, y) as in Example 3, and the condition for the central configurations now becomes ( a ( Y 2 - X2), 2 a X Y ) = 3 a ( X Y 2 - X3/3)(X, Y). By solving this equation, we find the six central configurations (\u00b11,0) and (+ 1/2, \u00b1,\u00a2~/2), which are all the sixth roots of the unity when the plane is thought of as the complex numbers. This symmetry goes even further, since for Oo= (E, 0) or Oo = ( - a / 2 , \u00b1, , /3/2) with E = \u00b1 1 , the homothetic solutions q(t) = h(t) Oo satisfy the equation ;t2/2 = EaA3/3 + h. If a = -1 , there are solutions only when h > 0, agreeing with the shape of the Hill regions in Figure 5. Looking at these regions, we see that escape to infinity can take place only in directions along three of the six symmetrical regions: indeed, on those where U > 0. As in the preceding example, the infinity manifold is the same for any energy h and can be described as follows. Passing to coordinates t9 = 1/x,,/~T y 2 , 0, 0 = - - p-UzlJ and u = 01n~J, we again get a system of differential equations (13) with the same change of timescale and energy relation. But in this case, the restriction of the potential to p = 1 has the form U(O) = or/3 cos 30, (15) which explains the above-described symmetry in the regions and in the central configurations, since U(O) has period 2~-/3" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003655_978-90-481-9262-5_29-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003655_978-90-481-9262-5_29-Figure5-1.png", "caption": "Fig. 5 Some singular configurations of the H4 robot.", "texts": [ " This condition corresponds to the constraint singularities of the robot that occur when the legs lose their ability to constrain the motion of the end effector, which gains one or several DOFs. By solving Eq. (6), we obtain the different cases for this type of singularity as follows: (a) s12 m \u00d7 s34 m = 0: s12 m and s34 m are parallel, which happens when the intersection line of two amongst the four planes \u03a0i, (i = 1, . . . 4), is parallel to the intersection line of the two other planes. For example, when n1 // n3 and n2 // n4 as shown in Fig. 5a. (b) s12 m // z, i.e., when the two planes \u03a01 and \u03a02 are vertical, their normal vectors n1 and n2 are in the horizontal plane and s12 m = n1 \u00d7n2 is parallel to z. A similar case happens when s34 m // z ; (c) n1 // n2, i.e., the two planes \u03a01 and \u03a02 are parallel, and as a consequence s12 m = 0. A similar case happens when n3 // n4 ; (d) s12 m , s34 m and z are coplanar but not parallel to each other. (e) s12 m // s34 m // z, i.e., when the four planes \u03a0i, (i = 1, . . . 4), are vertical as shown in Fig. 5b. In cases (a), (b), (c) and (d), the two constraint moments \u03c4\u0302 I \u221e and \u03c4\u0302 II \u221e are identical (z\u00d7s12 m // z\u00d7s34 m ) or one of these moments is null. The constraint wrench system of the robot becomes a 1-system and its twist system a 5-system, and as a result, 280 Singularity Analysis of Lower-Mobility Parallel Robots with an Articulated Nacelle the manipulator gains one DOF. In case (e), the two constraints moments \u03c4\u0302 I \u221e and \u03c4\u0302 II \u221e are null and the robot gains two DOFs. 2. [abd \u2022 f][cg \u2022 hj] = 0 \u21d4 ( abd \u2227 cgj ) \u2227 fh = 0 \u21d4 the projective line fh in- tersects with the intersection line of planes abd and cgj. This condition is expressed in vector form as follows: ( [s1 uv \u00d7 s2 uv]\u00d7 [(rg \u2212 rc)\u00d7 z] ) \u2022 (s3 uv \u00d7 s4 uv) = 0 (7) This condition occurs when the legs cannot control the linear velocity of the end effector. The different cases for this condition can be established by solving Eq. (7). For example, when s1 uv // s2 uv and s3 uv // s4 uv (Fig. 5c). In this paper, a general methodology was proposed to analyze the singularities of parallel manipulators with an articulated nacelle. The methodology consists of two main steps. First, the new concept of twist graph is used to simplify the constraint analysis. This graph is obtained with the theory of reciprocal screws. Then, a wrench diagram is obtained in order to derive a simplified expression of the superbracket decomposition. This expression is analyzed to provide geometric conditions for singular configurations" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000943_s0997-7538(01)01156-1-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000943_s0997-7538(01)01156-1-Figure2-1.png", "caption": "Figure 2. (a) Gradient of the yield locus curve for an isotropic initial state (r1,2 = 1); (b) example for possible changes of the yield locus curve because of planar anisotropy.", "texts": [ " For specimens parallel and normal to the rolling direction, two different r-values are defined in this way: r1 = \u03b5\u0307 pl 22 \u03b5\u0307 pl 33 , r2 = \u03b5\u0307 pl 11 \u03b5\u0307 pl 33 . (3.3) By substituting the flow rule (2.5), this reduces to: r1 = f22 f33 , r2 = f11 f33 . (3.4) By use of the incompressibility condition: \u03b5\u0307 pl ii = 0 (3.5) and the flow rule (2.5) the equations: f22 f11 \u2223\u2223\u2223\u2223 \u03c322=0 = \u2212 r1 1 + r1 , (3.6a) f11 f22 \u2223\u2223\u2223\u2223 \u03c311=0 = \u2212 r2 1 + r2 , (3.6b) can be formulated which describe the relations between the r-values and the components of the gradient of the yield condition in a plane principal stress state (cf. figure 2). Because of the definitions of r1 and r2, equation (3.6a) is valid for the point of intersection of the yield locus curve with the \u03c311-axis and equation (3.6b) is valid for the point of intersection with the \u03c322-axis. The angles \u03b31 and \u03b32 between the normals of the yield locus curve in these points and the coordinate axes are related to the components of the gradient vector by the relations: f22 f11 \u2223\u2223\u2223\u2223 \u03c322=0 = tan\u03b31, f11 f22 \u2223\u2223\u2223\u2223 \u03c311=0 = tan\u03b32. (3.7) Because of these equations and with (3.6a) and (3.6b), the components fij of the gradient vector are also related to r1 and r2, respectively. For the case of general planar anisotropy, r1 = r2, we have \u03b31 = \u03b32, which leads to changes in position or shape (or both) of the yield locus curve compared with the isotropic state (cf. figure 2b). The following representation is based on the assumption that from an uniaxial tension test in the x1-direction the yield curve \u03c3F(\u03b5 pl v ) and r1(\u03b5 pl v ) are known. The aim of the investigation is to describe the changes of the yield locus curve caused by anisotropic plastic hardening with special regard to a variable planar anisotropy. For isotropic, kinematic and distortional hardening the evolution equations (2.15) are employed. They are, however, not able to take into account a given function r1(\u03b5 pl v ) for the controlled change of planar anisotropy" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003624_978-3-642-03737-5_20-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003624_978-3-642-03737-5_20-Figure2-1.png", "caption": "Fig. 2. Biologically inspired localization of a biped robot: a) identification of the relative position and size of different landmark objects in the environment, b) determination of the azimuth angle with respect to the target landmark object", "texts": [ " In spite of that, infants learn quickly by exploration of the space around themselves. Human beings use the visual feedback to determine the exact position in 3D workspace as well as to plan their motion. Object-based localization is the crucial natural principle enables humans to guide themselves in the unknown environment. In the environment, humans determine their relative position and find their direction of motion with respect to the characteristic, well-visible object(s) as it is shown in Fig. 2. A lantern (light) represents a landmark object in this example shown in Fig. 2. Under the notion landmark object or marker we assume a real object or shape that dominates in a certain way comparing with other objects/shapes in surrounding by its size (length, height, width), brightness, color, etc. Conventionally, biped robots are equipped by a stereo-vision system (two cameras). The role of cameras is to identify the relative position d and direction of motion (azimuth) \u03b2 of biped robot with respect to the chosen landmark object (Fig. 2) with a satisfactory accuracy. The choice of the appropriate marker can be made by training an appropriate artificial connectionist structure (a kind of robot brain/memory) embedded into the robot\u2019s high-level control block. Such network structure is trained off-line to recognize the potential landmark objects, i.e. bright, large, high or colored objects that can be potentially well visible in the unknown scene. An arbitrary indoor scene with a biped robot and obstacles are presented in Fig. 2 in two geometry perspectives \u2013 side view and a top view. Elevation angles of robot eyes/cameras 1\u03b1 and 2\u03b1 as well as their attitude h are known (measurable). Robot relative position (distance d ) is calculated from the simple relation )(/ 1\u03b1tghd = while the height of the object H can be estimated as )( 2\u03b1tgdH \u22c5= . Elevation angles 1\u03b1 and 2\u03b1 can be obtained from the encoder sensor attached to the neck\u2019s pitch joint (Fig. 2) or by measuring the tilt (pitch) angles of cameras as alternative. Azimuth angle, i.e. angle of direction of motion \u03b2 is estimated by measuring the relative yaw angle of the neck joint as it is shown in Fig. 2. In such a way, a bioinspired, simple way of robot Simultaneous Localization and Mapping (SLAM) and advanced navigation algorithms will be realized. Determined geometry values 1\u03b1 , 2\u03b1 , \u03b2 , d and H acquired by corresponding robot sensor system are forwarded to the high-level (cognitive) control block of a humanoid robot. Beside the visual feedback information ensured by a pair of video cameras (see Fig. 2b), additional information about existence of obstacles is necessary for obstacle avoidance as well as robot trajectory prediction. The accurate distance(s) of the obstacle(s) inside the circle of 50.100.1~ \u2212r [ ]m can be obtained from the appropriate distance sensors. For that purpose Ultrasonic Range Finder (USRF) or laser Light Detection and Ranging (LIDAR) are commonly used in robotic practice depending on desired accuracy, assembling possibilities to the mechanical structure, price, etc. By implementation of the USRF sensors it is possible to detect existence of the obstacles in a robot collision zone as well as direction of motion of possible mobile obstacles/objects in the robot surrounding. By numerical differentiation of the identified/measured distance(s) between the robot and moving object(s) it is possible to estimate its/their speed(s) and acceleration(s) of motion. These are important indicators to be used for making the strategy of collision avoidance. During motion in unknown environment people comes in zones close to the obstacles (Fig. 2b). In order to avoid obstacles they make appropriate actions: change the course, i.e. direction of motion\u03b5 , vary the forward velocity v , step length s , step periodT , foot lifting height fh , etc. Mentioned variables\u03b5 , v , s ,T , fh represents the gait parameters pG . These parameters represent output vari- ables of the new cognitive block for robot trajectory prediction and planning (generation of feet cycloids) that will be integrated in the robot\u2019s high-level control structure. During a walk, humans do not know quantitative values how far they are from the closest obstacle or how fast they run" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003214_1.2839011-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003214_1.2839011-Figure4-1.png", "caption": "Fig. 4 Effect of singular configuration on homing", "texts": [ " 1 In the process that the limb Lu returns to its zero position, the limb Lu will be shortened till the nut fixed on the lower part of the extendible limb Lu runs against the home switch. If the machine tool is in the configuration as shown in Fig. 3, the nut cannot run against the home switch since it is already higher than the home switch. 2 Since actuation redundancy overcomes the singularity that limb Lu and the moving platform are collinear, the workspace of the machine tool is enlarged. When the machine tool is in the configuration as shown in Fig. 4 and begin to return to the homing position, it must pass its singular configuration to return to the home position. It is obvious that the machine tool with the above homing method cannot pass the singular configuration. Transactions of the ASME 7 Terms of Use: http://www.asme.org/about-asme/terms-of-use 5 s o p t s w t t o t t c a E p m r a p c 4 m i c z t c i m t a o d a L i E t J Downloaded Fr Assistant Homing Strategy For the redundantly actuated PKM discussed here, the position ensor of the redundant limb is absolute, and the position sensors f other limbs are all incremental. Based on the homing method resented in Sec. 4, an assistant homing strategy is proposed in his section. 5.1 Assistant Homing of Redundant Limb. To avoid the ingular configuration, the corresponding nonredundant PKM ith the redundant limb removed has a smaller workspace such hat it cannot move to the configuration shown in Fig. 4. However, he configuration shown in Fig. 3 can also occur in the workspace f the corresponding nonredundant machine tool. Before homing, he jog operation should be performed to lengthen limb E2B2 till he height of the nut is lower than that of the home switch. It is ertain that the jog operation is suitable for the redundantly actuted PKM in the configuration shown in Fig. 3 to lengthen limb 2B2. However, in a practical a application, the operation is comlex and the time of homing is so long that the efficiency of achining is debased greatly" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003297_j.rcim.2008.07.002-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003297_j.rcim.2008.07.002-Figure3-1.png", "caption": "Fig. 3. Setting of the coordinate system.", "texts": [ " 2, the equations of the tooth profile of the concave tooth section BD are x1 \u00bc u sin a; y1 \u00bc O0O\u00fe u cos a (2) On the pitch circle, we have x2 1 \u00fe y2 1 \u00bc R2 umax \u00bc \u00f0O 0O1\u00de cos a\u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 \u00f0O0O1\u00de 2 sin2 a q (3) For the same reason umin \u00bc \u00f0O 0O1\u00de cos a\u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 f1 \u00f0O 0O1\u00de 2 sin2 a q (4) uminpupumax (5) In substance, the spherical gearing of ratio 1 is equivalent to two pitch spheres of the same size rolling against each other in space. The engagement of concave teeth with convex teeth along the meridian line of the pitch surface is equivalent to that of a couple of planar gears of ratio 1. Therefore, the convex tooth profile can be found in the same way as the tooth profile of engaging planar gears. The calculation is the same. Shown in Fig. 3, 1 and 2 are two pitch circles with the same radius. P refers to the pitch point. The centers of the two pitch circles are expressed by O and O0. The center distance a \u00bc 2R. The coordinate system O1x1y1z1 is fixed to gear 1, while the coordinate system O2x2y2z2 is fixed to gear 2. XPY is a static coordinate system. The three axes y1y2y are coincided in the initial position. The coordinate equations are x y 1 2 64 3 75 \u00bc cos j sin j 0 sin j cos j R 0 0 1 2 64 3 75 x1 y1 1 2 64 3 75 (6) x2 y2 1 2 664 3 775 \u00bc cos j sin j R sin j sin j cos j R cos j 0 0 1 2 664 3 775 x y 1 2 664 3 775 \u00bc cos 2j sin 2j a sin j sin 2j cos 2j a cos j 0 0 1 2 664 3 775 x1 y1 1 2 664 3 775 (7) In order to see the profile of the convex tooth more clearly, a local coordinate system Ogxgygzg on the pitch circle of gear 2 is established: xg yg 1 2 64 3 75 \u00bc 1 0 0 0 1 R 0 0 1 2 64 3 75 x2 y2 1 2 64 3 75 (8) 4" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003655_978-90-481-9262-5_29-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003655_978-90-481-9262-5_29-Figure4-1.png", "caption": "Fig. 4 (a) Twists of leg li; (b) Constraint and actuation wrenches; (c) Wrench diagram in P3 of the H4 robot.", "texts": [ " Links 1, 2 and 3 are virtual links represented with dashed circles. 1 \u03c4\u0302 and \u03b5\u0302 stand for unit wrench and unit twist, respectively. 2 By applying a linear transformation. 276 Singularity Analysis of Lower-Mobility Parallel Robots with an Articulated Nacelle Since the twist system of a (4S)i linkage is represented with a virtual chain composed of two revolute joints and two prismatic joints, a twist graph of the H4 robot is obtained as shown in Fig. 3. The twist system Ti of the ith leg li = Ri\u2013 (4S)i (Fig. 4a) is equivalent to the twist system of a serial chain Ri\u2013Ri 1\u2013Ri 2\u2013Pi 1\u2013Pi 2 spanned by: \u03b5\u0302 i 01 = (si 1, ri 1 \u00d7 si 1) T , \u03b5\u0302 i 02 = (si mn, ri n \u00d7 si mn) T , \u03b5\u0302 i 03 = (si mp, ri p \u00d7 si mp) T , \u03b5\u0302 i \u221e1 = (0, ni)T and \u03b5\u0302 i \u221e2 = (0, si mp \u00d7 ni)T . Note that si 1 denotes a unit vector along the direction of Ri joint axis. For the ith leg li, si 1 // si mn // si pq [17]. The constraint wrench system Wi of li includes the wrenches that are reciprocal to all the twists in Ti. Thus, the axis of a \u03c40 in Wi is coplanar to the axes of \u03b5\u0302 i 01, \u03b5\u0302 i 02 and \u03b5\u0302 i 03 and orthogonal to the directions of \u03b5\u0302 i \u221e1 and \u03b5\u0302 i \u221e2", " This rotation is represented with the twist \u03b5\u0302012 whose axis is directed along s12 m = n1 \u00d7 n2. Therefore, T12 = W\u22a512 = span(\u03b5\u0302\u221ex, \u03b5\u0302\u221ey, \u03b5\u0302\u221ez, \u03b5\u0302012) where \u03b5\u0302\u221ex, \u03b5\u0302\u221ey and \u03b5\u0302\u221ez are the infinite pitch twists associated with translations along directions x, y and z, respectively. Similarly, the twist system of leg l34 is T34 = W\u22a534 = span(\u03b5\u0302\u221ex, \u03b5\u0302\u221ey, \u03b5\u0302\u221ez, \u03b5\u0302034) and the axis of \u03b5\u0302034 is directed along s34 m = n3 \u00d7n4. The twist system of leg LI = l12\u2013RI is TI = T12 \u2295 TRI . RI is the rotation about axis ZI (Fig. 4c) represented with the twist \u03b5\u03020ZI = (z, rc \u00d7 z)T . Thus, TI = span(\u03b5\u0302\u221ex, \u03b5\u0302\u221ey, \u03b5\u0302\u221ez, \u03b5\u0302012, \u03b5\u03020ZI ). Therefore, WI = T\u22a5I = span(\u03c4\u0302\u221eI) where \u03c4\u0302\u221eI = (0, z\u00d7s12 m )T . Likewise, WII = span(\u03c4\u0302\u221eII) where \u03c4\u0302\u221eII = (0, z\u00d7 s34 m )T . Legs LI and LII are mounted in parallel on the end effector of the H4 robot. Thus, its constraint wrench system is: Wc H4 = WI \u2295WII = span(\u03c4\u0302\u221eI, \u03c4\u0302\u221eII) (3) The end effector of the H4 robot is constrained by two pure moments: \u03c4\u0302\u221eI = (0, z\u00d7 s12 m )T and \u03c4\u0302\u221eII = (0, z\u00d7 s34 m )T ", " To obtain the six extensors of the H4 superbracket, we have to select twelve projective points on the six projective lines, i.e., two points on each one. The extensor of an infinite line is represented by two distinct infinite points. The extensor of a finite line can be represented by either two distinct finite points or one finite point and one infinite point, since any finite line has one point at infinity corresponding to its direction. We know that \u03c4\u03021 0 and \u03c4\u03022 0 intersect axis ZI . Likewise, \u03c4\u03023 0 and \u03c4\u03024 0 intersect axis ZII (Fig. 4). Let a (respectively c) denote the intersection point of \u03c4\u03021 0 (respectively \u03c4\u03022 0 ) and ZI and let e (respectively g) denote the intersection point of \u03c4\u03023 0 (respectively \u03c4\u03024 0 ) and ZII . Besides, ZI and ZII are parallel, i.e., ac and eg are parallel lines. They intersect in the infinite plane \u03a0\u221e at point j = (z, 0)T , which corresponds to the z direction. Note that an underlined letter stands for an infinite point. The finite line representing \u03c4\u03021 0 = (s1 uv, r1 v \u00d7 s1 uv)T can be defined by any two points on this line", " The infinite point of this line is expressed as: i = (n1 \u00d7 n2, 0)T = (s12 m , 0)T and corresponds to the intersection point of \u03c4\u03021 \u221e and \u03c4\u03022 \u221e. In the same vein, the intersection point of \u03c4\u03023 \u221e and \u03c4\u03024 \u221e is expressed as: k = (n3 \u00d7n4, 0)T = (s34 m , 0)T . Let us consider the constraint moment \u03c4\u0302\u221eI = (0, z\u00d7 s12 m )T . The vector z\u00d7 s12 m is normal to any finite plane spanned by the two vectors z and s12 m . The infinite point of s12 m is i and the infinite point of z is j. Therefore, \u03c4\u0302\u221eI = ij. Likewise, \u03c4\u0302\u221eII = kj. We have selected the twelve points of the H4 superbracket. The wrench diagram of the H4 robot is represented in Fig. 4c. The rows of the inverse Jacobian matrix of a parallel manipulator are Plu\u0308cker coordinates of six lines in P3. The superjoin of these six vectors in P5 corresponds to the determinant of their six Plu\u0308cker coordinate vectors up to a scalar multiple, which is the superbracket in GCA \u039b(V (2)) [8]. Thus, a singularity occurs when these six Plu\u0308cker coordinate vectors are dependent, which is equivalent to a superbracket equal to zero. In [20], the theory of projective invariants has been used to decompose the superbracket into an expression having brackets involving 12 points selected on the axes 279 S" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001247_robot.1990.126127-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001247_robot.1990.126127-Figure4-1.png", "caption": "Figure 4", "texts": [ " c- Apply the relations (1 3) to the parameters of translational links lying between ri andr2, as defined in section (3-1-2-2) to determine the possible supplementary regrouping. If these joints are parallel or perpendicular, we can find direct relations to obtain them in [ 161. d- Apply the relations (38), (39) and (42) for each parallelogram loop. e- The regrouping relations of the equivalent tree structure will be applied once more if step (d) generates parameters which can be eliminated by these relations. Find the minimum inertial parameters of the HITACHI-HPR robot, figure 4. The robot has 8 joints, 7 moving links, and one parallelogram closed-loop. The joints 1,3.4.6 and 7 are motorized and the joints 2,5 and 8 are not motorized. The geometric parameters of the robot are given in table 1. assuming that the joint 8 has been opened to construct the equivalent tree structure. I 4 1 2 1 0 1 0 1 0 1 0 I D4 I B d l 0 I 1 I I , I , I I = XX3 -YY3 - d52( Ms+ M g + M7) +XXq - YY4 = XZ3 -D5 ( MZj+ q) + = 223 +DS2(M5+ Mg+ M7) + = MX3 + D5 (Ms+ M g + M7) + MXq = XXs - YYs- D62 (Mg+ M7)+ XX2 -YY2 -W2(hZ1) = XYS + XY2 I X Z 5 - W Mzfj-xz2+D4Mz4 = XY3 + XY4 = m 3 + y z q =YZs-YZ2 = + m2 (M6+ M7) -b zz2 + M2( Mq) MXR5 =MX5+D6 (&+M7)--MX4 D DS xxR6 = x x 6 + YY7 - YY6 z2R6 = q + Y Y 7 XXR7 = XX7 - YY7 h\u2019f%%6 = M Y 6 - m 7 This mean that 38 parameters have been eliminated either because they have no effect or by regrouping to other parameters" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002134_1.5060506-Figure20-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002134_1.5060506-Figure20-1.png", "caption": "Figure 20. STL model of the buffer layer sliced with a rational B\u00e9zier surface", "texts": [ " As mentioned, the cladding regions (contour curves and their inclusion relationships) for non-planar layers can be generated by determining the intersection curve between a parametric surface and a CAD model. Page 317 Laser Materials Processing Conference ICALEO\u00ae 2005 Congress Proceedings For tool path generation the STL model of the buffer layer is sliced by a rational B\u00e9zier surface, which is generated by extrusion of a rational B\u00e9zier curve representing the planed cladding layers. A rational function is necessary for surface representation because the base material is cylindrical. Fig. 20 shows the buffer layer of the oil drilling tool sliced with a cylindrical B\u00e9zier surface. The results of the slicing procedure are the outer and inner contour curves. Fig. 21 shows the non-planar deposition paths for the buffer layer inside the outer and inner contour curves. Nonplanar slicing enables the fabrication of arbitrarily shaped layers on existing tool surfaces, as shown in Fig. 22. Non-planar deposition paths can be generated by nonplanar slicing planes, as mentioned before, or by direct slicing using so called \u201cdrive-surfaces\u201d [4]" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003745_tpwrd.2010.2068567-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003745_tpwrd.2010.2068567-Figure6-1.png", "caption": "Fig. 6. Deformation of the V-shape insulator string caused by windage yaw of transmission line.", "texts": [ " According to the meteorological condition and tower parameters of the transmission line, the load of the V-shape insulators (maximal wind velocity 35 m/s, no conductor icing) is calculated. The results are shown in Table I. The load ratio is represented as the vertical load/horizontal load from the conductors. The maximal wind velocity is from the weather record of the areas gone through by the transmission line. The displacement and stress distribution along the 750-kV insulator string caused by windage yaw of transmission line have been investigated. As shown in Fig. 6, the V-string (porcelain insulators) consists of string a and b. In wind, string a moves to and b to . Angle is generated by the movement of string a. The insulator string facing the wind was in tension status and tended upward. The leeward insulator string was bearing pressure and sagging. The parameters for showing the calculation results are follows: 1) horizontal displacement ; 2) vertical displacement ; 3) deflection angle , rotated by the insulator string a to ; and 4) the stress distribution along the insulators", " In the ordinary design consideration for the included angle of the V-shape insulator string, it is requested that the V-shape included angle be no more than twice that of the maximal windage yaw angle of I-shape insulators with the same configuration. In this situation, not one of the strings of the V-shape insulator would be bearing pressure when maximal windage yaw took place. In addition, it is proposed in some publications that the difference of the V-shape string\u2019s included angle with twice the amount of I-shape maximal windage yaw angle be less than 6 , or it is said that the deflection angle (as shown in Fig. 6) of the V-shape insulators is less than 7 . These considerations are based on experience, and little attention is paid to the calculation or experiment for the deformation of the V-string. In this paper, the improved selection method is discussed according to the calculation and experiment. The consideration for the selection of included angle meets the requirements: 1) avoidance of the insulators\u2019 broken in the condition of maximal windage yaw of transmission line and 2) assurance for the insulation performance of the air gap in the windage yaw of the transmission line" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003427_tmag.2006.891035-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003427_tmag.2006.891035-Figure1-1.png", "caption": "Fig. 1. Sketch map of the permanent magnet assembly. (a) An eight-segment magic ring. (b) The assembling procedure.", "texts": [ " The numerical results are compared with the ones of a conventional method, the electric current sheet equivalent, and the measured values to verify the validity of the presented method. Index Terms\u2014Finite element method, magic ring, Preisach hysteresis model, rotational magnetization. I. INTRODUCTION ACCURATE simulation of hysteresis phenomena in permanent magnet assemblies is necessary especially for the assemblies with high magnetic field strength. Such magnet assemblies are used in electronic devices, accelerators and medical systems. A typical intense magnetic flux source using permanent magnets is the so-called \u201cmagic ring,\u201d see Fig. 1(a), in which the permanent magnet segments are arranged in the form of hollow cylindrical arrays. A magnetic flux density level multi-times as much as the remanence of permanent magnet material can be achieved in the small air cavity at the center of the assembly. An extensively used method for simulating permanent magnets in numerical computation is surface current sheet model, with which only the demagnetization segment of hysteresis loop in the second quadrant is taken into account. This model is suitable to low field, e", " The rotational magnetization with magnetic field direction varying arbitrarily and the hysteresis characteristic including local loop are considered in the formulation of the model. The numerical computation of three permanent magnet assemblies with different materials are implemented using the method proposed. The comparison of the numerical results by the method with the results by the surface current sheet equivalent and by experiment verifies the validity of the method proposed in this paper. Fig. 1(a) shows the configuration of an eight-segment permanent magnet assembly. The arrows in the figure indicate the directions of magnetization for each segment, and the direction of magnetic field in the central cavity. The assembling procedure of the permanent magnet assembly is assumed as shown in Fig. 1(b). At the beginning of the procedure, the distances between the 8 magnet segments are large enough to make the interaction of these segments weak, so that the surface current sheet model, or voluminal current simulation with the operating point on the demagnetization curve 0018-9464/$25.00 \u00a9 2007 IEEE could be used to determine the initial magnetic field, then a set of spatial steps are performed forward to make all the segments touched (and fixed with special glue). For each step, a 2-D finite element analysis is implemented combined with a modified scalar Preisach model. The proposed method can trace the history of magnetization, and find the operating point in all the four quadrants easily. The effect of the arbitrarily direction-varying magnetic field to the magnetization is taken into account. The magnetic field equations for the problem depicted in Fig. 1(b) are given by (1) (2) where is magnetic field intensity, the magnetic flux density, the magnetic vector potential, is the magnetic polarization of medium, and is the equivalent voluminal current density in permanent magnets, which is given by (3) where stands for reluctivity of vacuum. In the case of 2-D analysis, the equation of magnetic vector potential is given by (4) where (5) In the finite element analysis of the permanent magnet structure the discretized equivalent voluminal current density is given by (6) in which (7) where is the direction angle of magnetization in element , and subscript denotes node number, and and are the parameters of element depending on node coordinates" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003449_09596518jsce656-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003449_09596518jsce656-Figure2-1.png", "caption": "Fig. 2 The membership functions of input and output: (a) E(B) membership function; (b) E\u0307 membership function", "texts": [ " In this paper, the G function with fuzzy reasoning regulation is defined. Let the error vector be e(k)5y*(k + 1) 2 y(k), where y*(k + 1) denotes the desired controlled variable. The input of fuzzy reasoning regulation are error and rate of error. The main steps of the fuzzy reasoning regulation are to build the membership functions, the fuzzy reasoning rules, and the fuzzy transducer. The structure diagram of fuzzy reasoning regulation and the membership functions of input and output are as shown in Fig. 1 and Fig. 2 respectively. Having analysed the arc welding process, the reasoning rules are defined. In general, the weld pool increases as the current increases. The reasoning rules are 1) if E is NB and E\u0307 is N then B is NB; 2) if E is NB and E\u0307 is Z then B is NS; A 15) if E is PB and E\u0307 is P then B is PB. The necessary condition that the MFC with G function can be used is that this algorithm is convergent. Let g k\u00f0 \u00de~ 1, 1zG= y kz1\u00f0 \u00de{y k\u00f0 \u00de\u00f0 \u00de, ( y kz1\u00f0 \u00de{y k\u00f0 \u00de~0 y kz1\u00f0 \u00de{y k\u00f0 \u00de=0 k~2,3, \u00f011\u00de Then if y*(k + 1) 2 y(k) " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000276_tmag.2003.816499-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000276_tmag.2003.816499-Figure1-1.png", "caption": "Fig. 1. Moving mesh and position determination.", "texts": [ " and in (4) are the magnetic forces decomposed in the and directions. Once the magnetic field is determined by the nonlinear time-stepping finite-element method, the magnetic force and torque are calculated by using the Maxwell stress tensor. Then mechanical motion is solved by the Runge\u2013Kutta method. After the mechanical equation determines a new angular and radial position of a rotor, the finite-element model is rearranged by moving mesh technique to recalculate the magnetic field. As shown in Fig. 1, moving meshes are composed of the 0018-9464/03$17.00 \u00a9 2003 IEEE meshes of the rotor and half of the air gap in the rotor side. New coordinates of the moving meshes are determined by locating moving meshes in the radial direction, and by rotating them along the sliding line in the air gap. By this process, the mesh sizes of the moving meshes in the air gap are changed to accomplish the nodal connectivity to the adjacent meshes. This procedure is repeated until it reaches a steady state from the standstill of a rotor" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003264_03093247jsa427-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003264_03093247jsa427-Figure2-1.png", "caption": "Fig. 2 Geometry of the contact interface: (a) a contactor node K penetrating a target segment Sl and (b) contact forces at the contact interface", "texts": [ " The contact interface is modelled by using the node-to-segment contact approach [44, 45]. In this approach, one of the contacting bodies is assumed to be a contactor, while the other is assumed to be a target. The contact interface is composed of contactor nodes that candidate to come into contact with the target segments. The contactor nodes should not penetrate the target segments, satisfying the first inequality condition of equation (4). A typical situation showing a contactor node K penetrating a target segment Sl, after j \u2013 1 increments within the time f +Df is shown in Fig. 2(a). The normal and tangential vectors, n and t, respectively, of the contact interface are constructed based on the target geometry. To satisfy the non-penetration condition, the node K should be located at a point P, where P is the physical contact point. The position vector of the physical contact point P can be expressed in terms of the position vectors of points K1 and K2, which connect the target segment Sl, using the interpolation shape function. The target segment that contains the contactor node K can be detected by the dot product of the tangent vector and the vector representing the projection of the contactor node K on the normal direction, such that L fzDfx j{1 P Lj : fzDfx j{1 K {fzDfx j{1 P ~0 \u00f032\u00f0a\u00de\u00de where fzDfx j{1 K and fzDfx j{1 P are the position vectors of the contactor node K and the physical contact point P, respectively, after j \u2013 1 increments within the time f +Df", " When the contactor node K lies on the target segment Sl, the condition, 21 ( jP ( 1, should be satisfied. Once the target segment containing the contactor node K is detected, the violation vector V j, defined by equation (30), is calculated to check if a new contact is detected. In case of contact, the interpenetration is eliminated, and, in turn, contact forces are developed at the contact interface throughout the jth increment. The contact force distribution for the contactor node K and target segment Sl is shown in Fig. 2(b). Now, the response of the problem is completely known at j \u2013 1 increment within the time f +Df. The algorithm of solution to obtain the contact status at jth increment is depicted as follows. Perform steps from 1 to 5 for the contactor domain. 1. Construct the element stiffness matrix fzDfKj e based on the residual time Dfj{1 r , such that fzDfKj e~ \u00f0 Ve BT fzDfC0 j B dV \u00f033\u00de where B is the strain-displacement transformation matrix and f +DfC9j is the relaxation modulus matrix, mechanical part, which can be expressed for a linear isotropic viscoelastic material as fzDf C0\u00bd j~ C" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000457_978-3-642-55848-1-Figure7.75-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000457_978-3-642-55848-1-Figure7.75-1.png", "caption": "Fig. 7.75. p-channel JFET. (a) The circuit symbol, (b) The bond graph representation", "texts": [ " The electrical circuit symbol used for n-channel JFETs is shown in Fig. 7.74 a. The corresponding bond graph component repre sentation is shown in Fig. 7.74b. It is assumed that power flows into the compo nent at the gate and the drain ports, and flows out at the source port. The compo nent can be created using the n-channel JFET button of the Electrical Component palette (Fig. 7.2). The text JFET is simply a label used for reference and can be changed when the component constructed or later. The polarities are just the opposite in a p-channel JFET (Fig. 7.75). Thus, the p-channel JFET component can be created from an n-channel component by re versing the power flow direction of all ports. This can be done by selecting the component and using the command Change Ports All. It is also possible to change only the gate port. In this case, the drain and the source of the p-channel JFET change places with respect to the n-channel JFET. The n-channel and p-channel JFETs differ in the sense of the gate port power flow. The drain of the n-channel component is a port where power flows in; for the p-channel, power flows out" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002001_1.3453240-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002001_1.3453240-Figure1-1.png", "caption": "Fig. 1 Geometry of porous journal bearing", "texts": [ " Also p = dp/dO = 0 at 0 = 'Y > 180 degrees. These are so-called Reynolds' conditions. (5) The flow in the oil film satisfies Reynolds' equation appropriately modified for the porosity of the shell. (6) The oil flow in the porous shell is governed by Darcy's law. (7) The permeability is constant. (8) The pressure is continuous across the porous bearing. (9) The normal component of the velocity across the porous boundary is continuous. Analysis (a) Constant Viscosity Oil. Assume that the flow in the porous shell in Fig. 1 is governed by Darcy's law if> of> ql = --- 71 0/ where if> is the permeability, 71 is the viscosity and f> is the pressure in the porous medium. Denote qx, qy, and qz as the respective flows in the x, y, and z directions of the medium. Then continuity of flow in the latter gives a a a - (qx ) + - (qy) + - (qz) = 0 ox oy oz or to the peripheral length of the bearing, it is reasonable to express the pressure gradient across the matrix in Cartesian coordinates. In ad dition it is also reasonable to assume that of>/oy is linear across the porous matrix ofthe bearing shell" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003496_6.2007-1806-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003496_6.2007-1806-Figure8-1.png", "caption": "Figure 8: (a) Experimental setup for membrane dynamics. Membrane specimen with a single transverse crease is shown in this figure. (b) Vacuum chamber used for membrane dynamics experiment.", "texts": [ " The consistent decrease in frequency for the addition of further compliance in membrane was observed in the numerical response. An experiment was then performed to investigate the vibration behavior of the four-corner loaded square membrane model. The purpose of this experimental analysis was to validate the numerical results for the pristine and creased membranes. An Ometron VPI 4000 Scanning Laser Vibrometer System was used during this experiment. The experiment is challenging for several reasons that will become clear from what follows. A view of the experimental membrane setup is shown in Figure 8. The Kapton membrane corners were truncated and glued with load spreaders. The lower corners of membrane were attached with tension springs, whose stiffness was known. The other ends of the springs were connected to the aluminum frame. The upper corners of the membrane were connected with frame by Nylon thread passing through turnbuckles. The corner force applied to the membrane was determined from the spring stiffness and corresponding spring deflection. The membrane was excited by a small permanent magnet bonded to the membrane and a stationary electromagnet placed towards the uncoated membrane side. The membrane specimen was then placed in a vacuum chamber, as shown in Figure 8. The natural frequencies of the membrane with equal corner tension of 0.25 N were identified in the range of 0-100 Hz. This range was initially preferred based on the numerical results. The amplitude of the excitation was selected small enough to minimize any noise and coupling effects generated from the springs and load spreaders. A broad-band (0 \u2013 100 Hz) pseudo random excitation was supplied from a signal generator to the membrane through the magnet. A FFT (Fast Fourier Transform) analyzer was used to identify the membrane response" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002033_ij-epa:19790022-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002033_ij-epa:19790022-Figure4-1.png", "caption": "Fig. 4 Torque/linear-force conversion x experimental results", "texts": [ " 3 in which the peak force was found to be 38-33N for x = 0-838 tw, corresponding to values of da/d(p = \u2014 3-22 and a = 8-66. x experimental results o calculated results least square approximation ELECTRIC POWER APPLICATIONS, AUGUST 1979, Vol. 2, No. 4 3 Experimental results 3.1 Torque/force characteristic A static test was carried out by applying various values of torque to the armature and measuring the maximum linear force exerted on the sleeve. It was found that the static friction torque was 5x 10\"3Nm. The torque/force curve is shown in Fig. 4 which gives a torque (Nm)/Force (N) = 1-29 x 10~3m. With the lead angle of the screw thread of 2\u00b0 42', the component Fy of the normal force on the thread acting at the armature radius of 0-027m expressed as a ratio of the rectilinear force Fx in x-direction is calculated to be 0-047. Thus torque _ Fy x 27 x 10\"3 force Fy = 4 -7x27x 10~5 = 1-27 x 10~3m Thus the calculated and experimental conversion ratios correspond very closely. The efficiency, at low velocities, of the convertor, 77, is given by F x 71 = ~7d x 1 0 0 % where 6 = angular displacement (rad) and x/2p = Q\\2TI computed results 137 It was found that with a torque T = 56-9 x 10~3 Nm the maximum force moved through a linear displacement was 38-26 N" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003564_978-1-4020-8600-7_38-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003564_978-1-4020-8600-7_38-Figure4-1.png", "caption": "Fig. 4 Geometric meaning of the condition \u03b4s (\u03b81, \u03b82) < \u03c6.", "texts": [ " On a unit sphere, centered at the center of the spherical motion, such an angle measures the length of the great-circle arc between two points that lie on the equatorial circle perpendicular to the rotation axis, and coincide with each other after the above-mentioned finite rotation. A limitation on \u03b4s(\u03b81, \u03b82) (e.g. \u03b4s(\u03b81, \u03b82) < \u03c6) has a clear geometric meaning. In fact, it means that each body-frame axis at the second orientation is confined to lie inside a circular cone with vertex at the center of the spherical motion, cone axis coincident with the homologous body-frame axis at the first orientation, and vertex angle given by the imposed condition (Figure 4). 365 R. Di Gregorio The distance metrics (1) and (2), and Proposition 2 can be used to generate the following family of distance metrics of SE(3): \u03c1u(x1, x2) = \u03b4T (O1,O2)+ u\u03b4s(\u03b81, \u03b82), (3) where x1 = (OT1 , \u03b8 T 1 ) T , x2 = (OT2 , \u03b8 T 2 ) T , and u is an arbitrary positive constant that is evaluated in the same unit as \u03b4T . The analysis of definition (3) reveals that a limitation on \u03c1u(x1, x2) expressed in the following form: \u03c1u(x1, x2) < h, (4) implies the following limitations on \u03b4T and \u03b4s , and the associated geometric meanings: \u03b4T (O1,O2) < h, (5a) \u03b4s(\u03b81, \u03b82) < h u " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000318_ijcnn.1991.170676-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000318_ijcnn.1991.170676-Figure4-1.png", "caption": "Fig. 4 Knowledge acquisition by DEFAnet (41 neurons) for the inverse kinematics of an industrial robot by learning with zero and calculated initialization (solid lines) and by calculation (dotted lines). Mean position error in a teat area of 450 mm x 600 mm.", "texts": [ " 1999 of network size showed that the mean position error decreased better than proportionally to the inverse of total number of neurons, and that for a given accuracy the adjustment of the smoothing factors may save up to 90% of neurons, so that comparatively small numbers of neurons achieved high performance (Fig. 3). For training by the delta rule the teacher was taken from the inverse kinematics calculated by conventional methods [l]. Examples were distributed homogeneously in the test area whithout repetitions. Training may indeed improve accuracy, if calculation cannot yield good results due to inappropriate smoothing (Fig. 4, a = 0). However, with suitable smoothing (Fig. 4, a = 1.4) calculation alone may produce almost optimal results. In simulations initialized with zeros, learning did not reach the same level of performance within lo6 steps (Fig. 4). In simulations initialized with calculated weights learning could not reduce the mean of position error by more than 0.1% (not shown). In spite of the randomization of teaching examples, the inverse kinematics tended to be acquired in a similar fashion - regarding position and orientation - in each training session. Development of the inverse kinematics is demonstrated by test trajectories along the edges of the test area after increasing lengths of training sequences (Fig. 5). Conclusion A deterministic network concept has been presented, that is capable of approximating arbitrary continuous functions with any desired accuracy" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003406_13506501jet418-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003406_13506501jet418-Figure2-1.png", "caption": "Fig. 2 High-temperature bearing test rig", "texts": [ " In each case, the solid lubricant should be used in conjunction with a self-lubricating bearing cage to provide additional lubrication. The recommended configurations are listed in Table 1. Bearing tests were conducted for both of these lubrication configurations. The self-lubricating materials relevant to the work described in this article are listed in Table 2. A test rig was designed and manufactured at ESTL to enable torque measurements of bearings operating at high temperature in vacuum. The rig (Fig. 2) enables heating of the bearings up to 300 \u25e6C. The test bearings are driven by a shaft connected to a stepper motor mounted external to the vacuum chamber. Electrical heaters mounted above and below the bearing housing are used to control the temperature. The reactive torque of the bearing housing is measured using a piezoelectric torque transducer (accurate to 0.2 mN m). The torque transducer table is thermally isolated from the bearing housing by means of a stack of ceramic discs and cooled by a recirculating fluid bath" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002052_iecon.2005.1569174-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002052_iecon.2005.1569174-Figure6-1.png", "caption": "Fig. 6. Local minimum test : the robot plan the optimal path when the direct path is closed.", "texts": [ " In this paper, the robot that have two wheels and twelve sonar sensor is simulated. The environment is Visual C 6.0 in windows XP and Pentium 4 2.4Ghz. There are deadreckoning error and sensor noise with Gaussian distribution. The sonar beam angle is 22.5 degree that of Polaroid 6000 series. fig.5 shows the simulator in this paper. the robot has sixteen sonar sensors that cover 360o and dense front sensing. Following examples show the situation for static local minimum problem and dynamic environment examples. See the fig.6 and fig.7. In the fig.6, the robot resolve the local minimum problem with grid map and path-planning. This result is almost same as the EPF. In the fig.7, the robot met the unknown object - centered one and move with another optimal path. These results show that the MREPF can navigate appropriately for static and dynamic environment as the EPF navigate the environments. We will discuss the difference from EPF in next section. Fig. 7. Dynamic environment test : When the first path is closed by dynamic obstacle, the robot generate another path" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001615_tpas.1981.316711-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001615_tpas.1981.316711-Figure4-1.png", "caption": "Fig. 4 Damping torque arising from the mutual attraction of the carrier N-S poles in the rotor with the counter rotating N-S poles of (a) upper sideband and (b) lower sideband stator currents. Viewed from carrier frame.", "texts": [ "(6), (7) and (8) the resultant stator flux is: -s s s -a -a Dli Ql 1 2 V (10 + ;3 exp j (-wv)t Electromechanical Torque The electromechanical torque acting on the rotor may be expressed as a vector cross product [8]: (b) R-L-C case. 2213 2214 + R ST = k (4~X 4) e e In terms of complex pha -R S T = Imagtk ( H) e e e RlsQ R SDl e DilQ1 Ql Dl vectors in the D1-Qi frame of the carrier. N-rn (11-a) At t=Q, the upper and lower sideband stator flux vectors make phase angles Ya and Y3 asors respectively. The carrier vector -f remains fixed in the diagram whereas 2 and b are (11-b) rotating at r/s in the counter-clockwise and clockwise directions. 1In Fig.4, the' north(N) and south(S) magnetic poles are (11-c) where the flux components are as defined in eq.(9) and (10). Bilateral Torque Coupling The torque component which couples bilaterally to the source oscillations of the rotor must have the same frequency Wv. Substituting eq.(9) and (10) into eq.(11), one finds that the relevant terms are f + f3) x a and $.fx( 2a + -)* However, the first term makes no contribution to damping, because it is not in time phase with the rotor velocity. This leaves: kT( ,, XI f X -", "3(b), a a%= -akbkceVIfR wo + W ~D-4~ 2 2 2D2D3 ~~~R +[(w +w )L - 1/(w +w )C] 0 IV 0 V d8 dt kef X w - W 0 V 2 2 R +[(w-w )L -l/(w-w)Cv0 V 0 V (15) Clearly when (\u00a2D2 -4D3)>.0, the damping torque component becomes unstable. A PhXsical Intelkretation of Electromechanic- kt'X (O3. 3 a77 -W-<~~~~~ I~~~~~~~d IA' 1Di 4- <7 Wvt wV t wt WVt At this point, it is instructive to draw a physical pict_pre of the damging torque component based on (bl x\u00a22) and (l X\u00a23) of eq.(12). These are illustrated respectively in Fig.4(a) and (b) which show the flux Fig. 5 Time function of (a) displacement (b) velocity of rotor oscillations (c) torque of Fig. 4(a), (d) torque of Fig. 4(b). w affixed on stator and rotor iron along the axes of the flux vectors. The polarity convention used, is that the magnetic flux emanates from the iron structure at the north pole. The rotor torque can be viewed as due to the attraction of unlike poles and the mutual repulsion of like poles which quantitatively is expressed by eq.(11). As the upper and lower sideband stator fluxes rotate with respect to the rotor field flux, it 'is evident that they produce pulsating torque components at an angular frequency wv and with phase angles ya and Ya as shown in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000781_0898-1221(86)90093-3-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000781_0898-1221(86)90093-3-Figure2-1.png", "caption": "Fig. 2. Nonrotating and hub-fixed unit vector triads.", "texts": [ " which are fixed to the hub and rotate with a constant angular velocity of magnitude .Q. is described by the rotation sequence (0.., 0:., 00 indicated in Fig. 3111]. The third rotation 0x takes place about the ~ principal axis of the cross-section. An additional rotation equal to the blade's pitch angle 0 brings the blade's principal axes (6, rl, 4) to their actual orientation in space. The angular orientation of the hub-fixed (x, y, z) axes relative to a set of inertial (X, Y, Z) directions is described as shown in Fig. 2. The angle 13 is the blade's precone angle and d) = f~t, with t denoting time. The angle e~ shown in that figure is the angle of attack of the rotor. In addition to the angular orientation of the cross section at x = x, the components of the elastic displacement vector of C are also needed to describe the motion of the blade. The components relative to the rotating (x, y, x) hub-fixed axes, denoted by u l, v l and w l, respectively, are used. The six variables (u l, v l, wl, 0:, 0:., 0r) are functions of x and 0, of course" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003773_s11668-009-9268-4-Figure16-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003773_s11668-009-9268-4-Figure16-1.png", "caption": "Fig. 16 Schematic diagram of self-loading", "texts": [ " A brittle fracture with inter- and transgranular features was observed. No striations were found on the fracture surface. The results were compared with the original fractured surface of the shaft. The fracture was at one side of the inner race \u2018A\u2019. The inner race of the bearing was damaged and there were roller marks on the inner race, Fig. 2. This shows that the bearing was unbalanced and the separating oil film was destroyed. This resulted in self-loading (radial binding) of the bearing [2], as illustrated in the schematic diagram Fig. 16 and caused metal-to-metal contact resulting in adhesive wear or seizing [3]. Due to relative movement at high speed of the shaft the adhering regions broke, and particles/debris from the shaft were pulled out of the inner race \u2018A\u2019. This caused scoring or gouging on the shaft beneath the ring [4, 5]. The loose particles increased the severity of the wear system and resulted in scoring as deep as 2.5 mm on the shaft, Fig. 6. Optical microscopy confirmed that the material on the inner surface of bearing ring was superficially stuck, and the SEM-EDS analysis confirmed that the adhering material had the same composition as the shaft" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002122_eurcon.2005.1630169-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002122_eurcon.2005.1630169-Figure2-1.png", "caption": "Fig. 2. Robot pair mechanism.", "texts": [ " By superposing the particular solution of oscillatory nature, and the stationary solution of forced nature, any elastic deformation of a considered mode may be presented in the following general form: Y (x1 t) =X1, (k1,1 ) (Tst1,I (t) + Tto1,I (t)) (5) T (t) is the stationary part of elastic deformation stl,1 caused by stationary forces that vary continuously over time. Only transversal deformations of prismatic beam will be analyzed in detail in this paper. LINK IN THE PRESENCE OF THE SECOND MODE The behavior of a robot pair with an elastic joint and elastic link in the presence of the second mode is analyzed (See Fig. 2.). We obtain the model of elastic line of first mode: 2 1,1 1,1 ae 2 6 1,1 The equation of the elastic line of the second mode should be defined by an analogous procedure. To set equilibrium equations for the tips of modes considered (LMA), the equilibrium equation defining the behavior of elastic joint as well as the mathematical model of the motor, boundary conditions. Thus we obtain the mathematical model of the system: U = H + h + C 0 + B + JT u (7) Equation (7) can be used for defining bending angles of the tip of each mode, but it cannot be used for defining the motions of single points on the elastic line of the modes present", " Remark IV: The first equation of model (7) follows directly from equation (6), upon defining ordered boundary conditions. Equation (6) cannot replace the first equation of model (7) because they are equations of different types. System (7) comprises equations of the same type. We can use them to analyze robot tip motion. HeR 4 is the matrix of inertia, heR is the vector of centrifugal, Coriolis and gravitation forces, CeR 4x4 is rigidity matrix. BeR is matrix of damping. Control is denoted byU . Je is the Jacobian matrix, F> is environment force. A robot starts from point \"A\" (Fig. 2.) and moves to point \"B\" within a specified time T = 2 [s] . Environment force dynamics is included in system motion dynamics. The accepted velocity profile is trapezoidal with an 0.2 T acceleration/deceleration period. As may be seen from Fig. 3, during its motion in the direction from point \"A\" to point \"B\" the robot tip tracks properly the nominal trajectory in the Cartesian coordinate's space. The presence of oscillations during robot task performance is evident (if we consider the change in velocity with respect to the nominal in the x-direction)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003188_j.mechmachtheory.2007.07.001-FigureA.1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003188_j.mechmachtheory.2007.07.001-FigureA.1-1.png", "caption": "Fig. A.1. Representation of rotation of vector.", "texts": [ " Indirect generating method and the method to obtain moulding surface by the structure condition are complementary each other. The authors express their deep gratitude to the National Natural Science Foundation of P.R. China for the financial support of this research project under Contract No. 50275017. All authors are thankful to the anonymous reviewers for their thoughtful and positive criticism, which allowed them to make this paper more readable. A.1. Rotation group Rotation group is an effective tool to investigate the vector rotation. In Fig. A.1, {O,abX} is a unit orthogonal right-handed frame, therein, rotation group B(u) around X is represented by the equation: B\u00f0u\u00de \u00bc \u00f0aa\u00fe bb\u00de cos u\u00fe \u00f0 ab\u00fe ba\u00de sin u\u00fe XX \u00f0A:1\u00de where u is the rotation angle, aa, bb, . . .,XX denote the dyads. Suppose that R is an initial position vector, r is the image of R after the rotation about X by the angle u, the following expression can be obtained: r \u00bc B\u00f0u\u00deR \u00f0A:2\u00de Referring to the rules of dyadic operation, r can be further represented in dyad notation as r \u00bc \u00bda\u00f0a R\u00de \u00fe b\u00f0b R\u00de cos u\u00fe \u00bd a\u00f0b R\u00de \u00fe b\u00f0a R\u00de sin u\u00feX\u00f0X R\u00de \u00f0A:3\u00de When there is u = 0, the following expression can be obtained B\u00f00\u00de \u00bc \u00f0aa\u00fe bb\u00de \u00feXX \u00bc E \u00f0A:4\u00de where E is called unit group and denotes an identical transformation, i" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001793_13552540510623576-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001793_13552540510623576-Figure1-1.png", "caption": "Figure 1 A structural fitting for helicopter frame", "texts": [ "eywords Rapid prototypes, Alloys Paper type Research paper Closed die hot forging processes are cost competitive for large volume production of parts. This high volume requirement is primarily due to long manufacturing lead times associated with the forging die development. For a typical low volume helicopter part shown in Figure 1, the delivery times for forging and post-forge machining often approach one year. Consequently, the helicopter companies are resorting to machining the part shapes from rolled plate stock even with material and fatigue performance penalties. For forgings to be acceptable, the lead times have to be reduced to a few weeks and at the same time they have to be affordable. The primary objective of this study was to investigate the feasibility of die manufacturing times using rapid prototyping (RP) techniques (Altan et al" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000243_095441002321029035-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000243_095441002321029035-Figure5-1.png", "caption": "Fig. 5 Pit orientations", "texts": [], "surrounding_texts": [ "The main parameters are: (a) the contact geometry, (b) the applied load, (c) speeds of rotation, (d) the oil viscosity, (e) roughness (Abbot\u2019s curve), (f) hardness of the contact materials, (g) elastic characteristics (elasticity module, Poisson coef\u00aecient) of materials, (h) fatigue endurance limit and yield strength of hard cases. There are six steps of calculation to perform before an estimation of the micropitting formation can be obtained: Step 1: Hertzian theory for a perfect contact. Calcula- tion of contact dimensions and Hertzian pressure. Step 2: calculation of oil-\u00aelm thickness (taking pressure into account). Step 3: con\u00aermation of a mixed contact (integration of roughness values). Step 4: surface plasti\u00aecation estimation. Calculation of plasticized depths. Step 5: calculation of overpressures. Step 6: calculation of maximum stresses. Estimation of a margin on micropitting formation. This methodology is represented by a graph given in the Appendix." ] }, { "image_filename": "designv11_32_0003062_s1560354708050067-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003062_s1560354708050067-Figure4-1.png", "caption": "Fig. 4.", "texts": [ " To study the disc dynamics one should construct on the phase plane the domain \u03a9 and level lines of the reduced energy, defined by T\u0303 + \u03a0\u0303 = const. (2.11) REGULAR AND CHAOTIC DYNAMICS Vol. 13 No. 5 2008 The contact mode of motion corresponds to trajectories that are completely in \u03a9. Key points of the phase portrait are stationary points of the function \u03a0\u0303, which can be found from equation mga cos \u03b8 + A\u03c4\u03c4 \u2032 = 0. (2.12) Depending on values of first integrals, equation (2.12) has one or three roots; the corresponding phase portraits have a unique elliptic fixed point (Fig. 4a) or a hyperbolic fixed point and two elliptic fixed points (Fig. 4b) [7, 8]. Equilibrium positions of system (2.5) (i. e., stationary motions of the disc) are always in \u03a9. Besides, when the domain \u03a9 is disconnected (Fig. 3b), one of the equilibrium position is in the left component of \u03a9 and two other equilibrium positions (if they exist) are in the right component of \u03a9. This analysis is valid for the case \u03b1 > 0; one can obtain results for the opposite case using symmetry considerations from above. 3. A DISC WITH THE SHARP EDGE ON AN ICY SURFACE In this case the friction is anisotropic: the disc can freely rotate about its axis and the velocity vector of a contact point is parallel to a horizontal disc diameter [4]", "2) can have two or none equilibrium positions depending on a value of c0. Typical phase portraits are shown on Figs. 5b and 5c. Note that equilibrium positions are necessarily in \u03a90, but not necessarily in \u03a9. In this situation there is a non-uniqueness of the motion, i.e., both equilibrium (corresponding to a stationary motion of the body) and detachment of the disc from the support are possible. 3. For p\u03c6 = p\u03c8 all phase trajectories of the system (3.2) are bounded; the corresponding model phase portraits are shown on Fig. 4. Likewise the previous case all equilibrium positions are necessarily in \u03a90, but not necessarily in \u03a9. REGULAR AND CHAOTIC DYNAMICS Vol. 13 No. 5 2008 ACKNOWLEDGMENTS This work was supported by the Russian Foundation of Basic Research (grant 08-01-00718). The author is grateful to A.V. Borisov and to participants of the Seminar on Nonlinear Dynamics for idea of this paper and useful discussion. REFERENCES 1. Deryabin, M.V. and Kozlov, V.V., On the Theory of Systems with Unilateral Constraints, Prikl" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000457_978-3-642-55848-1-Figure7.77-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000457_978-3-642-55848-1-Figure7.77-1.png", "caption": "Fig. 7.77. Model of junction diodes", "texts": [ " If VTO < 0, then at Vgs = 0 the device is in the on condition and, under a positive drain to source voltage, current will flow from drain to source. To cut off the device it is necessary to apply a negative gate to the source voltage. Such device operation is known as the depletion mode. In the en hanced mode VTO > 0, the device is pinched-off initially and it is necessary to ap ply a positive voltage larger than the threshold to enable the device to conduct the current. The diode models consist of a non-linear resistor and a capacitor (Fig. 7.77). Because in JFETs the diodes normally are reverse-biased, there is no diffusion charge. Hence, the charges consist of fixed ions in the depletion region and are represented by a junction capacitor. Eq. (7.51) shows that at a relatively small drain-to-source voltage Vds the cur rent increases with the voltage until the saturation voltage (equal to Vgs-VTO) is reached. This region is called the linear region of operation. When the drain-to source voltage increases above the saturation voltage, the drain-source current is practically independent of the voltage and the device is saturated", " The change in polarity of the voltages across the terminals and of the direction of current is taken care of by a change in the power flow direction through the p channel device (Figs. 7.74 and 7.75). The model of the p-channel JFET is similar to the n-channel model of Figs. 7.76 to 7.78, but with direction of power flow be tween external ports reversed. The change of power flow direction should be ap plied only to the bonds through which power is transferred between external ports. The others are not affected, e.g. the power flow direction to the non-linear resis tive element and of the capacitive element of the diode model in Fig. 7.77, as well as that of the controlled resistive element of the resistor in Fig. 7.78. These are the same for both n-channel and p-channel devices. In addition, we need to change the signs of the summator inputs of Fig. 7.78, because these components are used to evaluate Vgs, the voltage used in Eq. 7.51. This way, the p-channel JFET model can be created from the n-channel model by changing the port power flow direc tions. This is done by using the Change Ports All command for all component ports, or the Change Port command for a particular port, then changing the sum mator input signs", " In MOSFET there is no direct resistive current path between the gate and either the drain or source because of the oxide isolation layer. There is charge accumula tion, however, that is modelled by capacitors CGO and GCS, between the gate and the drain and the gate and the source, respectively. In a first-order analysis these can be described by constant capacitances. The capacitance between gate and body is neglected. There also are junctions between the body, the source, and the drain that are represented by diodes (Fig. 7.83). These junctions are reverse-biased. We use the same model of diodes as in JFET (Fig. 7.77). The capacitances Cj in that model describe the accumulation of junction charges. The discussion regarding direct and reverse operation of JFET applies here, as well. Thus, Vgs in Eq. (7.52) is replaced by Vgd, Vbs is replaced by Vbd, Vds is changed to -Vds, and the sign of the current is changed. 7.4 Modelling Semiconductor Components 28S The same applies to PMOSs. The direction of power transfer trough the com ponent is opposite to that of NMOS. Thus, the PMOS model can be created from the NMOS model in the same way as discussed for JFETs" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure8.1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure8.1-1.png", "caption": "Fig. 8.1. 3D Cartesian robotic system", "texts": [ " The server will process the client\u2019s request and serves up the front panel image to the client\u2019s browser. Snapshots of the browser executing the monitoring and diagnostic modes of the vibration analysis are given in Figures 7.37 and 7.38 respectively. 7.3 Real-time Vibration Analyser 227 228 7 Vibration Monitoring and Control 7.3 Real-time Vibration Analyser 229 230 7 Vibration Monitoring and Control 8 A control system, based on the above developments, is developed and applied to a precision 3D Cartesian robotic system as shown in Fig. 8.1 with a travel of 250\u00d7400\u00d750 (dimensions are in mm). Other engineering aspects are signficant to the overall development effort, such as sizing and choice of components, hardware architecture, software development platform, user interface design and performance assessment. Details of these aspects are described in the ensuing sections. The control specifications are given in Table 8.1. Linear electric motors manufactured by Anorad Corporation, U.S.A. are used for the construction of the robot. The LE series of high efficiency brushless linear servo motors are selected for the high continuous force specification of 78 N and a peak force of 191 N" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003998_09544062jmes1329-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003998_09544062jmes1329-Figure2-1.png", "caption": "Fig. 2 Cutaway view of the spindle showing components of the drawbar mechanism", "texts": [ " Two radial gas bearings at the front (right side of the figure) and back ends support the spindle in the radial direction. The thrust gas bearing at the end of the spindle provides longitudinal support during the cutting process. However, the spindle is still driven with the conventional electromagnetic force as in ordinary motors. A series of 16 copper bars are casted onto the slots along the spindle circumference to serve as the rotor, which is driven by the stator with its coils situated at the housing to drive the spindle. Figure 2 is a cutaway of the inside of the drawbar mechanism of the spindle (designated with a dashed line in Fig. 1). It consists of the bush, collet, and disc springs. The bush and collet are screwed together as a single unit, and the set of six disc spring pieces is mounted at the shoulder of this assembly. During the installation of the drill bit, the air cylinder pushes the bush/collet assembly a step forward so that the end of the collet is exposed for mounting the drill bit; meanwhile, the stacked disc springs are compressed", " The following formulae include the concept of loading (\u2212sign) and unloading (+sign) phases F = 4Es D2 e [ (h \u2212 s) ( h \u2212 s 2 ) Cf t + Df t 3 ] Cf = [(\u03b1d + 1)/(\u03b1d \u2212 1) \u2212 (2/ log \u03b1d)]\u03c0[\u03b1d/(\u03b1d \u2212 1)]2 1 \u2213 f [(2(h \u2212 s + t)/De \u2212 Di)] Df = (\u03c0/6) log \u03b1d[\u03b1d/(\u03b1d \u2212 1)]2 1 \u2213 f {[2(h \u2212 s + t)]/(De \u2212 Di)} (3) In general, the conventional tool-holder or the collet is used to hold the cutting tools in the machine during the work process. The high-speed gas spindle system has four slots cut into the collet body that allow the collet to expand to some extent when holding the drill bit (see Fig. 2). The drawbar force then generates a contact pressure on the collet\u2013spindle interface to hold the drill bit. Figure 7 shows the typical holder of traditional machine tools such as those used in milling machines or machining centres. This kind of tool-holder has a Proc. IMechE Vol. 223 Part C: J. Mechanical Engineering Science JMES1329 \u00a9 IMechE 2009 at UNIVERSITE DE SHERBROOKE on April 11, 2015pic.sagepub.comDownloaded from Fig. 7 The contact area and related notations of the tool-holder in traditional machine tools \u2018full contact\u2019 on the tool-holder\u2013spindle interface" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000765_1.3168978-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000765_1.3168978-Figure2-1.png", "caption": "Fig. 2 Theoretical profile of dovetail joint", "texts": [ "org/about-asme/terms-of-use r\u0302 Loading bolt Load cel l \u2014 6 mm o o ST2 1 50 rec tangu lar g ra t i ng J V Fig. 1 General arrangement of test piece Description of the Experiment Test Piece. Figure 1 shows a general arrangement of the test piece and loading rig. The test piece consisted of a 3 mm-thick sheet with two blades of the same thickness dovetailed into it. Both faces were ground. The material used was bright carbon steel with a tensile strength of 600 MPa. The dovetail was finished by form grinding, to the profile shown in Fig. 2, leaving all edges sharp. The test piece was assembled and held flat in the frame and loaded through 3/8 in. (9.5 mm) diameter pins. After assembly, the test piece was thoroughly degreased and loaded repeatedly between 1 kN and 4.5 kN. It was then preloaded to 1.33 kN. The grating was then replicated onto it following the technique described in reference [5], over the whole of the dovetail. To facilitate the interpretation of the fringe pattern, as will be discussed later, two \"bridges\" consisting of thin flexible plastic arches were fixed between blade and sheet-as shown in Fig", " The difference between displacements (us \u2014 ub) and (vs \u2014 vb) is proportional to the difference bet ween the fringe orders at the sheet and at the blade, for the point considered, in accordance with equation (9). Along the straight flanks, data from Fig. 5(a) and (b) is reduced in the form shown in Fig. 7(a) and {b), where, from the relevant fringe orders, the variation of (Ns-Nb) is plotted. The slight asymmetry will be noted. Similar plots were made for the other loads, an even greater asymmetry being found under increasing than under decreasing loading. The slip and opening between the points of tangency A, B in Fig. 2, were then calculated using equations (10) and (11) and plotted in Fig. 8. These, and similar results obtained for the other load levels analyzed, are summarized in Table 1. The mean of the slip on the left and right-hand sides is compared to the opening of the back gap, calculated in the same manner, in Fig. 9. Finally, Fig. 10 shows the opening (closure) of the joint at the maximum load. Discussion The asymmetry already observed in the photographs is made even more patent by Table 1, where the results for the right and left-hand flank are compared", " This figure shows the average of slip on the two flanks, but analysis of Table 1 also indicates that the hysteresis for slip on the left flank is considerably more pronounced than for the right flank. Indeed, the back gap opens linearly under increasing load and the nonlinearity under decreasing load is less than \u00b1 10 percent of its maximum value. A sharp change in the friction coefficient between the stick and slip conditions together with minor errors in manufacture and differences between the two surfaces in contact are the most likely cause of this behavior. In the theoretical shape of Fig. 2, contact occurs between points A and B. At the point of tangency B, the gap between blade and sheet is already IOAMI, or an order of magnitude higher than the higher closure of Table 1. Contact is therefore limited to the straight flank, the contact pressure decreasing toward the throat as predicted by numerical analysis [2]. The peak closure at B, Fig. 8, does not necessarily imply that at that point the contact pressure also peaks, since a slight tapering or blending between the straight flank and the radius results in the effective separation between blade and sheet, creating a gap at B prior to load application" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002150_s021984360500034x-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002150_s021984360500034x-Figure1-1.png", "caption": "Fig. 1. Mechanism configuration with five DOF.", "texts": [ " This comes from the fact that fingers can move very precisely but cannot stand long-term fast movement. To measure the finger involvement, an integral criterion has been suggested5: IKI \u2014 the integral kinematic involvement, being the sum of amplitudes of fingers motions. Some other reasonable criteria (reducing energy or motor temperatures) produced results rather comparable with IKI ones.18 4.2. Example In a simplified (but still representative) example we consider a planar arm consisting of the shoulder q1, the elbow q2, and the wrist q3 (Fig. 1). In writing, the fingers work together to produce two translations as shown in Fig. 2. Hence, with the robot arm, true fingers are substituted by two linear joints (q4 and q5 in Fig. 1). The motion ranges for such \u201csliding fingers\u201d are \u22064 = q4max \u2212 q4min = 0.05 m and \u22065 = q5 max \u2212 q5min = 0.05 m. The complete set of parameters used in the example is given in the Appendix. The task consists of writing a prescribed sequence of letters shown by solid lines in Fig. 3. Under (a), an x\u2013y representation is presented (x and y being operational coordinates), while (b) and (c) show the time histories x(t) and y(t). This reference sequence is set so as to be close to real letters and, at the same time, to be easy to describe mathematically (cycloids, circles, and straight lines have been used)", " The second order model (for the jth joint motor) is Trj\u0398\u0307rj = Zrj \u00b7Rj i 2 j \u2212(\u0398rj\u2212\u0398hj), Thj\u0398\u0307hj = Zhj Zrj (\u0398rj\u2212\u0398hj)\u2212(\u0398hj \u2212\u0398a), (9) where \u0398rj and \u0398hj are the rotor and housing temperatures, Trj and Thj are the thermal time constants, Zrj and Zhj are the energy-transfer resistances rotor-to-housing and housing-to-ambient, \u0398a is the ambient temperature, and Rji 2 j represents the Joule power loss. The time constants influence the slope of the temperature progress while the resistances define the steady state levels. The thermal dynamic model can be reduced to first order if the appropriate choice of parameters is made. All the relevant effects will be preserved.15\u201317 The first order model is Tj\u0398\u0307j = ZjRji 2 j \u2212 (\u0398j \u2212 \u0398a). (10) The thermal model, along with the dynamic model of the arm [Eq. (2)], enables simulation. 5.3. Example We consider the robotic arm shown in Fig. 1 in Sec. 4. The task (i.e. the reference) in that example was defined to be flexible, allowing different inclinations of letters. For the present analysis, we set the inclination to \u03b1 = 20\u25e6 [as can be seen in Fig. 10(a)]. In t. J. H um an . R ob ot . 2 00 5. 02 :1 05 -1 24 . D ow nl oa de d fr om w w w .w or ld sc ie nt if ic .c om by M O N A SH U N IV E R SI T Y o n 08 /2 5/ 15 . F or p er so na l u se o nl y. Simulation in this work is performed to prove the feasibility of the concept. Thus, the system parameters need not be realistic but rather chosen so as to stress the relevant effects" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure5.28-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure5.28-1.png", "caption": "Fig. 5.28. XY table testbed", "texts": [ " The tool attached to the table may be moved in either the X or Y-direction. The X and Y travel together span a 100\u00d7100 (mm) 2D space. The digital encoder resolution is 2.5 \u03bcm after a fourfold electronic interpolation, which also corresponds to the minimum step size. The motor uses screw threads for translating a rotation into a linear motion. Highly non-linear displacement errors are thus expected, in which case, linear interpolation may not be adequate and a non-linear error model will be necessary if high-precision requirements are to be satisfied. Figure 5.28 shows a picture of the XY table used. It is the primary objective of this section to introduce an improved calibration method to reduce the positioning errors of the XY table arising from the geometrical errors. Error modelling typically begins with a calibration of the errors at selected points within the operational space of the machine. For a 3D working space, the resultant geometrical errors in positioning may be decomposed into 21 underlying components (Satori et al. 1995). For the XY table with zero tool offsets, the error sources reduce to six components, including two linear errors, two straightness errors, one angular error, and the orthogonality error between the X- and Y-axes" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002406_0094-114x(74)90016-0-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002406_0094-114x(74)90016-0-Figure3-1.png", "caption": "Figure 3", "texts": [ " We have to establish first that joints 1 and 3 are mobile, and second that their motion is not such as to permit replacement by joints of lower connectivity. To this end, we examine these to see that they produce rotational movements . If they do not, they are either locked or are replaceable by prismatic joints. Now if either joint does not permit rotational movement , the indicatrix becomes a three-bar spherical linkage. Thus, the two mobile joints 2 and 4 must at least be parallel. In the indicatrix they must appear coaxial; so the indicatrix appears as a folded spherical linkage (Fig. 3a). It can be seen that such a linkage has two alternative configurations: the folded configuration in which 02 = 27r - 04, and the open configuration (Fig. 3b) in which 02 = 0,. Since, f rom (II.1), R 2 - o-R4 = 2mTrh and sO2 = ors04 for each of the above solutions, we can in fact find the correct sign ~r for each case. For example, Fig. 3 applies to the s u m m a r i s e d in T a b l e 1. Of t h e s e on ly the para l l e l s c r e w case 1 s e e m s to have p r e v i o u s l y been d e s c r i b e d . T h e re su l t s m a y be c o m p a r e d wi th t h o s e o f Savage [8 ] , W a l d r o n [ 6 ] and D i m e n t b e r g [ 1 6 ] fo r the C - R - C - R - case . I t is seen tha t the C - R - C - R - f o r m s o f all the so lu t ions p r e s e n t e d he re a p p e a r in s u m m a r y fo rm in r e f e r e n c e [ 6 ] , bu t tha t not all C - R - C - R - so lu t ions are spec ia l c a s e s o f C - H - C - H - fo rms " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002855_07ias.2007.334-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002855_07ias.2007.334-Figure6-1.png", "caption": "Figure 6. Resonance of yoke frame, 6600 Hz", "texts": [ " In this case, stator design is chosen in order to have only one resonance in audible spectrum corresponding to mode 2 at 8200 kHz. A finite element model developed with Ansys\u00ae software confirms that only one vibration mode (resonant frequency) exists in the audible spectrum (Figure 4.). Yoke frame and end shields are necessary to SRM functioning. In order to reduce influence of yoke frame and end shields on the stator resonance and mode shape, joining are placed on vibration antinodes (Figure 5.). Indeed, yoke frame and end shields have their own resonant frequencies but have in this way low influences on stator strain (Figure 6.). Figure 7. shows the experimental spectrum of vibratory acceleration measured on stator, yoke frame and end shields excited by symmetrical piezoelectric actuators. In respect with yoke frame and end shields location, stator vibratory acceleration spectrum has only one resonance. Vibratory acceleration spectra of the yoke frame and the end shields have multiple spectral lines due to different part of them (bolt, teeth \u2026). Vibration sources (aerodynamic, mechanical and magnetic) create forces on stator", " shows the relative vibration damping for sinusoidal excitations (magnetic and piezoelectric) at stator mode 2 resonance (Figure 5.) at 8200 Hz. Like Figure 7. has shown, piezoelectric actuators have a great influence on stator vibration but also on 3D part (Yoke frame and End shields). Note that piezoelectric actuators have been supplied in order to generate 2D forces (and consequently 2D strain) and at this frequency, the nodal strain is essentially 2D. Table III. shows the relative vibration damping for sinusoidal excitations (magnetic and piezoelectric) at yoke frame resonance (Figure 6.) at 6600 Hz. Contrary to the stator mode 2 resonance, the strain generated on this frequency is essentially 3D. For a same piezoelectric voltage, the relative vibration damping on stator has been decreased. In case of 3D strain, on 3D part (yoke frame and end shields), the vibratory acceleration generated by actuators can be out of phase with the magnetic vibratory acceleration. Thus relative vibration damping can be out of relative vibration wanted (0 to 100 %). Active control problem is composed by an input variable, the PZT actuators voltage, an output variable, the vibratory acceleration, and disturbance inputs (Figure 10" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000388_872115-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000388_872115-Figure2-1.png", "caption": "Figure 2: Inlet Valves Greased with Lubricant", "texts": [ "8 1300 The deposit mass was determined on the basis of the weIght dIfference of the inlet valve before and after the test (FIg. 1). By removing the deposits from the combustion chamber side only those of interest for the present investigation, located on the inlet side were measured. The deposits were also submersed in polar solvents, according to a defined procedure, in order to determine the soluble fractions. During all investigations one charge of leaded premium fuel without any additives was used. Figure 2 shows the oil greasing arrangement of the valves. They were greased with a lubricant having a viscosity according to SAE lOW 50. 872115 The oiling device continuously introduces the lubricant via a capillary tube into the valve guide. In addition, an air seal is used in the upper region of the valve guide to prevent the lubricant escaping out the top of the guide and to prevent the cylinder head lubricant from entering the clearance between guide and stem through the stem seal. The first tests revealed that there was a large scatter in deposit masses when the engine is operated with standard stem seals and without the oiling device shown in Figure 2. The sensitivity of the test method was not sufficient to measure changes in the deposit masses when varying the parametes. When the oiling device was applied the repeatability was lowered to approximately +/- 15 %. The valves were not allowed to turn in order to observe the zones of varying deposit layer thickness and morphology on the valve. Several authors /1, 2, 3/ have observed that the valve deposits contain fuel and lubricant fractions. The lubricant reaches the valve head via the valve stem and forms deposits as a result of the valve temperature /7/ and the level of vacuum in the intake pipe" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000655_0954407011528194-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000655_0954407011528194-Figure3-1.png", "caption": "Fig. 3 Band brake engagement test stand", "texts": [ " The Fpreload (N) 0 \u00a4 [(N m/s) K] 150 electric motor brings the drum to a speci ed rotationalApis (m2) 0.0075 Cdrum (N m/K) 100 speed to prepare for the engagement. One end of the band brake is anchored to the test stand housing. When the engagement is commanded, the servo pneumaticallyabsorption type band engagement test stand (SAE No. 2 pulls the other end and tightens the band brake aroundtest stand) [3 ]. The drum is connected to an electric the drum with a speci ed pressure level. This action gen-motor and an inertial ywheel as shown in Fig. 3. erates both viscous and dry engagement torque at theAutomatic transmission oil lubricates the band\u2013drum interface with a speci ed owrate. The oil rst ows band\u2013drum interface. The engagement torque tends to D05900 \u00a9 IMechE 2001 Proc Instn Mech Engrs Vol 215 Part D at UNIV CALIFORNIA SANTA BARBARA on June 29, 2015pid.sagepub.comDownloaded from twist the entire test housing through the anchored end band. As shown in Fig. 2c, the double-wrap band can of the band and is measured using a torque sensor", " For segment I, the spatial integration of the diVerent friction material permeability and dry friction partial diVerential equation system starts at \u00f5 0 and procharacteristics are also evaluated. The experimental con- ceeds towards \u00f5 2 at each numerical time step. The model ditions are summarized in Table 2. In the table, T oil is takes into account the change in band width at \u00f5 1 to the oil temperature measured at the band\u2013drum interface calculate a drop in the band contact pressure. It is using the thermocouples shown in Fig. 3 while the drum assumed that segments I and II have the same lm rotates at a speci ed speed before the band actuation. thickness distribution over the bridge area and that it is determined from the segment I calculation. Thus, for segment II, the numerical integration of model equations 3 SIMULATION SET-UP starts at \u00f5 2 and ends at \u00f5 3 . At \u00f5 2 , the model accounts for the width change to calculate the contact pressure. The band model described in reference [2 ] is extended 3.2 Model inputto predict the engagement behaviour of the double-wrap This section describes the model input variables which are required in addition to the system speci cations and experimental conditions listed in Tables 1 and 2" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000416_iecon.2002.1187482-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000416_iecon.2002.1187482-Figure1-1.png", "caption": "Fig. 1. Elementary Induction Machine.", "texts": [ " The mechanical equations for the machines are, where 8, is the rotor position, o is the angular speed and J,I is the combined rotor-load inertia. TI is the load torque and T, is the machine electromagnetic torque which can be obtained form the magnetic co-energy, (9) The magnetic co-energy is the energy stored in the magnetic circuits and can be written as, 1 1 1 1 2 2 2 2 wc, =-I$L,I, +--I$L,I, +--ITL,,I, +-ITL,I,. (10) 111. EXTENSION OF THE MODIFIED WINDING FUNCTION APPROACH An elemental scheme of the machine is presented in Fig. 1 to obtain the equations that allow the induction machine inductance calculation. To make things clearer, stator windings and rotor end-rings are not shown in the scheme. There are no restrictions about the winding and rotor bar distribution and the skewing of the rotor bars for the analysis. Furthermore, restrictions over the air-gap eccentricity are not assumed. Then the machine can exhibit non-uniform either static or dynamic eccentricity down the axial length of the motor. The stator reference position of the closed loop abcda, the angle $, is measured at an arbitrary point along the air-gap. The path stretches along the axial axis a length z. Points a and b are located in $0 and zo (both equal zero), points c and dare located in $ and z. On the other hand, points a and dare located on the stator internal surface whereas points b and c are located on the rotor external surface. 8, is the rotor angle with respect to a fixed stator point. Applying the Ampere's law over the closed path abcda shown in Fig. 1, where H is the magnetic field intensity, J is the current density and S is the surface enclosed by abcda. Since all the wires enclosed by the closed path carry the same current i, (1 1) results as follows, $ H($,z,Q,)dl= n($,z,Q,)i abcda The function n($,z,0,) can be called the 2-0 spatial winding distribution and represents the number of the winding turns enclosed by the path abcda. This distribution, unlike previous proposes, depends on the geometry of the windings down the axial length of the motor" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-FigureA.4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-FigureA.4-1.png", "caption": "Fig. A.4. Set-up for yaw measurements", "texts": [ " An angular measurement is concerned with the measurement of the angular displacement (tilt) of the moving part (on which the angular reflector is mounted) from the ideal position. This angular displacement may vary with the linear travel distance of the moving part. The primary causes of an angular deviation include the physical guide imperfections and possibly cogging related effects. The optics and accessories used for the angular measurement are rather similar to those used for linear measurements. A breakdown of these devices and accessories is given in Figure A.2. The set-up for pitch and yaw measurements are given respectively in Figure A.3 and Figure A.4. A closed-up view of the traverse path of the laser beams is given in Figure 5.7 which illustrate that the angular measurement is comprised of two linear measurements at a precisely known separation. Roll measurement is addressed separately in the next section as this measurement will typically require a level-sensitive device to be used. The objective of a straightness measurement is to determine whether the moving part is moving along a straight path. The main source for a straightness 5.3 Overview of Laser Calibration 137 error is the straightness profile of the guiding mechanisms which guide the motion of the moving part" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000525_iros.2000.893185-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000525_iros.2000.893185-Figure1-1.png", "caption": "Figure 1: The twist basis in Cartesian space.", "texts": [ " The new basis BL is no longer coordinate basis because they do not commute with each other [24, 61. s2 = s 4 = Based on this twist basis, equation (3) can be rewritten as T-'T(t) = Slsl + S 2 s 2 -k S 3 s 3 4- S 4 s 4 -k S 5 s 5 + SgS6 where the twist coordinates S I , . . . , s 6 are identical to velocity of the rigid body [wz, q,, uz, w,, wy, wZlT in the Cartesian space. Namely, [sl, s2, s3IT is related to the translational motion along the X,Y, and Z axes, respectively, and [ s4 , s5, s6IT is related to the consecutive rotational motion about the same axes as shown in Figure 1. ( 6 ) 4 Derivation of the Cartesian Stiffness Matrix Cartesian stiffness matrix describes how the components of the Cartesian wrench applied at a rigid body change as the body moves along the twist basis. We will present the property of Cartesian stiffness matrix through the congruence transformation between coordinates. First, we discuss the coordinate transformation through the relationship between bases. Secondly, we present the stiffness formulation with respect to the valid coordinate transformation matrix" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003745_tpwrd.2010.2068567-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003745_tpwrd.2010.2068567-Figure2-1.png", "caption": "Fig. 2. Dimensions of the V-shape insulator string. (a) Composite insulators. (b) Porcelain insulators.", "texts": [ " Assuming that there is no relative displacement among the adjacent parts, the spherical hinge is applied to the simulation of the constraint relation among adjacent parts. Relative angular displacement and friction exists among adjacent parts. The suspended U-shape rings in the insulator model, which are used for connecting the insulator with tower in engineering, restricting the movement of the V-shape insulator model in the 2-D plane. The dimensions of the V-shape insulator string (composite and porcelain), including connection hardware and link plate, are illustrated in Fig. 2, and the dimension of the porcelain insulators is presented in Fig. 3. The structure height of thecomposite insulator applied in 750-kV compact transmission line is selected to 6800 mm for the electric requirements, and the diameter of the core rod is selected to 30 mm for the tensile strength requirements. The composite insulator strength rating is 320 kN and connection hardware strength is 300 kN. The weight of composite insulator in the calculation mode is 45 kg. In addition, two types of porcelain insulators (XP1-300 and XWP2-300) with a minimum mechanical failing load of 300 kN can be applied to the lines" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003167_gt2008-50257-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003167_gt2008-50257-Figure2-1.png", "caption": "FIG. 2 RIGHT HAND FLOW OF TEST RIG WITH COMBINED BRUSH AND LABYRINTH SEAL CONFIGURATION (BSS)", "texts": [ " For this purpose, an experimental setup to measure swirl is described in the next section, followed by a description of numerical seal modeling. All results are presented, compared and discussed in the second part of the paper. The experimental investigations of this paper have been carried out using an existing test rig which was developed and improved in previous works to study static and dynamic characteristics of several sealing configurations (see for example [11]). The main components of the double-flow test rig are an inflow casing (swirl vane), a seal arrangement consisting of several seal chambers, and a rotor (Fig. 2). The seal Copyright \u00a9 2008 by ASME Terms of Use: http://www.asme.org/about-asme/terms-of-use Dow geometry is variable and can be assembled from a series of rings. The modular assembly enables time efficient testing of different sealing configurations. Two configurations are presented in this study: a combination of three sealing teeth (SSS) and a combination of a brush seal at the upstream position and two sealing teeth (BSS). The SSS configuration serves as a reference. The radial cold clearance between bristle pack and rotor is approx. 0.2 mm. The clearance under the sealing knifes is 0.31 mm. In Fig. 2 the test rig is shown with its BSS sealing configuration. The rotor with a diameter of 180 mm is driven by a speed regulated direct current motor with a rotational speed up to 12000 rpm. The test rig is supplied with compressed air. The maximum pressure difference between the first and the last sealing tooth is up to 900 kPa. The seal assembly has an axial length of about 60 mm from prechamber to outlet; the seal chamber height between rotor and chamber walls is 6 mm. The preswirl is generated in the inflow casing (Fig", " The velocity component cu or swirl velocity is then calculated from these pressures in the following way, using the equations for compressible flows: ( ) 1\u03ba 1pp2 Ma \u03ba 1\u03ba st \u2212 \u2212\u22c5 = \u2212 (1) TRMacu \u22c5\u22c5\u03ba\u22c5= (2) Copyright \u00a9 2008 by ASME Terms of Use: http://www.asme.org/about-asme/terms-of-use The temperature is also measured in each chamber and is nearly equal to the ambient temperature (see Fig. 4, top). In the prechamber, only one set of static and total pressure probes is used for the determination of the swirl. In the subsequent chambers 1 and 2 (see Fig. 2) the determination of swirl is repeated at four locations over the circumference as shown in the bottom sketch of Fig. 4. The results of these individual measurements are averaged to obtain the mean swirl in the two chambers, cu1 and cu2. The swirl downstream of the last sealing tooth was not measured. An overview of further metering points in both sealing chambers is shown in Fig. 4. The circumferential pressure distribution at the casing wall of chamber 1 and 2 is measured by ten static bores, plus an additional two wall taps in the 4 Downloaded From: http://proceedings" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002935_978-3-540-77296-5_15-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002935_978-3-540-77296-5_15-Figure2-1.png", "caption": "Fig. 2. Conceptual drawing of the bacteria integrated swimming microrobot: the microrobot is propelled by the attached array of bacteria, and its motion is controlled by turning the bacterial flagellar motors on/off using chemical stimuli. The robot body diameter would be of the order of 10s or few 100s of microns.", "texts": [ " Moreover, a continuous supply of ATP is required to move the biomotor, which could be a limitation for some liquid environments and applications. This work investigates bacteria assisted propulsion for swimming microrobots as a novel microrobotic actuation approach. The authors propose to use peritrichous bacteria for controlled propulsion of a swimming microrobot robustly and efficiently. An inorganic microrobot body is propelled by the helical flagella \u2013 only about 20 nanometers in diameter (Fig. 1) \u2013 of the bacteria attached to it. Fig. 2 shows the conceptual drawing of a hybrid (biotic/abiotic) swimming microrobot propelled by the bacteria attached to one of the flat ends of a polymeric micro-disk attached to the base of the microfabricated body of the robot. Here, a large number of couple of micrometer long bacteria are attached to a functionalized polymer surface by their bodies rather than their flagella, so that the flagella can rotate freely and propel the robot body. Using chemical stimuli, bacterial flagellar motors are turned on or off when desired for on/off motion control" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001001_s1388-2481(00)00141-7-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001001_s1388-2481(00)00141-7-Figure1-1.png", "caption": "Fig. 1. Scheme of microdisc surface on the large sphere.", "texts": [ "n this paper, we demonstrate a new approach for simulation of the 2D microdisc problem in spherical co-ordinates and apply it to the solution of the non-steady-state electrogenerated chemiluminescence (ECL) problem at a microdisc electrode. \u00d3 2001 Elsevier Science B.V. All rights reserved. Keywords: Microdisc electrode; Spherical co-ordinates; Electrochemiluminescence; Non-steady-state bipolar electrolysis There are many analytical approximations and digital approaches for the solution of the microdisc problem. Our approach is based on an idea to solve this problem not using cylindrical r; z but spherical co-ordinates r;H (Fig. 1). We consider a large sphere (with radius of say centimetre dimensions) as an insulator and a microdisc electrode (of radius say of microns) on the surface sphere. When rd rsph we assume that microdisc electrode surface is almost planar (Fig. 1). This fact allows us to compare obtained results with traditional solutions (analytical and numerical) in cylindrical coordinates. We have used this idea for the solution of the microdisc problem and applied it to electrogenerated chemiluminescence (ECL) under conditions of nonsteady-state bipolar impulse electrolysis (Fig. 2), and compared our new results with previous solutions for the microdisc problem [1\u00b14]. This approach allows us also to investigate the progressive shift from an almost planar disc electrode to an almost complete sphere electrode by simple adjustment of the geometric parameters in the program. ECL involves the formation of electronically excited states by an energetic electron transfer (ET) between redox species generated at an electrode surface [5]. In this work, the mass transport di usion-controlled kinetics in an ECL cell with a microdisc electrode on large spherical insulator (Fig. 1) under bipolar impulse non-steady electrolysis (Fig. 2) is considered. A microdisc in an ECL cell is electrolysed by bipolar voltage impulse of amplitude being enough to form reduced and oxidised organoluminophor forms. It is possible to separate the model into two time phases, where the \u00aerst phase is anodic, when the positive voltage impulses is applied to an electrode, and the second is a cathodic phase, which corresponds to a negative voltage impulse. Simulation area is (Fig. 1) rsph6 r6 rmax rsph 6 DTe p ; 06H6Hmax rd 6 DTe p rsph ; where Te is the total electrolysis time, D is the di usion coe cient, which is considered equal for all species in the solution, rd is the disk radius, rsph is the sphere radius. Anodic phase Ag \u00ff \u00ff e\u00ff ! A * Corresponding author. Tel.: +38-0572-409-107; fax: +38-0572- 409-113. E-mail address: svir@kture.kharkov.ua (I.B. Svir). 1388-2481/01/$ - see front matter \u00d3 2001 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 8 - 2 4 8 1 ( 0 0 ) 0 0 1 4 1 - 7 The equation of di usion processes in spherical co-ordinate for model (Fig. 1) is oc ot D o2c or2 2 r oc or 1 r2 o2c oH2 1 r2 tan H oc oH ; 1 c cg c0; 2 where c and cg are the concentrations of A and Ag species, respectively, and c0 is the initial concentration. The initial and boundary conditions are t 0; rsph < r < rmax; 0 < H < Hmax; c r;H; t 0; 0 < t < T1; r rsph; 06H6Hd; c c0; Hd < H < Hmax; oc or r rsph 0; rsph < r < rmax; H 0; oc oH H 0 0; r ! 1; H P Hmax; c 0; 0 < H < Hmax; c 0: 3 where Hd rd=rsph. Cathodic phase Ag e\u00ff ! A\u00ff; A e\u00ff ! Ag A A\u00ff!kbi 1A Ag 1A !kf cecl Ag 0B@ 1CA: Equations, which describe behaviour of the system in cathodic phase are: oc ot D o2c or2 2 r oc or 1 r2 o2c oH2 1 r2 tan H oc oH \u00ff kbic c\u00ff; 4 oc\u00ff ot D o2c\u00ff or2 2 r oc\u00ff or 1 r2 o2c\u00ff oH2 1 r2 tan H oc\u00ff oH \u00ff kbic c\u00ff; 5 oc ot D o2c or2 2 r oc or 1 r2 o2c oH2 1 r2 tan H oc oH kbic c\u00ff \u00ff kfc ; 6 c c\u00ff c cg c0; 7 where c\u00ff and c are the concentrations of A\u00ff and A species, respectively, kb the bimolecular interaction rate constant, kf ufl=s is the pseudo-monomolecular rate constant of `light' homogeneous ET reactions, where ufl is the \u00afuorescence quantum e ciency and s is a lifetime of species 1A " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002176_11505532_4-Figure4.3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002176_11505532_4-Figure4.3-1.png", "caption": "Fig. 4.3. The geometric principle of the proposed guided formation path following scheme in 2D for an individual formation agent and its support particle.", "texts": [ " the dynamic equations that the formation agent must adhere to given that its support particle employs the guidance laws from the preceding section. Denote the position and velocity vectors of the ith support particle by ps,i = [xs,i, ys,i] \u2208 R2 and p\u0307s,i = [x\u0307s,i, y\u0307s,i] \u2208 R2, respectively, where i \u2208 I = {1, ..., n}. Then denote the position constraint corresponding to the formation position of the ith formation agent by \u03b5f,i = [sf,i, ef,i] \u2208 R2. Consequently, the INERTIAL frame position of this formation agent can be stated by: pf,i = ps,i + Rsv,i\u03b5f,i, (4.29) which is illustrated in Figure 4.3. Here Rsv,i = R(\u03c7s,i) is of the same form as (4.10), while \u03c7s,i adheres to (4.19). This means that each formation agent must satisfy the following dynamic relationship: p\u0307f,i = p\u0307s,i + R\u0307sv,i\u03b5f,i + Rsv,i\u03b5\u0307f,i = p\u0307s,i + Rsv,iSsv,i\u03b5f,i + Rsv,i\u03b5\u0307f,i, (4.30) in order to converge to and follow its assigned position in the formation. Here Ssv,i = S(\u03c7\u0307s,i) is of the same skew-symmetric form as (4.8). Note that (4.30) allows for a time-varying formation position. However, in practice it suffices to consider that \u03b5\u0307f,i = 0, implying that formation reconfigurations nominally are conducted discretely" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure2.13-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure2.13-1.png", "caption": "Fig. 2.13. Tubular linear motor", "texts": [ " One of the drawbacks of this architecture is the low mechanical stiffness of the epoxy-filled armature blade which might lead to resonance under servo control in high acceleration applications. The U-shaped geometry captures and traps the hot air next to the coils, and therefore U-shaped linear motors can only be efficiently cooled by mounting a heat sink on the motor blade or via forced cooling. In addition, the U-shaped motor is characterized by magnetic flux utilisation inefficiencies similar to those of the forcer-platen type. 2.2 Permanent Magnet Linear Motors (PMLM) 29 Tubular motors, as shown in Figure 2.13, consist of two main elements: the thrust rod containing the permanent magnets (typically stationary) and the thrust block containing the motor coils (typically the moving element). From a force generation and energy efficiency perspective, these motors have significant design advantages over other linear motor architectures. The device consists of a single conductive wire cylindrically wound and encapsulated comprising the motor armature (thrust block) and a cylindrical assembly of sintered NdFeB high performance permanent magnets arrayed in an on-axis N-S stack contained within an encasing tube which comprises the stator" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002291_detc2006-99222-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002291_detc2006-99222-Figure2-1.png", "caption": "Figure 2 Schematic view of the LAR feed positioning system, planar representation and not to scale.", "texts": [ " Dewdney and Veidt presented in [4] a first refinement to Legg\u2019s initial suggestion. They concluded that a promising way to position the feed plate is to use a cable-driven parallel mechanism kept under tension by an aerostat filled with helium. This possibility was studied in more detail in [3] where the authors suggested the use of another level of actuation (the confluence point mechanism, CPM) at the focal apparatus to obtain the precision needed. The complete feed positioning system they envisioned is shown schematically in figure 2. It consists of two parallel mechanisms mounted in series. The large cable mechanism links the ground to the confluence point (CP) structure and performs coarse positioning and orientation Copyright \u00a9 2006 by ASME rms of Use: http://www.asme.org/about-asme/terms-of-use Down of the latter structure at low frequencies using winches. It is kept under tension by a helium filled aerostat that is linked to the CP structure by the leash. The CPM isolates the feed plate from the high-frequency perturbations occuring at the CP structure" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001744_135065004322842799-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001744_135065004322842799-Figure1-1.png", "caption": "Fig. 1 Diagram of the lip seal and details of A", "texts": [ " However, if the objective is to reduce the observed differences, it is necessary to integrate all the knowledge within this domain as well as to improve the proposed models that still remain quite limited in the modelling of a seal structure. Indeed, these models suppose that the compliant part of the lip seal has a bidimensional mechanical behaviour (axisymmetric), which is far from being the case at the lip edge. The present work proposes elastohydrodynamic model improvements which consider a three-dimensional elastic behaviour of the seal edge. The cross-section of a lip seal is presented in Fig. 1. If the seal is free of constraint, the diameter of the lip is always smaller than the diameter of the shaft. The difference between these two dimensions is the pre-load, which pushes back the lip edge when the seal is assembled and causes a radial strength whose effect is to compress the lip against the shaft. The magnitude of this strength depends on the elastomer used, the temperature, the geometric pro\u00aele of the lip as well as the stiffness of the spring. The radial strength of the lip produces, taking into account its geometric shape lip angle and the spring location, an asymmetric distribution of the tightening pressure ps, leading to a strong rise on the lubricant side and a smooth decrease on the other side (details shown in Fig. 1). The approach used for the structure modelling is new and original. Indeed, the compliant part of the seal is not supposed to have a totally elastic axisymmetric behaviour; it is divided into two parts with different mechanical behaviours (Fig. 2). Part (1), whose height h3 is de\u00aened according to the lip seal, is assumed to have a three-dimensional elastic behaviour, while part (2) remains axisymmetric. The shape of part (1) in contact with the rotating shaft can be considered as a strip whose length b depends on the pre-load" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003068_1.3555027-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003068_1.3555027-Figure1-1.png", "caption": "Fig. 1\u2014Seal geometry.", "texts": [ " = fluid viscosity v = fi/p p = fluid density T = shear stress = phase angle between eccentricity line of centers and till reference line CJ = angular velocity of tilted surface Q, = angular velocity of eccentric surface Journal of Lubrication Technology OCTOBER 1 9 6 9 / 695 Copyright \u00a9 1969 by ASME Downloaded From: https://tribology.asmedigitalcollection.asme.org on 06/19/2019 Terms of Use: http://www.asme.org/about-asme/terms-of-use 9T\u00ab dz = o dp = 0 [2] [3] oz When the flow is laminar, these equations take the form d2U dp ~dr~ p - - + ix \u2022 r oz1 iL = i ! l = o dz dz2 [4] 1.5] Velocity Distribution The seal geometry is shown in Fig. 1. For small angles of tilt A the vectorial velocity of a point on the upper tilted disk is given by Vw = [rco cos 9 sin 9 tan A sin X]er + [no cos A]e\u201e + [no sin A sin 6]ez [6] while the vectorial velocity of a point on the lower disk is given by Vn = [eQ sin ( - 0)]er + [rQ]es [7] Equation [5] indicates that the tangential velocity profile is linear in the axial coordinate. The linear profile satisfying the boundary conditions of Eqs. [6] and [7] is v \u2014 rlu cos A \u2014 Q,) \u2014 + rO h [8] where h is a function of r and 9", " The radial velocity profile which satisfies the conditions imposed by Eq. [10] is z2 - hz \\ dp \u00bb\u2022 Pf& + efi sin ( 1 2 t I dr (rco sin 6 cos 9 cos A tan2 A) Q \\/ z3 - zh2 h pi- ll v-~>-^=n + &\u2022 (- zh ) + (-as^A )\u2022 Iz4 -zh*\\ [11] Pressure Distribution The integrated form of continuity equation is f * l - i - ( w ) c b + f * A ^ & + f * ^ c f a a = 0 [12]Jo r dr Jo r d9 Jo dz The first term of this equation can be written as 1 Ch d , v , 1 d Ch , > , ( dh\\ \u2014 \u2014 (ur) dz = (\u00abr) dz \u2014 [u I r Jo drK ' r dr Jo K ' \\ dr ) z~h [13] For the geometry shown in Fig. 1 the film thickness is given by h = ho \u2014 r cos 9 tan A [14] so that \u2014 \u2014 (ur) dz = I (ur) dz r Jo dr v ' r dr Jo v ' + rco sin 9 cos2 9 cos A tan3 A [15] The second term of the continuity equation can be integrated using Eq. [8] to yield Transactions of the ASME Downloaded From: https://tribology.asmedigitalcollection.asme.org on 06/19/2019 Terms of Use: http://www.asme.org/about-asme/terms-of-use fh^ dz = ~ (co cos X-U)r sin 9 tan X [16]_1 Ch dv r The third term can also be integrated in a straightforward manner, and making use of Eq", " Fortunately, when the gross performance quantities such as leakage, load and torque are evaluated, even the direct effect of the boundary radial velocity disappears because it is self-cancelling for the seal as a whole. The result is that higher order terms involving the tilt angle appear in the equations for leakage, load, and torque only as a consequence of geometric integrals such as appear in Eqs. [32] and [37]. To put it another way, from an analytical point of view the rotation of the upper surface in Fig. 1 is an unnecessary complication which does not contribute to the effects being studied. The absence of w from Eqs. [32], [37] and [42] confirms this assertion. For this reason the turbulent investigation will be carried-out assuming that co = 0 which will greatly simplify the analysis. It was shown in (2) that the tangential velocity in turbulent flow could be represented by k\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\^ Vi = til 4te)\">^\"/2 02 2 V h/2 rQ/h- z \\ 1 / 7 2 V h/2 ) - ~ [43] satisfying the boundary conditions V* = 0 ov v = rfl, z = 0 v = 0, z = h [44] Figure 4 shows the assumed profile" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003370_aina.2008.53-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003370_aina.2008.53-Figure2-1.png", "caption": "Figure 2. (a) IEEE802.15.4-Ethernet Gateway. (b) and (c): IEEE802.15.4 field devices desgned for long-term battery operation", "texts": [ " Using a device with 64 kB ROM and 4 kB RAM it is possible to have a basic stack and some high level services like an HTTP 1.0 server and a simple XML parser on the device [9]. Even when implementing a rudimentary UPnP stack there is some program memory left for a small sensor or control application. In the SARBAU project also wireless field bus devices are investigated. We chose IEEE802.15.4 as lower layer, and implemented an IP over 802.15.4 protocol [8], currently using a star topology where the field bus devices communicate with a dedicated 802.15.4-to-ethernet gateway. This gateway (Fig. 2a), also realized with an 8 bit \u00b5C, converts the IP frames to IEEE802.15.4 frames and routes them to the corresponding wireless device, and vice versa. Address translation between the ethernet MAC addresses and the IEEE802.15.4 MAC addresses is performed on the gateway. Wireless connectivity is especially interesting for \u201cpush-only\u201d devices, which do not normally listen to network requests but only operate when they want to signal an event. Typical candidates are for example light switches, which are active only to transfer the switch event or temperature sensors, which are not queried but push their values periodically to a controller. This type of device can operate several years on a small battery. Since it operates wireless and on battery, it does not need any wiring which reduces installation costs. Our \u201cWeBee3\u201d [7] is an example of such a device (Fig. 2c). Commissioning is the initial assignment of a logical name or high level address to the device, and the setting of parameters on the device. Such parameters may include information about connected sensors, actuators, parameters for HVAC systems, and others. Binding is the assignment of relationships from the given device to other devices. A common binding use case is the assigning of lighting controllers to a light switch. Normally the commissioning and binding data is created forehand as a database which contains the devices and the network structure" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000952_21.105084-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000952_21.105084-Figure4-1.png", "caption": "Fig. 4. Position constraint in the second method.", "texts": [ " The maximum force/moment capability of a single robot arm, however, was earlier studied by Tarn, Bejczy, and Li [12], and will not be addressed again in this paper. Here, we are only concerned how to reduce the load of a Cartesian force to the arm, and at the same time minimize the energy consumption by the mainbody in adjusting its configuration. 2, The constraints imposed On the system magnitude of the Cartesian force is unlimited when the X , + R,bXh = X , (21) configured in a degenerate status. Therefore, the force 4r min 41 G 41 max (23) and (24) 6 @b < @ , m a . Equation (21) defines position constraint of the end-effector (Fig. 4), (22) describes the limitation of the joint torque, (23) describes the limitation of the arm motion and (24) represents the limitation of the mainbody orientation. In comparison with the first method, the second method uses torque limitations as new constraints. With ZHENG AND YIN: COORDINATING MULTILIMBED ROBOTS 855 more constraints involved in the nonlinear programming, the second method requires more computation. The first method, on the other hand, selects arm joint positions without considering the energy consumption" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003178_s12206-008-0124-3-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003178_s12206-008-0124-3-Figure2-1.png", "caption": "Fig. 2. Schematic diagram of pushrod type valve train system.", "texts": [ " However, due to the contact geometries between cam and follower around the contact spot that are totally different from each other, the cam profile shape to the flat follower is not generated in the same way as that to the rolling one. The relative contact velocity between cam and follower is another important parameter for the computation of lubricant load capacity, because it determines the entraining velocities of the lubricant into the gap. In this study, a perfectly flat follower type, Stone [13] (Fig. 2) is selected for simplicity of computation. The contact geometry with the curvaturefaced follower which is rather complex will be easily investigated with the results of our work. The instantaneous radius of curvature for the contact between cam and flat follower in Fig. 3, is described as below: [13] 3 2 2 2 2 2 2 22 2 2 2 2 2 d d d d d d d d d d d d d d d d (2) where, 2 dRR d (3) and 1 1tan dR R d . (4) Using the values of and , the distance and angle from the center of cam to the contact point, respectively, the velocity components at the contacting point between cam and flat follower are given by the following: coscu , (5) 2 2t d d Ru dt d " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000222_tmag.2002.802291-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000222_tmag.2002.802291-Figure1-1.png", "caption": "Fig. 1. Basic structure of the moving-magnet type linear oscillatory actuator (unit: mm).", "texts": [ " There are the various driving methods in the LOA drives. Of the various driving methods, sinusoidal current drives require a complicated electronic circuit structure, whereas, rectangular voltage drives has a simple electronic circuit [3]. In this paper, the following are described for the LOA under the simulated compressor load. 1) The efficiency of the LOA driven by two kinds of driving method, i.e., sinusoidal and rectangular wave. 2) Consideration of the iron loss for the LOA under base driving conditions. Fig. 1 shows the basic structure of the moving-magnet type linear oscillatory actuator. The LOA is symmetrical structure to a shaft. The LOA is composed of yokes, permanent magnets, coils, and brackets. The yokes of the LOA are made of laminated magnetic steel sheets. The LOA has the Nd\u2013Fe\u2013B magnets as the moving part. The two coils are connected in parallel, and each coil has 680 turns. The shaft is supported by linear ball bearings. The basic specifications of the LOA are listed in Table I. Fig. 2 shows the schematic diagram of the system for measuring the efficiency characteristics of the LOA under simulated compressor" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003955_6.2009-1999-Figure9-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003955_6.2009-1999-Figure9-1.png", "caption": "Figure 9. Canon G9 camera and roll-axis gimbal mount providing +/- 45 degree of roll compensation and side-look pointing.", "texts": [ " A Pelco NET300T video server is used to stream the analog video feed from the camera, and all network devices are linked through a Linksys 5-port hub. An overhead view of the avionics is shown in Fig. 8. The camera used here is the Canon G9, with a 12MP sensor, 6:1 optical zoom lens, and optical image stabilization. In the first trials the camera was hard-mounted in the bottom of the aircraft, but in the present version it is mounted in a roll-axis gimbal to compensate for bank angle and provide a limited side-look capability. The camera and gimbal mount are shown in Fig. 9. The gimbal is driven by hobby servos, one for the roll axis, and one American Institute of Aeronautics and Astronautics to operate the camera power switch. Both servos are driven via serial-to-PWM interfaces driven by the onboard computers. The gimbal is controlled by the real-time computer while the powering is controlled by the Linux computer, functionally separating sensor operation and platform movement. While the network control and the high-resolution imaging system perform adequately with conventional waypoint navigation as used in virtually all fielded UAV platforms, we have been developing a path-following algorithm that uses a secondary controller to augment the autopilot control using an L1 adaptive controller [18-24]" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001038_elan.1140020211-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001038_elan.1140020211-Figure6-1.png", "caption": "FIGURE 6. Calibration plots for the simultaneous flow-injection determination of ascorbic acid and glucose. 1, Calibration plot for the first series of standard solutions with different AA concentrations; 2, calibration plot for the second series of standard solutions with different glucose concentrations and a constant AA level (C&,).", "texts": [], "surrounding_texts": [ "The flow-injection system consisted of an MP13-GJ4 rnultichannel peristaltic pump (Ismatec, Switzerland), a homemade rotary injection valve with an exchangeable sample loop, and a Pt wire flow-through cell. A polarograph, PLP-225C (Zalimp, Poland), was used as the potentiostat and an E436 potentiograph (Metrohm, Switzerland) served as the recorder for the potentiostat output. The flow cell arrangement is shown in Figure 1; inset indicates the details of the working Pt wire electrode (0.3 mm in diameter, 4 mm long). The microreactor with the enzyme immobilized on controlled porous ghss (CPG) was made of glass tubing (3 mm id. , 80 mm long). The flow-injection manifold was made of Teflon tubing ( i d , 0.7 mm) and homemade perspex connectors." ] }, { "image_filename": "designv11_32_0003434_6.2008-4505-Figure13-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003434_6.2008-4505-Figure13-1.png", "caption": "Figure 13. Test rig used to assess leakage of 3.88 inch and 4.0-inch diameter test items.", "texts": [ "031 inches high and between 6\u00b0 and 10\u00b0, flow in this gap is turbulent, even for differential pressures as low as 2 psig. Thus, when the end flanges are introduced at the OD and the pads overlap one another, the primary leakage path will be through the very narrow hydrodynamic film region, which, at about 0.001 inch, will result in leakage rates well below any present technology. Two rigs were used to assess leakage characteristics of the baseline compliant surface axial face seals, as shown in Figure 13 and Figure 14. Testing was initially conducted under non-rotating conditions to assess the influence of static preload on leakage for each configuration. The static test procedures called for installing the test seal into the rig; applying an axial preload, introducing pressurized air into the seal cavity. Measured parameters included air mass flow, air pressure, axial preload force, and gap between the seal and runner. Following static testing and data analysis, two configurations with different L/Ro ratios were tested under conditions from 24,000 to 60,000 rpm in the test rig Figure 13. The L/Ro ratios and angular gaps tested are listed below: Outer Diameter L/Ro ratio Angular Gap (Deg) 3.88 0.516 10 3.88 0.327 10 4.37 0.351 6 4.37 0.223 6 9 0.665 10.5 9 0.665 3.5 American Institute of Aeronautics and Astronautics 092407 5 The preliminary model used to assess leakage flow is presented in equation 1 below. 3 0 9/4 4/7 14 )(7.1 \u239f\u239f \u23a0 \u239e \u239c\u239c \u239d \u239b \u23a5 \u23a6 \u23a4 \u23a2 \u23a3 \u23a1 \u0394= h h P L Dq new\u03c0 Equation 1 The above equation is based on the Reynolds flow equation but has been simplified so that the influence of the critical parameters and their impact on design could be readily evaluated" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000244_iros.1995.525929-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000244_iros.1995.525929-Figure2-1.png", "caption": "Fig. 2. Mobile robot for service use developed", "texts": [], "surrounding_texts": [ "or posture. Robot\u2019s position and direction related to global reference coordinate are the information for the detection of robot\u2019s posture. The robot\u2019s position related to the global reference coordinate is computed by the measured value from encoder that is fixed on the wheel. The robot\u2019s position related to the global refer- ence coordinate can be computed approximately in the following two equaitons: xi+, = X ; + :E-+:\\) (sin (8; + M ? ~ M ~ ) - sin 0,) , M - M W ( M * + M 1 ) {cos 8; - cos (8i + +) } , Y , + 1 = y i + ~ ( M . - M I ) where X ; and Y; are the robot\u2019s position related to the global reference coordinate a t i th step; 8; is robot\u2019s direction related to the global reference coordinate at ith step; Ml and M, are wheel\u2019s movement value; W is the distance between left and right wheel. B. Recognition o n obstacles. To avoide the obstacle and locomote the robot, it\u2019s needed to detect the robot\u2019s posture related to the obstacle. In the robot\u2019s real time locomotion control, the detection, recognition and judgment on information are needed, so it\u2019s better for robot to use minimal but enough sensors in the system, and the handling time on the information should be short. Thus, only 5 ultrasonic sensors are used for the detection of rotot\u2019s position related to the obstacle. C. Locomotion control. We can get information from the sensors fixed on the robot, for the autonomous locomotion control, it\u2019s necessary to change the detected information to recognizeable information. In our study, we propose to take fuzzy inference inethod for this problem. The fuzzy inference method is also adopted for the choice of path tracking control or obstacle avoidance control. Example 3. Path tracking. The locomotion control for tracking the path determined by working plan part as a connected line is conducted by the usage of fuzzy inference method. Following 4 kinds of parameters are taken as the input of fuzzy inference for the path tracking control (see Fig. Sa). 7 fuzzy levels are set for Dp, AP and AG, while, 4 fuzzy levels are set for DG. Following 2 parameters are used as output of fuzzy inference: * * S T : Steering angle; **VT: Movement speed, (7 fuzzy levels for S T , and 4 fuzzy levels for VT). In our method for simplicity Mamdani fuzzy inference is used. The inference is conducted by the product of fuzzy set in the max-min form. The output control is obtained by the defuzzi- fication of control rule with weight method. Example 4. Obstacle Avoidence. The robot will avoide the obstacle according the information about the distance between robot and obstacle from environment recognition part . T h e input parameter is the distance information froin robot to obstacle measured by sensors in the direction of left side D S L , left ahead D L , front D F , right ahead D R and right side DSR (Fig. 6b). A layout fuzzy inference method is proposed for the obstacle avoidance control. In this method, the infered output result a t this time will be used as input a t next time in the fuzzy inference. By this method, the whole rule number will be decreased, and make i t easy to construct a rule base. The control rule is set in below, in t h e first layout, values from 5 sensors will be divided to three groups as left, center aiid right, by this way, the fuzzy inference is conducted. Control ratio decision coefficient KoUT is used for the determination of ratio of Path Tracking fuzzy output and Obstacle Avoidence fuzzy output in the calculation of practical control ouput. Steering angular speed So and robot\u2019s speed bb are computed in equation (1) and ( 2 ) . K o U T is a value changedin [0.0,1.0], aiid the re are 4 fuzzy levels with K o U T where KSTR- angular speed translate coefficient. Example 5. Simulat ion and Ezperimental results. Simulation shows the proposed fuzzy inference method is valid in the modelling of movement environment or robot, and in the robot\u2019s locomotion control. Fig. 7a and 7b are t,he simulation result about path tracking control with obstacle avoidance. The robot can avoide the obstacles and move to the desired target in narrow corridor by changing the control ratio decision coefficient on the basis of obstacle\u2019s sit.uation. The experiment on this robot is carried out in real situation by the method proposed iri the above. Fig. 8a and 8b are the experiment result of pa th tracking control with obstacle avoidance on the corridor of building or on the floor of room. In the experiment, the obstacle is placed in the experimental surrounding, and experiment shows the robot can arrive a t target by avoiding obstacle in real surrounding. 5 Conclusion (1). To develop an intelligent locomotion robot for service use, the investigation on robot's working plan, environment recognization and locomotion control is conducted by simulation and experiment. (2). I t was investigated that for intelligent flexible control system must have hierarchical structure and 2 subsystem (global path planning on basis of HNM and GA and local for correction of trajectory basis on FC) are nedeed to introduce. (3). By adding the necessary items to the introduced estimation fitness function and setting the suitable gains to the estimation fitness function, the robot can arrive at the desired target successfully. The sirnulaiton results show tha t the proposed HNM is effective on the reducing G u i d a n c e a E l e v a t o r le b Fig.1. Mobile robot for service use a - Structure of mobile robot for service use b - Technological operations of work planning cost and better work planning can be achieved by this method. (4). Development of intelligent fuzzy control system realize the human interaction between mobile robots. References 1. Yamafuji K., Yamazaki Y., Watanabe T., Ogino K., Hamuro M. and Saeki K., Development of intelligent mobile robot for service use, Japan Soc. Mech. Engineers Ann. Conf. Robotics and Mechatronics (ROBOMEC '92)( 1992), Kawasaki, Vol. B, pp. 269-270. 2. Ishikawa A., Miyagawa K., Tanaka T. and Yamafuji K ., Development of intelligent mobile robot for service use, Japan Soc. Mech. Engineers Ann. Cod. Robotics and Mechatronics (ROBOMEC '94)(1994), Kobe, Vol. A, pp. 353-358. 3. Fukuda T. and Shibata T.,Integration and synthesis of neural network fuzzy logic and genetic algorithms for intelligent systems, J.Soc. Mech. Eng. (1993), Vo1.59, No. 564, pp.22822289. a b l e 1. Difference in results between two maps 1 I lnnul - 1 - -0. 2 i t . 1 . I . 1 . I Oulput Obstacle -0. 2 Kour V O 1 - h ' Locus Obstacle Oulpul Planned mote - I - --0. 2 t l . I * 1 . 1 . E e' 0 1 I ' ) / Wall,Obstacle 1 .1 \\ E 0 s\"" ] }, { "image_filename": "designv11_32_0002704_j.oceaneng.2007.09.005-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002704_j.oceaneng.2007.09.005-Figure8-1.png", "caption": "Fig. 8. Rule 2: matching the velocity with teammates.", "texts": [ " The steering angle factor is the direction angle towards the average position of teammates within the sensor range as the following equations described: pxave \u00bc px1 \u00fe \u00fe pxi 1 \u00fe pxi\u00fe1 \u00fe \u00fe pxN N 1 , (3) pyave \u00bc py1 \u00fe \u00fe pyi 1 \u00fe pyi\u00fe1 \u00fe \u00fe pyN N 1 , (4) b1 \u00bc arctan pyave pxave , (5) ARTICLE IN PRESS Y. Hou, R. Allen / Ocean Engineering 35 (2008) 400\u2013416404 where b1 is the steering angle factor calculated from rule 1, \u00f0px; py\u00de is the position of each of the teammates in the reference frame of coordinates, N is the number of the teammates and i is the ith teammate. This rule keeps vehicles\u2019 velocities as similar as possible when they are manoeuvring. A vehicle receives information of its teammates and then calculates the steering angle factor b2 by Eq. (8). As shown in Fig. 8, the central vehicle intends to turn b2 degree to keep matching the velocities of teammates within the sensor range: vxave \u00bc vx1 \u00fe \u00fe vxi 1 \u00fe vxi\u00fe1 \u00fe \u00fe vxN N 1 , (6) vyave \u00bc vy1 \u00fe \u00fe vyi 1 \u00fe vyi\u00fe1 \u00fe \u00fe vyN N 1 , (7) b2 \u00bc arctan vyave vxave , (8) where b2 is the steering angle factor calculated from rule 2 and \u00f0vx; vy\u00de is the velocity of each vehicle in the reference frame of coordinates. Rule 3 ensures that vehicles do not hit each other when they are close. In Fig. 9, Lmt is the minimum tolerable distance between two vehicles" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003008_j.mechmachtheory.2007.05.001-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003008_j.mechmachtheory.2007.05.001-Figure4-1.png", "caption": "Fig. 4. Optimal grasps on a bulb for different manipuation task.", "texts": [ " /;w, and h can be written as G \u00bc ri \u00bc pOH \u00fe ROH piH rz\u0302i; r4 \u00bc rpji \u00bc 1; 2; 3 The vector z\u0302i is just the unit normal at the contact point ri towards the interior of the object O. From the above arguments, the feasible grasps on an object can be sought in the domains of /;w; h. The proposed algorithms are implemented using MATLAB on a PC with P4 2.8 GHz processor, 1 MB cache memory, and 512 MB RAM. Assume that the friction coefficient li = 0.2 and the force upper bound f U i \u00bc 10 N for each contact. Each friction cone is linearized into a 10-side polyhedral cone, i.e., l = 10 in (26). Example 1. It is required to manipulate a bulb (Fig. 4), whose surface contains a sphere S of radius R0 = 20 mm and a cone C. The origin of frame FO is selected at the center of S. The cone C is expressed in frame FO by C \u00bc conv [2 k\u00bc1 r 2 R3 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2 x \u00fe r2 y q \u00bc Rk; rz \u00bc hk n o ! where R1 \u00bc R0 cos a0; h1 \u00bc R0 sin a0;R2 \u00bc R1 \u00fe H 0 tan a0; h2 \u00bc h1 H 0; a0 \u00bc p=6, and H0 = 18 mm. Two dynamic external wrenches will be applied on the bulb, which are specified in frame F O by wa ext \u00bc 0:5 cos 2:4pt \u00fe 10 \u00f02\u00fe 0:5 sin 2:4pt\u00de sin 0:4pt \u00f02\u00fe 0:5 sin 2:4pt\u00de cos 0:4pt cos\u00f0sin 1:2pt\u00de sin\u00f0cos 0:4pt\u00de sin\u00f0sin 1:2pt\u00de cos\u00f0sin 1:2pt\u00de cos\u00f0cos 0:4pt\u00de 2666666664 3777777775 and wb ext \u00bc 0:5 cos 2:4pt 10 \u00f02\u00fe 0:5 sin 2:4pt\u00de sin 0:4pt \u00f02\u00fe 0:5 sin 2:4pt\u00de cos 0:4pt cos\u00f0sin 1:2pt\u00de sin\u00f0cos 0:4pt\u00de sin\u00f0sin 1:2pt\u00de cos\u00f0sin 1:2pt\u00de cos\u00f0cos 0:4pt\u00de 2666666664 3777777775 They are periodical and their periods are both 5 s", " Locate the palm on S. Then rp \u00bc \u00bdR0 cos / cos w R0 cos / sin w R0 sin / T; np \u00bc \u00bd cos / cos w cos / sin w sin / T op \u00bc \u00bd sin / cos w sin / sin w cos / T; tp \u00bc \u00bd sin w cos w 0 T where / 2 \u00bd0; p=2 and w 2 \u00bd0; 2p\u00de. The steps of /;w, and h are taken to be p=8, p=4, and p=12, respectively. Using Algorithm 1 to search the domains for /;w, and h satisfying the above three conditions, we obtain 176 feasible grasps on the bulb with the CPU time of 55.40 min. Running Algorithm 3 w.r.t. wa ext yields the optimal grasp bGa (Fig. 4a) at / \u00bc 0;w \u00bc p, and h \u00bc 0, for which Q\u00f0G\u0302a;wa ext\u00de \u00bc 0:8322. Then b\u03021 \u00bc b\u03022 \u00bc b\u03023 \u00bc 0:0724p and the contact positions r1 \u00bc \u00bd 6:764 0 18:820 T; r2 \u00bc \u00bd 6:764 16:299 9:410 T; r3 \u00bc \u00bd 6:764 16:299 9:410 T, and r4 \u00bc \u00bd 20 0 0 T. Running Algo- rithm 3 w.r.t. wb ext, we obtain grasp bGb (Fig. 4b) at / \u00bc 0;w \u00bc 0, and h \u00bc 0, for which Q\u00f0bGb;wb ext\u00de \u00bc 0:8321. At that time, b\u03021 \u00bc b\u03022 \u00bc b\u03023 \u00bc 0:0724p, and r1 \u00bc \u00bd 6:764 0 18:820 T; r2 \u00bc \u00bd 6:764 16:299 9:410 T; r3 \u00bc \u00bd 6:764 16:299 9:410 T, and r4 \u00bc \u00bd 20 0 0 T. The required CPU times are 113.08 min and 126.21 min. Example 2. The object O to be manipulated is a bottle (Fig. 5), which consists of an intercepted ellipsoid E and the spherical extension H of a hexahedron. The origin of frame FO is selected at the center of E. The piece of surface E can be formulated in frame FO as E \u00bc conv \u00bd a cos c1 cos c2 a cos c1 sin c2 b sin c1 Tj p=6 6 c1 6 p=6; 062 6 2p n o where a \u00bc 10 mm and b \u00bc 20 mm" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000981_a:1017905723120-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000981_a:1017905723120-Figure3-1.png", "caption": "Fig. 3. Cyclic volt-ampere diagrams for complex I (1.3 \u00d7 10\u20133 mol/l) in MeCN/0.05 M [Bu4N]PF6 on a glassy-carbon electrode at v = 0.2 V/s and T = 20 \u00b1 2\u00b0\u00eb: (a) single-electron reduction, (b) two-electron reduction.", "texts": [ " Layer B is only formed by the disordered cations with a central N(6) atom, while layer A contains alternating anions and tetrabutylammonium cations with a central N(5) atom. Layers A and B are parallel to the crystallographic plane 0xz and alternate along axis 0y. The redox properties of complex I were studied using cyclic voltammetry in CH2Cl2 and MeCN. The electrochemical behavior of complex I in both solvents is very similar, except for the potentials of cathodic peaks A and B observed in the data from cyclic voltammetry. The volt-ampere diagram of complex I in CH2Cl2/0.05 M [Bu4N]PF6 and MeCN/0.05 M [Bu4N]PF6 (Fig. 3) contains two cathodic peaks A and B with nearly equal heights. Both peaks are diffusion-controlled (Ipv\u20131/2 = const, where Ip is the peak height, i.e., the current of the peak at the maximum, and v is the rate of the potential linear sweep) [17] and single-electron peaks, which follows from comparison of their heights with the height of the peak known beforehand to be a single-electron peak of a binuclear Cp2Mo2(CO)4 complex [18] under identical conditions. The choice of Cp2Mo2(CO)4 as a standard instead of ferrocene was made with regard to the close sizes of the molecules and, hence, close diffusion coefficients of this compound and I. In addition to the reduction peaks A and B for I in CH2Cl2, one can clearly observe irreversible oxidation of I (peak D, which is not shown in Fig. 3, but can be seen from Table 4) accompanied by blocking of the electrode surface. In MeCN, this peak is not observed, although in both studied solvents, in the presence of I, the anodic range of the working potentials becomes significantly narrow as compared to the background electrolyte, which points to electric oxidation of the com- 660 RUSSIAN JOURNAL OF COORDINATION CHEMISTRY Vol. 27 No. 9 2001 RAKOVA et al. plex in MeCN. The above data give evidence that the complex oxidation is most likely accompanied by destruction of its binuclear structure. Since the electrode surface was blocked by the products formed, it was impossible to study the oxidation in greater detail; this process will not be discussed in this paper. Unlike irreversible oxidation, the two-electron reduction of complex I, which runs in steps, is fully reversible at the first step, which is confirmed by its equal cathodic (A) and anodic (A') reflexes (Fig. 3a) and by the value of \u2206E = \u2013 ( and are the potentials of peaks A and A') being equal to 60\u201365 mV in both CH2Cl2 and MeCN. Moreover, the equal heights of peaks A and A' in the v range under study (0.02\u2013 0.2 V/s) suggest that the product of the single-electron reduction of I, namely, [Fe2(\u00b5-S2O3)2(NO)4]3\u2013 containing Fe0 and Fe+, is stable at least within the time interval of the cyclic voltammetry measurements. The further single-electron reduction of this three-charge anion is irreversible (peak B in Fig. 3b), which suggests instability of the obtained [Fe2(\u00b5-S2O3)2(NO)4]4\u2013. The product formed in the course of its decomposition is oxidized at the potentials of peak C, which appears on the anodic Ep a Ep c Ep c Ep a branch of the diagram only after the peak B potentials are attained. The presence of peak C indicates that the four-charge anion containing two Fe0 atoms is unstable. Perhaps it decomposes with destruction of the binuclear structure, however, this question requires further study. Some differences in the standard potentials (E0 = ( + )/2) for A/A' redox pair and the potentials of the cathodic and anodic peaks (B and C, respectively) in CH2Cl2 and MeCN, as in the case of the previously studied cluster (Bu4N)[Fe4(\u00b53-S)3(NO)7] (IV) [19], are due to the different donor\u2013acceptor properties of the solvating solvents" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002406_0094-114x(74)90016-0-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002406_0094-114x(74)90016-0-Figure2-1.png", "caption": "Figure 2", "texts": [], "surrounding_texts": [ "Now a C - H - C - H - linkage with two pairs of parallel joint axes is known to be mobile [13, 17, 18]. Thus we need not further investigate this case, and can exclude from the following the possibility of parallel joint axes. The C - H - C - H - linkage with two pairs of parallel joint axes is listed as solution no. l in Table I." ] }, { "image_filename": "designv11_32_0002457_cdc.2005.1582362-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002457_cdc.2005.1582362-Figure3-1.png", "caption": "Fig. 3. Constrained area on the surface of the sphere.", "texts": [ " (10) Note that the start direction of the closed path, \u03d5, is not constrained. This means that the rolling motion can be generated in arbitrary directions at the start position of the closed path Af . Remark 1: In order to apply a method in this paper to control of contact points by multi-fingered robot hands, it is necessary to obtain the area on the sphere by the constrained rolling motion. When the parameters are constrained as in (9) and (10), the constrained area on the sphere is the circled area surrounded by the dashed line shown in Fig. 3. This area is depicted by rotating the point Cf through 2\u03c0 about x- axis. This circled area is characterized by the angle \u03b8r := AfOCf . It follows that the boundaries of \u03b1f := [ uf vf ]T are |uf | \u2264 \u03b8r, |vf | \u2264 \u03b8r, (11) where \u03b8r = cos\u22121(cos \u03b8\u03041 cos \u03b8\u03042) (12) is given by applying Law of cosines to the triangle AfOCf . In the following sections, we propose a method for \u03b7\u0303 to converge to the origin by finite iterative closed paths with constrained rolling motion. The fundamental ideas are composed of the following items: (1) (Section III) To determine the parameter \u03d5 from the viewpoint of the norm minimization independent of the other two parameters" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002892_1.5061067-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002892_1.5061067-Figure2-1.png", "caption": "Figure 2: LC IN-625 demonstration piece with conical top, (a) CAD drawing and (b) LC part.", "texts": [ "81 mm thick), (4) a circular fin (2 mm thick), and (5) substrate disk (50 mm in diameter and 9.4 mm thick). Laser consolidation of IN-625 was performed with a 5- axis motion system to build the demonstration piece on a 1020 steel substrate in the following sequence: cylinder #1, cylinder #2, conical top on a short cylinder and finally the circular fin. A hole with a diameter of 8 mm was pre-drilled in the middle of the substrate to allow the release of the loose powder inside the part after laser consolidation. The steel substrate forms the part of the final demonstration piece. Figure 2 shows the CAD drawing and the as-consolidated LC IN-625 demonstration piece after removing the loose powder. It is evident that the as-consolidated part shows very good surface finish. The cross-sectional view of the part (Figure 3a) reveals that, as per the CAD design requirement, the laser consolidation process managed to build the LC IN-625 conical top with very uniform wall thickness and the tip was sealed very well. Figure 3b shows that all four sections of the LC IN-625 piece demonstrate uniform wall thickness" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002035_iros.2003.1249296-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002035_iros.2003.1249296-Figure3-1.png", "caption": "Figure 3 shows image when performing a contact task. The left side figure shows command, telemetry, and reference manipulators. The reference manipulator denotes the command one sent before duration of the time delay. A static external forcehorque applied to the manipulator end tip can be calculated ftom the telemetry and the reference", "texts": [], "surrounding_texts": [ "I. INTRODUCTION\nSpace robot systems are performing and expected to perform important missions, for example, large-scale structure on-orhit construction (as in the International Space Station or the Solar Power Satellite) and on-orbiting servicing tasks in Low Earth Orbit (LEO). It is difficult to develop an intelligent robot, which performs various tasks autonomously in complex environments. Current technology makes necessary to rely on human operator for providing overall task guidance and supervision, and for banding special situations. The benefits of teleoperation of a space robot have already been proved many times by Shuttle Remote Manipulator System, which is operated by astronauts inside the spacemfi to perform complex tasks, such as satellite handling and repairing [I].\nControlling space robots from ground is potentially much more effective than controlling them in space [2]. There are many advantages: first, the total hourly cost of a ground operator is orders of magnitude lower than that of an astronaut in space; second, ground control stations can have greater computing resomes available; thud, ground teleoperation permits to reduce crew workload; and forth, ground control permits terrestrial scientists to perform remotely experiments, etc. Hence, ground control of space robots seems very attractive, but on the other side there are some important drawbacks or limitations that must be overcome: (i) communication time delay; (ii) a low communications bandwidth (iii) lack of telepresence with difficult control in operation.\nUnder such a condition, special attention should be paid to contact forces and torques wben performing a contact task with a space-based manipulator teleoperated from ground Therefore, the manipulator should he controlled\n0-7803-78601103/$17.00 Q 2003 IEEE 2809\nautonomously with compliance feature. Note that some sort of compliance feature on the manipulator, either active or passive, is effective for contact tasks. Compliance is useful to cope with the error caused by an imperfect model. It can reduce execution time and overall forces applied upon the environment. The only problem is that it consists of an automatic remote feature and the operator can get confused if not fully aware of its behavior. Experimental researches for teleoperation have been well studied. The robot in the German space robot experiment, ROTEX, which was teleoperated both from within the space shuttle by an astronaut and from ground by an operator, was equipped with a forcehorque sensor [3]. In addition, ground-based experimental Studies on teleopemtion under time delay have been performed as in [4]-[6l. The Engineering Test satellite W, which was launched at tbe end of 1997 by the National Space Development Agency (NASDA) 171, performs tbe most recent experiment for space teleoperation.\nThis paper proposes a new strategy for space teleoperation under communication time delay, which makes it possible for an operator to notice through force reflection of a band controller: occurrence of contact; force release of the manipulator; and manipulator moving. Organization of the paper is the following. Section 2 explains the concept, the algorithm, and virtual images of the proposed approach. Section 3 introduces an example task that the proposed approach can be applied, and how to notice contact by the proposed approach. Finally, the teleoperation experiment confirms the proposed approacb in section 4.\nIt. TELEOPERATION BY FORCE REFLECTION\nA. Concept of the Proposed Approach\nIn teleoperation for a space-based manipulator fiom ground, a ground operator sends a command to the manipulator, which executes it. After duration of communication time delay, the operator receives telemetry data as a result of manipulator motion. Then, the current telemetry data is a result of the command data sent before duration of tbe time delay, when sending the current command. In the proposed teleoperation approach, difference of the current command and the current telemetry is displayed to the operator by force reflection through a hand controller. The manipulator is moving or begins to move when the operator feels the force reflection. On the other hand, wben a contact force is applied to the manipulator, it is added to the force reflection of tbe time", "delay. In operation without contact, the force reflection becomes to he zero when receiving telemetry data expressing that the manipulator finishes its motion. Under condition of contact, the force reflection continues to be applied even if the manipulator stops its motion. Also,\u2019 an operator feels change of the force reflection when contact of the manipulator occurs, when a contact force applied to the manipulator is reduced, and when the manipulator is moving. Thus, the operator can know conditions of the manipulator.\nIn order to apply the proposed approach, autonomous compliance control has to be used for the remote manipulator. On tbe other hand, two features can be considered for operation: type of a force reflecting input device; and command control mode to employ. Master arm and joystick can be considered for input devices. Also, two basic types of control modes are position control and rate conwol. Rate control with a master arm is very difficult and position control is advantageous only when doing dexterous tasks at rather bigh velocity, not very recommended for space teleoperation. Joystick can be used either way, but rate control seems more intuitive doe to the small working range of joystick joints and the abitity to stop the manipulator very precisely on a given point. Hence, position control with joystick is preferable as a hand controller for the proposed approach.\nB. Force Reflection Algorithm\nThe reference is same as the command sent before duration of the communication time delay. Also, the telemetry and the reference are same when no forces and no torques are applied to the remote manipulator, and they are different when forceltorque is applied In order to calculate force reflection F, the following equation is employed\nF = F, + F, (1)\nwhere F, denotes a force reflection of the time delay described as:\nand F, denotes a force reflection of contact described as:\nwhere K, and K, are control gains\nC. Virtual Feeling for Operation\nFigure 2 shows image of the proposed teleoperation approach without contact. A remote manipulator is operated as if the operator moves it through a virtual spring. The left figure shows command and telemetry manipulators. Sending a command and receiving telemetry data configure them, respectively. The difference of the command and the telemetry of the manipulator end tip positions are uanslated to extension of the virtual spring, which generates force reflection F,. As a result, the operator can recognize the time delay by extension of the virtual spring. when F, becomes to be zero, the manipulator has executed the command and the operator feels no forces.", "x - x\n:ir ' Fig. 2 Virtual fkecling of c0\"unieation timc delay without contact\nmanipulators. Both differences due to a contact force and the time delay are translated to extension of the virtual spring, which generates force reflection F, + F,. When the manipulator is moving, the operator feels that a length of the virtual spring is changing, not constant. When the manipulator stops, and an external forcehorque is applied to the manipulator, the operator feels that the virtual spring is extended at a constant length. Thus, the operator can h o w conditions of the manipulator.\nIII. EFFICIENCY OF THE PROPOSED APPROACH\nLet's consider an example task to make contact of the remote manipulator with a target surface. A sequence for this task is considered as follows: the operator sends a command whose point overshoots the target surface, and\nthen sends a next command in order to reduce a contact force. During the task, the operator should notice the following three conditions:\n(a) contact of the manipulator with the target;\n(b) geometrical contact point for detach;\n(c) detach of the manipulator from the target." ] }, { "image_filename": "designv11_32_0003745_tpwrd.2010.2068567-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003745_tpwrd.2010.2068567-Figure3-1.png", "caption": "Fig. 3. Dimension of the porcelain insulators. (a) XP1-300. (b) XWP2-300.", "texts": [ " Assuming that there is no relative displacement among the adjacent parts, the spherical hinge is applied to the simulation of the constraint relation among adjacent parts. Relative angular displacement and friction exists among adjacent parts. The suspended U-shape rings in the insulator model, which are used for connecting the insulator with tower in engineering, restricting the movement of the V-shape insulator model in the 2-D plane. The dimensions of the V-shape insulator string (composite and porcelain), including connection hardware and link plate, are illustrated in Fig. 2, and the dimension of the porcelain insulators is presented in Fig. 3. The structure height of thecomposite insulator applied in 750-kV compact transmission line is selected to 6800 mm for the electric requirements, and the diameter of the core rod is selected to 30 mm for the tensile strength requirements. The composite insulator strength rating is 320 kN and connection hardware strength is 300 kN. The weight of composite insulator in the calculation mode is 45 kg. In addition, two types of porcelain insulators (XP1-300 and XWP2-300) with a minimum mechanical failing load of 300 kN can be applied to the lines" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002001_1.3453240-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002001_1.3453240-Figure2-1.png", "caption": "Fig. 2 Pressure distribution for a long, porous bearing for various values of Co. E = 0.5, 12<1>1/c3 = 0.25, ,., = constant", "texts": [ " Various porous metal bearings have permeabilities ranging from 15 X 10-12 in2 (100 X 10-12 cm2) to about 300 X 10-12 in2 (2000 X 10-12 cm2) [10]. Thus for a bearing material having = 1500 X 10-12 cm2, t = 0.508 cm and c = 2.54 X 10-3 cm, 12<1>t/c3 is about 0.54. Thus values of 12<1>t/c 3 = 0.25 and 1.0 were used in the calcula tions. Graphs of normalized pressure j5 = pc 2/6Uwfi 1 were plotted using the numerical scheme previously outlined. Typical plots for constant viscosity oil and 12<1>t/c3 = 0.25 and 1.0 are given in Fig. 2, 3, 4, and 5 for values of eccentricity ratio E = e/c of 0.5 and 0.75, respectively, and with various values2 of Co = 6U,.,oR1t(1 - va)/Ec 3. It is observed that, for fixed values of eccentricity ratio, the normalized pressures p reduce with increasing values of 12<1>t/c3 from 0.25 to 1.0, particu larly for the smaller Co values. It is also observed that, for fixed values of Co, the normalized pressures increase with increasing values of E from 0.5 to 0.75, particularly for smaller values of 12<1>t/c3. It was already concluded by Conway and Lee [7] that the normal ized pressures for non-porous long bearings are quite sensitive to 2 For a rotational speed N = 1500 rpm, t = 0.2 in (0.50S em), ~o = 3.3 X 10-6 Rey. for SAE 30 oil at 160\u00b0F, Rl = 1 in (2.54 em), E = 106 psi (6.S9 X 109 Pal, \"0 = 0.3, c = 10-3 in (2.54 X 10-3 em), the constant Co is about 0.57. 452 / OCTOBER 1977 variations in the value of the parameter Co. As observed from Fig. 2, 3, 4, and 5, a similar behavior is found for both porous and impervious bearings, especially for larger values of eccentricity ratio. It is also seen that, for fixed values.of E and Co, the normalized pressures for a porous bearing are smaller than those for a corresponding nonporous one. The reductions in the normalized pressure increase with increase in the value of the permeability. Transactions of the ASME Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/26/2016 Terms of Use: http://www" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002514_ias.2006.256617-Figure9-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002514_ias.2006.256617-Figure9-1.png", "caption": "Fig. 9: Proposed simplified thermal model for the prototype.", "texts": [ " In any case, Starting from the thermal model proposed in [6], it is possible to define a simplified thermal model, which describes the thermal behaviors of the motor prototypes under study. Since, the rotors are realized in plastic, the heat flux in the airgaprotor-shaft thermal path can be neglected for any rotor speed condition. Due to the temperature difference between the endwindings and the copper embedded in the slots measured in the MA160 motor prototype, a thermal resistance between these two winding parts has to be considered in the proposed thermal model. On the base of these considerations, the thermal network shown in Fig. 9 has been adopted. The meaning of the parameters is listed in the following: \u2022 R0: natural convection thermal resistance between the external motor frame and the surrounding ambient. \u2022 RS-MF: equivalent thermal resistance between the copper embedded in the slots and the motor frame. \u2022 RS-EW: thermal resistance between the copper inside the slots and the endwindings. \u2022 REW-MF: equivalent thermal resistance between the endwinding and the motor frame. \u2022 PS: power losses in the winding part inside the slots (taking into account the actual temperature)", " It is an author opinion that the internal air whirls contribute to reduce the temperature spread on the motor frame surface. In the proposed thermal model the RS-MF and RS-EW are considered constant with reference to the rotor speed. This is reasonable taking into account that these thermal resistances describe the thermal exchange inside massive materials and, in any case, the motor inner air does not influence their values. Obviously, the REW-MF thermal resistance depends on the rotor speed. This resistance can be considered as the parallel of three thermal resistances, as shown in the circle of Fig. 9. In particular, it is possible to define the following thermal resistances: \u2022 RNC: natural convection thermal resistance between the endwinding and the motor frame. \u2022 RRAD: radiation thermal resistance between the endwindings and the motor frame. \u2022 REW-IA: forced convection thermal resistance between the endwindings and the end space inner air. \u2022 RIA-MF: forced convection thermal resistance between the inner air and the motor frame. The REW-IA and RIA-MF resistances have to be considered infinite when the rotor is still because they are depending on the inner air whirls", " This coefficient can be computed using the data reported in the last row of Table II, Table V and Table VIII, with exception of the point at zero rotor speed. The obtained results are reported from Fig. 14 to Fig. 16 as function of the peripheral rotor speed. In the same picture the regression lines of the computed data are reported too. The agreement between the heat transfer coefficient values reported in Fig.1 and the estimated hEquivalent ones is well evident. It is interesting to observe that the hForced Convection results equal zero when the rotor is still because the forced convection thermal path is not active in this condition (see Fig. 9). On the base of the results reported in Fig.14, Fig.15 and Fig. 16, the following consideration can be done: \u2022 In the considered speed range, for each prototype a linear dependence of the heat transfer coefficients versus the inner air speed has been found. \u2022 For the MA160 and MA132 motor prototypes, the obtained heat transfer coefficient values are comparable. This means that the inner ventilation play a similar role in the endwinding cooling, even if the endwinding enlargement in the end space regions is quite different (Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002985_apex.2007.357543-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002985_apex.2007.357543-Figure5-1.png", "caption": "Fig. 5. Magnetization curve of primary due to Iq Primary", "texts": [ " It must be noted that according to (1) a change in sign of quadrature axis current represent switching between motoring and generating modes of operation. The present investigations have been conducted using Finite Element Analysis (FEA) on a single sided, 3 phase, 4 pole LIM (Detailed information is given in Appendix A). Configuration along with distribution of the three phase winding is illustrated in figure 4. As can be seen the secondary is formed by an aluminum plate backed by a ferromagnetic plate. Maximum thrust force of 15 N (generating) 1-4244-0714-1/07/$20.00 C 2007 IEEE. 390 0.4 l 1.5 2 2.5 3 3.5 Iq (A) 4 4.5 5 5.5 6 Motor Generator Figure 5 illustrates the peak magnitude of flux density in the primary due to Iq, when Id is fixed at 1 A. Figure 6 is the similar characteristic due to Id, when Iq is fixed at 1 A. From both curves, one can notice that there is a difference between motoring and generating conditions in Fig. 5. However, curves representing motoring and generating conditions in Fig. 6 match reasonably. Figure 7 illustrates the peak magnitude of flux density in the back iron of the secondary due to Iq, when Id is fixed at 1 A. Fig. 8 is the similar characteristic due to Id, when Iq is fixed at 1 A. Again, there is a difference between motoring and generating conditions in Fig. 7. Curves of both motoring and generating conditions in Fig. 8 match well. The above observations indicate that the effect of Iq is not symmetric between motoring and generating conditions" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000610_ip-d:19830007-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000610_ip-d:19830007-Figure1-1.png", "caption": "Fig. 1 Third-order linear operator and null space", "texts": [ " 2 Switching function as a linear operator Consider the set of state equations for an \u00abth-order dynamic system in companion form: x = Ax + bu (20) Consider also a linear operator m* operating in rcth-order vector space such that a = nSx (21) The operator m1 will have a nullity of n \u2014 1 and a first-order range space if ml has the form m* = (m0.. . m n _ ! ) (22) As m* will indicate a direction in state space, we can arbitrarily setmn_, to 1. The range space of a linear operator mt = (23) is shown in Fig. 1. The linear operator m* can be represented by a vector normal to the operator null space. This follows directly from the definition of the scalar product: = 0 (24) In the third-order state space the null space is a second-order plane such that any trajectory confined to the plane obeys the characteristic equation = 0 (25) 2.7 Fixed gain control onto null space Consider a control signal u(t) such that state feedback of the form u = -k*x,Ak = 0 (26) is used on the system described in eqn. 20. The choice of k* will revolve around trying to maintain x within the null space of ml'. So, for any state x lying in the null space of m1, x will also lie in the null space. This is most easily achieved by placing n \u2014 \\ eigenvectors of the closed loop system in the null space, and so \u2014 bklx = Anx (27) 34 IEEPROC, Vol. 130, Pt. D, No. 2, MARCH 1983 where Ac = (A-bk*) (28) As the null space has a nullity of n \u2014 1, only n \u2014 1 distinct eigenvectors will be required to form a basis in the null space. The remaining eigenvector will not lie in null space. Fig. 1 shows this for a third-order system with the eigenvectors zx and z2 lying in the null plane with the third eigenvector z3 lying outside the null space. As the total set of eigenvectors z{ form a basis set for the wth-order space, we have, for any state x, X = (29) where a,- are scalar constants. The eigenvalues Xf associated with eigenvectors zt will be assumed distinct but not necessarily real. The eigenvector zn with associated eigenvalue Xn will be shown to determine the null space dynamics and will therefore be real", " Figs, la and b show the switching between two complex conjugate responses. Both result in a nonlinear oscillation about o = 0 with the stable system producing less oscillation than the unstable system. Figs. 1c and d show the effect of real eigenvalues with both stable and with one unstable. Note that for the case of one unstable eigenvalue the product term XnXn_j in eqn. 78 is negative; hence Ak*x is the same IEEPROC, Vol. 130, Pt. D, No. 2, MARCH 1983 as a. Again, both conditions produce a nonlinear oscillatory system with the stable system of Fig. 1c producing less excursion in a. The case for two unstable eigenvalues shown in To design a reduced-order switched system with adequate range space dynamics requires the two range space eigenvalues to be as fast as possible compared with the null space dynamics. Stable real or well damped complex eigenvalues give the best response, but one unstable or unstable complex eigenvalues can be used. In all cases the range space dynamics will be oscillatory. Consider as an example the same system as in full state a System output for reduced-order null space b Null space variable a time response c Null space trajectory switching but with a null space operator mT given by m* = (0.4226 1 0) The gain vector kt required for this is kt = (0.385 0 0) (79) (80) The magnitude of Ak* is kept the same as the full state switching system. For this system the range space eigenvalues are X2 = -0.4226 X3 = -2 .154 (81) This corresponds to Fig. 1c and should produce a reasonably well damped range space dynamics. The responses are shown in Figs. 8a to c. Fig. 8a shows the system output time response which exhibits some evidence of the range space dynamics as a slight oscillation at the beginning of the trajectory. The IEEPROC, Vol. 130, Pt. D, No. 2, MARCH 1983 39 range space variable is shown in Fig. Sb, and as expected is oscillatory. The state diagram for the range space is shown in Fig. 8c, illustrating the switched modes of Fig. 7c. If the null space operator is now changed so that m1 contains the fastest eigenvalue m* = (2" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000749_tmag.1984.1063217-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000749_tmag.1984.1063217-Figure1-1.png", "caption": "Fig. 1. Magnetization curves for (1).", "texts": [], "surrounding_texts": [ "INTRODUCTION\nIn order to represent the hysteretic properties of magnetization, Preisach has proposed a model which assumes that each of the domaines possesses a rectangular hysteresis loop and interaction between domaines can be introduced by assuming local fields acting on the domains [l]. Even though the Preisach type model is based on such simple assumptions, it gives valuable results that are in agreement with experimental results L21. There is however an instability problem 131 for which the Preisach's function takes an different value depending on the previous path in the magnetization processes.\nmodel for nonlinear inductors exhibiting hysteresis loops [ 4 ] . Furthermore, they have generalized their model to a static hysteresis model [ 5 ] . Their model is based on the fact that a trajectory of flux linkage vs. current is uniquely determined by the last point at which the time derivative of flux linkage changes sign. Their model exhibits many important hysteretic properties commonly observed in practice. However, their model is too complex to use the two- or threedimensional magnetic field calculations.\nto the Chua type model for analyzing the threedimensional magnetic field distributions in electromagnetic devices [6,71.\nand Chua type models can be derived from a common picture. We also propose a specific model that can embrace essential parts of both Preisach and Chua type models.\nChua and Stromsmoe have worked out a lumped circuit\nSaito had proposed a specific model that is similar\nIn this paper, we elucidate that both the Preisach\nTHE MAGNETIC HYSTERESIS MODEL\nChua Type Model --- The specific model belonging to Chua assumes that\nH = (UIJ)B + (l/s)aB/at, (1)\nwhere H,B,!JrS and t denote the field intensity, flux density, permeability, hysteresis coefficient and time, respectively [6,7] .\nFrom an experimental point of view, the magnetization is accomplished in essence through the time varying flux density. In (11, a magnetization hystory is implicit through the value of the peak flux density. The time derivative of the flux density aB/at takes an different signs on the ascending branch Or descending branch of the hysteresis loop, and takes different values depending on the rate of change aB/at. determined by the sign of aB/at as well as the rate of This means that a magnetization trajectory is uniquely change aB/at.\nSince the term aB/at in (1) becomes zero when the flux density B arrives at the positive or negative maximum value, a trace of the peak points on the B vs. H trajectories yields a single valued function of permeability !.I shown in Fig. l(a)., where the hysteresis coefficient s becomes to quite small in value but not zero. Similarly, a trace of the peak points on the aB/at vs. H trajectories yields a single valued function of the hysteresis coefficient s shown in Fig. l(b), because the flux density B becomes to zero when the time derivative of the flux density aB/at in (1) arrives at the positive or negative maximum value.\nPreisach Type Model\nAccording to the [21, the reversing point field intensity Hn and applied field intensity Hp are defined as shown in Fig. 2. By considering Fig. 2 , it is obvious that the B vs. \u20ac3 trajectory takes different paths depending on the reversing point field intensity Hn. Thereby, the flux density B is represented as a function of the applied field intensity Hp as well as reversing point field intensity Hn,\nB = B(H H ). P' n\n0018-9464/84/0900-1434$01.0001984 IEEE", "Moreover, by considering a saturation point of flux density on the nonsymmetrical hysteresis loop shown in\nThe Chua type model is based on the fact that the magnetization path is uniquely determined by aB/at. On the other side, the Preisach type model is based on a behavior that the change of slope aB/aH depends on the reversing point field intensities.\nIn order to find a relationship between them, application of (1) to the states of Fig. 2 gives the following relations:\nwhere the field intensity AHn in Fig. 2 s so small that the permeability p and hysteresis coefficient s may be assumed to be constant. By subtracting ( 4 ) from (5) and rearranging, it is possible to obtain\nAB/u = (L/p) (Ba - Bb)\nFurther rearrangement of (6) yields\nIn Fig. 2, if the limit of AHn goes to zero, then ' AB/V term in ( 7 ) is simultaneously reduced to zero. Thus an assumption of AH,=AB/p leads to\nFrom ( 3 ) , ( 7 ) and (81, a relationship between the hysteresis coefficient s and the Preisach's function Y is obtained as\n1435\n(9)\nMAGNETIZATION CHARACTERISTICS\nClassification\nm e n the flux B in (1) is sinusoidally varying with time, the resulting hysteresis loops can be roughly classified into two kinds of shapes: the one is normal and the other is square in their shapes. Each of them is further classified into two-types according to the frequency dependence. Figs. 3(a) and 3(b) show the typical B VS. H curves for P and @/at vs. H curves for s in (1) , respectively. combination of these curves in (I) when the flux B is sinusoidally varied yields the four kinds of shapes of hysteresis loop shown in Fig. 4.\n(a) Curves A and C. (b) Curves B and C." ] }, { "image_filename": "designv11_32_0001251_icit.2002.1189888-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001251_icit.2002.1189888-Figure5-1.png", "caption": "Figure 5 : Locating point P on local x-axis and et determination (xp > 0)", "texts": [ " Accordingly, the truck bed position and por:ture, (Xrrucki Ytruckr @truck) is translated into (x f j -wk> Yfruck, @truck) with respect to A, a particular point P(xp, y p ) on the local x-axis ofA classifies the algorithm into 3 cases. The point P is a cross point of the local x-axis and a line passing through (&ck, Am,) whose angle is @jruck. Then classified cases are: 1 1. 2 >OandO: c k # O 2. X' < 0 and @ruck # 0 3. e!ruTk=o. Casel: xb > 0 and Ofruck # 0 2. Drawing dotted line passing through point P(xb, 4) which divides H?Q into 2 equal half angles, HFD and D?Q. This step will produce @:(Figure 5) . 3. S(xb, A) is on the dotted line at distance rl, where rl = m, and in different quadrant from (.I,,,> d,,k)(Figure 5 ) . y , = rlsineb (6) Algorithm for locating the summit of v-shape S(x;,A) and orientation 0; can be concluded as follows: 1. After the local coordinate system A is set up, we draw line from T(xfrUckr with slope of tan e:, to local x-axis. This step will create point P(xb, .I{) at the intersection point on local x-axis. r2 is the distance from T to P(Figure 5). After a summit of the v-shape, S ( x t , A) and orientation e;, are located, two different paths on which WL is able to move can be demonstrated depend on the following two criteria: 1. rl 5 rz, then, the symmetrical clothoids, 0-S, and A section S-T' will be defined (see Section 3.). 188 IEEE ICIT'02, Bangkok, THAILAND 2 between T' and T will be tilled with a line, seginent(Figure 4). demonstrated as follows: The svmmetrical clothoid. 0-S will be defined. A section _ I , between S and 2 will be filled with a line segment, where will be ri > rz, then, the symmetrical clothoid, 0--S will be = r2/2, consequently, the symmehical c]othoid, Z-T defined" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002455_tmag.2005.862760-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002455_tmag.2005.862760-Figure2-1.png", "caption": "Fig. 2. Structure of the electromechanical converter.", "texts": [ " Nowadays, electromagnetic actuators have been successfully employed to convert electrical signals into mechanical movements in many applications due to their high level of driving force, rugged structure, and compact volume; however, the conventional high-response electromagnetic actuators such as solenoid or energy-stored actuator, are only suitable for ON\u2013OFF applications [1]\u2013[3], and the microelectromagnetic systems (MEMS) actuator could not provide sufficient driving force [4], [5]; therefore, they do not meet the demands of continuous control of the engraving system. This paper puts forward a new high-response moving-iron electromagnetic actuator; both the theoretical and experimental analysis are presented, and the actuator is practically applied into a real electronic engraving system to testify its engraving performance. The actuator shown in Fig. 2 consists of permanent magnets, \u201c \u201d type armature, an upper magnetic conductor, a bottom magnetic conductor, a magnetic isolator, a driving coil, and a linking rod that is linked to the engraving needle (not drawn out). The \u201c \u201d type armature, together with the output components, is shown in Fig. 3. The armature is fixed on the magnetic conductor by two cantilever beams, which not only support the armature but also act as high-stiffness springs through their elastic Digital Object Identifier 10.1109/TMAG" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003779_0369-5816(65)90138-9-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003779_0369-5816(65)90138-9-Figure4-1.png", "caption": "Fig. 4. Geometrical relations.", "texts": [ " APPLICATION OF THE THEORIES TO INTERSECTING SHELLS In o r d e r to be able to make use of the y ie ld loci for i n t e r s ec t i ng she l l s as r e p r e s e n t e d in sec t ion 2, some approx ima t ions to the shel l conf igura t ion mus t be in t roduced. Although the fo l - lowing a rgumen t holds t rue for any she l l of r e v o - lution, we r e s t r i c t o u r s e l v e s to the spec ia l c a se of a r a d i a l out let f rom a s p h e r i c a l she l l subjec t to in te rna l p r e s s u r e as shown in fig. 4. F o r the c y l i n d r i c a l p a r t of the she l l , the equat ions of equ i l ib r ium, with the notat ion of f ig. 5, a r e given by: dQ NO dMx + - - r = P ' dx - Q ' N x = \u00bdpr \" (10) F o r N o = const the in teg ra t ion of eq. (10) y i e ld s to (11) M x = \u00bd( , - ~ - ) x ' 2 + A x , B . The constants A and B can be evaluated using any suitable stress distribution, provided this assumed stress field nowhere exceeds any of the chosen yield surfaces of section 2, e.g. / a t x = l , Q = 0 , M x = M c , N o = N c , (12) a t x : 0 , Q : Q ' , M x : M ' c , NO : N c " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000028_auto.2000.48.4.157-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000028_auto.2000.48.4.157-Figure1-1.png", "caption": "Figure 1: The Acrobot", "texts": [], "surrounding_texts": [ "In the case of exact feedback linearization the control design problem is largely complete once the system is linearized. For partial feedback linearization with asymptotically stable zero dynamics local stabilization is easily achieved, but global or semi{ global stabilization requires consideration of issues such as peaking, etc. For the class of systems considered here, the collocated linearization approach above, generally result in systems having unstable zero dynamics. Thus the second stage control, i.e. the design of the outer loop terms u in (9), more to the point, the choice of u in (10), is nontrivial. To deal with this we will outline methods for the design of u that combines high gain and/or saturating controls with methods based on passivity and energy concepts. By exploiting the physical structure of the system in this way, we can achieve closed loop stability without requiring stable zero dynamics. In general, though, the stability achieved is not asymptotic to a xed point, but only to a manifold. For this reason, for problems such as swing up control of inverted pendula or the Acrobot, the control must eventually switch to a separate controller that achieves local asymptotic stability to the desired equilibrium con guration. We will illustrate these designs on several examples, without proof." ] }, { "image_filename": "designv11_32_0002338_j.jmatprotec.2006.03.081-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002338_j.jmatprotec.2006.03.081-Figure1-1.png", "caption": "Fig. 1. The kinematic structure of the developed robot.", "texts": [ " According to Pereira [3] and Tremonti [4] automated weldng would be the natural alternative for presenting advantages n relation to the manual process, such as: reduction of the ime that welders are exposed to unhealthy environment, better niformity and quality of the welding in the repaired areas, etter control of the geometry of the blades and reduction of he total cost in the recovery of hydraulic turbines. However onventional robot manipulators cannot be used for this task ecause constrains caused by limited workspace inside the otor of a hydraulic turbine. In the Roboturb project, a special robot was designed and uilt in a partnership among UFSC, LACTEC, COPEL and, ore recently, FURNAS. This robot, as shown in Fig. 1, has six 232 N.G. Bonacorso et al. / Journal of Materials Pro d a m T v d a \u201c d a t o t P t 2 a t o i f s r f 2 d s o z i p i e b s t z t z s i t t p r t m egrees of freedom and seven degrees of mobility. Six of them re due to revolute joints, J2\u2013J7, while the seventh degree of obility, joint J1, is given by the displacement on a flexible rail. his rail is conformed and fixed on free from surface through acuum clampers or magnetic bases. This robot has two end-effectors that are used alternately uring the tasks of recovery of eroded surfaces by cavitation, ccording to Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003458_tec.2007.895865-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003458_tec.2007.895865-Figure6-1.png", "caption": "Fig. 6. P \u2013Q diagram showing the stability limit of PSPRG.", "texts": [ " The air gap power is given by Pag = P + (I2 ds + I2 qs)Rm. (19) Substituting (12) and (17) into (19) yields Pag = V 2 m 2D2 Rm(2R2 m + X2 ds + X2 qs \u2212 2RmD) +(Xds \u2212 Xqs)(D \u2212 2Rm) sin 2\u03b4 \u2212Rm(X2 ds \u2212 X2 qs) cos 2\u03b4 . (20) Stability limits of this generator can be obtained by putting dPag/dt = 0; after some manipulations, an expression for the critical load angle can be derived as \u03b4cr = 1 2 tan\u22121 (2B/Xqs) \u2212 B2 \u2212 R B(R + 1) (21) where B = Rm/Xqs, and R = Xds/Xqs. Equation (21) gives the critical value of load angle in terms of machine\u2019s parameters. Fig. 6 gives the (P\u2013Q) power diagram corresponding to (18) with constant terminal voltage Vm. For given machine\u2019s parameters and terminal voltage, the maximum and minimum real and reactive power components can be easily computed. A standard stator frame initially used for a single-phase induction motor (capacitor-start, capacitor-run) rated at 1 HP, 220 V, four-pole, and 50 Hz was employed. A salient-pole rotor made of solid steel with dimensions chosen according to stator bore dimensions was used. The prime mover employed was a separately excited dc motor rated at 1" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001945_s0022-460x(77)80051-5-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001945_s0022-460x(77)80051-5-Figure7-1.png", "caption": "Figure 7. Composite of transition curves; co~ = 0\"0, 0.2 ..... 2.0.", "texts": [ " Ranges for t5 and ~ are given with each figure. Shading is intended to emphasize that the previously considered transition curves become surfaces when co~ is allowed as a third dimension. Hence, Figures 5-7 can be regarded as three-dimensional Strutt diagrams. In Figure 5, 1/o~ is varied from 0.0 to 0.1 in increments of 0.01. A decrease in em~x and the bending of the transition curves is evident as col ---> 2. Figure 6 also displays these features. These same features are once again evident in Figure 7, where cot is varied from 0.0 to 2.0 in increments of 0.2. The outstanding feature of Figure 7 is that transition curves emanating from 6 = 0 have positive ordinates. From this one can conclude that for col< 2, the equilibrium position 0 = rr cannot be rendered stable. 1. V. V. BOLOTIN 1964 The Dynamic Stability of Elastic Systems. San Francisco: Holden-Day. See p. 139. 2. W. MAGNUS and S. WINKLER 1966 Hill's Equation. New York: Interscience Publishers. See Section 1.2 and Chapter 7. 3. L. MEmoVITCH1970 Methods of Analytical Dynamics. New York: McGraw-Hill Book Company, Inc. See Sections 7" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001487_j.mechmachtheory.2004.05.004-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001487_j.mechmachtheory.2004.05.004-Figure1-1.png", "caption": "Fig. 1. A point-line.", "texts": [ " ie \u00bc ei; je \u00bc ej; ke \u00bc ek: \u00f05\u00de The conjugations 2 of the eight units are as follows: 1 \u00bc 1; i \u00bc i; j \u00bc j; k \u00bc k; \u00f0ie\u00de \u00bc ie; \u00f0je\u00de \u00bc je; \u00f0ke\u00de \u00bc ke; e \u00bc e: \u00f06\u00de The dual quaternion algebra has applications in spatial displacements [4,15,31]. A point-line contains a directed line 3 and the location of an endpoint along the line. A directed line can be represented with a unit line vector [30] or signed Pl\u20acucker coordinates [22]. The pointline representation can be constructed thereupon, and appears as a dual vector or signed Pl\u20acucker coordinates. The directed line passing through points E and H (see Fig. 1) can be represented by a unit line vector a _ : a _ \u00bc a\u00fe ea0 \u00f0jaj \u00bc 1; a a0 \u00bc 0\u00de; \u00f07\u00de in which a represents the unit vector along the oriented line, and a0 is the moment vector of the oriented line with respect to the origin of reference frame O-xyz. A unit line vector has six parameters, of which four are independent due to the two constraint conditions. The remaining issue is to define the location of the endpoint along the directed line. Let P be a reference point, N is the foot of the perpendicular from P to the point-line, and h the distance from N to the endpoint E" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003333_iccas.2008.4694276-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003333_iccas.2008.4694276-Figure1-1.png", "caption": "Fig. 1 Inverted pendulum on cart.", "texts": [ "nternational Conference on Control, Automation and Systems 2008 Oct. 14-17, 2008 in COEX, Seoul, Korea Control of the inverted pendulum on cart is a classical problem in control theory. The inverted pendulum on cart is the SIMO system where the force applied to the cart is the input and cart position and pendulum angle are the outputs of the system. Its structure, shown as in Fig. 1, composes of a cart and pendulum where the pendulum is hinged in series to the cart via a pivot and only the cart is actuated. These limited travels of the cart can be changed by changing the values of some designed parameters (a0 and b0). Although the inverted pendulum on cart is easy to be described, it is not easy to be controlled given its inherent instability and nonlinear characteristics. It is also a more challenging task to autonomously move the pendulum to the upright position from its pendent position and to keep it there", " For instance, the method using a PD controller for swinging up the pendulum is described in [1] which controls the cart\u2019s position to preassigned values obtained by observation, and the method using the energy control is explained in [2] in which the limitation of the cart travels is not considered. In this paper the controller is designed based on Energy Control Method [3] to swing up the pendulum from its pendent position to around the upright position within a limited travel of the cart without preassigned cart\u2019s position and Coefficient Diagram Method (CDM) [4] to stabilize the pendulum in the upright position while maintaining the cart at a certain position. The inverted pendulum on cart to be controlled is shown in Fig. 1. Where \u03b8 is the pendulum angle (rad), x is the cart position (m), M is the mass of the cart (kg), m is the mass of the pendulum (kg), l is the distance from turning center to center of mass of the pendulum (m), L is the length of the pendulum (m), c is the cart\u2019s friction coefficient (kg/s) and F is the force applied to the cart (N). The mathematical model of inverted pendulum on cart can be derived using Lagrange\u2019s equation. First, determine the kinetic energy T and potential energy E of the system\u2019s components in terms of generalized coordinates q " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001925_004051750507500216-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001925_004051750507500216-Figure1-1.png", "caption": "FIGURE 1. Air vortex twister in air-jet spinning.", "texts": [ " Oxenham and Basu [6] also studied the effect of jet design parameters, such as diameter and orifice angle, on the properties of air-jet spun yarns. In this paper, we take an analytical approach to the problem, and our design formulation embodies the essential relationships needed by engineers who have to design practical systems. In earlier work, (Zeng and Yu [12]) we used the CFD technology to simulate air flow in the nozzle of an air-jet spinning machine, and our numerical results showed that the vortex velocity (u) in the horizontal plane scales as u rn , (1) where n is a constant and r is the radius coordinate. Analytical Model Figure 1 illustrates the model of the air vortex twister (the nozzle) in air-jet spinning. Compressed air is forced into the twisting chamber from the air reservoirs through the jet orifices. The vortex air then twists the yarns. The system must obey the basic laws of mechanics. The momentum in the horizontal direction (Figure 2), ignoring the energy loss, gives N d 2 2 u0 cos D d 2 0 2 0 D/ 2 ur2drd , (2) where is the air density, u0 is the velocity at the jet orifice, u is the vortex velocity, D and d are diameters of the nozzle and the orifice, respectively, is the orifice angle, and N is the number of the orifices" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002625_978-1-84628-372-7_8-Figure8.18-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002625_978-1-84628-372-7_8-Figure8.18-1.png", "caption": "Figure 8.18. Snakelike robot using IPMC", "texts": [ " On the other hand, when m=1 g, the actuator with Cs+ can realize a wide range of walking speeds with low energy consumption. Note here that even if the average input power is increased in the case of Cs+, the walking speed is not increased because the walking pattern is not proper and the energy dissipated in a collision is increased. In the last section, it was shown that the efficiency of walking with different walking speeds was confirmed by numerical simulation. In this section, the effect is checked by a snakelike robot swimming in water experimentally. Figure 8.18 shows an experimental machine, a three-link snakelike swimming robot with IPMC actuators. The frame of the robot is made of styrene foam. Thin fins are attached to the bottom of the body frame, and each frame is connected by an IPMC film. The total mass of the robot is 0.6 g and its total length is 120 mm. The IPMC film which we used in this experiment is Nafion\u00ae117 (by DuPont) plated with gold; the thickness of this film is about 200 m in a wet condition, and it was cut into a ribbon with a width of 2 mm and length of 20 mm. To check the performance of the robot, we also performed experiments using the snakelike robot as shown in Figure 8.18. Figure 8.19 shows the experimental results with input signals whose cycle is 2 s, amplitude is 2.5 V, phase shift is 90 , and the kind of counterion is sodium (Na+). From figures (a) and (b), it can be confirmed that the robot performs an undulating motion and moves forward. Figure 8.20 shows sequential photographs of the experiment. For more details of the experimental setup and the properties of the motions, refer to 0. To verify the doping effect, we performed experiments on IPMC actuators which were doped with Na+, Cs+ and TEA+ as counterions" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003467_iccas.2008.4694197-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003467_iccas.2008.4694197-Figure1-1.png", "caption": "Fig. 1 Schematic Model by using Brush Motor.", "texts": [ " FLOOR-TYPE IDENTIFICAITION In this section, we describe sensing method for floor-types identification. We decided to use a side brush attached on a vacuum cleaning robot for the identification of floor-types such as wood, marble and carpet. Keywords: Wheel robot, Floor-types identification , Sensing method, Impedance variation, Brush motor The side brush is used to clean and sweep the dust in the vacuum cleaning robot. The presented method uses existing components, side brush, to identify floor-types by using impedance variation. Fig. 1 shows the method that perceives the variation of a load while spinning the brush on the floor. Then the load\u2019s variation causes voltage level to change depending on the floor-types. The proposed method is to perceive the differences between the soft and hard floor based on load variation. For example, the brush motor\u2019s load increases in the soft floor-types: a carpet. However, the brush motor load decreases in the hard floor-types: a wood. The purpose of modeling an electrical motor is to describe observable phenomena while keeping the model representation" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003876_2013.38674-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003876_2013.38674-Figure4-1.png", "caption": "FIG. 4 Vibrometer consisting of a spring supported mass driving a pententiometer by means of a stranded cable.", "texts": [ " The seat was attached to the top end of a verti cal guide to which the cylinder was also mounted so that moments would TRANSACTIONS OF THE ASAE 1970 not be transferred to the relatively small cylinder piston rod (Fig. 3) . Also shown in this figure are the physi cal relationship of the components to each other. The c h a s s i s - m o u n t e d vibrometer which was used as a detector of vibra tional motion consisted of a springsupported se i smic mass m o u n t e d around a vertical shaft on a linear bearing with freedom to move verti cally (Fig. 4 ) . In order to effectively sense position for low frequency, the mass was sprung very softly having a natural frequency of about 0.5 Hz. To circumvent the problems of large spring deflections commonly associated with such a low natural frequency, a lever was used so that the spring could be attached to a short arm and the mass to a long arm. A light-stranded cable attaching the lever arm to the mass passes over a pulley on a poten tiometer shaft which it rotates to pro duce a signal proportional to the posi tion of the mass" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002891_1.5061089-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002891_1.5061089-Figure6-1.png", "caption": "Fig. 6 Schematic representation of microfocused X-ray transmission in-situ observation system during CO2 laser welding and specimen used .", "texts": [], "surrounding_texts": [ "Matsunawa Laboratory In Matsunawa laboratory, a variety of studies were performed from 1980 to 2002. The themes are as follows: \u201cPlume behavior and its interaction to laser during pulsed YAG laser irradiation\u201d, \u201cSurface nitriding and boronizing by laser irradiation\u201d, \u201cLaser production of various ultrafine particles\u201d, \u201cLaser surface amorphization of alloys\u201d, \u201cInterpretation of laser-rapidly solidified microstructure of stainless steel\u201d, \u201cCeramic coating by Laser PVD/CVD\u201d, Modeling of laser spot melting and solidification\u201d, \u201cLaser weldability of shape-memory alloy, aluminum alloys, stainless steels, etc.\u201d, \u201cLaser rapid solidification microstructure and microsegregation of aluminum alloy single crystals\u201d, \u201cLaser welding of Zn-coated steels\u201d, \u201cLaser welding of magnesium alloys\u201d, \u201cElucidation of laser welding phenomena\u201d, \u201cElucidation of formation mechanisms of laser welding defects and development of their remedies\u201d, \u201cEffect of pulse-shaping on laser spot weldability of stainless steels and aluminum alloys\u201d, \u201cLaser welding of dissimilar metals\u201d, \u201cLaser spot welding under vacuum and microgravity\u201d, \u201cSimulation of front keyhole wall dynamics during laser welding\u201d, \u201cMonitoring during laser spot welding\u201d, \u201cEffect of superimposed laser beams of different wavelengths on melting-ability\u201d, \u201cMelt flows inside molten pool during laser welding or arc welding\u201d, and so on. TEM photos of ultrafine Fe particles (at lower and higher magnifications) formed during YAG laser spot welding are shown in Fig. 115). It was confirmed that ultrafine particles were always formed during laser welding. Figure 2 shows simultaneous optical measurement methods of temporal variations in transmission of a He-Ne probe laser (\u03bb=633 nm), intensity of neutral atomic spectral line (\u03bb=411 nm) and scattering of an incident YAG laser beam to the right angle during laser irradiation3). The measured results are shown in Fig. 33). As shown in (a), the transmittance of Page 361 Laser Materials Processing ConferenceICALEO\u00ae 2007 Congress Proceedings the probe laser drops sharply at a certain period after YAG laser irradiation initiation and keeps low level until the laser power decays. Accordingly, variations in spectral line intensity and scattering intensity of incident laser are detected in (b) and (c). Such variations are attributed to the Rayleigh scattering due to ultrafine particles during laser welding3). The effects of pulse shaping on weldability were elucidated as shown in Figs. 4 and 55,6). Welding defects such as porosity, cracking and underfilling could be reduced under the proper pulse shapes of laser power obtained on the basis of welding phenomena. Two systems using microfocused X-ray transmission apparatuses were constructed for the evaluation of effect of porosity on mechanical properties of the welded joints and observation of porosity formation situation18,20). The observation system during hybrid welding is shown in Fig. 623). Keyhole behavior, melt flows and the situation of bubbles and porosity formation inside the molten pool were observed. Examples of observation results in Type 304 and A5083 during CO2 laser welding at 10 kW in He shielding gas are shown in Fig. 718). It was understood that a keyhole was fluctuated and melt flows inside the molten pool were caused by recoil pressure of evaporation and sometimes surface tension. In N2 or Ar shielding gas, a big gas plasma was formed, as shown in Fig. 823). Welding phenomenon was similar to pulsed laser welding. The melt flows inside the pool and bubble and porosity formation mechanisms were different depending upon the welding conditions, as shown in Fig. 917). Porosity decreases with the increase in welding speed. Full penetration welding, pulse modulation welding, vacuum welding, forward inclined laser beam welding, etc. were confirmed to be effective to the reduction in porosity. Porosity was reduced in austenitic stainless steels welded with CO2 laser or YAG laser in N2 gas22). Page 362 Laser Materials Processing ConferenceICALEO\u00ae 2007 Congress Proceedings Page 363 Laser Materials Processing ConferenceICALEO\u00ae 2007 Congress Proceedings III. Some Fruitful Results Obtained in Succeeded Katayama Laboratory The plume-laser interaction during YAG or fiber laser welding was investigated by the special visualized observation and measurement system, as schematically shown in Fig. 1016). Fiber laserinduced plumes and probe laser beams were simultaneously observed by high speed video camera during fiber laser welding at the extremely high power density of 0.9 MW/mm2, and Fig. 11 shows the results17). The blue white plume and the orange one were observed near the surface and in the upper part, respectively. The plume was periodically ejected from the keyhole inlet. It was confirmed that the interaction between the plume and the probe laser was small since the maximum and average refraction angles were less than 2 and 0.4 mrad, respectively, and the attenuation of the probe laser at 3 mm above the surface was about 4.5 %. The attenuation was clearly attributed to the Rayleigh scattering (which expresses that the attenuation is proportional to \u03bb-4 in the case of particle sizes < \u03bb) caused by ultrafine particles during laser welding, as shown in Fig. 12. According to the spectroscopic analysis result of the plume at 2 mm above the keyhole inlet from Type 304 steel, neutral lines of Fe and Cr were mainly detected, but neither clear lines of alloying element ions nor Ar atom neutral lines were detected. According to the Saha equation, the temperature of the plume was estimated to be about 6,000 K, which suggests that the plume should be in the weakly ionized state. Consequently, a focused 10 kW fiber laser beam produced a weakly-ionized plume. However, the weakly ionized plume exerted slight effects on the Las LasBubKeyhpo Page 364 Laser Materials Processing ConferenceICALEO\u00ae 2007 Congress Proceedings refraction and the attenuation of the fiber laser beam. From such high-speed video observation pictures, the mechanisms of humping and spattering or underfilling can be interpreted. To understand melt flows on the molten pool surface during TIG-YAG hybrid welding, the movement of ZrO2 particles was observed with a high-speed video camera. Examples of surfaces observed at 100 and 200 A are shown in Fig. 14 (a) and (b), respectively17,26). At 100 A, ZrO2 particles approached a keyhole inlet but flew out accompanying with plume ejection. Nevertheless the particles approached again probably due to the surface tensiondriven flows and the electromagnetic convection. At 200 A, the surface of the molten pool was concave due to the arc pressure, and ZrO2 particles approached a keyhole inlet but soon flew away due to a strong arc plasma stream in addition to the plume ejection. The cross sections and X-ray inspection results of weld beads, and transmission observation results of molten pools during hybrid welding are shown in (P1 = 3.3 kW, v = 10 mm/s, fd = 0 mm, \u03b1 = 55 deg, h = 2 mm, d = 5 mm, Shielding gas: Ar ( 5 x 10 \u20134 m3/s )) Page 365 Laser Materials Processing ConferenceICALEO\u00ae 2007 Congress Proceedings the air are schematically summarized in Fig. 1626). In the YAG laser welding, bubbles are generated from the bottom part of the keyhole probably due to intense evaporation of metal or keyhole collapse. The bubbles are trapped by the solidifying front, resulting in the formation of porosity. At 100 A, a keyhole is slightly larger and deeper, since the surface tension driven flows and electromagnetic flows superimpose the downward flows of the melt near the keyhole wall and thereafter the melt flow from the keyhole tip to the rear part along the bottom of the molten pool. The formation of bigger bubbles increased the porosity. At 200 A, the surface of the molten pool is concave, the keyhole inlet diameter is larger, and other fast melt flows due to arc plasma stream exert to widen the bead width. Laser brazing phenomena were also observed by high-speed video camera and microfocused X-ray transmission observation system, as shown in Fig. 1728). It was confirmed that the formation mechanisms of pit and pore (porosity) were different. The method using monitoring and adaptive control is in the advanced stage. Figure 18 shows pulsed YAG laser welding system with monitoring and adaptive control9). The spot lap welds produced by YAG laser are shown in Fig. 199). An example of monitoring results of a reflected laser beam and heat radiation signal is shown in Fig. 209). Under normal pulse laser irradiation, some good or bad spot welds are formed, but sound spot welds can always be produced under the monitoring of heat radiation signal (in this case) and adaptive control of laser power and irradiation period. It is feasible to make a sound spot weld with YAG laser under the monitoring and adaptive control. Such adaptive control work has been extended to cw laser welding and performed during welding12). Page 366 Laser Materials Processing ConferenceICALEO\u00ae 2007 Congress Proceedings Page 367 Laser Materials Processing ConferenceICALEO\u00ae 2007 Congress Proceedings" ] }, { "image_filename": "designv11_32_0002625_978-1-84628-372-7_8-Figure8.12-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002625_978-1-84628-372-7_8-Figure8.12-1.png", "caption": "Figure 8.12. Model of bipedal walking robot", "texts": [ " In figure (b), the control voltage of the experiment and simulation are shown and we can see some deviation. Especially, the actual control voltage gradually increased due to integral operation. The reason inferred for the deviation is that such a slow mode was not identified by our Hammerstein model. We consider, however, that our model is valid for a periodic motion with a short period considered below. This section addresses an application of the linear actuator to a small-sized bipedal walking robot shown in Figure 8.12, and realization of walking with the proposed actuator is investigated by numerical simulations. The parameters of the robot are set as ml =5 g, mh =10 g, a=50 mm, b=50 mm, l=100 mm, rh =4 mm, g=9.81 m/s2, and rf =0 mm. This small bipedal robot can exhibit passive dynamic walking 0 without any actuator on a gentle slope. In the following simulation, we assume that actuators are attached between legs, as in the right side of Figure 8.12. In the simulations, we assume that contact between a leg and ground is pin contact and collision of the swing leg with the ground is perfectly inelastic. Figure 8.13 shows the simulation results of walking on level ground. The number of units connected in parallel and series is set as 4 and 3, respectively. In this simulation, we applied a square pulse as input voltage whose cycle was 0.48 s and whose amplitude was 2.5 V. From the results, it can be seen that a one-period walking gait is generated and the walking cycle synchronizes with the cycle of the input signal" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003745_tpwrd.2010.2068567-Figure18-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003745_tpwrd.2010.2068567-Figure18-1.png", "caption": "Fig. 18. Deformation of the V-shape porcelain insulator string (XP1-300, 80 ). (a) Initial status. (b) Deformation in the maximal load.", "texts": [], "surrounding_texts": [ "presented in Fig. 16. The structure height of the 750-kV composite insulator is 6.8 m and the diameter of the core rod is 30\nmm. The weight of the composite insulator is 45 kg. The types of porcelain insulators were XP1-300 and XWP2-300.\nThe applied vertical load was 47.6 kN. The maximum horizontal force was 94 kN. Cx represents the V-shape insulators. P is the link plate. V is the basket for the vertical load. L is the equipment for applying the horizontal load.\nThe load performance of the V-shape insulators (composite and porcelain) has been investigated in the condition of different included angles (70\u2013105 ). The initial and deformation shape of the V-shape composite insulator when loaded gradually is presented in Fig. 17. It is found that the insulator bearing pressure would be deformed of buckling. The buckling shape is similar to the results of stress calculation. The initial status and deformation shape of porcelain insulator strings (XP1-300 and XWP2-300) are presented in Figs. 18 and 19. When the horizontal load is strong enough, one string of the V-shape porcelain insulator will begin to sag and appear to be catenary, which is agreed with the calculation results for the deformation shape of the porcelain insulator string.\nThe displacements of the V-shape insulators were varied when the horizontal load was increased gradually. The experimental relation of displacements and load ratio (vertical load/horizontal load) is shown in Figs. 20 and 21. It is found that the displacements were increased after the V-string was deformed with the horizontal loads applied strong enough. The deformation of theV -string occurred easily with a small included angle. Comparing the experimental results of Figs. 20 with 21, under the large horizontal load, the displacement of composite insulators is smaller than that of the porcelain", "insulator string because of the composite insulator\u2019s buckling performance.\nThe calculation and experimental results of the composite and porcelain insulators are shown in Tables II\u2013IV. The load ratio in the table is calculated from the parameter of three tower types shown in Table I. The experimental value is obtained from the fitting value of measurements. Good agreement between calculation and experimental results is demonstrated. It is shown that the calculation results are reliable in the application of engineering. The reasons for the discrepancies are: 1) resolution limitations of the range finder and force sensor; 2) revised force for the movement of the link plate; 3)influence of friction among the parts (connection hardware and insulators) in the calculation model; and 4) absent consideration of the single insulator performance in the string. The discrepancy of relative rotation in the adjacent insulators can be cumulated to influence the entire mechanical performance of the insulator string.\nIn the ordinary design consideration for the included angle of the V-shape insulator string, it is requested that the V-shape included angle be no more than twice that of the maximal windage yaw angle of I-shape insulators with the same configuration. In this situation, not one of the strings of the V-shape insulator would be bearing pressure when maximal windage yaw took place. In addition, it is proposed in some publications that the difference of the V-shape string\u2019s included angle with twice the amount of I-shape maximal windage yaw angle be less than 6 , or it is said that the deflection angle (as shown in Fig. 6) of the V-shape insulators is less than 7 . These considerations are based on experience, and little attention is paid to the calculation or experiment for the deformation of the V-string.\nIn this paper, the improved selection method is discussed according to the calculation and experiment. The consideration for the selection of included angle meets the requirements: 1) avoidance of the insulators\u2019 broken in the condition of maximal windage yaw of transmission line and 2) assurance for the insulation performance of the air gap in the windage yaw of the transmission line.\nThe first requirement has been discussed in Section II, the conclusion about mechanical performance of composite and porcelain insulators has been drawn from Figs. 8 and 14, respectively. For the second requirement, when an included angle of V-string is more than 80 , the insulation distance between the electrical conductor and tower is agreed with the demand", "of an ac flashover voltage of 750-kV compact transmission in the situation of maximal windage yaw. Consequently, a smaller included angle can be selected appropriately. The consideration applied in the design can make the tower size smaller and reduce the right of way of the overhead line to some extent.\nIt is noted that the drop of V-shape insulators has occurred in the overhead transmission line because of the broken connection between the hardware and insulator in the windage yaw of the transmission line [9], [10]. Thus, the deflection angle of V-shape insulators should be limited to a certain range in the windage yaw. In this paper, the deflection angle of composite and porcelain insulators is limited less than 15 and 10 , respectively. Referring to Figs. 7(c), 12(c), or Fig. 13(c), the recommended value of the V-shape include angle selected for 750-kV compact transmission line is shown in Tables V and VI. The two type of porcelain insulators (XP1-300 and XWP2-300) have similar results, so the recommended conclusion is shown in Table VI accordingly.\nThis paper presented a new approach for calculating the deformation of the V-shape insulator string. The solution, including calculation and experiment, will be applied to included angle selection for the V-string in the 750-kV compact transmission line. The degree of swing and stress in the structure of V-shape insulators is related closely to the included angle. The calculation for the deformation of the V-shape insulator string (composite and porcelain) with different included angles shows good agreement with the experimental results. According to" ] }, { "image_filename": "designv11_32_0002483_s00542-006-0305-x-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002483_s00542-006-0305-x-Figure7-1.png", "caption": "Fig. 7 Distribution of static friction coefficient over contact zone in herringbone groove bearing", "texts": [ " This interesting result explains well why extremely light sliding contacts lubricated with activated additives, as observed in high precision sliding guides, etc., generally exhibit very low friction and wear characteristics. In this case, thick adsorbed surface films are formed through the chemical adsorption of activated additives in the lubricant. Table 1 shows the geometrical parameters of the herringbone groove and multi-taper bearings used in the following friction and wear analysis, and Table 2 shows the combined roughness parameters and other physical parameters. Figure 7 shows the distribution of the static friction coefficient at the contact between the journal and herringbone groove bearing (HB). It can be seen that the static friction coefficient is not distributed uniformly and the maximum values occur at the circumferential contact border where the contact pressure is decreased to near zero. Thus, the static friction coefficient used in common practice represents the mean value of a non-uniformly distributed friction. Figure 8 illustrates the trajectories of the journal in herringbone groove and multi-taper bearings during the beginning of startup" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001057_007-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001057_007-Figure4-1.png", "caption": "Figure 4 Courbes experimentales de la loi de vitesse en fonction du temps aprts llchage pour trois billes, dont les caractkristiques sont donnies sur le tableau 1 (Bchantillons 3, 1, 2, de bas en haut). Les nombres B l\u2019interieur des cercles representent la distance parcourue B ces diffirents temps comptee en termes du nombre de diamttres de billes. Le dicrochement, analysb dans cet article, se produit pour un temps correspondant au parcours par la bille de 1.5 diamttres. La ligne en tirets verticale correspond au temps, le m&me pour les trois billes, ob celles ci quittent une trajectoire verticale.", "texts": [ " 5 0 ~ 50x 60 cm de haut rempli d\u2019eau, nous avons Ctudit la loi de montCe de billes sphkriques rigides de diamgtre (2R = 1 i 5 cm) et de masse volumique pR inftrieure i celle de I\u2019eau IachCes sans vitesse initiale i partir du fond i un instant initial par un dispositif ClectromagnCtique. Dans la bille a CtC noyCe une petite aiguille magnCtique placCe symetriquement ou non par rapport au centre de masse de la bille. Dans ce dernier cas, I\u2019aiguille introduit un petit couple de rappel dans son mouvement. Le mouvement de la bille CclairCe h intervalles rCguliers par un stroboscope est suivi en pose sur une plaque photo (figures 1 i 3). Le tableau 1 et la figure 4 rassemblent un certain 228 P Boum\u2018er, E Guyon and J P Jorre nombre de rCsultats pour trois billes diffCrentes par leur diamktre et leur masse volumique. Nous allons en dCcrire successivement les ClCments en prenant l\u2019example de la sphkre No 1, dont la figure 5 donne la loi de vitesse en fonction du temps. On distingue Figure 4 Experimental curves giving the ascent velocity as a function of time for three spheres whose characteristics are given in table 1 (spheres 3,1,2 from bottom to top curve). The numbers inside the circles give the disiance, evaluated in terms of number of diameters of the sphere. The sharp break in the curve, analysed in the article, takes place after a displacement of 1.5 diameters for the different spheres. The vertical dotted line gives the time of departure of the vertical trajectories (see figure 2) and is the same for the three spheres" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003759_1.3650622-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003759_1.3650622-Figure3-1.png", "caption": "Fig. 3 Free-body diagram of foil near central boundary", "texts": [ " Equation (146) is a linear third-order equation, the solution to which is The conditions stated in the foregoing come from the definition of the problem. In addition to these conditions, the gap has to be the same in both regions at the boundary between the two regions, AC AH = Aemyx + Bemyx + De'\"\u2122 + \u2014 where ?ii, n2, and n3 are roots of the equation n* - \u2014 n2 + 1 = 0 7 (15) (16) (10) The slope of the foil at the boundary between regions 1 and 2 has to be the same. This can be seen by examining a small piece of foil near the boundary, Fig. 3. Equating forces along x on both sides of the boundary pAx sin 9i \u2014 T cos 0i = pAx sin 02 \u2014 T cos 0-, (11) Equating forces along y on both sides of the boundary pAx cos Qi - T sin ft - pAx cos 02 + T sin 02 (12) At the boundary where Ax = 0, equations (11) and (12) can be satisfied only if Ot = 0> or The form of equation (15) is thus a function of the parameter A / 7 only. It is therefore this parameter, and not A alone, which determines the effect of fluid compressibility in foil bearings. Equation (16) has one real and two complex roots when A / 7 is less than 1" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002754_j.mechrescom.2007.01.001-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002754_j.mechrescom.2007.01.001-Figure2-1.png", "caption": "Fig. 2. Elastic body with defects at positions 1 and 2 displaced within the material by k1 and k2, respectively.", "texts": [ " Equating (6) and (7) and cancelling equal terms results in Eq. (1). The objective of the present contribution is to establish novel reciprocity theorems in material space (i.e., in Eshelbian mechanics) analogous to the classical (or standard) reciprocity theorems in Newtonian mechanics mentioned above. For this purpose, we focus attention on two localized defects at points 1 and 2 in a linearly elastic stressed body of arbitrary shape and arbitrary distribution of further defects and possibly inhomogeneities, Fig. 2. As already mentioned, the material forces are the negative gradients of the total potential energy with respect to the position of the defect within the material (details may be found, e.g., in the monographs Kienzler and Herrmann, 2000; Maugin, 1993; Gurtin, 2000). Thus, in general, in an arbitrarily stressed body, material forces will be acting throughout and will be especially concentrated at the two localized defects under consideration. In consonance with the meaning of materials forces, if a defect is displaced within the material by a certain amount, work will be done by the material force in this material displacement and the stored energy of the whole system will also change as a consequence", " The work done by k1 then is W 21 \u00bc k1 \u00f0B10 \u00fe B12\u00de \u00fe 1 2 k1 B11; \u00f011\u00de and again, the material force at 2 does not contribute to W21. Since the total work after application of material displacements k1 and k2 is independent of the order of application we obtain the result k1 B10 \u00fe 1 2 k1 B11 \u00fe k2 \u00f0B20 \u00fe B21\u00de \u00fe 1 2 k2 B22 \u00bc k2 B20 \u00fe 1 2 k2 B22 \u00fe k1 \u00f0B10 \u00fe B12\u00de \u00fe 1 2 k1 B11; \u00f012\u00de or, after cancelling terms k2 B21 \u00bc k1 B12; \u00f013\u00de which states a novel theorem in Eshelbian mechanics, analogous to Betti\u2019s theorem according to Marguerre (1962); or Maxwell\u2019s theorem according to Barber (1992); cf. Fig. 2. Introducing analogously to physical space the component of B21, in the direction of k2 as BP 21, the component of B12 in the direction of k1 as BP 12 and the magnitudes of k1 and k2 as k1 and k2, respectively, we arrive at a scalar version of (13) as k2BP 21 \u00bc k1BP 12: \u00f014\u00de For k1 = k2 we have BP 21 \u00bc BP 12; \u00f015\u00de which is analogous to Maxwell\u2019s theorem according to Achenbach (2003). It states that the change in the component of the material force at point 2 in the direction of the material displacement produced at point 1, equals the change in the material force component at point 1 produced by an equal material displacement at point 2" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002830_13506501jet258-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002830_13506501jet258-Figure1-1.png", "caption": "Fig. 1 (a) Bearing geometry and nomenclature. (b) Unwrapping of bearing. The cross-sectional areas of the two regions are equal. (c) Isometric view of the FE mesh of the model", "texts": [ " The energy equation is likewise discretized using the SUPG FE formulation to produce Nv\u2211 j=1 \u222b e { w\u0303i ( 1 \u2212 \u03bb\u0304 ( Nve\u2211 k=1 N ve k T\u0304 e k \u2212 1 )) \u00d7 [( Nve\u2211 k=1 u\u0304e kN ve k ) \u2202N ve j \u2202 x\u0304 + ( Nve\u2211 k=1 v\u0304e kN ve k ) \u2202N v j \u2202 y\u0304 + ( Nve\u2211 k=1 w\u0304e kN ve k ) \u2202N v j \u2202 z\u0304 ]} + 1 Pe [( \u2202Wi \u2202 y\u0304 \u2202N v j \u2202 y\u0304 )] T e j = \u222b e w\u0303i PrEc Pe ( exp ( \u2212 ( Nve\u2211 k=1 N ve k T\u0304 e k ))) \u00d7 \u23a1\u23a3 \u2202 \u2202 y\u0304 \u239b\u239d( Nve\u2211 k=1 u\u0304e kN ve k )2 + ( Nve\u2211 k=1 w\u0304e kN ve k )2 \u239e\u23a0\u23a4\u23a6 \u2212 [( Nve\u2211 k=1 u\u0304e kN ve k ) ( d dx\u0304 ( Nve\u2211 k=1 N ve k p\u0304e k )) + ( Nve\u2211 k=1 w\u0304e kN ve k ) ( d dz\u0304 ( Nve\u2211 k=1 N ve k p\u0304e k ))] (2) where Nv is the number of volume (brick) elements, N ve k is the shape function of the kth volume element, Wi and w\u0303i are the Galerkin and SUPG weighting functions, respectively, T\u0304 = \u03b2(T \u2212 Ti) is the nondimensional temperature, \u03bc\u0304 = exp[\u2212T\u0304 ] and \u03c1\u0304 = 1 \u2212 \u03bb\u0304(T\u0304 \u2212 1) are used for non-dimensional viscosity and pressure, respectively, and the superscript e represents the variable at the elemental level. Figures 1(a) and (b) show the journal bearing template while Fig. 1(c) is the isometric view of the FE mesh. Appropriate boundary conditions must be applied at the rupture and reformation interfaces [4]. Periodical boundary conditions are applied at both the ends of the bearing template. 2.2 Formulation of model equations The method proposed here follows Jang and Khonsari [5] and Khonsari et al. [12]. A brief procedure of the method is given here for continuity. 1. Compute the Sommerfeld number S. Proc. IMechE Vol. 221 Part J: J. Engineering Tribology JET258 \u00a9 IMechE 2007 at UNIV PRINCE EDWARD ISLAND on February 24, 2013pij", "9 (4) where the coefficients were determined empirically by Gadala and Zengeya [2] who simulated pressurefed bearings in the literature and did curve-fitting to the data given that Q\u0304L = f (\u03b5, \u03bb). Results from equation (4) consistently gave better predictions compared to Jang\u2019s equation for the bearings simulated. Leakage due to supply pressure Qp is determined as proposed by Martin [13]. A brief description of the method is included here for continuity. For the case where the oil groove is opposite the load line (Fig. 1(b)) Qp = fg(1 + \u03b5 cos \u03d5)3(psC 3/\u03bci), where fg is a groove function which depends on the groove location and dimensions. Total leakage is determined by finding a datum flow, Qm, which calculates the flowrate by ignoring oil film continuity Qm = QL + Qp \u2212 0.3 \u221a QLQp, then corrected for film reformation. Total leakage is determined as QL,tot. = QS \u2032 m Q1\u2212S \u2032 p where S \u2032 = 0.7(Lg/L)0.7 + 0.4 for an axial groove of length Lg. An important consideration in flow computation is where the hydrodynamic film starts", "comDownloaded from lb lower bound L bearing width (z-dimension) (m) Lg length of groove (m) Ni finite element basis functions Nv number of volume elements N ve k shape function of the kth volume element Ns journal speed, revolutions/second (rps) pa maximum allowable pressure (Pa) Pe Peclet number, Pe = \u03c1acp\u03c9C 2/kf ps supply pressure (N/m2) PL power loss (W) Pr Prandtl number Pr = cp\u03b7/kf P\u0304 non-dimensional pressure Q volumetric flowrate (m3/s) QL leakage flowrate (m3/s) R1, R2 bush, shaft radius (m) T lubricant temperature (K) Ti inlet temperature (K) To ambient temperature (K) Ts shaft temperature, (K) ub upper bound U shaft surface velocity (m/s) wg width of groove (m) W load on bearing (N) Wi Galerkin weighting function x, y, z coordinates in the circumferential, radial, and axial bearing directions \u03b1 thermal diffusivity of lubricant (m2/s) \u03b11, \u03b12 weighting parameters \u03b2 temperature-viscosity coefficient (1/K) \u03b21, \u03b22 scaling parameters 1 boundary surface on domain \u03b4 thermal compressibility of fluid (m3/K) \u03b5 eccentricity ratio, \u03b5 = e/C \u03b8 circumferential coordinate of angle from line through minimum film thickness position (Fig. 1) (rad) \u03ba1, \u03ba2 temperature rise parameters \u03bb length to diameter ratio (L/D) \u03bc fluid viscosity (Pa s) \u03bci inlet viscosity (Pa s) \u03c0D bearing length (x-dimension) (m) \u03c1 density of lubricant (kg/m3) \u03c1o inlet density (kg/m3) \u03d5 attitude angle (Fig. 1) (rad) \u03d5cav angle from load line to the cavitation boundary/interface (rad) \u03c9 angular speed (rad/s) \u03c9cr critical whirl speed (rad/s) volume domain, discretized for finite element Superscript \u2018\u2212\u2019 indicates a non-dimensional parameter Non-dimensional parameters Note: Re, Pe are local, not global). u\u0304 = u U v\u0304 = R C v U w\u0304 = w U x\u0304 = x 2\u03c0R y\u0304 = y h z\u0304 = z L/2 T\u0304 = \u03b2(T \u2212 Ti) \u03bc\u0304 = \u03bc \u03bci \u03c1\u0304 = \u03c1 \u03b4\u03c1o h\u0304 = h C \u03b2\u0304 = \u03b2Ti \u03b1 = kf \u03c1cp P\u0304 = C 2P \u03bcR2Ns \u03bc\u0304 = exp[\u2212\u03b2\u0304(T\u0304 \u2212 1)] Re = \u03c1CU \u03bc Pr Ec = \u03b7aU 2 kf Ti \u03ba1 = \u03b1 kf \u03bci\u03b2\u03c9 ( R C )2 \u03ba2 = \u221a \u03bci\u03b2 kf U APPENDIX 2 Optimization procedure The procedure presented here will help designers to implement the optimization model proposed" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003383_iccas.2007.4407013-Figure9-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003383_iccas.2007.4407013-Figure9-1.png", "caption": "Fig. 9 Diagram for NGL.", "texts": [ " NGL is motivated from Proportional Navigation (PN). NGL contains an anticipatory control feature which overcomes the inherent limitation of feedback control in following curved paths. NGL is composed of two elements. The first element is the selection of a reference point, and the second element is the generation of lateral acceleration command. First, the reference point at each instant is chosen on the desired path, and at a certain distance ( 1L ) from the vehicle in the forward direction as shown in Fig. 9. Then, the lateral acceleration command is generated by the following Equation [10]. \u03b7sin2 1 2 L Va cmds = (1) Where V is velocity, 1L is the reference point on the desired path at a distance ( 1L ) forward of the vehicle. In this simulation, the leader UAV maintains the airspeed to 20 m/s and altitude 200 m . The leader sends its position and velocity information 20 times a second to GCS while GCS sends leader information at the same rates to other formation members. Each UAV has its own formation position in the formation group" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001933_05698190590948232-Figure14-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001933_05698190590948232-Figure14-1.png", "caption": "Fig. 14\u2014Structure drawing of face-to-face double seal with self-circulating screw pump: 1, primary ring; 2, rotating seat; 3, 0-ring secondary seal; 4, spring; 5, case; and 6, retainer.", "texts": [ " D ow nl oa de d by [ E rc iy es U ni ve rs ity ] at 1 5: 28 2 9 D ec em be r 20 14 Example 1 The wet-gas compressor is the key equipment in the oil-refining process. To meet the requirement of production with long period, high reliability, and low leakage, it is very important to select the type of its shaft end seal. The main parameters of the centrifugal compressor used in a certain oil refinery are given as follows. The sealed gas media is wet gas, suction pressure 0.25 MPaA, discharge pressure 1.70 MPaA, rotating speed 10,000 r/min, and seal size 137 mm. As shown in Fig. 14, a noncontacting, zero-leakage double seal with double-row spiral grooves was used. Its supporting system is like that shown in Fig. 4, in which a self-circulation screw pump combined with a controller of oil-gas-pressure difference is adopted. As compared with the supporting system by means of outside circulation, it has the advantages of power savings and simplicity of operation. Because wet gas is very dirty and inclinable to coke, a prepositive buffer seal near the process gas side was adopted to ensure the face seal with spiral grooves had an ideal working environment, in which a patented technology was used (Wang (4)). A section of sleeve-type seal combined with a section of labyrinth seal, shown in Fig. 14, was used as the buffer gas seal. The sleeve-type seal is mainly used to prevent the process gas concentration diffusion D ow nl oa de d by [ E rc iy es U ni ve rs ity ] at 1 5: 28 2 9 D ec em be r 20 14 Fig. 16\u2014Principle of the supporting system adopting an outside circulation manner. with a very high efficiency (Wang (5)). The buffer gas flow rate is controlled by a sonic orifice and its control principle is shown in Fig. 15. So, a very small buffer gas flow rate about 5 standard cubic meters per hour for one shaft end of the compressor is enough to completely keep the dirty process gas from the face seal" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003328_08ias.2008.180-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003328_08ias.2008.180-Figure2-1.png", "caption": "Fig. 2. BEGA steady state vector diagram at unity power factor a) motoring mode b) generating mode", "texts": [ " During the unity power factor operation (with zero dI and zero q\u03a8 ), from (1)-(5), the steady-state dq equations of BEGA become: constIILIRV qksfmfrqkss ==+= I \u03c9 (6) qksqkfmfe jIIIIpLT == ; 2 3 (7) where Iqk=\u03a8PM/Lq. Implicit unity power factor operation is obtained. The machine operation can be switched from motoring to generating in two ways: a) by changing the sign of qi current, but in this case the machine does not operate at unity power factor b) by changing the sign dc. excitation current. The vector diagram at steady state and unity power factor operation is illustrated in Fig. 2. For the prototype data in Table 1, the saturation effect of d- axis flux, considering id=0, is illustrated in Fig 3. III. EXPERIMENTAL PLATFORM A set of experiments was carried out to prove the validity of the proposed solution (zero id and zero \u03a8q). The structure of experimental platform is shown in Fig. 4. BEGA (Table 1) is fed through a 48Vdc, 350A Sauer-Danfoss three phase inverter from a 48V, 55Ah valve regulated lead-acid battery pack. The BEGA was mechanically coupled with a three phase induction machine (IM) via a transmission belt (nIM/nBEGA=1/2)", " The total copper losses vs electromagnetic torque at id=0 and different iq * values, taking into account the saturation effect in d axis, are represented in Fig. 7. and are expressed as follows: f qfmf e sqffsqcopper R IIL TRIRIRIP 2 222 )(3 3 \u239f \u239f \u23a0 \u239e \u239c \u239c \u239d \u239b +=+= (17) Fig. 7. demonstrates that the proposed simplified current referencer reduces the total copper losses at minimum. The dotted red line in Fig. 7. represents the minimum losses that can be achieved using the proposed current referencer (Fig. 6). A theoretical analysis of the effect of the current referencer on the BEGA power factor during operation is done in what follows. As seen in Fig. 2. for peak torque values ( 0 / =\u03a8== dqPMqkq iandLii ), during BEGA operation, unity power factor is achieved. Also, for low and very low torque levels, the unity power factor operation is possible, but with efficiency penalty. Using the current referencer (Fig. 6), for lower torque levels, the unity power factor can not be maintained anymore, so we are interested to see how much is the power factor degradation. The BEGA power factor angle (\u03d5), at id=0, can be expressed: ( ) ( ) \u239f \u239f \u23a0 \u239e \u239c \u239c \u239d \u239b + \u03a8\u2212\u2212 \u2212== fmfqs PMqqq ss iLir il atanVi \u03c9 \u03c9 \u03d5 ,\u227a (12) The power factor angle vs speed, for different torque levels, using the proposed loss minimization strategy is illustrated in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000457_978-3-642-55848-1-Figure2.20-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000457_978-3-642-55848-1-Figure2.20-1.png", "caption": "Fig. 2.20. See-saw platform plane motion", "texts": [ " For example, a resistive component R could be used instead of the source effort. The signal taken from the effort junction is integrated to get the platform rotation an gle. The governing equations are again very simple: The platform acts as a transformer of the velocities of the attached bodies. Si multaneously, transformation of the reaction forces of the bodies also takes place. To develop the bond graph model describing these interrelations we analyse the 52 2 Bond Graph Modelling Overview general plane motion of the platform in the global co-ordinate frame Oxy (Fig. 2.20). The position and orientation of the platform is described with reference to a body frame CX'y' with the origin at its mass centre. The position vector of the ori gin C is described by a column vector of its global co-ordinates, i.e. (2.73) Orientation of the body is defined by the rotation matrix (see e.g. [5]) R = (c~scp - Sincp) SInCP COscp (2.74) The vector of the relative position of a point P in the body with respect to the ori gin of the body frame can be expressed in the body frame by a vector of its coor dinates ", " In addition to these force effects, any moment at a port is transmitted di rectly to the rotation effort junction e. An inertial element added to the junction represents the rotational inertia of the platform. The translation inertia is repre sented in component CM which consists of two effort junctions that add inertial elements corresponding to the x and y motion (Fig. 2.21 CM). The platform grav ity is also added here. The mathematical model of the platform can be written directly from the Fig. 2.21. Respective variables are given in the figure, and parameters a, b, and care dimensions shown in Fig. 2.20; m is the platform mass, and Ic is its mass moment of inertia about its mass centre. The equations read: 1 Because of space limitation, only one of the f and LinRot components is shown. The oth ers have a similar structure. 56 2 Bond Graph Modelling Overview Platform -left side: V 1x - V C1x - V Cx = 0 V 1y - V C1y - V Cy = 0 VC1x =(a\u00b7sin~+c\u00b7cos~)\u00b7(O V C1y = (-a\u00b7 cos ~ + c . sin ~) . (0 M1x = (a\u00b7 sin~ + c\u00b7 cos~)\u00b7 F1x M1y =(-a\u00b7cos~+c\u00b7sin~)\u00b7F1Y - MC1 + M1x + M1y = 0 Platform - right side: V 2x - V C2x - V Cx = 0 V 2y - V C2y - V Cy = 0 VC2x = (-a\u00b7 sin~+c \u00b7cos~)\u00b7 (0 VC2y =(a\u00b7cos~+c\u00b7sin~)\u00b7(O M2x =(-a\u00b7sin+c\u00b7cos~)\u00b7F2x M2y = (a \u00b7cos~+c\u00b7 sin~)\u00b7F2y -MC2 +M2x +M2y = 0 Platform - upper side: - V 3x + V C3x + V Cx = 0 -V3y +VC3y +VCy =0 V C3x = -(b\u00b7 cos ~) ", " The pendulum will be represented in classical state-space form and solved using the implicit Runge-Kutta code RADAU5 of [11 ]. 6.5 The Pendulum Problem 217 To simulate the see-saw problem using BondSim, we retrieve the problem from program library (using Get From command on Project menu) and build the model. We use the following model parameters: 1. Body 1 mass m1 = 80 kg 2. Body 2 mass m2 = 20 kg 3. Platform mass m3 = 40 kg 4. Platform mass moment of inertia (centroidal) J3 = 90 kg\u00b7m2 5. Geometric parameters (Fig. 2.20) a =1.5 m, b = 1.125m, c = 0.375m 6. Initial angle of the platform = 1 rad The simulation interval was taken equal to 55 and the output interval was 0.05 s, the error tolerances both absolute and relative are equal to 1\u00b710-6 (default). Some results of the simulation are shown in Figs. 6.64 and 6.65. From Fig. 6.64 it can be seen that the see-saw oscillates about the equilibrium position that is at

0 and the polar coordinates of the vector x(t) \u2212 P(t) are given by 1(t) + \u03041, 2(t) + \u03042 where \u03041 and \u03042 are two constants such that \u2212 2 < \u03041< 2 and \u2212 2 < \u03042< 2 . Therefore x(t) is given by x(t)= P(t)+ d (cos( 1(t)+ \u03041) cos( 2(t)+ \u03042) sin( 1(t)+ \u03041) cos( 2(t)+ \u03042) sin( 2(t)+ \u03042) ) . Now if we set z(t)= ( 1(t)+ \u03041, 2(t)+ \u03042) T and make the change of variable u= A(z)z\u0307, where A(z)= ( d cos z2 0 0 d ) , adding process and measurement noise, the motion of x(t) is governed by the following system: x\u0307 = v(t) (cos(z1(t)\u2212 \u03041) cos(z2(t)\u2212 \u03042) sin(z1(t)\u2212 \u03041) cos(z2(t)\u2212 \u03042) sin(z2(t)\u2212 \u03042) ) + (\u2212 sin z1(t) \u2212 cos z1(t) sin z2(t) cos z1(t) \u2212 sin z1(t) sin z2(t) 0 cos z2(t) ) \u00d7u(t)+ ex(t), z\u0307 = A\u22121(z)u(t)+ ez(t), (1) where x0, z0 are the initial conditions and the noise terms ex : [0,+\u221e) \u2192 R3, ez : [0,+\u221e) \u2192 R2 are continuous mappings such that \u2016ex\u2016 Bx, \u2016ez\u2016 Bz" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000378_3-540-44869-1_23-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000378_3-540-44869-1_23-Figure1-1.png", "caption": "Fig. 1.Model of the humanoid robot with the position and orientation of the rotational joints; the global coordinate frame considered is also represented", "texts": [ " Each leg is composed of six degrees of freedom, which are distributed as follows: two for the ankle |one rotational on the pitch axis and the other one rotational on the roll axis|, one for the knee |rotational on the pitch| and three for the hip |each of them rotational on each of the axes|. The total height of the robot is 280 mm. The links dimensions considered are 113, 65 and 102 mm for the links between the ground and the ankle, the ankle and the knee, and the knee and the hip respectively. The hip length is 200 mm [11]. A diagram of the robot legs with the dimensions of each segment is shown in Fig. 1. The direct kinematics of the robot as regards what the relative position and orientation of one foot from the other is can be solved easily considering our model as a robotic chain of links interconnected to one another by joints. The rst link, the base coordinate frame, is the right foot of the robot. We assume it to be xed to the ground for a given nal position or movement, where the robot global coordinate frame will be placed. The last link is the left foot, which will be free to move. The assignment of the coordinate frames to the robot joints is ilustrated in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003259_jp075849h-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003259_jp075849h-Figure1-1.png", "caption": "Figure 1. Schematic graph showing two nonmagnetic microparticles (magnetic hole) of radius r1 and r2, suspended in a ferrofluid under an applied magnetic field H.", "texts": [ " As an illustration, in section V, we perform molecular dynamics simulations to give a picture of the microparticle size distribution in the formation of a bct lattice in bidisperse inverse ferrofluids. The paper ends with a discussion and conclusion in section VI. II. Interaction Model for Two Nonmagnetic Microparticles We start by considering a simple situation in which two nonmagnetic spherical microparticles (also called magnetic holes) are put nearby inside a ferrofluid which is homogeneous at the scale of a sphere in an applied uniform magnetic field H, see Figure 1. The nonmagnetic microparticles create holes in the ferrofluid, and corresponding to the amount and susceptibility of the ferrofluid, they possess the effective magnetic moment, which can be described by25 m ) -\u00f8f /(1 + 2/3\u00f8f)VH ) -\u00f8VH, where \u00f8f (or \u00f8) means the magnetic susceptibility of the host (or inverse) ferrofluid. When the two nonmagnetic microparticles placed together with distance rij away, we can view the magnetization in one sphere (labeled as A) as induced by the second (B). The central point of dipole-multipole technique is to treat B as the dipole moment m at the first place and then examine the surface charge density \u03a3 induced on the sphere A", " The induced solid structure is supposed to be the configuration minimizing the interaction energy, and here, we assume first that the microparticles with two different sizes have a fixed distribution as discussed below. By using the cylindrical coordinates, the interaction energy between two microparticles labeled as i and j considering both the dipole-dipole and the dipole-multipole effects can be written as where the center-to-center separation rij ) |ri - rj| ) [F2 + (zi - zj)2]1/2, and \u03b8 is the angle between the field and the separation vector rij (see Figure 1). Here, F ) [(xi - xj)2 + (yi - yj)2]1/2 stands for the distance between chain A and chain B (Figure 2), and zi denotes the vertical shift of the position of microparticles. Since the inverse ferrofluid is confined between two plates, the microparticle dipole at (x, y, z) and its images at (x, y, 2Lj ( z) for j ) (1, (2, ... constitute an infinite chain. In this work, we would discuss the physical infinite chains. After applying a strong magnetic field, the mismatch between the spheres and the host ferrofluid, as well as the different sizes of the two sorts of spheres will make the spheres aggregate into lattices like a bct (body-centered tetragonal) lattice" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure5.13-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure5.13-1.png", "caption": "Fig. 5.13. Example of deadpath error", "texts": [ ", the Abbe\u0301 offset should be as small as possible. Deadpath is the part of the measurement path between the interferometer and the reflector when the reflector is at the zero point. It is ideally zero, so that a Doppler frequency shift is only associated with a translation. Otherwise, the linear measurement may include an additional part which arises due to the deadpath. When there is a variation in the air refractive index, a deadpath error may manifest in an apparent shift of the zero point, resulting in poor machine repeatability. Figure 5.13 shows an example of a deadpath error. To minimise this error, the interferometer optics <2> should be placed as close as possible to the retroreflector <5> without allowing them to touch. Cosine error arises when the laser and the desired measurement axis are not straightly aligned, so that the recorded measurement is shorter than the actual travel of the machine. The error increases with the travel distance and the misalignment. An exaggerated illustration is given in Figure 5.14 5.6 Factors Affecting Measurement Accuracy 143 The accuracy of an angular measurement can be affected even by a small change in the distance between the retroreflectors" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003806_icelmach.2010.5608274-Figure10-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003806_icelmach.2010.5608274-Figure10-1.png", "caption": "Fig. 10. Magnitude of the fifth (left) and tenth (right) harmonic of magnetic flux density.", "texts": [], "surrounding_texts": [ "The four-pole energy-saving small induction motor with core made from the non-oriented silicon steel M600-50A was examined. The supply voltage was 230 V for the frequency 50 Hz. Stator windings were delta connected. The number of series turns of stator windings was 368. The external diameter of the stator core was 120 mm, the internal diameter is 70.5 mm, and stator core lengths is 102 mm." ] }, { "image_filename": "designv11_32_0003227_s11071-007-9225-2-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003227_s11071-007-9225-2-Figure3-1.png", "caption": "Fig. 3 A redundant manipulator with joint actuators moving in a vertical plane", "texts": [ " Therefore BT B + V V T becomes (BT B + V V T) = \u23a1\u23a2\u23a3\u2212z2 1 0 \u23a4\u23a5\u23a6 [\u2212z2 1 0] + \u23a1\u23a2\u23a3 1 1 z2 z2 k1 k1 \u23a4\u23a5\u23a6 [ 1 z2 k1 1 z2 k2 ] = \u23a1\u23a2\u23a32 + z4 z2 k1 + k2 z2 2z4 + 1 (k1 + k2)z2 k1 + k2 (k1 + k2)z2 k2 1 + k2 2 \u23a4\u23a5\u23a6 (41) Springer Using cofactors, the inverse of BT B + V V T is then: (BT B + V V T)\u22121 = 1 \u23a1\u23a2\u23a3k2 1 + k2 2 + z4(k1 \u2212 k2)2 2k1k2z2 \u2212(k1 + k2)(z4 + 1) 2k1k2z2 z4 ( k2 1 + k2 2 ) (k1 \u2212 k2)2 \u2212z(k1 + k2)(z4 + 1) \u2212(k1 + k2)(z4 + 1) \u2212z2(k1 + k2)(z4 + 1) 2(z4 + 1)2 \u23a4\u23a5\u23a6 (42) where is the determinant of BT B + V V T having the value: = (k1 \u2212 k2)2(z4 + 1)2. (43) Substituting from Equation (42) into Equation (10), we obtain Equation (39). Observe, however that here the computational effort is considerably greater. Example 2. A Redundant Manipulator (Huston et al. [31]). To illustrate the use of the method with controlled systems, consider a simple planar redundant manipulator consisting of three identical pin-connected rods moving in a vertical plane as in Fig. 3. Let the orientations of the rods be defined by the inclination angles \u03b81, \u03b82, and \u03b83 as shown. Suppose now that the movement of the rods is kinematically constrained so that the angular speeds \u03b8\u03071, \u03b8\u03072, and \u03b8\u03073 of the rods are related by the expressions: \u03b8\u03071 + \u03b8\u03072 \u2212 \u03b8\u03073 = 0 and 2\u03b8\u03071 \u2212 \u03b8\u03072 = 0. (44) In matrix form, Equation (44) may be written compactly as: A\u03b8\u0307 = b (45) where, by inspection, the arrays A, \u03b8 , and b are A = [ 1 1 \u22121 2 \u22121 0 ] , \u03b8 = \u23a1\u23a2\u23a3\u03b81 \u03b82 \u03b83 \u23a4\u23a5\u23a6 , b = [ 0 0 ] (46) As before, let the system initially be considered as being unconstrained", " In matrix form, these equations may be written as: M \u03b8\u0308 = f (50) where, by inspection, the M and f arrays are: M = mL2 \u23a1\u23a2\u23a3 7/3 (3/2)c2\u22121 (1/2)c3\u22121 (3/2)c1\u22122 4/3 (1/2)c3\u22122 (1/2)c1\u22123 (1/2)c2\u22123 1/3 \u23a4\u23a5\u23a6 (51) Springer and f =mL2 \u23a1\u23a2\u23a3(3/2)\u03b8\u03072 2 s2\u22121 + (1/2)\u03b8\u03072 3 s3\u22121 \u2212 (5g/2L)s1 (3/2)\u03b8\u03072 1 s1\u22122 + (1/2)\u03b8\u03072 3 s3\u22122 \u2212 (3g/2L) s2 (1/2)\u03b8\u03072 1 s1\u22123 + (1/2)\u03b8\u03072 2 s2\u22123 \u2212 (g/2L) s3 \u23a4\u23a5\u23a6 (52) Next, let there be actuators at the joints which can exert control moments (or \u201ctorques\u201d) T1, T2, and T3 between adjoining rods as represented in Fig. 3. The contributions to the generalized forces from these control torques may be assembled into the 3 \u00d7 1 array C using Kane\u2019s method with partial angular velocities. Specifically, as in Equation (25), the partial angular velocity array H and the control torque array \u03bc are seen to be H = \u23a1\u23a2\u23a31 0 0 0 1 0 0 0 1 \u23a4\u23a5\u23a6 and \u03bc = \u23a1\u23a2\u23a3T1 \u2212 T2 T2 \u2212 T3 T3 \u23a4\u23a5\u23a6 (53) Hence C is: C = \u23a1\u23a2\u23a3T1 \u2212 T2 T2 \u2212 T3 T3 \u23a4\u23a5\u23a6 (54) When C is given, we can conveniently use Equation (8) to determine the response of the system. To illustrate the procedure and the concept of equivalently controlled systems, consider two sets of constraints for the control torques" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002076_vppc.2005.1554564-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002076_vppc.2005.1554564-Figure1-1.png", "caption": "Fig 1. Exploded Assembly View of DLC Motor", "texts": [ " This, in turn means that excessive temperature rises \u2013 which means that bore core and winding dimensions can be reduced. Furthermore, in the case where good thermal coupling is provided between the winding and the core; the core may be used as a heat sink for the winding. This means that winding heat flux may be increased which in turn means that increased current densities can be accommodated. This leads to the reductions in overall size and mass. The exploded assembly view of the DLC Motor [2] is presented in Fig 1. The bulk component thermal model developed by Mellor [1, 3] was chosen for the proposed thermal modeling for its simplicity and compactness and for the fact that it had already been proven, under transient conditions, to give accurate predictions of the stator winding \u2018hot spot\u2019 temperatures for small Totally Enclosed Fan-Cooled TEFC induction motor. The Model was retained in its basic form which consists of ten components. 1. The frame 2. The stator back iron. 3. The stator teeth. 4. The stator slot winding" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003779_0369-5816(65)90138-9-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003779_0369-5816(65)90138-9-Figure3-1.png", "caption": "Fig. 3. Yield hexagonal prism.", "texts": [ " she l l s by e l imina t ing rn 8 f rom the Hodge \" twomoment l i m i t e d - i n t e r a c t i o n \" su r face [18]; i t i s r e f e r r e d to a s a \"one -momen t l i m i t e d - i n t e r a c - t ion\" y ie ld sur face . This hexagonal p r i s m is much s i m p l e r but is by no means as good a f i t at some points . 1 R e - ducing a l l i t s v e r t i c e s by the f ac to r \u00bd(5~,- 1) p r o d u c e s an i n s c r i b e d y ie ld sur face . A t h r e e - q u a r t e r s i ze p r i s m , however , l i e s within the a c - Another approx ima t ion to the y ie ld su r face i s shown in fig. 3. Th is y ie ld condi t ion i s defined by the fo l lowing eight p l anes : E4 AXISYMMETRIC INTERSECTING SHELI.~ OF REVOLUTION 89 tual y ie ld su r f ace ove r an extended range of v a l - ues of p r a c t i c a l i n t e r e s t for p r e s s u r e v e s s e l s . 3. APPLICATION OF THE THEORIES TO INTERSECTING SHELLS In o r d e r to be able to make use of the y ie ld loci for i n t e r s ec t i ng she l l s as r e p r e s e n t e d in sec t ion 2, some approx ima t ions to the shel l conf igura t ion mus t be in t roduced", " The results thus obtained are restr icted to those shell configurations where the assumed s t ress profile, NO= const, and conditions (14) or (15) can be imposed. By choosing his boundary conditions to satisfy face I of the yield surface of fig. 1 and the set of eq. (16), Lind [19] has been able to establish such a collapse pressure. The complexity of the equations obtained makes it necessary to use a trial and e r ro r procedure. Gill [20], on the other hand, by taking face I of the hexagonal pr ism yield locus of fig. 3, in association with the boundary conditions (12) and (18) and the set of eq. (17), arr ives at a fairly simple expression for the collapse pressure. The solution by Cloud [21] may also be derived as a particular case of Gill 's expression for the collapse load. An upper bound on the collapse pressure can be found by equating the external rate of doing work to the internal rate of energy dissipation for a kinematically admissible pattern of three hinge circles. A velocity field of the form U= c[1-cos(E-q)] , W= -csin(~-\u00a2) satisfies these hinge conditions" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003347_imtc.2007.379200-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003347_imtc.2007.379200-Figure5-1.png", "caption": "Fig. 5. Robotic arm prototype.", "texts": [ " The GUI is formed by five horizontal LEDs which represent, from left to right, the most significant bits that are converted into a decimal value. A remote user sets the LED values by a mouse click: a light coloured turned-on led button means a programmed \"1\", a darker turned-off led button means \"0\". The binary sequence in Fig. 3 is \"01011\" and the corresponding decimal value \"11\" is shown on the on-board display, monitored by the web-cam. The second and third experiments implemented for the remote laboratory are automation applications: the former (Fig.4) drives a two-wheel vehicle based on M\\AX7000S chip, the latter (Fig.5) controls movements and actions of a robotic arm prototype (Lynxmotion Lynx5 Satellite Arm without electronics) [16]. The hardware realizing the two-wheel prototype consists of the UPIX board, two servos Futaba S3003, a 7.2 Volt battery and an infrared sensor. The control algorithm, written in VHDL for the M\\AX7000S FPGA, allows the remote students to drive the robot in all of the four perpendicular directions (ahead, behind, left and right). The VI control panel (Fig.6) is formed by six vertical LEDs which, when are on, operate as follows (from the top to the bottom): 1) supply voltage to the UPIX board is switched off" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000219_20.877668-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000219_20.877668-Figure2-1.png", "caption": "Fig. 2. The coercive and interaction fields on the Preisach plane.", "texts": [ " The single domain particle changes its easy axis to the nearer direction from the direction of magnetization between the direction of the original easy axis and negative direction of the original easy axis when the applied field satisfies the following condition [8]: (4) where . After the direction of the magnetization is decided, the component of the magnetization of the domain parallel to the applied field is computed using the following equation: (5) The coercive force, , and interaction field, , can be found easily at the Preisach plane as shown in Fig. 2. If the domain particle turns to the positive magnetized state at and negative magnetized state at , the coercive and interaction fields are computed as follows: (6) The component of the total magnetization parallel to the applied field due to all the domain particles that have easy axis of is, using the Preisach plane, given as (7) where is the distribution density of the domain particles which have easy axis of , and switching fields and , which should be determined from the experimental data, and is the output of the single domain particle that will be computed using (5), and is the applied magnetic field", "1 [T] is applied to the specimen for 40 minutes using the electromagnet, shown in Fig. 3, which is cooled by water. Since the specimen is very slowly bound in the strong magnetic field, all the single domain particles are supposed to be aligned in one direction, and the specimen can be assumed to have only one easy axis. For the specimen, the first order transition curves are measured using VSM and represented in Fig. 4, from which the distribution density for an element in Preisach plane, shown in Fig. 2, is calculated using Everett function as follows: (9) where is the Everett function value when the applied field is decreased to from . For the anisotropic specimen, using the developed algorithm, the major loop of the hysteresis curve is simulated for the different directions of the applied field, and compared with the experimentally measured curves in Fig. 5. It is shown, at the figure, that the simulated coercive force is smaller than the measured one when the external field is applied to the direction of the easy axis" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003152_elan.200704127-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003152_elan.200704127-Figure1-1.png", "caption": "Fig. 1. Schematic representation of A) the electrochemically driven anion transfer (the EI-process) and B) the electrochemically driven ion transfer coupled to a regenerating chemical reaction step within the organic phase (EIC\u2019-process).", "texts": [ " When dissolved into an organic water-immiscible solvent such as 4-(3-phenylpropyl)-pyridine (PPP), FDA\u00fe remains in the organic microphase even upon prolonged contact to the aqueous electrolyte and therefore the electrochemical behavior in this liquid j liquid redox system can be studied. The electrochemical behavior of FDA\u00fe in PPP microdroplets is investigated in several electrolyte media. In the absence of sulfite, the transfer of PF6 , ClO4 , and nitrate are shown to follow a simple EI-mechanism (see Fig. 1A), where the electron transfer at the electrode surface (E-step) is associated with an anion transfer at the liquid j liquid interface (I-step) to maintain the charge neutrality in the organic phase. With sulfite present in the aqueous phase, the mechanism changes and an EIC\u2019-process is proposed to compete with the EI-process. In the EIC\u2019-process (see Fig. 1B) the electron transfer step (E-step) is associated with the ion transfer of the sulfite (I-step) which is then reducing the ferrocenyl derivative back into the 18 electron state while finally being converted into sulfate (catalytic C\u2019-step). The effectiveness of this process, the role of the supporting electrolyte, and the affects of the liquid j liquid interface on the overall process are investigated. In addition, the sensitivity towards sulfite solutions are studied, and future improvements in the microdroplet based sensor electrode are discussed" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000901_ac00276a058-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000901_ac00276a058-Figure1-1.png", "caption": "Figure 1. Absorption spectra of the product by the nitrite-5,7dlhydroxy-4-imlno-2-oxochroman reaction vs. reagent blank (A) (nitrite nitrogen = 0.140 ppm) and reagent blank vs. water (B) in 10 mL of the mixed solvent of n-butyl alcohol and ethyl acetate (2:3).", "texts": [ " These reagents are expected to react similarly with nitrite to 4,5-dihydroxycoumarin, which has been proposed for the rapid and selective spectrophotometric determination of nitrite (8, 11). From the results of this screening study, 5,7-dihydroxy-4-imino-2-0~0chroman was chosen from the point of view of high sensitivity, high stability of the colored product, high selectivity, and good reproducibility. Absorption Spectra. The absorption spectra of the nitrite-5,7-dihydroxy-4-imino-2-oxochroman reaction product and the reagent blank in the mixed solvent are shown in Figure 1. The pale yellow product exhibited the maximum absorbance at 361 nm. Therefore, all subsequent studies were made at 361 nm. The product in the mixed solvent gave a constant absorbance for at least 3 h. Effect of Acidity. The acidity of the reaction solution was varied from pH 3 to 1.0 N hydrochloric acid. The reaction of nitrite and the reagent produced the maximum color intensity in the pH range of 1.3 to 1.9 as shown in Figure 2. A pH of 1.6 was chosen for subsequent experiments. Effect of Reagent Concentration" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000943_s0997-7538(01)01156-1-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000943_s0997-7538(01)01156-1-Figure3-1.png", "caption": "Figure 3. Yield locus curve, rotated in the \u03c311\u2212\u03c322-system: (a) by \u03d5; (b) by d\u03d5 < 0 dependent on r1(\u03b5 pl v ).", "texts": [ " The orientation of the initial yield locus curve can be determined by a coordinate transformation. After the transformation the direction of the gradient vector at the point of intersection with the \u03c311-axis corresponds to the given initial value of r1. The equations for this transformation in a plane principal stress state are: \u03c311 \u03c322 = cos\u03d5 \u2212 sin\u03d5 sin\u03d5 cos\u03d5 \u00b7 \u03c3 11 \u03c3 22 + 1 \u2212 cos\u03d5 \u2212 sin\u03d5 \u03c3F0. (3.8) The angle \u03d5 indicates the deviation from the orientation of Mises\u2019s ellipse (cf. figure 3). Equation (3.8) is then substituted into the yield condition of second order (cf. (2.8)): f = f ( \u03c3ij (\u03c3 kl, \u03d5),K0,Kij ,Kijkl ) . (3.9) By replacing \u03c3 ij by \u03c3ij , we get the equation of the yield locus curve which is rotated by \u03d5 in the original system (\u03c311, \u03c322). The dependence on \u03d5 is now realised by the transformation of the internal variables which results from a comparison of coefficients between f and f : f = f ( \u03c3ij ,K0(\u03d5),Kij (\u03d5),Kijkl(\u03d5) ) . (3.10) After reordering and collecting the terms of the yield function we get the equations (Grewolls, 1998): K0 =K0 + [ K11(1 \u2212 cos\u03d5)\u2212K22 sin\u03d5 ] \u03c3F0 + [ (1 \u2212 cos\u03d5) [ K1111(1 \u2212 cos\u03d5)\u2212 2K1122 sin\u03d5 ] +K2222 sin2 \u03d5 ] \u03c3 2 F0, K11 = [ 2K1111 ( cos\u03d5 \u2212 cos2 \u03d5 ) + 2K1122(1 \u2212 2 cos\u03d5) sin\u03d5 \u2212 2K2222 sin2 \u03d5 ] \u03c3F0 +K11 cos\u03d5 +K22 sin\u03d5, K22 = [ 2(cos\u03d5 \u2212 1) sin\u03d5K1111 + 2 ( sin2 \u03d5 \u2212 cos2 \u03d5 + cos\u03d5 ) K1122 \u2212 2 cos\u03d5 sin\u03d5K2222 ] \u03c3F0 \u2212K11 sin\u03d5 +K22 cos\u03d5, K1111 = 2K1122 cos\u03d5 sin\u03d5 +K2222 sin2 \u03d5 +K1111 cos2 \u03d5, K1122 = (K1111 \u2212K2222) cos\u03d5 sin\u03d5 +K1122 ( cos2 \u03d5 \u2212 sin2 \u03d5 ) , K2222 =K1111 sin2 \u03d5 \u2212 2K1122 cos\u03d5 sin\u03d5 +K2222 cos2 \u03d5. (3.11) Internal variables with indices \u20183\u2019 must be determined from the condition of plastic incompressibility. This is necessary to ensure that the axis of the yield cylinder is parallel to the diagonal of the principal stress space at any time. By the transformation (3.8) which is related to the new internal variables corresponding to (3.11), the principal axes of the yield locus curve rotate by the angle \u03d5 (figure 3a). If the centre of the rotation is the point of intersection with the \u03c311-axis, changes of the angles \u03b2 and \u03d5 are equal. Taking into account the equations (3.6a), the rotation \u03d5 of the yield locus curve with respect to the isotropic state is: \u03d5 = arctan ( r1 \u2212 1 2 + 3r1 ) . (3.12) For many materials the value of r1 is initially greater than 1 and decreases during plastic deformation (figure 3b). This leads to changes of the yield locus curve which shall now be taken into account in the evolution equations by a term depending on r1(\u03b5 pl v ). Therefore the differential changes of the internal variables are needed which can be obtained from the differentiation of the transformation (3.11): K\u030711 = K22\u03d5\u0307 \u2212 2K1122\u03d5\u0307\u03c3F , K\u030722 = \u2212K11\u03d5\u0307 \u2212 2K2222\u03d5\u0307\u03c3F , K\u03071111 = 2K1122\u03d5\u0307, K\u03071122 = (K2222 \u2212K1111)\u03d5\u0307, K\u03072222 = \u22122K1122\u03d5\u0307. (3.13) The rates (3.13) describe the rotation of the yield ellipse when the material axes are constant" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000457_978-3-642-55848-1-Figure9.15-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000457_978-3-642-55848-1-Figure9.15-1.png", "caption": "Fig. 9.15. The initial configuration of the mechanism", "texts": [ " Weare interested in the rotation angles of the mechanism. Hence we need a display component. We create such a component as an X- Y Plotter using the me chanical components palette (Fig. 9.12). 342 9 Multibody Dynamics The display component is created with one input port. Thus we add another one. The upper one is connected to the Crank component output port and is la belled as Phi. The lower one, however, is not simply the body rotation angle, but angle alpha, which the other member (Body) makes with the vertical direction (Fig. 9.15). For this a function component is created that converts the body angle of rotation to the angle required. The angle is calculated as a = rc/2 -

W (Fig. 9.68a). At a point in this range the robot arm could be moved to one of two possible postures: elbow down or elbow up (Fig.9.68b). To illustrate the behaviour of the complete system we move the tool tip over the wall along a straight segment as shown in Fig. 9.68a. This can be achieved by ~: ~2y :i:(2ntlPER)} Z = A z sin(2ntlPER) (9.145) Using the data in Table 9.12 with w = 0.1 m, the radius of the bounding circle is 0.48990 m. Thus, the amplitudes in Eq. (9.145) are taken as Ay = 0.2 m and Az = 0.3 m. The period is PER = 5 s. The program trajectory is defined in the components RefP and RefF of Fig. 9.65 by Eq. (9.146). The parameters are defined as TO = 2 S, T1 = 3 S, T2 = 15 s, T3 = 16 s, RET = 0.5 s, and Fw = 50 N. The yend and zend are the values of the respective coordinates at t = T3" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002278_09544097jrrt75-Figure10-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002278_09544097jrrt75-Figure10-1.png", "caption": "Fig. 10 Simulation model \u2013 rolling and sliding. (a) Limit state (rolling) and (b) limit state (sliding)", "texts": [ " Equations of motion for the loading mass are given by Z: Fj2 sin (wD2)\u00feN2 cos (wD2) Fcyl sin (aH ) \u00bc m(g \u00fe \u20acqZ ) (10) X: Fj2 cos (wD2) N2 sin (wD2) \u00fe Fcyl cos (aH ) \u00bc m \u20acqX (11) a: Fcyl{ cos (aH ) P25Z \u00fe sin (aH ) P25X } \u00fem(g \u00fe \u20acP03Z) P24X m \u20acP03X P24Z \u00bc (mjP24j2 \u00fe J) \u20acaF (12) and further Fj2 cos (wD2) N2 sin (wD2)\u00fe Fcyl cos (aH ) \u00bc km VflexFX (13) where km is a simplified representation of the stiffness of the loading mass assembly, where P03 \u00bc A1 \u00fe A2 B1 \u00fe B2 \u00fe C \u00fe D1 D2 E1 E2 \u00fe VflexC (14) P24 \u00bc E1 E2 \u00fe F\u00fe VflexF (15) P25 \u00bc E1 E2 \u00fe G (16) VflexF \u00bc qX \u00fe jFj sin aF p 2 P03X 0 \" # (17) In this particular test setup, the angles are small. Therefore \u20acqZ g sin (aF ) aF (18) In every time step, initial rolling conditions according to equation (2) are assumed. The normal and tangential contact forces are calculated from the Proc. IMechE Vol. 220 Part F: J. Rail and Rapid Transit JRRT75 # IMechE 2006 at UNIV OF PITTSBURGH on March 18, 2015pif.sagepub.comDownloaded from equation system given by equations (3) to (5) and (9) to (13). If the tangential force Fj0 . m0N0, as shown in Fig. 10(a), i.e. if the friction break-out force is exceeded, sliding occurs and a new point of equilibrium, as shown in Fig. 10(b), is calculated. The resulting force Flink in the link is assumed to be constant when calculating angle a for the normal to the contact. The equations defined are formulated as a system of first-order differential equations. The system is solved numerically using a classical fourth-order Runge\u2013Kutta routine. As stated earlier, the link simulation model is used to investigate and explain the principal link suspension behaviour found in the laboratory tests. Although not all parameters in the model are known by \u2018exact\u2019 numerical values \u2013 particularly the structural flexibilities in links, end bearings, and loading mass assembly \u2013 the model should be able to explain the real behaviour by applying approximately estimated values of such parameters" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002040_rtd2004-66044-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002040_rtd2004-66044-Figure4-1.png", "caption": "Fig. 4 \u2013 Wheel rail contact geometry.", "texts": [ " The contact model of the wheel and the rail is an important element of train dynamic studies. Unlike usual train models, yaw and vertical motion of the axles have also been considered here in addition to their side motions. The wheel position relative to the rail must be determined at each computation step. Considering the complex geometry of the wheels and rail contact for each of the axles and the number of the wheels in the train, a large portion of computation time must be allocated for the determination of the contact geometry (Fig. 4). To overcome this difficulty, a system of 10 equations for the 10 geometrical unknowns of each axle was constructed. It must be mentioned that each wheel is considered to have two degrees of freedom, namely; lateral and yaw motions. The solution of these equations during main computations will reduce the calculation speed. Therefore the equations were completely solved for different contact conditions. The results were used in training a neural network (Fig. 5) which will be employed to estimate the contact geometry during computation stage" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000373_int.10025-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000373_int.10025-Figure2-1.png", "caption": "Figure 2. Sensing a wall perpendicular to sensor 4.", "texts": [ " In our system we use a fuzzy perceptual model developed by the authors3 that allows us to build an approximate world model giving us various levels of interpretation, the possibility for reasoning and planning about the robot motion in the world, and allows behavior-based navigation using the hybrid deliberative-reactive architecture. First, the influence of multiple error sources is studied to establish a process that reduces the influence of these phenomena, and to define a new fuzzy model sensor that gives us a belief degree about the possible existence of a piece of wall that is being sensed perpendicular to the direction of the ultrasound sensor. Figure 2 shows an example in which a wall perpendicular to sensor s4 is being perceived. The value of belief in a possible wall perpendicular to sensor si is noted by B(si ), and it is a number that belongs to the interval [0, 1]. Then, fusing information gathered from different sensors, the contours around the robot can be determined and classified in perceptual objects like walls, corridors, corners, hallways, and others distinguished places using an incremental process. Fuzzy logic is the tool that is used to manage the uncertainty and vagueness of the sensor data, and for modeling the different perceptual objects" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000514_3-540-45118-8_49-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000514_3-540-45118-8_49-Figure3-1.png", "caption": "Figure 3. shows Puma-like manipulator moving out of elbow (and wrist) singularity, following the path which lies in the degenerate direction", "texts": [], "surrounding_texts": [ "Type 1 Singularity, or in the case of PUMA, the elbow lock, is one where null space torque would generate motion in the singular direction. This means, for the case of PUMA, null space motion of joint 3 would generate motion in the singular direction (see Figure 2 for singular direction). Comparing the tracking error (position and orientation) of the manipulator moving out of elbow singularity into the degenerate direction with that of non-singular motion, no significant increase in position and orientation error is observed. (Compare Figure A7 and A8 to Figure A1 and A2)." ] }, { "image_filename": "designv11_32_0002228_05698190600614882-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002228_05698190600614882-Figure1-1.png", "caption": "Fig. 1\u2014Photograph of test facilities. (a) Gear test rig. (b) Test Gearbox and Instrumentation.", "texts": [ " Some success has been achieved by the authors in applying the WVD to recognize and locate surface faults in a gear transmission system (Choy, et al. (20); Polyshchuk, et al. (21), (22)). Based on the results of this comparative study, general conclusions are drawn concerning the effects of local damages to the global vibration signatures of the gear transmission system. In order to conduct experimental investigations on the effects of gear tooth damage on the vibration signature of the system, the gear test rig shown in Fig. 1a is used for this study. The test rig consists of two identical spur gears, with one attached to the electric motor while the other is attached to a water-braking system to provide loading to the gears. The driver of the gear test rig consists of a 75-HP motor connected through a belt-pulley drive system that can provide a maximum speed of up to 8000 rpm. The motor speed was controlled by a Quantum III microprocessor-controlled DC variable speed drive unit and the rotational speed of the shaft is monitored by an optical triggering unit. The loading of the gear mesh is provided by another belt-pulley drive system to a 50-HP Atd-114 Kopper-Kool Brake unit with the disc clutches with the brakes liquid-cooled through an external fan-forced radiator. The gearbox, Fig. 1b, consists of a set of identical 26-teeth spur gears with 10DP, pressure angle of 20 degrees, and a face width of 11/4 inches. The gears are cooled by circulating oil through an oil reservoir using a 1.5-HP AC hydraulic power unit. During the experiment, vibration data are collected using four 5-mm non-contacting proximeter sensors at the two rotors and four accelerometers at the bearing housing. A high-speed computer-based multi-channel analog-to-digital converter is used to convert and store the acquired vibration data including the optical triggering signal into the computer memory" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001927_s026357470500158x-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001927_s026357470500158x-Figure2-1.png", "caption": "Fig. 2. Graphical Representation of the Arm.", "texts": [ "0000409 radians per encoder count. There is also an available analog velocity signal for each link of the robot arm coming through a frequency to voltage converter which is proportional to the joint velocities of the links,5 but since this signal is noisy, the velocity of each link is obtained by using the position signal and utilizing first order backward differencing technique. Figure 1 shows the experimental test bed used in this study. Detailed experimental setup and modelling can also be found in reference [6]. Figure 2 shows the schematic diagram and basic dimensions of the 2 axis SCARA robot arm. The dynamic equations of the manipulator provides a description of the relationship between the joint actuator torques and the motion of the structure. These equations can be found by using the Lagrange formulation and the dynamic model of the manipulator can be obtained in the form, M(\u03b8)\u03b8\u0308 + V (\u03b8, \u03b8\u0307)\u03b8\u0307 = \u03c4 \u2212 F (\u03b8\u0307) (4) where M(\u03b8) is the 2\u00d72 symmetric positive definite mass matrix, V (\u03b8, \u03b8\u0307 )\u03b8\u0307 is the 2\u00d71 vector of Coriolis and centrifugal terms, F (\u03b8\u0307) is the 2\u00d71 vector of friction forces and \u03c4 is the 2\u00d71 vector of joint torques with \u03b8 = [ \u03b81 \u03b82 ]T being the joint position vector, \u03b8\u0307and \u03b8\u0308 being the joint velocity and joint acceleration vectors, respectively, for our case" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000286_iros.1994.407498-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000286_iros.1994.407498-Figure1-1.png", "caption": "Fig. 1 Redundant iiiacro niicro manipulator", "texts": [ " That is, by specifying a suitable set of the desired mechanical impedance, a compliant motion can be realized without any excessive joint torque of the macro manipulator, and a wide motion range of the macro manipulator can be used effectively to compensate a small motion range of the micro manipulator. In section 2, basic equations are described. In section 3, an impedance controller for redundant macro-micro manipulators is proposed. In section 4, a method for specification of stiffness of the macro manipulator for realizing the desired position of the micro manipulator is presented. In section 5 , simulation results are given to show the validity of the proposed controller. 2 Basic Equations A redundant macro-micro manipulators discussed in this paper is shown in Fig.1. It is assumed to move in three dimensional space and both of the macro and micro manipulators are assumed to have 6 degrees of freedom. In the figure, Cb, E M , and C, mean the base coordinate frame, the macro coordinate frame, and the micro coordinate frame, respectively. The origin of C M is located at the tip of the macro manipulator, and the origin of C m is located at the endpoint of the manipulator. Text is the external force, and TM is the internal force applied at the tip of the macro manipulator by the micro manipulator" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000964_j.1471-4159.1984.tb06095.x-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000964_j.1471-4159.1984.tb06095.x-Figure2-1.png", "caption": "FIG. 2. Competitive inhibition of the ['4C]serotonin oxidation (type A MA0 activity) by NAP-5-HT. The assay was performed in the same manner as described in Fig. 1. The [14C]serotonin concentrations ranged from 10 to 100 kM. The NAP-5-HT concentrations were 0 (o), 0.1 (o), and 0.3 pM (b). K , determination is shown on the left. The line of best fit was determined by linear regression analysis.", "texts": [ " The dark condition for our experiments was maintained by working without the overhead laboratory lights, and the dark control samples were covered with aluminum foil to prevent any possibility of photoactivation. Inhibition of MA0 activities by NAP-5-HT Figure 1 shows that NAP-5-HT inhibits both types of M A 0 activities in rat brain cortex with similar potency. A 50% inhibition of type A and type B activities was obtained with 0.40 F M and 0.28 FM NAP-5-HT, respectively. Kinetic studies revealed that NAP-5-HT inhibited each type of M A 0 activities by competing with the substrate (Figs. 2 and 3). The K i value for NAP-5-HT inhibition of serotonin deamination was determined to be 0.19 F M (Fig. 2) and 0.21 p M for inhibition of phenylethylamine deamination (Fig. 3). These latter results indicate again that NAP-5-HT has similar binding affiiliry to both types of MAO. The K , values for serotonin and P-phenylethylamine were determined to be 70 F M and 9 F M , respectively, which are similar to that reported for rat liver J . Neuroc'rem., Vol. 43, N o . 6 . 1984 1682 S. CHEN ET A L . MAOs, 71 F M for serotonin and 1.7 p M for phenylethylamine (Tipton and Mantle, 1981). Photodependent effect of NAP-5-HT on MA0 NAP-5-HT has a typical nitroazidophenyl derivative spectrum with absorption maxima at 258 nm and 470 nm (Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002323_bf00382472-Figure11-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002323_bf00382472-Figure11-1.png", "caption": "Fig. 11. A \" f a m i l y \" of superellipses, {x/a} n + {y/b}n = 1.", "texts": [ " On those machines, the inner tube is orten omitted. The product itself supports the film. F r o m a generalised version of the foregoing theory, this rectangular model of a shoulder can be calculated too. In order to achieve this, the circumference of the inner cylinder was represented by a superellipse [11. I t s shape is decribed by I f a = b, n ~ 2, eq. (9) r e p r e s e n t s a eircle; if a ~ b, s ~ 2 i t is an ellipse. I f \u00ab~ > 2, shapes ly ing b e t w e e n a r e c t a n g l e a n d an el l ipse are r ep re sen t ed . I n Fig. 11, s o m e of these shapes are shown [2, 3] : I t can be seen t h a t for suf f ic ient ly large va lues of n , ac tua l ly rec tangles wi th r o u n d e d angles are ob ta ined . S u b s t i t u t i o n of (1) in to (9) y ie lds a fo rmu la t i on of the superel l ipse in po la r coord ina tes .* = + ; 7:/2 < 9 --< 7: (10) a r(9 ) = r ( - - q9) = r(~ + ~). F r o m (10) i t follows t h a t r(0) - a and r ( n / 2 ) = b. (1) and (2) are n o w genera l i sed in to x = - - r (~) cos 9; Y - - r(9) sin 9; z = ~b(u(9 ), 9) (11) x 0 = e c o s ~ - - a ; y o - - ~ - - e t a n f l ; z 0 = e s i n ~ + h (12) * x n is for real \u2022 only defined for z > 0" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001051_bf02335932-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001051_bf02335932-Figure4-1.png", "caption": "Fig. 4. Calibration device for the calibration of the force measuring system", "texts": [ " At that moment the electromagnet can be switched off to prevent the weight pulling back on the subject. The weightholder then drops on the buffer (N). The displacement of the seat is registered by an incremental encoder (0) (Leine & Linde AB, Sweden, model 58, type 5806/A/15V/400) which is coupled to a non-elastic loop (P) attached to the seat (Fig. 2 and 3). The angle between the horizontal plane and the direction of the force is registered with an angle transducer (D). Calibration The force-measuring system can be calibrated using the device depicted in Fig. 4. The construction ~ '\" \" :D'] 9 r l I II t ,IF, E c H ~P ,,~ \" - ~,/I Fig. 2. Func t iona l par ts o f the d y n a m o m - eter du r ing d y n a m i c m e a s u r e m e n t s . For fur ther exp l ana t i on see text . O N ELAST,C LOOP r { - k ' ! . . . . . . . E N C O D E R \\ ~ . . . . . II . . . . . . - - - - ~ - B A L L B E A R I N G S / / / / / / / / / / / / / / / Fig. 3. Attachment of seat to rail with ballbearings and the coupling of the displacement t ransducer to the seat with a non-elastic loop shown permits the application of a very large range of forces, by using a few calibration weights" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001612_robot.2003.1241973-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001612_robot.2003.1241973-Figure5-1.png", "caption": "Fig. 5. Distinctive marks attached to the object", "texts": [ " S h i g h denotes a high-pass filtering operation to eliminate the stationaq factors from e;. K,; and K,, are gain matrices. B. Visual selvoing In the last decade, there are a lot of researches on the advanced visual servoing that is called the feature-based approach. This approach has advantages of being simple and robust to the calibration error 171, [SI. Therefore, the feature-based visual servoing is applied for the relative positioning between the end-effectors and the surface of the object. I The distinctive marks are attached to both the sides of the object as illustrated in Fig. 5. Feature vector si is defined as follows (Fig. 6): si = [ X l i Y l i '.. ~ 4 i 2/4iITI (3) T where [zji yji] represents the median points of the j-th mark on the image plane. Subsequently, the control command 8,,i is given so that the end-effector squarely faces to the surface of the object (Fig. 4 (b)). 8,; is given by: &vi = JTo:%iJ:iKui ( E d ; - \u20ac,I1 (4) where J,e; is the camera Jacobian matrix that relates the rates of change of the end-effector mounted camera positions and the joint angles" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure7.23-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure7.23-1.png", "caption": "Fig. 7.23. Membership function for the the input MAX ERR, \u03bcHIGH(MAX ERR)", "texts": [ " The value of the attribute is then evaluated as a weighted average of the uis: HEALTH = \u2211p i=1 \u03c9iui\u2211p i=1 \u03c9i , (7.22) where the weight \u03c9i implies the overall truth value of the premise of rule i for the input and it is calculated as \u03c9i = \u03a0n j=1\u03bcFij (EVij). (7.23) \u03bcFij (EVij) is the membership function for the fuzzy set Fij related to the input linguistic variable EVij (for the i-th rule). For example, in this application, the evaluation criterion (EVi) may be the maximum error (MAX ERR) and Fij may be the fuzzy set HIGH. The membership function \u03bcHIGH(MAX ERR) may have the characteristics as shown in Figure 7.23. The decision as to whether any rectification is necessary can then be based on a simple IF-THEN-ELSE formulation as follows: IF HEALTH \u2264 \u03b3, THEN STRATEGY=TRIGGER ALARM ELSE STRATEGY=CONTINUE TO MONITOR. \u03b3 can be seen as a threshold value. Suitable values for \u03b3 may be in the range 0.6 \u2264 \u03b3 \u2264 0.9. Under this framework, it is relatively easy to include additional criteria for analysis and decision making on the system. The procedure will involve setting up the membership functions for the criterion, formulating the additional fuzzy rules required, and adjusting the scaling parameters\u2014the \u03b1s in Equation (7" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000603_memsys.2000.838545-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000603_memsys.2000.838545-Figure4-1.png", "caption": "Figure 4. SEM micro-graph of a 6pm thick released rotating micro-actuator.", "texts": [ " 3c) in an HF:HN03:H20=1: 1:20 solution at room temperature [9], the sacrificial layer was removed and the structure released. The completed structure is schematically shown in Figure 3d. 37 1 The as-sputtered amorphous films were crystallized for 30 minutes at 750\u00b0C and aged for 100 hours at 5OO0C in a 0.44pTorr vacuum. Mf was engineered to be higher than the room temperature so that no deliberate cooling is needed for normal operation of the device. A typical micro-actuator, with a rotating beam (C) held by two opposite and offset fixed beams (A and B), is shown in the micro-graph in Figure 4, taken using a secondary electron microscope (SEM). The performance of the actuator is characterized by studying its response to temperature and electric current cycling. The rotation amplitude of the actuator is measured against the integrated marker rulers using a IOOOX optical microscope. The device is set at an ambient temperature of 10'C and the rotation amplitude is measured while an alternating current (ac) with a constant amplitude of 15mA is applied. The measured response (Fig. 5) as a function of the ac frequency is capped at a low 15Hz" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001197_iros.1998.724648-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001197_iros.1998.724648-Figure3-1.png", "caption": "Figure 3: A planar system", "texts": [ " On the other hand, by comparing dynamics of each subsystem, it seems interesting to define strategies optimizing the path for the mobile platform : the arm is assumed to be able to adapt its configuration easier and more quickly. All this leads to consider a lower-dimensional optimization problem and a new criteria Np(q,f) i.e. (recall : q: = (o,o,o)). Examples are given in the next section. 6 Example : a planar system We study the mechanical system composed of a HILARElike mobile platform on which is mounted an horizontal double-pendulum arm (i.e. such that both rotation axis are vertical) [lo, 121 (see Fig. 3). The arm generalized coordinates are: q b = (qbl, q b z ) (n = 2) and the mechanical system generalized coordinbtes are: operational coordinates (in \u2018R) are: x = ( z ~ , Q , z ~ ) = ( I , m, qb); the two Cartesian coordinates 1 and m specify the position of the center of the EE in R and the third component qb characterizes the orientation of the EE with respect to the axis (0,Z). Here, it is easy to see that it is possible to choose arbitrarily the position and the orientation of the EE in the plane; we will verify, by simple computations, that indeed p = A = 3" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003130_13506501jet226-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003130_13506501jet226-Figure1-1.png", "caption": "Fig. 1 Geometry and coordinates of the problem", "texts": [ " Christensen and Tonder [17\u201319] dealt with the modelling of random roughness and suggested a comprehensive general analysis for investigating the effect of transverse as well as longitudinal surface roughness. This approach of Christensen and Tonder [17\u201319] formed the basis for analysing the effect of surface roughness in a number of investigations (Ting [20], Prakash and Tiwari [21, 22], Prajapati [23, 24], Guha [25], Gupta and Deheri [26], and Andharia et al. [27]). Here, it has been sought to analyse the performance of a magnetic fluid-based squeeze film between rough porous truncated conical plates. 2 ANALYSIS The configuration of bearing system is shown in Fig. 1. The assumptions of usual hydrodynamic lubrication theory are taken into consideration in the analysis. The porous matrix is taken to be homogeneous and isotropic. The lubricant film is considered to be isoviscous and incompressible and the flow is laminar. The bearing surfaces are considered to be transversely rough. The thickness h(x) of the lubricant film is h(x) = h\u0304(x) + hs where h\u0304(x) is the mean film thickness and hs is the deviation from the mean film thickness characterizing the random roughness of the bearing surfaces" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003062_s1560354708050067-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003062_s1560354708050067-Figure1-1.png", "caption": "Fig. 1.", "texts": [ " 1) In the domain \u03a9 \u2229 \u03a90 the contact is continuous; 2) in the domain \u03a9 \u2229 \u03a90 (the bar over a symbol of a set denotes the complement of this set) the constraint is weekened; 3) the paradox situation of the non-uniqueness of motion, when it is possible both the detachment and the continuous contact, corresponds to the set \u03a9 \u2229 \u03a90; 4) another paradox situation, when both these types of motion are impossible, corresponds to the set \u03a9 \u2229 \u03a90. Example. A heavy circular disc of the radius a is moving in a fixed vertical plane. This system is subject to the ideal bilateral constraint: the center of mass moves along a fixed vertical line and also to the nonideal unilateral constraint in the form of a horizontal plane with viscous friction (Fig. 1a). Consider the inertial reference frame OXY such that its origin lies on the plane of support and its ordinate axis contains the mass center G. As Lagrange coordinates we chose the ordinate y of the center of mass and the angle \u03b8 between the vector CG (C is the geometrical center of the disc) and the absciss axis. The constraint (1.1) can be written in the form \u039b = y \u2212 h(\u03b8) 0, h(\u03b8) = a + b sin \u03b8, b = |GC|. (1.3) The friction is given by the formula F = \u2212\u03bcv, v = \u03b8\u0307h(\u03b8), (1.4) where v is the sliding velocity in a contact point and \u03bc is the coefficient of viscous friction", " 5 2008 Since for an unilateral constraint it holds N 0 the domains \u03a9 and \u03a90 can be defined by the following conditions \u03a9 : \u2212 g(2C + mh\u20322) \u2212 2Ch\u2032\u2032\u03b8\u03072 < 0, (1.10) \u03a90 : \u03bch2h\u2032\u03b8\u0307 \u2212 g(2C + mh\u20322) \u2212 2Ch\u2032\u2032\u03b8\u03072 < 0 (1.11) (formula (1.11) differs from (1.10) by presence of the friction term). Comparing these inequalities, one can note that in the domain determined by the formula \u03b8\u0307 cos \u03b8 > 0, (1.12) condition (1.11) implies (1.10), i. e., \u03a90 \u2282 \u03a9. For the opposite sign in inequality (1.12) it holds the opposite inclusion \u03a9 \u2282 \u03a90. On Fig. 1b the domains \u03a9 and \u03a90 are marked by the horizontal and inclined hatching correspondingly. The difference between these sets is bigger for a bigger coefficient of friction. Here is also the phase portrait of the system on the cylinder evolvent (\u03b8, \u03b8\u0307) \u2208 (\u2212\u03c0, \u03c0)\u00d7R. The equilibrium positions \u03b8 = \u03c0/2 and \u03b8 = \u2212\u03c0/2 are correspondingly the saddle point and the stable focus. The location of domains \u03a9 and \u03a90 with respect to each other shows that the continuous phase curve can penetrate into the domain \u03a9 \u2229 \u03a90, but the domain \u03a9 \u2229 \u03a90 can be reached only provided the initial conditions belong to the domain" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000120_1.1539059-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000120_1.1539059-Figure2-1.png", "caption": "Fig. 2 Face seal kinematical model: 1,2-seal rings", "texts": [ " It was possible then to analytically solve the Reynolds equation as well as, by integrating the obtained distribution of pressure over the surface area of the seal faces, determine the forces and moments applied by the fluid film. The analysis concerns a non-contacting FMRR face seal ~Fig. 1! with two rings flexibly mounted in the housings, which are rigidly attached to the shafts rotating with constant but different velocities\u2014v1 , v2 . Both sealing rings are characterized by conical faces determined with angles b1 , b2 respectively. A kinematic model of an FMRR seal with assumed coordinate systems is shown in Fig. 2. In the analyzed seal model, each sealing ring has four degrees of freedom, that means its motion is composed of an axial displacement ~translation! along the common axis of rotation going through their centers of mass and three angular displacements ~rotations! ~see Fig. 2!. The description of kinematics will begin with an assumption that there are no positive drive devices in the seal construction. This configuration corresponds to a seal with elastic bellows. For example the ring flexibly mounted in the elastic ~metal! bellows is shown in Fig. 1~b!. Thus, to describe the ring motion, four independent coordinates were assumed: z1 , w1 s , w2 s , w3 s , for sealing ring 1, and z2 , w1 r , w2 r , w3 r for sealing ring 2. Figure 3 shows the sequence of the assumed angles of rotation for either of the rings", "; After applying simplifications for small angles w1 , w2 , it is: w\u03071w\u03072w2'0; w\u03081w2 2'0; w\u03071w2'0, the components ~derivatives! of the kinetic energy, will be written as follows: d dt S ]T ]w\u03071 D'Jw\u030811Jo~ w\u03073w\u030721w\u03083w2!; d dt S ]T ]w\u03072 D'Jw\u03082 ; d dt S ]T ]w\u03073 D'Jow\u03083 ; d dt S ]T ] z\u0307 D5mz\u0308; ]T ]w2 'Jow\u03073w\u03071 ; (13) The potential energy of the ring depends mainly on the energy of stiffness and damping of its flexible housing. The energy in the field of gravity forces can be omitted in this case. The flexible housing of sealing ring 1 ~Fig. 2! can be composed of a single central spring or multiple springs arranged on the ring circumference and a rubber ~elastomer! static seal ~the so-called secondary seal! most frequently in the shape of an \u2018\u2018O\u2019\u2019 type ring. If we assume the Kelvin-Voit model for elastomer rings and uniform distribution of these elements and clamping springs with the stiffness ks on the central radius rm of the surface of contact, i.e., rm50.5(ro1ri), then we can write the unit coefficients of stiffness: ki50.5(k/prm), and similarly define the unit coefficient of damping: ci50", " After substituting the components of the angular velocity into the OXYZ system performing simple transformations and assuming simplifications for small angles w1 , w2 , we obtain: Qw1 5M x ; Qw2 'M y ; Qw3 5M z . The derived equations ~20! describe the motion of a flexibly mounted ring in a housing without the positive drive device. Now if we assume that the mechanism is true for the configuration shown in Fig. 1, we have to take account of the kinematical constraints in the description of the ring motion. It is known that the positive drive devices cause kinematical constraints between the angular velocity w\u03073 and the angular velocity about the axis Z ~Fig. 2!, w\u0307Z5v . If we apply simplifications for small angles of rotation w1 i w2 , we can write that w\u03073'v . Moreover, if we assume that the angular velocity v is constant (v5const.), the third equation of motion ~20! for the angle of rotation w3 vanishes. An identical system of Eqs. ~20! is derived for the other ring so, finally, we obtain a complete description of the dynamics of the FMRR case. If we use the superscripts \u2018\u2018r\u2019\u2019 and \u2018\u2018s\u2019\u2019 to denote angular displacements and the subscripts \u2018\u20181\u2019\u2019 and \u2018\u20182\u2019\u2019 to denote linear ones, the equations of motion will be written as follows: 800 \u00d5 Vol" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003791_optim.2010.5510483-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003791_optim.2010.5510483-Figure2-1.png", "caption": "Fig. 2. Finite element mesh.", "texts": [ " It consists of 3D finite element modelling of the magnetic field of the actuator and solution of the electric circuit \u2013 mechanical motion problem based on the functions obtained from the magnetic field modelling. These functions are the coil flux linkage, its derivatives with respect to the current and the displacement and the electromagnetic force. For the 3D magnetic field modelling, the finite element method and ANSYS\u00ae program [19] are used. An example of the finite element mesh is given in Fig. 2. The three-dimensional finite element modeling is carried out using edge flux formulation and tetrahedral finite elements. The studied domain consists of the actuator and a buffer zone around it, on the boundaries of which fluxparallel boundary conditions are imposed. The total number of nodes of the mesh is about 100 000. For both current in the coil and for the stroke minimal and maximal values are defined. Then a grid of points currentstroke is generated by setting values of the current and of the stroke to be uniformly distributed within the defined ranges" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003458_tec.2007.895865-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003458_tec.2007.895865-Figure1-1.png", "caption": "Fig. 1. Phase currents relationship of SESPRG.", "texts": [ " Two modes of operation for such a generator are analyzed and studied, namely, the two-stator winding generator and the single-stator winding generator. A fixed-capacitor (FC) thyristor-controlledreactor (TCR)-type static var compensator is used to regulate its 0885-8969/$25.00 \u00a9 2007 IEEE terminal voltage. The active and reactive (P\u2013Q) power diagram of a SESPRG is developed. Experiments were performed on a laboratory machine to confirm the validity of the theoretical analysis. Steady-state analysis of SESPRG is based on the d\u2013q axis model and the phasor diagram shown in Fig. 1. The following assumptions are made in the analysis of machine. 1) All the machine parameters except the d-axis magnetizing reactance are assumed to be constant (only the d-axis magnetizing reactance is assumed to be effected by saturation). 2) The core loss in the machine is ignored. 3) The MMF space harmonics and the time harmonics in the induced voltage and current waveforms are ignored. 4) The turns ratio between the main and auxiliary windings is assumed to be unity (balanced conditions are considered)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003188_j.mechmachtheory.2007.07.001-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003188_j.mechmachtheory.2007.07.001-Figure5-1.png", "caption": "Fig. 5. Sketch for conjugate moulding surfaces.", "texts": [ " When one of them degenerates into a surface of revolution, it can be deemed as the tool surface to be in cutting another surface. As for a pair of moulding surfaces R(1), R(2) with a same generator Cm, they are in continuous tangency at the generator in the meshing process, thus such a case is termed as moulding-surface conjugation in this paper. Here its fundamental equations and conditions are discussed. Here, a pair of moulding surfaces to be in meshing is generated by a general planar curve Cm. In Fig. 5, Z(1), Z(2) are the rotation axes, A, a are the center distance and its unit direction vector. X(1), X(2) are the angular velocities of R(1) around Z(1)-axis and R(2) around Z(2)-axis, and are collinear with Z(1), Z(2), respectively. For the convenience of analysis, it is supposed that the magnitude of X(1) is equal to 1. The following relationships can be obtained: du\u00f01\u00de \u00bc dt; jX\u00f02\u00dej \u00bc I ; du\u00f02\u00de \u00bc Idt X\u00f01\u00de X\u00f02\u00de \u00bc I cos c; X\u00f01\u00de X\u00f02\u00de \u00bc I sin ca \u00f08\u00de Here, u(1), u(2) are the rotation angles of R\u00f01\u00de;R\u00f02\u00de, respectively, t is the time parameter,I is the speed ratio, c is the crossing angle between X(1) and X(2)", " (3), the equations and the basic frames of the directrixes C\u00f0i\u00dep0 and C\u00f0i\u00dep are presented as C\u00f0i\u00dep0 : R\u00f0i\u00dep \u00bc R\u00f0i\u00dep \u00f0si\u00de; fR\u00f0i\u00dep ; e \u00f0i\u00de 1 e \u00f0i\u00de 2 e \u00f0i\u00de 3 g x \u00f0i\u00de 0 \u00bc k\u00f0i\u00den e \u00f0i\u00de 2 \u00fe k\u00f0i\u00deg e \u00f0i\u00de 3 C\u00f0i\u00dep : r\u00f0i\u00dep \u00bc r\u00f0i\u00dep \u00f0si\u00de \u00bc Bi\u00f0u\u00f0i\u00de\u00deR\u00f0i\u00dep \u00f0si\u00de; fr\u00f0i\u00dep ; a \u00f0i\u00de 1 a\u00f0i\u00de2 a \u00f0i\u00de 3 g x\u00f0i\u00de \u00bc Bi\u00f0u\u00f0i\u00de\u00dex\u00f0i\u00de0 \u00bc k\u00f0i\u00den a \u00f0i\u00de 2 \u00fe k\u00f0i\u00deg a \u00f0i\u00de 3 \u00f09\u00de Here, si is the natural parameter of the directrix C\u00f0i\u00dep ; a \u00f0i\u00de j \u00bc Bi\u00f0u\u00f0i\u00de\u00dee\u00f0i\u00dej \u00f0j \u00bc 1; 2; 3\u00de, Bi\u00f0u\u00f0i\u00de\u00de is a rotation group aboutZ(i)-axis (see Appendix A). Due to the tangency of R\u00f01\u00de;R\u00f02\u00de at the generator Cm, the points on the directrixes corresponding to the common generator at every instant are called the conjugate point in the present paper. Actually, the conjugate condition of two moulding surfaces can be transformed into the geometric condition at conjugate point of the directrixes. In general case, the directrixes C\u00f01\u00dep ;C\u00f02\u00dep are tangent at conjugate point P, as shown in Fig. 5. Further, we consider that the basic frames at point P of two directrixes coincide with each other and constitute a common frame fP ; a1; a2; a3g. The fundamental equation of general moulding-surface conjugation can be given as r\u00f01\u00dep r\u00f02\u00dep \u00bc Aa aj \u00bc a \u00f01\u00de j \u00bc a \u00f02\u00de j ( \u00f010\u00de where aj denotes the common frame at conjugate point P of C\u00f01\u00dep and C\u00f02\u00dep . Now we start to investigate the intrinsic relationships of conjugation. Referring to Eq. (8) and (A.10), (A.11) in Appendix A, the differentiation of the first expression in Eq", " Obviously, some special problems on moulding-surface conjugation should be resolved. As for the conjugate condition of normal-circular-arc surface, Eq. (25) is equivalent to two scalar equations, i.e. v\u00f021\u00de p a2 \u00bc v\u00f021\u00de p a3 \u00bc 0, thus the following equations are obtained X\u00f021\u00de \u00f0r\u00f01\u00dep a2\u00de A\u00f0X\u00f02\u00de a\u00de a2 \u00bc 0 X\u00f021\u00de \u00f0r\u00f01\u00dep a3\u00de A\u00f0X\u00f02\u00de a\u00de a3 \u00bc 0 ( \u00f033\u00de According to Eqs. (9) and (A.7) in Appendix A, Eq. (33) is further transformed into X\u00f021\u00de B1\u00f0u\u00f01\u00de\u00de\u00f0R\u00f01\u00dep e2\u00de A\u00f0X\u00f02\u00de a\u00de B1\u00f0u\u00f01\u00de\u00dee2 \u00bc 0 X\u00f021\u00de B1\u00f0u\u00f01\u00de\u00de\u00f0R\u00f01\u00dep e3\u00de A\u00f0X\u00f02\u00de a\u00de B1\u00f0u\u00f01\u00de\u00dee3 \u00bc 0 ( \u00f034\u00de In Fig. 5, fO\u00f01\u00de; abX\u00f01\u00deg is a unit orthogonal right-handed coordinate system. Referring to Eq. (A.1) in the Appendix A, rotation group B1(u(1)) about X(1) in this coordinate is represented by B1\u00f0u\u00f01\u00de\u00de \u00bc cos u\u00f01\u00de\u00f0aa\u00fe bb\u00de \u00fe sin u\u00f01\u00de\u00f0 ab\u00fe ba\u00de \u00feX\u00f01\u00deX\u00f01\u00de \u00f035\u00de Substituting Eq. (35) into Eq. (34) yields P e2 cos u\u00f01\u00de \u00feQ e2 sin u\u00f01\u00de \u00bc U e2 P e3 cos u\u00f01\u00de \u00feQ e3 sin u\u00f01\u00de \u00bc U e3 P \u00bc I sin cb R\u00f01\u00dep \u00fe AI cos cb Q \u00bc I sin ca R\u00f01\u00dep \u00fe AI cos ca U \u00bc \u00f0I cos c 1\u00deX\u00f01\u00de R\u00f01\u00dep AI sin cX\u00f01\u00de 8>>>< >>>: \u00f036\u00de where P;Q;U; e2; e3 are the functions of natural parameter of the directrix C\u00f01\u00dep " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002219_cdc.2006.377706-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002219_cdc.2006.377706-Figure1-1.png", "caption": "Fig. 1. Sketch of the sets O1, \u21261, and \u2126\u2032 1", "texts": [ "2: A patchy control Lyapunov function for (1) with the attractor A consists of a set Q and a collection of functions Vq and sets \u2126q, \u2126\u2032 q for each q \u2208 Q, such that \u2022 Q is a totally ordered countable set; \u2022 {\u2126q}q\u2208Q and {\u2126\u2032 q}q\u2208Q are locally finite families of nonempty open subsets of O\u0303 such that O \u2282 O \u2282 O\u0303, where O := \u22c3 q\u2208Q \u2126q = \u22c3 q\u2208Q \u2126\u2032 q, and for all q \u2208 Q, the unit (outward) normal vector to \u2202\u2126q is continuous on ( \u2202\u2126q \\ \u22c3 r q \u2126\u2032 r ) \u2229 O, and \u2126\u2032 q \u2229 O \u2282 \u2126q; \u2022 for each q, Vq is a smooth function defined on a (relative to O) neighborhood of \u2126q; and the following conditions are met: there exist a continuous function \u03b1 : (0,\u221e) \u2192 (0,\u221e), class-K\u221e functions \u03b3, \u03b3, and a function \u03c9 which is a proper indicator of A with respect to O\u0303 such that: (i) for all q \u2208 Q, all x \u2208 \u2126q \\ \u22c3 r q \u2126\u2032 r, \u03b3(\u03c9(x)) \u2264 Vq(x) \u2264 \u03b3(\u03c9(x)); (ii) for all q, r \u2208 Q, r q, all x \u2208 \u2126q \u2229 \u2126\u2032 r, Vr(x) \u2264 Vq(x); (iii) for all q \u2208 Q, all x \u2208 \u2126q \\ \u22c3 r q \u2126\u2032 r, there exists uq,x \u2208 U such that \u2207Vq(x) \u00b7 f(x, uq,x) \u2264 \u2212\u03b1(\u03c9(x)); (iv) for all q \u2208 Q, all x \u2208 ( \u2202\u2126q \\ \u22c3 r q \u2126\u2032 r ) \u2229 O, the uq,x of (iii) can be chosen such that nq(x) \u00b7 f(x, uq,x) \u2264 \u2212\u03b1(\u03c9(x)), where nq(x) is the unit (outward) normal vector to \u2126q at x. Example 3.3: (Artstein\u2019s circles, revisited) We now re- turn to the system (5) and display a smooth patchy control Lyapunov function for it. Let Oq, Vq, q = 1, 2 be as in Example 3.1. Pick any two angles \u03b2 > \u03b1 in (\u03c0/2, 3\u03c0/4) and let \u2126\u2032 1 = {x = (r, \u03b8) : r > 0, \u2212\u03b1 < \u03b8 < \u03b1} , \u21261 = {x = (r, \u03b8) : r > 0, \u2212\u03b2 < \u03b8 < \u03b2} , while \u2126\u2032 2 = \u2212\u21261, \u21262 = \u2212\u21261. The sets O1, \u21261 and \u2126\u2032 1 are sketched in Figure 1, with \u03b3 = 3\u03c0/4. The sets and functions just defined form a smooth patchy control Lyapunov function. The index set Q = {1, 2} can be ordered via 2 1. The families {\u21261, \u21262}, {\u2126\u2032 1, \u2126 \u2032 2} consist of nonempty and open sets and form a locally finite cover of O = \u21261 \u222a \u21262 = \u2126\u2032 1 \u222a \u2126\u2032 2 = R 2 \\ {0}. We have( \u2202\u21261 \\ \u22c3 r 1 \u2126\u2032 r ) \u2229 O = (\u2202\u21261 \\ \u2126\u2032 2) \u2229 O = \u2205, (6) while ( \u2202\u21262 \\ \u22c3 r 2 \u2126\u2032 r ) \u2229 O = \u2202\u21262 \u2229 O (7) consists of two half lines that do not contain their endpoints, and the (outward) unit normal vector to \u2202\u21262 is constant (so continuous) relative to each of these lines" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002188_1.2401563-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002188_1.2401563-Figure1-1.png", "caption": "FIGURE 1. Schematic of ATMI\u2019s Ion Source Test Stand", "texts": [ " ATMI is continually working towards providing process efficiency solutions to the semiconductor industry. ATMI\u2019s recent research efforts have been directed at continuing to improve both the safety and efficiency of ion implantation processes and tools. As part of these efforts we recently installed a state of the art ion source test facility at our Danbury CT facility. In this paper, we describe the test stand, and show data to illustrate its capabilities and the type of research in progress. The ion source test stand (Figure 1) features a single filament Bernas source, an 80 degree analyzing magnet with a mass resolution M/ M > 50, and a magnetically suppressed Faraday located immediately downstream of the analysis slit. The gas box is currently configured for three low pressure gases and one high pressure cylinder, with a fifth gas slot available for future expansion. Beam energy is variable from 10 to 60 keV with analyzed beam currents of about 10 mA for B+, P+ and As+. The primary purpose of the test stand is to facilitate ATMI\u2019s research into innovative materials which can optimize operation of ion implant sources and beamlines" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003662_s12239-009-0025-1-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003662_s12239-009-0025-1-Figure5-1.png", "caption": "Figure 5. Multibody dynamics vehicle model for ADAMS.", "texts": [ " The ADAMS program is a multibody dynamic analysis software that is generally used for vehicle dynamic analyses in automobile companies. This is a useful method to test mechanical systems because it can save time and money. The multibody model considers the geometric and component nonlinearities in mechanical systems, and a comparatively precise modeling can also produce a physical prototype. 5.1. Multibody Dynamics Vehicle Modeling in ADAMS The vehicle system for a multibody dynamic simulation is shown in Figure 5. This system is a small passenger car model (Park et al., 2001) in which all the parts are modeled as rigid bodies and kinematic joints, as shown in Figure 5. The parameters T*, R*, and S* in Figure 5 represent a translational joint, revolute joint, and spherical joint, respectively. SS* and RS* represent a spherical-spherical joint and a revolute-spherical joint, respectively (Nikravesh, 1988). This model possesses 15 degrees of freedom (DOF), which includes 6 DOF in the chassis, 8 in the suspension and wheel rotation, and 1 in the steering. The Fiala tire model (MSC Software, 2003), which is very common in the ADAMS program, was employed. The vehicle model has to communicate variables to the \u03b5 k( )=er k 1+( )\u2212 e\u03b4 k( ) e\u00b7 e\u03b4 = t t+ t\u03b4 \u222b e\u00b7dt e\u00b7\u2248 \u03b4t=\u03b4tA+\u03b4tBub J ub, k( )=\u03b5 T k 1+( )Q\u03b5 k 1+( )+ub T k( )Rub k( ) J ub( )= M N\u2013( ) T Q M N\u2013( )+ub T Rub M=er k 1+( )\u2212\u03b4tA, N=\u03b4tBub \u2202J \u2202ub -------=\u22122 \u03b4tB( ) TQM+2 \u03b4tB( ) TQN+2Rub=0 ub= \u03b4tB( ) TQ \u03b4tB( )+R( ) 1\u2013 \u03b4tB( ) TQM x y MATLAB program for the co-simulation" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001952_0165-022x(80)90024-x-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001952_0165-022x(80)90024-x-Figure3-1.png", "caption": "Fig. 3. Fluorescence of various amounts of norepinephrine after isolation with the stan-", "texts": [ " These facts prove that it is not necessary to employ the generally [1,4--7] accepted large 200--400 mg A1203 batches; much less is sufficient. The present data (Fig. 2) confirm tha~ the volume of the eluent is critical in terms of the efficiency of elution [1] : 0.5 ml was not sufficient for a full recovery while either 1.0 or 2.0 ml was enough. Still, when the adsorbent : eluent ratio was sufficiently low, as when using only 25 mg alumina and 100 pl acetic acid, a volume low enough to match the requirements of microcuvettes gave 95- - !00% recoveries. As Fig. 3 shows, the fluorescence of a given amount of catecholamines was considerably higher after subjecting it m the present isolation procedure adapted to the requirements of microcuvettes (detailed in Scheme 1) than RFI % ~ 0 0 - 50- ii . . . . . ~ . . . . . . ; . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . y . io ~ 50 100 200 rng At203 25 Fig. 2. Rela t ive f luorescence of 100 ng n o r e p i n e p h r i n e a f te r (1) a d s o r p t i o n to var ious a m o u n t s of a l u m i n i u m oxide and e lu t ion w i th 2", "0 ml) (1) and wi th t he p r o c e d u r e descr ibed in S c h e m e 1 (2). Each p o i n t r epresen t s t he m e a n of at least 5 m e a s u r e m e n t s ; S.D. was invar iab ly tess t han 1.5. Values are given as the pe rcen tage of the f luorescence of 100 ng of n o r e p i n e p h r i n e sub jec t ed to t he ' n o n - m i c r o ' p r o c e d u r e (RFI) . The s t anda rd was added to t he 0 .01 N HC1 (see S c h e m e 1). after extracting them in a more dilute form with one of the original methods [1,4--7] (Fig. 3). Though only data on norepinephrine are presented in Figs. 2 and 3, experiments with dopamine gave an identical picture. One may therefore assume that the introduction of filter tubes for the isolation of catecholamines increased the sensitivity of the method as well as shortening it by considerably simplifying the procedure. The h a n d l i n g of so lu te- -so l id mix tu re s is great ly fac i l i ta ted by the i n t r o d u c t i o n of f i l ter tubes . Shak ing of t he a d s o r b e n t is done in the f i l ter tubes , a valve p reven t ing dripping" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000457_978-3-642-55848-1-Figure10.30-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000457_978-3-642-55848-1-Figure10.30-1.png", "caption": "Fig. 10.30. Coriolis mass flowmeter with two straight parallel tubes", "texts": [ "20% of the flow rate, practically over the range from zero and up [13]. The range of fluid densities that can be measured varies widely, running from about 100 kg/m3 or less to over 3000 kg/m3; certain flowmeters even can be used for gases. CMFs are highly insensitive to temperature and pres sure variations. They are very accurate and reliable instruments. The principle of their operation is rather simple. We will explain it with an example of a straight parallel tube CMF. There are other configurations as well, but the basic principles are the same. Fig. 10.30 shows a Coriolis mass flowmeter consisting of two parallel tubes hydraulically connected in parallel. The incoming flow divides and flows into two separate and practically identical tubes; the flows again combine at their exits. The tubes' ends are clamped to the meter body. They are excited by a drive-located at their middle-which vibrates in their first vibration mode. On the left and the right of the driver are two sensors that detect displacements between the tubes. They are used to measure the difference between times when the tubes cross their middle positions (time delay)", "6 Coriolis Mass Flowmeter 433 ment ports are modified by addition of tangential and normal inertial force terms. The coefficient matrix of the first is the same matrix as in the Coriolis term, and matrix C of the other term is given by Eqs. (10.74) and (10.75). After the tube element with fluid flow is developed, we start model develop ment by defining a project called Coriolis Mass Flowmeter. The system-level model is shown in Fig. 10.33. It mimics the structure of the Coriolis flowmeter with two straight tubes in Fig. 10.30. The model contains two Measuring Tube components clamped to the Wall at both ends. This means that velocities (trans versal and angular) at the tube ends are zero, a condition that is enforced by suit able source-flow components in the Wall. In the middle of the tube components are power ports to which the tubes driver is attached. The Driver is connected to the tubes by an effort node f component consisting of two flow junctions. These describe relative velocities at the tube-driver connections" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002939_s11071-007-9215-4-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002939_s11071-007-9215-4-Figure4-1.png", "caption": "Fig. 4 Reachable area of the tip of the free link (rmin =\u221a", "texts": [ " Thus, radius of the trajectory described by the tip of the free link can be varied. In the following section, we clarify the reachable area of the tip of the second link by changing \u03b81off and \u2217 0. 3.3 Reachable area of the tip of the free link We define rtip as rtip = [{l0 + l1 cos \u03b81 + l2 cos(\u03b81 + \u03b82)}2 + {l1 sin \u03b81 + l2 sin(\u03b81 + \u03b82)}2]1/2/(l0 + l1 + l2), which stands for dimensionless radius of the trajectory described by the tip of the free link, i.e., dimensionless distance between the rotation center of the base and the tip of the free link, as shown in Fig. 4. As rtip is normalized by l0 + l1 + l2, the maximum value of rtip is rtip = 1 in the condition where the four points including the rotation center, the active joint, the free l2 0 + l2 1 + l2 2 + \u221a 2l0(l1 \u2212 l2)/(l0 + l1 + l2)) joint, and the tip of the free link lie in the same straight line as the configuration (c) in Fig. 4. The relative angles \u03b82 in the configurations (a), (a)\u2032, (b), and (c) correspond to the points indicated with the same labels as in Figs. 2 and 3. The distance rtip is determined by the angles of the first and second links (\u03b81 and \u03b82). Therefore, as mentioned in the previous section, rtip is governed by the offset of the excitation \u03b81off and \u2217 0. Now we consider that the offset \u03b81off is in the rage of 0 \u2264 \u03b81off \u2264 \u03c0/4 corresponding to the measurement restriction of the after-mentioned experiments. Since the maximum value of \u03b82 is \u03c0/2 for any values of \u03b81off and \u22172 0 , the minimum value of rtip is realized in the case of \u03b81off = \u03c0/4 and \u03b82 = \u03c0/2 as shown in Fig. 4 (a)\u2032; the minimum value is rtip =\u221a l2 0 + l2 1 + l2 2 + \u221a 2l0(l1 \u2212 l2)/(l0 + l1 + l2) and we define the value as rmin. Thus, it is obvious that the reachable area of the tip of the free link is the gray zone in Fig. 4. From Equation (8), we can obtain stable equilibrium surfaces of rtip depending on \u03b81off and \u22172 0 as in Fig. 5. The upper surface is connected to the lower on the junction line at \u03b81off = 0. In order to change the distance rtip from the maximum value at the point (c) in Fig. 5 to the minimum at the point (a)\u2032, rtip needs to go through the junction line to reach the lower surface on which the point (a)\u2032 exists. Therefore, we first increase \u22172 0 as the arrows indicate in Fig. 6 (from (c) to (a) through (b)). Then, by keeping the excitation frequency constant and varying the offset of the excitation \u03b81off from 0 to \u03c0/4 (from (a) to (a)\u2032 along the arrows in Fig. 7), the minimum value of the distance rtip = rmin at the point (a)\u2032 can be realized. The magnitude of the minimum value for the Springer parameters of the after-mentioned experimental apparatus is rtip = 0.6373. In this way, the tip can reach any point in the clarified reachable area described in Fig. 4. 4 Experiments 4.1 Experimental setup The validity of the proposed control method is experimentally examined by using an apparatus shown in Fig. 8. The base is levitated above a planar glass by air bearings [New Way Air Bearings, Flat air bearing (40 mm Dia.)] and the links are configured to be horizontal so that there is no gravity effect. Compressed air is supplied to the air bearings from the air tanks on the base. The first link is mounted on the base through a DC motor with an encoder [Maxon Motor, RE40 + MR Encoder (maximum torque: 2" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000162_b107541c-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000162_b107541c-Figure1-1.png", "caption": "Fig. 1 Schematic representation of (a) the cross-section and (b) the plan view of a RAM electrode.", "texts": [ " It consisted of seven RAM electrodes in a hexagonal array and thus contained more than 8000 microelectrodes. The RAM electrodes were random assemblies of inlaid microdisks.11,12 These comprised conducting carbon microdisks wired in parallel and embedded in epoxy resin. The individual microdisks were the sectioned ends of the carbon fibres. To ensure a good seal between the carbon fibres and the epoxy resin, the fibres were pre-oxidised to create oxygen-containing functionalities on their outer surfaces. The general outline of a RAM electrode is shown in Fig. 1. The radius of each microelectrode was 3.5 mm and their median nearest-neighbour distance was approximately 70 mm. Prior to each experiment, the working surface of the very large assembly was prepared as follows: (1) The assembly was abraded with an aluminium oxide slurry on a new, clean polishing cloth (from Buehler Ltd., Illinois, USA) for at least 30 s. It was then thoroughly rinsed with deionised water. (2) In order to remove all traces of slurry, the assembly was washed on a clean, damp polishing cloth without slurry and rinsed with deionised water" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003434_6.2008-4505-Figure9-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003434_6.2008-4505-Figure9-1.png", "caption": "Figure 9 3.88\" diameter seal with L/R=0.516", "texts": [], "surrounding_texts": [ "Six different configurations of proof of concept foil face seals were fabricated in order to assess the impact of flow path radial length, axial preload and surface velocity on leakage. The six test articles are shown in Figure 5 through Figure 10. Two 9-inch OD thrust foil bearings, two 4.37-inch OD and two 3.82-inch OD configurations were fabricated providing different L/Ro ratios, angular gaps between pads and different flow paths. For each test seal, the outer periphery of the compliantly supported foil pads was open to atmosphere, thereby presenting a leakage path along the radius as opposed to the closed ends shown in Figure 3. Figure 11 and Figure 12 schematically show the tested configurations with the open ends and the primary flow paths. The importance of the open ends for these initial tests was to determine the baseline resistance to flow due to the total axial gap (htotal) in the angular segments between pads, the gap beneath the bump foils (hb) and the gap between the top smooth foil and the disc (hfilm), all without the end flanges and secondary seal elements to restrict flow. This would allow for an assessment of critical design parameters for the fundamental seal shape, such as an assessment of the importance of L/Ro ratio. Additionally, tests of the candidate seals with this arrangement and conducted under rotating conditions would, when compared to static/non-rotating tests, verify that the hydrodynamic pressures were generated and reduce total leakage. As shown in Figure 2 and Figure 3, both the angular gap and open ends will be eliminated in the final configuration, thereby only allowing leakage flow to pass through the minimum film height (hfilm). By eliminating the larger gaps associated with the pad angular spacing and the region beneath the compliant bumps in the face seal configuration, the leakage will be substantially reduced from the measured baseline configuration. It should be noted that during testing the total gap height was on the order of 0.031 inch, whereas hfilm was either zero when static tests were conducted or on the order of 0.001 inch when dynamic testing was conducted at speeds from 24,000 to 60,000 rpm. While hfilm initially increases during dynamic testing (see Figure 11), the generated hydrodynamic film pressure resists the radial inflow/outflow of high pressure air. Thus, the air is forced to flow behind the top smooth foil and through the passages formed by the bumps (approximately 0.021 inch high) as well as the gaps between individual pads. It should also be noted that with the high pressure at the OD, the inward directed pressure driven flow will also be restricted by the inherent outward self pumping action of the disc. Finally, while the gap between pads is approximately 0.031 inches high and between 6\u00b0 and 10\u00b0, flow in this gap is turbulent, even for differential pressures as low as 2 psig. Thus, when the end flanges are introduced at the OD and the pads overlap one another, the primary leakage path will be through the very narrow hydrodynamic film region, which, at about 0.001 inch, will result in leakage rates well below any present technology." ] }, { "image_filename": "designv11_32_0002872_s000192400000186x-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002872_s000192400000186x-Figure2-1.png", "caption": "Figure 2. The climb turn of agricultural aircraft.", "texts": [ " 3 it is evident that the flight path becomes steeper when the normal load coefficient n increases, especially for relatively moderate values of the bank angle \u03d5 (<45\u00b0). This is logical, as the path angle in the vertical plane \u03b3 and the rate of turn, d\u03c8/dt, as a function of the bank angle \u03d5, during turning flight. Generally, the normal and tangential load factors are changed during turning flight. However, these factors are assumed to be constant for the approximate calculation, during some parts of turn path (the first part of the path is 0\u00b0 < \u03c8 < 60\u00b0, the second part of the path is 60\u00b0 < \u03c8 < 95\u00b0 and the third part of the path is 95\u00b0 < \u03c8 < 180\u00b0, see Fig. 2). The results of numerical calculation are not affected significantly by this assumption(8-11). Substituting the relation dh/dt = VSin\u03b3 into the system of differential equations of motion (Equation (4)), we eliminate time from the system and obtain the following system of differential equations: as a function of the path angle in the horizontal plane (\u03c8). The fourth equation, which results directly from the last equation of the system (Equation (4)), can also be added to the system of equations" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000348_1.1523143-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000348_1.1523143-Figure3-1.png", "caption": "FIG. 3. ~a! Proposed groove configuration of the unidirectionally rubbed substrate. ~b! Proposed groove configuration of the multidirectionally rubbed substrate. In the figure, f m represents the elastic anchoring energy per unit area in the first rubbing direction; f n represents the elastic anchoring energy per unit area in the final rubbing direction.", "texts": [ " Therefore, the groove density can be reasonably assumed to increase with the cumulative number of rubs, increasing the rubbing strength. Notably, rubbing tends to shear the top surface of the PVA-coated substrate. Consequently, microgrooves on a ~7,1! rubbed substrate are not as well defined as those on a ~1,0! rubbed substrate.11 According to the AFM surface images shown in Fig. 2, a model that assumes substrate with various groove densities along various rubbing directions is presented. Consider a cell with sufficiently deep and narrow grooves, as depicted in Fig. 3~a!: The LC molecules align parallel to the grooves.9,20\u201322 However, if the LC molecules are forced to lie against the surface while the director lies across, rather than parallel to, the grooves, then the additional elastic energy per unit volume d f equaling 1/2k(Aq2)2 exp(22qz) is required, where k is the elastic constant, A is the peak to valley groove depth, q5 2p/L is the wave vector, L is the groove wavelength and z is the distance from the grooved surface.19 Therefore, the additional elastic energy per unit area generated by the distortion due to the gratinglike wavy surface is f 5*0 `d f dz51/4kA2q3" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001268_cca.2000.897429-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001268_cca.2000.897429-Figure1-1.png", "caption": "Figure 1: Definition of state space regions.", "texts": [ " 1 Choose the nonlinear feedback control law U* = --f^(z1 , Q ) - ~ 1 x 2 - Y ' s a t ( s , ~ ) (17) Then the derivative of Lyapunov function candidate is v 5 -[Is[ 5 0. (19) With this sliding-mode control law(u*) the nonlinear system can be stabilized.To avoid the chattering effect, we used the saturation function as the smooth control law in Eq.(17), g' iven as 1, S > E (20) sat(s,-E) = S I \u20ac , --E 5 s 5 E { -1, s < --E . 3 Control Algorithm Implementation The proposed control algorithm invokes three different computations, depending on categorizations of the system state into one of three regions. The regions are illustrated in the phase plane in Fig.1. In fig.1, E is determined from the singular solution with E = I lz;:a2 I. In region I, bang-bang time optimal control is appropriate with the performance index J 1 . In region 11, linearized feedback control law is to be used along the sub-arc of singular solutions. Finally in region 111, sliding-mode control is added to improve the robustness and stability of system. Actually near the target set of states, it prevents the oscillation of control law by changing values smoothly. All combined algorithm can be implemented with a computer" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003429_09544054jem898-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003429_09544054jem898-Figure1-1.png", "caption": "Fig. 1 Schematic drawing of a wingbox", "texts": [ " Section 3 discusses positional displacements of an individual rib foot, and section 4 considers the influence of tightening bolts. Both theoretical and experimental considerations are presented. The production of a commercial airplane requires the integrated assembly of several sections including wings, body, tailcone, etc. Each section consists of several frames of assemblies and skin panels. Each assembly is further divided into several subassemblies. For example, an aircraft wingbox consists of three main components as shown in Fig. 1; the ribs, the longitudinal spars, and about four skin panels. The wingbox is approximately 36m long and about 7.5m wide [14]. The longest skin panel covers an area of about 27 ribs, i.e. about 18m [15]. The assembly of these large components involves the use of large and complex jig and fixture structures [16]. The components are subject to geometric variations at the time of assembly, which can slow down the assembly process and affect manufacturing efficiency. The lead time to assemble a typical Airbus wingbox is up to 3 weeks" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002483_s00542-006-0305-x-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002483_s00542-006-0305-x-Figure1-1.png", "caption": "Fig. 1 Model of lubricated roughness contact with sliding. a Two lubricated roughness surfaces in sliding contact. b Composite roughness surface with adsorbed surface film", "texts": [ " Such point contact is reasonably considered to be a representation of a single asperity contact in microcosm. Since asperities are randomly distributed in height, we assume that all the three lubrication regimes exist simultaneously in lubricated rough contacts with sliding. In addition to the lubricated contacts, direct metallic contacts formed between higher asperities are inevitable as well due to thermal desorption of the adsorbed surface film (Wu and Cheng 1991). The currently accepted lubricated friction and wear model, which is shown in Fig. 1, consists of four regimes according to the deformation of the asperities in contact, i.e., the adhesion regime, boundary lubrication regime, micro-EHL regime and partial lubrication regime. The micro-EHL regime is considered to be formed by transition of the boundary lubrication regime when two contacting surfaces are brought into sliding. Since this transition is usually incomplete, concurrence of these two regimes is possible. As shown in Fig. 1b, we assume that all asperities on the composite surface are covered with an adsorbed surface film of uniform thickness tb before contact. The formation of the adsorbed surface film is attributed to either physical or chemical adsorption of additives in lubricants. From the experimental results measured with point contacts by Johnston et al. (1991), the thickness of the adsorbed surface film is generally not greater than 15 nm. Direct metallic contacts occur only in asperities whose heights are greater than a specific value xM above the plane of the opposing surface, where xM represents the critical interference below which direct metallic contact is avoided" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002947_978-3-540-75103-8_18-Figure12-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002947_978-3-540-75103-8_18-Figure12-1.png", "caption": "Fig. 12. Morphed mesh on cyclic symmetry faces. The entire rotationally symmetric model is shown in Fig. 1.", "texts": [ " A triangular mesh is created using the TQM algorithm on a four-edged quadrilateral flat face (Fig. 11a). The elliptical face in Fig. 11b, represents the target face that is still flat and 4-edged, but is elliptical in shape. The triangular mesh on the elliptical face is morphed from the mesh on the quadrilateral face. All nodes and elements of the source face have a one-to-one correspondence with the nodes/elements on the target face. A radial sector of an Aluminium impeller as shown in Fig.1, is substructured with cyclic symmetry boundary conditions. Two radially cut faces, as shown in Fig. 12, represent the cyclic symmetry faces. A boundary condition needs to be applied to these faces that equate the degree of freedom of each node on these faces in the Hoop direction ( -direction). In order to achieve this, it is necessary to have the same number of nodes/elements on these faces. The proposed mesh morphing technique is used to morph the mesh on the source face (any one of the symmetry faces) to the target. The meshes are shown in Fig. 12. Cyclic symmetry boundary conditions are applied on the nodes of the source and target faces. Next, this radial sector of the impeller, is analyzed for centrifugal load (rotating at 3000 RPM). Table 1.0 lists the maximum displacement, maximum Von Mises and maximum Octahedral shear stress for the radial substructure in comparison with those obtained from a full model solve. The cyclic symmetry model has about a fifth of the DOFs of the full model. The results indicate the accuracy of the sub-structured finite element model" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001793_13552540510623576-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001793_13552540510623576-Figure6-1.png", "caption": "Figure 6 Schematics of measurements for parts", "texts": [], "surrounding_texts": [ "R. Shivpuri, X. Cheng, K. Agarwal and S. Babu" ] }, { "image_filename": "designv11_32_0003518_s0001924000052763-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003518_s0001924000052763-Figure1-1.png", "caption": "Figure 1. The local sub-element within a SHEBA element.", "texts": [ " To simplify reference to figures and equations of TN 15(1), their numbers are postfixed with a roman one or two to indicate in which part they appeared; no further identification tag to the Technical Note in question is used. In contrast, the numbers of figures and equations of refs. 2 and 3 are prefixed with I or II to denote the relevant part; in addition, the reference number is also quoted. We first introduce within a SHEBA element and at a point \u00a3i. \u00a32, \u00a33 the local sub-element defined by the vectors 3x dx. dx \u2014\u2014 = \\ a = maea ; -^\u2014 =x / 3 = msef( ; -^\u2014=x v = m v e Y \"feci \"iff \"feY r . . . (i) see also Fig. 1 and the local infinitesimal triangle shown in Fig. (3,1). A similar definition for the local sub-element is given in ref. 2 for the TRIC and TEC elements. Follow ing the theory of ref. 3 (section 1,3), we consider the natural modes in the sub-element, which we write in the partitioned forms PLM = px,i = n\u00bb\u00a3No= {maea0 mfao myey0} \u2022 (2) P L B = P M = H\u00bbX\u201e= {maXa m^Xs myXy} \u2022 (3) corresponding to membrane and bending actions respec tively. Comparison with the definitions of ref. 3 confirms that pLM and p i B may be understood as the first two natural modes of the sub-beams in the a, B, y directions", " Using the standard relation between component stresses and total strains the typical stress cra at a distance \u00a3 is obtained from cra (\u00a3) = \u00a3 S I Km0 + \u00a3 -^ Kavl I T (15) in which the elements of the (3 X 3) material stiffness matrices KNO a n d Km \u0302 & denoted by K^O and KMV1 respec tively. The measure R is explained in section 6.1 of Part II. Since the ratios may be considered as small against 1, eqn. (15) reduces to a first approximation to o-, (0 = E ^ ( *cav0 + \u00a3 \u2014 Kav] j (e v 0 +\u00a3e v l ) l l - \u00a3 - ^ \u2014 I . (16) Consider a cross-section perpendicular to an cu-curve. The resultants of the component stresses applied to it may be represented by a membrane force Na and a bending moment Ma per unit length; see Fig. 2. Following Fig. 1 the typical height ha of a local sub-element in the middle surface is given by ha = 2ClL/ma = S/ma. If we introduce a strip of width dha between two infinitely close a-curves in the middle surface, the corresponding width dha' at a distance z is / = ( 1 + ^ ) d ^ ( 1 + ^ ) ^ - ( 1 7 > where Paa is the radius of curvature in a cross-section per pendicular to the a-curve. We immediately deduce from eqn. (38,1) using the mean radius of curvature Rm dh 1 _2_ Rm 1 R\u201er (18) The contribution of the component stress flow crad/ia'dz to the normal force Na and bending moment Ma is now dJVBdAa = o-", " The triangular local sub-element is then represented in the adirection by an a sub-beam. For the evaluation of the geometrical stiffness we also require the natural load vector PL3. From the theoretical and computational point of view it is most convenient to establish PL3 by considering the equilibrium on each com ponent sub-beam. We can then apply the standard beam theory as in ref. 3. Since P13 is effectively associated with the shear forces hQ in the sub-beams, we may write for a typical fi component ^ ( ^ G H ) = - ^ d P ^ dsu (29) which may also be deduced from Fig. 1,1 of ref. 3. Using eqn. (27a) in eqn. (29) we find m \u2022 1 3 ( 1 - -fsr^^\u2014i d (Mf J (30) which completes the analytical derivation of the PL vector. For computational purposes it is suggested to determine the derivatives of (/J\u201eMw) by numerical interpolation. When computing the loads P by way of eqn. (11,67) of ref. 3, we can ignore the contribution of P13 as in the case of a single beam {see eqns. (11,67, 70)CS)). Thus we obtain P=J [a 1 i t P L 1 + al2 tPl2] ^ - . (31) 4. The Geometrical Stiffness of the SHEBA Element Clearly, the theory for the geometrical stiffness of a local sub-beam in space developed in sections 11,4" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003350_vppc.2008.4677571-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003350_vppc.2008.4677571-Figure5-1.png", "caption": "Figure. 5 control-winding phasor diagram.", "texts": [ "00\u25cbC 2008 IEEE In the similar way, the commanded active power and hysteresis controller can be written as: * * DC DC DCPI( , )s s s sp U U U= \u22c5 (8) s s 1 if 0 if p p p p d p H d p H = >\u23a7\u23aa \u23a8 = < \u2212\u23aa\u23a9 (9) where PI( , ) ( ) ( )d ix y K x y K x y dt= \u2212 + \u2212\u222b , * \u02c6s s sq q q= \u2212 , * \u02c6s s sp p p= \u2212 . Via the digitized variables qd , pd and the output of the sector identifier, the appropriate vector can be selected from the OST. The optimal switching table (OST) can be determined in the following section. This section analyses the effect of the basic voltage vectors on the instantaneous power. Assuming that the orientation of the three phase control-winding in space at any instant of time is shown as Fig.5, the six active switching states will result in the voltage vector 1U , 2U ,\u2026 6U at that time. The space plane is subdivided into 12 sectors. Considering the anti-clockwise direction of rotation of flux to be positive, it should be noted that s\u03c8 lags behind r\u03c8 in the generating mode. s\u03c8 can be controlled by the control-winding voltage su according to s sdt\u2248 \u222bu\u03c8 . Assuming that s\u03c8 locates in Sector 1, as shown in the Fig.6. 1U , 5U and 6U make s\u03c8 move away from r\u03c8 . This results in the increase of angular \u03d5 in the negative direction, which augments the active power drawn from DWIG" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003429_09544054jem898-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003429_09544054jem898-Figure3-1.png", "caption": "Fig. 3 FEM of whole rib", "texts": [ " Furthermore, of the five stages in the wingbox assembly process, this study concentrates on the bolting of the skin panels to the ribs. All deformations of the rib and positional variations of the rib feet during the installation of the skin panel are investigated. OF THE NEXT JOINT The FEM has been used to investigate the geometric variations during the assembly process. It was assumed that the material has a linear behaviour in terms of geometric variations. A three-dimensional finite element model of the rib structure of the wingbox was constructed using ABAQUS CAE, and it is shown in Fig. 3. The rib was meshed using hexahedra nodes and three-dimensional solid elements (reduced integration C3D8R elements) with a higher mesh density in the rib feet than in the rest of the model. This resulted in 10 190 nodes and 4322 elements. Fixed constraint conditions were applied around the lines AB and CD to restrict any movement on the top and bottom of the rib on the three orthogonal axes in order to represent the pre-fastening condition of both the front and rear spars of the rib respectively" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000673_1.1478075-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000673_1.1478075-Figure3-1.png", "caption": "Fig. 3 Cross section of test stator: inlet annulus", "texts": [ " Data reduction is also expedited using software. A comprehensive logic-controlled monitoring and fault detection system provides partially or totally unassisted safe shutdowns to protect the test facility and apparatus. OCTOBER 2002, Vol. 124 \u00d5 959 17 Terms of Use: http://www.asme.org/about-asme/terms-of-use 960 \u00d5 Vol. 124, Downloaded From: http://gasturb Impedance Identification Two hydraulic shakers, mounted orthogonal to one another, are attached to the test stator via isolation \u2018\u2018stingers.\u2019\u2019 The \u2018\u2018stingers,\u2019\u2019 as shown in Fig. 3, were designed using guidelines from Mitchell and Elliott @11#. The shakers can apply dynamic loads up to 4,450 N ~1000 lb.! at frequencies up to 1000 Hz. The seal reaction forces are measured as the stator is excited using the hydraulic shakers. The equation of motion for the stator mass M s in Fig. 3 is M sH x\u0308 s y\u0308 s J 5 H f x f y J 1 H f xg f yg J , (2) where x\u0308 s and y\u0308 s are the ~measured! orthogonal stator accelerations, f x and f y are the ~measured! shaker component input forces, and f xg and f yg are the ~measured! annular gas seal reaction forces. The stator is simultaneously shaken at multiple discrete frequencies using a predetermined pseudo-random waveform. The pseudo-random waveform is an ensemble of discrete sinusoids with frequencies every 10 Hz from 40 out to a potential maximum of 440 Hz" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002846_tie.2007.900323-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002846_tie.2007.900323-Figure5-1.png", "caption": "Fig. 5. Diagram of Hall-effect sensor states relative to rotor position (\u03b8rh).", "texts": [ " It is noted that any one of (25)\u2013(27) can be used to determine position; however, calculating all three and taking an average has been found to be most effective in terms of reducing error associated with measurement noise as shown in [22]. The second component of the CPSH observer uses the Hall sensor to provide rotational-based estimation. Prior to describing the component, it is useful to define angles and axes used in its derivation. For simplicity, and without lack of generality, position angles are defined using the cross-sectional view of a two-pole machine shown in Fig. 5. Therein, the angle \u03b8r = \u03b8rh + \u03c6h (28) is shown where \u03b8r is defined as the angle between the q-axis and the as-axis, \u03b8rh is defined as the angle between the q-axis and the h-axis (herein defined orthogonal to the location of the phase-a Hall-effect sensor), and \u03c6h is the angle between the h-axis and the as-axis. In the machine used, the Hall-effect sensor (labeled ha,) is mounted on the inside of the endplate. The observer proposed utilizes transitions in sensor states to detect position. Ideally, transitions occur at every \u03c0 interval with the first occurring at \u03c0/2 radians relative to the h-axis, as shown in Fig. 5. Transition angles, labeled as \u03b8rhti, relative to sensor states are shown in Table I. To estimate the rotor position between state transitions, the angle is updated using \u03b8rh = \u222b \u03c9rdt+ \u03b8rhti (29) where \u03b8rhti is the angle at the \u201cith\u201d transition and \u03c9\u0304r is the average rotor angular velocity during the previous Hall-effect sensor state. The average rotor speed is determined from \u03c9r = \u2206\u03b8rh \u2206t (30) where \u2206\u03b8rh is the angular displacement of the rotor position over the previous Hall-effect sensor state and \u2206t is the difference in time between transitions" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002483_s00542-006-0305-x-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002483_s00542-006-0305-x-Figure3-1.png", "caption": "Fig. 3 Geometry, parameters and coordinate system. a Geometry and parameters of herringbone groove bearing. b Coordinate system of herringbone groove bearing. c Geometry, parameters and coordinate system of multi-taper bearing", "texts": [ " Thus, the rough contact pressure is given by pc;absorption \u00bc 4 3 E\u00f0NsRsrs\u00de ffiffiffiffiffi rs Rs r x3=2 p W\u00f0d\u00de; \u00f011\u00de where W\u00f0d\u00de \u00bc Zd\u00fexM d tb d d\u00fe tb xp 1:5 ws\u00f0d\u00de dd: \u00f012\u00de Based on the assumptions of the previous section, the real contact area, ac,absorption, and shear stress, sc,absorption, of the boundary lubrication regime are both equal to zero. 3.3 Partial lubrication regime The governing equations for the hydrodynamic pressure of rough contact, ph, have been derived by Patir and Cheng (1978, 1979). In the coordinate system shown in Fig. 3, the average flow Reynolds equation takes the form of @ R@U /pU h3 g @ph R@U \u00fe @ @Z /pZ h3 g @ph @Z \u00bc 6 _HZ @E hT\u00f0 \u00de @U \u00fe 6r _HZ @/sU @U \u00fe 12 @E hT\u00f0 \u00de @t ; \u00f013\u00de where /pF, /pZ and /sF are the pressure and shear flow factors, respectively, and r is the standard deviation of the combined surface. E(hT ) denotes the expectancy of local clearance, hT, and can be expressed as (Feng et al. 2003) E hT\u00f0 \u00de \u00bc h\u00fe F1 h\u00f0 \u00de \u00f014\u00de with Fn h\u00f0 \u00de \u00bc Z1 h d h\u00f0 \u00denw d\u00f0 \u00de dd; \u00f015\u00de where w (d) is the PDF of the combined rough surface and h is the clearance measured from the mean plane of the combined rough surface to the opposing surface. Considering the geometry of the journal bearing and coordinate system in Fig. 3, the clearance can be written as h \u00bc h0 \u00fe D hp \u00fe eX cos U\u00fe eY sin U \u00f016\u00de where h0 is the nominal clearance, hp the depth of groove, and D = 1 for the groove region while D = 0 for the land region. For simplicity, the two contacting surfaces are assumed to have an isotropic roughness structure and the same standard deviation. Thus, the shear flow factor /sF equals zero and the pressure flow factors, /pF and /pZ, are given by /pU \u00bc /pZ \u00bc 1:0 0:9 exp\u00f0 0:56H\u00de; \u00f017\u00de where H = h/r. From the reference (Patir and Cheng 1979), the stress arising from shear of the lubricant in rough contact is given by sh \u00bc gR _HZ h /f \u00fe /fs /fp h 2 @ph R@U ; \u00f018\u00de where /f, /fs and /fp are the correction factors due to averaging the shear flow, transportation flow and pressure flow, respectively, of the shear stress", " For the herringbone groove bearing, the journal slips over the bearing surface before taking off from the contact. For the multi-taper bearing, the trajectory has two patterns depending on the journal\u2019s contact position. When the journal contacts the land of the bearing, the trajectory is similar to that of the herringbone groove bearing but the slipping distance is much shorter. However, when the journal is located in the groove, the journal leaves the contact in a direction almost opposite to the load (see Fig. 3). For this reason, friction and wear of the multi-taper bearing are strongly dependent on the journal\u2019s contact position. The power consumed at the beginning of startup is shown in Fig. 9. Clearly, the power consumption of the herringbone groove bearing is much higher than that of multi-taper bearings. Thus, the latter outperforms the former in regard to lowering power consumption. Within the multi-taper bearings, power consumption increases with the number of tapers. Figure 10 shows the starting torque of herringbone groove and multi-taper bearings for different groove width ratios, hp\u00f0\u00bc hp=h\u00de (see Fig. 3a). In contrast to the power consumption, the starting torque of the herringbone groove bearing is generally lower than that of multi-taper bearings. For multi-taper bearings, the starting torque varies with hp both when the journal lies on the land and in the groove. Note that there exists an optimal value of hp for each multi-taper bearing at which the starting torques of journal-on-land and journal-in-groove are equal, so that the starting torque becomes nearly independent of the journal\u2019s initial position" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002839_tmag.2007.891390-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002839_tmag.2007.891390-Figure1-1.png", "caption": "Fig. 1. Elementary scalar play hysteron.", "texts": [ " These obstructions to the displacements lead to the hysteretic behavior of the material and associated to energy losses. With the Play model the material induction is calculated by the sum of the inductions associated with a set of pseudo-particles called hysterons as follows: (1) Generally, the hysterons can be assumed with equal weights, i.e., (2) Other functions can also be chosen but in this paper (2) was employed. The losses associated to each hysteron depend on the width of the operator. For instance, Fig. 1 shows, for the scalar case, a Play hysteron with its associated width . 0018-9464/$25.00 \u00a9 2007 IEEE The inductions associated to the hysteron can be evaluated using an anhysteretic function. In the 2\u2013D case, we use the following equation: (3) In (3) and are, respectively, the unity vectors in and directions and , , , and are material parameters to be obtained from experimental hysteresis loops. The time evolution of hysteron depends on its previous value , and on the actual effective field vector value and follows the next rules if if (4) where is a distribution factor of hysterons and (5) The effective field is calculated from the magnetization and the magnetic field value by (6) In (6) (7) is a tensor which must also be determined from experimental hysteresis loops obtained accordingly to the rolling and transversal directions if the anisotropy is considered" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000073_1.1494081-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000073_1.1494081-Figure2-1.png", "caption": "FIG. 2. Schematic of laser drilling model.", "texts": [ " and liquefaction ~suffix l!, as in Eq. ~1!: f5JeLe1JlLl . ~1! This model assumes that all the optical energy is absorbed at the base of the hole, with vaporization occurring 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: 202.28.191.34 On: Fri, 19 Dec 2014 09:42:12 above the surface of a thin layer of liquid material. The resultant vapor pressure forces the liquid region to be ejected ~see Fig. 2!. The assumption that laser beam absorption only takes place at the base of the hole means that we must also assume that the melt region adhering to the walls acts in a purely reflective manner. As light is absorbed, the liquid layer at the bottom of the hole grows in thickness, and the pressure from the vapor layer above it increases until it reaches a point at which this vaporization pressure overcomes the surface tension holding the liquid layer in place and liquid ejection occurs. The thickness of this liquid layer region depends on the optical energy of the laser pulse" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001047_12.478510-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001047_12.478510-Figure6-1.png", "caption": "Figure 6. Prediction of second measurement.", "texts": [ " (Several of the transformed sample points are below ground because the initial distribution of tilt and acceleration magnitude was broad enough that for some values the missile would fall over immediately after launch. This leads to a large uncertainty in the predicted slant range.) In addition, there are lines from the center of the ellipse to the mean estimated launch point and to the actual observation (whose uncertainty is too small to show up here). The updated launch point estimate is shown in Fig. 5. The prediction for the third observation is shown in Fig. 6, and the prediction for the fourth observation is added Proc. SPIE Vol. 4728 269 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 05/19/2015 Terms of Use: http://spiedl.org/terms in Fig. 7. Its elevation from the launch point is intermediate between the first two predictions. The uncertainty in predicted slant range has not improved much. The estimated launch point after three updates is shown in Fig. 8. The estimate has a bias in crossrange. Let dll = [L\u0302\u03bb\u0302]T \u2212 [L\u03bb]T be the error in the estimated launch position, and Pll be the corresponding part of the estimated covariance" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000299_robot.2001.932795-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000299_robot.2001.932795-Figure2-1.png", "caption": "Figure 2 . Determine the layer thickness according to the AC", "texts": [ " Then, according to maximum acceptable thickness, t, , that we defined before slicing process, the algorithm pre-slices the 3D CAD model into 2D layer contour at height, h=t,,, . At present, scan level is intersecting the edge of the triangles, thus the points of contour are generated. The contour circumference of the layer can be calculated by those point data. Similarly, the contour circumference of adjacent layers also can be calculated and then the difference in contour circumference between adjacent layers can be easily obtained. Based on calculating the relation of the geometry, the layer thickness, t , can be determined, as shown in Figure 2. The symbol A c expresses the difference in extended contour circumference between adjacent layers. And p\u2019 is the projection point of the exixemity point, p,+, of the extended contour circumference, c,+, . According to calculate the geometric relation between the triangle p\u2019p,p,+, and the triangle gp\u2019p,,, , the layer thickness, t , to the slice layer is obtained. As shown in Figure 3, if there is more than one contour at the slice level, the algorithm must sort them and ascertain exterior and interior contous at the slice level" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003377_ijvas.2007.016408-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003377_ijvas.2007.016408-Figure2-1.png", "caption": "Figure 2 Wheel and its contact with the ground", "texts": [ ", 2005) on Figure 1: with wind 1 2 3 4 1 2 3 4 cos( )( ) cos( )( ) sin( )( ) sin( )( ) LF F F F F F F F F F \u03b4 \u03b4 \u03b4 \u03b4 = + + + + \u2212 + \u2212 + \u2211 x f r f r x x x x y y y y and 1 2 3 4 1 2 3 4 sin( )( ) sin( )( ) cos( )( ) cos( )( ) SF F F F F F F F F \u03b4 \u03b4 \u03b4 \u03b4 = + + + + + + + \u2211 f r f r x x x x y y y y 2 1 1 2 1 2 1 1 2 2 3 4 3 4 4 3 3 4 {cos( )( ) sin( )( )} {sin( )( ) cos( )( )} {sin( )( ) cos( )( )} {cos( )( ) sin( )( )}. I F F F F F F F F F F F F F F F F \u03b4 \u03b4 \u03b4 \u03b4 \u03b4 \u03b4 \u03b4 \u03b4 = \u2212 + \u2212 + + + + + + \u2212 + + \u2212 + \u2212 Z f f f f f r r r r r t x x y y L x x y y L x x y y t x x y y \u03c8 (3) The model representing the dynamics of each wheel i is found by applying Newton\u2019s law to the wheel and vehicle dynamics Figure 2: In this paper, the task is to design virtual sensors (observers) for the vehicle to estimate the states, parameters and forces which need expensive sensors for their measurement. But due to the fact that it is not easy to apply an observer for the global model, equation (4) are taken at first, a second order sliding mode observer based on the modification of super-twisting algorithm is proposed for each equation (4) to observe the angular velocity of the wheel and to identify the longitudinal force" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002576_rd.186.0521-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002576_rd.186.0521-Figure2-1.png", "caption": "Figure 2. Details of the test fixture in Fig. I. (a) Schematic view of the head and tape region. (b) Closeup of the glass head region of the test fixture.", "texts": [], "surrounding_texts": [ "The desire to gain a better understanding of the pheno mena associated with tape transport in magnetic record ing is frequently cited as one of the main motivating fac tors in foil-bearing studies of the last two decades. The impact of this important application on the development of foil bearings continues because the technological re quirements for recording on flexible media demand that these phenomena be even better understood and con trolled. The trend toward higher recording bit densities and higher data transfer rates requires smaller separation between head and tape and larger relative velocity be tween the two. Moreover, significant and rapid damage to the medium and undue wear of the head must be avoided, hence the importance of maintaining and con trolling a suitable air filmat the head-to-tape interface. The interaction between an elastic foil and a fluid film has been extensively studied in recent years. This effort has provided considerable insight into the behavior of foil bearings, but it has not been effectively applied to investigating the performance of noncircular heads and to wave propagation phenomena in tape. In an attempt to analyze such problems, Stahl, White, and Deckert (I] developed a model of the interaction between tape and fluid film that differs in a number of respects from con ventional foil bearing studies. In [1] the undeflected straight-line configuration of the tape is used as a refer ence configuration, whereas in conventional approaches the coordinate system is attached to the surface of the cylindrical head. Conventional foil-bearing analyses employ asymptotic foil boundary conditions; the Stahl, White, and Deckert model, on the other hand, allows one to consider a finite piece of tape and to write appropriate conditions at each end. Finally, the time-dependent terms are an integral part of the formulation in [1], whereas these terms are not usually present in conven tional theory because it is mainly concerned with steady state solutions. The intent of this paper is to present an experimental study that complements and verifies some aspects of the theory presented in [1]. In particular, we have focused our attention on comparing theory and experiment for the case of the steady-state separation between tape and head. Licht [2] and Ma [3] have provided such a com parison between conventional theory and experimental data. However, because conventional theory is con cerned only with asymptotic boundary conditions, those authors did not provide some of the geometrical details which would be required if Stahl et ai. were to simulate their experiments. Moreover, most of their tests would constitute a case of large penetration of the head into the tape; a situation for which the linearized theory of [1] is not particularly appropriate. As a consequence, it was decided to design an experiment that closely duplicates the conditions underlying the theoretical considerations in [1] .Another feature of the experimental investiga tions reported in the literature is that the conditions of the experiment lead to rather large separations between the foil and the head, usually greater than three Mm. In 521 NOVEMBER 1974 WHITE LIGHT INTERFEROMETRY technique is difficult to use and the interpretation of the photographed fringe patterns is a laborious task. Lin and Sullivan [7] report on a white light interferometric method for measuring thin air films. In contrast to the method presented in [5, 6], this technique uses rela tively simple equipment to create and monitor the white light interference pattern. In addition, the resolution for spacings under one f-Iom is excellent and, of course, the interference pattern provides a direct full-field view of the spacing. These features make it an attractive alterna tive to the commonly used techniques of gap measure ment by means such as the capacitance probe [2, 3] or by finding the signal-amplitude loss of a prerecorded sig nal [4]. In fact, the utility of white light interferometry in measuring sub-urn spacing on flexible media has been demonstrated very recently by Tseng and Talke [9]. The head-medium configuration investigated in their paper, however, is different from the one presented here. Tape loop \\ ~/ Glass cylindrical head (a) +12V -12V Power + 6V Power Capstan supplies driver IL motor -48V t~ Tachometer I Square wave Counter generator .[]. Photonic - Oscilloscope f- Stroboscopic - Microscope psensor light source / Tape loop with reflective marker / Photonic probe 1 522 (b) Figure 1 Apparatus for measuring the gap between glass model of the magnetic recording head and the moving tape. (a) Block diagram of system. (b) Photograph of apparatus. magnetic recording, however, the air film should be one f-Iom or less, as was pointed out in [1]. Only limited data seem to exist for spacings in this region [4]. Hence, another objective of the present work is to provide more data for these low spacings and to compare these data with the model. To measure these spacings it was decided to explore the use of light interference methods. Some of the early work in this area is that of Lipschutz [5] and Harper, Levenglick, and Wilczynski [6]. These investigators de termined the separation of a foil from a cylindrical sur face by interpreting the fringe pattern obtained from a specially constructed three-color camera. However, their Interferometric technique The essential elements of the experimental apparatus are shown in Figs. 1 and 2. The test fixture is a parallel track tape deck using a capstan motor to move the tape, a vacuum column to provide tape tension, a number of air bearings for support and guiding, and a dummy head. The tape deck accomodates a tape loop 0.025 m (1 in.) wide. The tape loop used in the experiments is made of clear Mylar and is approximately 2.44 m in length. A laser goniophotometer used to measure the surface roughness of the Mylar indicates that over 95 percent of the surface area the peak-to-valley distance was under 0.1 f-Iom. The head is a plano-convex cylindrical lens that is considerably wider than the foil. A flexible precision microscale with 127-f-Iom spacing between lines is at tached to the lens and is useful in accounting for head curvature when measuring distance along the head from the apex. The micro scale is shown in Fig. 3. The head assembly and the air bearings on either side of this assembly are mounted on precision slides which permit adjustment of head penetration and the wrap an gles over the head [Figs. 2(a) and 2(b)]. The distance between these air bearings is set at 0.084 m. The tape speed is measured by means of an electronic counter and a phototube pickup in conjunction with a 360-line circular digital tachometer disk. The error in the speed measurement is estimated to be less than 0.5 percent. The tape tension is determined from the dimensions and pressure in the vacuum column. The vacuum is monitored on a Dwyer Magnehelic pres sure gauge; the estimated error in the measurement is of the order of one percent. The contribution to the total error in the determination of tension due to inaccuracies involving the measurement of the tape width and the tape loop is negligible. s. M. VOGEL AND J. L. GROOM IBM J. RES. DEVELOP. 523 the influence of head curvature on the path length of a light wave, but this contribution is negligible. Since the field of view is about 1.9 mm and the smallest head radius used in the experiments is 12 rnrn, the maximum error due to curvature is approximately one percent. For the more frequently used larger radius this error is, of course, significantly smaller. In some preliminary testing with the apparatus, it proved difficult to obtain stationary fringe patterns be cause of the large amount of debris that collected at and passed through the head-tape interface. In the initial at tempt to alleviate this problem a static eliminator, which prevents the buildup of electrostatic charges, was intro duced into the tape path by fastening it between two of the air bearings. This arrangement did not sufficiently alleviate the problem, so that clean air had to be blown across the fixture. The cleaner environment was achieved by placing the apparatus in an enclosure that was open at one end and had a laminar flow bench at the other. The static eliminator was not removed after the fixture was located in front of the flow bench. These modifications to the setup corrected the debris problem. At the heart of the measurement system is an Ameri can Optical 3015 T industrial microscope. Using a Gen eral Radio 1538-A Strobotac as the microscope illumi nation source, we can obtain a single flash picture of the interference fringe pattern on 35 mm film. The micro scope is mounted to allow viewing the interface through the lens head and was placed on a slide that traverses a direction normal to the stationary frame of the fixture. This feature is important because the field of view of the microscope encompasses only a small portion of the tape. When the microscope is moved from one edge of the tape to the other, the entire spacing at the head-tape interface can be viewed. To ensure that the pictures are not taken when the splice in the tape is in the vicinity of the head, a reflective marker, detected by a photonic sensor, is affixed to the foil to trigger the Strobotac. Because detailed discussion of the interference pheno mena that occur at the head-tape interface and of inter pretations of the interference pattern created by a white light source can be found in [7] and in texts such as [8], we confine ourselves to a few brief comments. The color that appears at any point in a thin film depends on the light intensity at those wavelengths that undergo con structive interference. Light at other wavelengths is not visible because of destructive interference. Moreover, because a variation in film thickness leads to a variation in the wavelength intensities that are either strength ened or weakened, the colors that appear depend on film thickness. Newton's color chart shows the colors as a function of the film thickness. An artist's rendition of this chart was published in [7]. Such charts, however, are frequently misleading because they do not exactly match the photographed fringe pattern. This problem can be overcome by constructing a color band chart us ing the same light source, color correction filters, optics and film as is used in the white light interferometer. The scale shown in Fig. 4 is an example of such a chart. It was made by photographing the fringe pattern produced by placing one optical flat on another in a slightly non parallel position. Such an arrangement produces a thin wedge-like air film that produces all the colors for vari ous gap widths-from zero to the spacing at which colors become indistinguishable. The color band chart shown in Fig. 4 covers spacings only up to 1.27 110m. Beyond this spacing the interference pattern degenerates into a sequence of light and dark bands, each pair of light and dark fringes representing an order. Each order spans a spacing of approximately 0.31 110m. We estimate that our measurement for head-to-tape separations less than 1.27 110m is accurate to within \u00b10.05 110m, and for distances greater than 1.27 110m the measurement is believed to be correct to within\u00b10.15 110m. The principal source of error in these estimates is due to color interpretation. Some error is introduced because of NOVEMBER 1974 WHITE LIGHT INTERFEROMETRfr 524" ] }, { "image_filename": "designv11_32_0000449_jahs.45.118-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000449_jahs.45.118-Figure4-1.png", "caption": "Fig. 4. Face-gear grinding setup.", "texts": [ " Oil inlet temperature was set at 74\u00b0C (165\u00b0F). In addition, theoil system was equipped with a chip detector as well as a three-micron filter. Face Gear Grinding Setup The face gears used in the current tests were precision ground using a true generating method. The goal was to produce face gears having a quality of American Gear Manufacturers Association (AGMA) Class 12 or better. The method used employed a worm thread grinding wheel to generate the face gear teeth in a setup similar to that shown in Fig. 4. The worm wheel rotational axis was located oemendicular to the face gear . . axis at an offset distance. Duringgrinding, the worm rotatedabout its axis as it translated across the face gear teeth along a nearly radial line. The JOURNAL OF THE AMERICAN HELICOPTER SOCIETY Table 1. Test gear design data AGMA quality desired, achieved Number of teeth; pinion, face gear Module (mm) Pressure angle (deg) Shaft angle (deg) Face width (mm); pinion, face gear Hardness (R,); pinion and face gear RMS surface finish (km) AGMA pinion bending stress (MPa); translation was ataslnall angle to thctn~cradial lineand related to thelead angle of the worm" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003579_s00107-009-0324-2-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003579_s00107-009-0324-2-Figure3-1.png", "caption": "Fig. 3 Schematic diagram of the peeling test on a microlathe Abb. 3 Schematische Darstellung des Scha\u0308lversuchs auf einer Labordrehbank", "texts": [ " Then scanning electron microscopy (SEM) \u2013 energy dispersive spectroscopy (EDS) were made to characterize their microstructures. M2 peeling tools with 20\u25e6 sharpness angle and 0\u25e6 clearance angle were prepared from a M2 melted sample, M2 clad sample, and M2 conventionally hardened bar by using a cutting and grinding technique (Figs. 1b and 2b). Both the M2 melted and M2 clad peeling tools were tempered at 560 \u25e6C three time for one hour each prior to wear testing. The wear resistance tests for the M2 peeling tools were performed in a peeling microlathe (Fig. 3a) without replication. Wood disks were prepared from a bar of beech log with a length of 2 m. The log was rounded in a peeling lathe up to a diameter of 380 mm. The wood disks were cut from the rounded log with a thickness of 18 mm. Considering the fact that about 50% of the prepared disks contained the defect of knot, the disks for the wear test were in combination between disks free of knots (30 pieces) and disks with knots (30 pieces). Only one tight knot with a diameter less than 5 cm near the outer circle was allowed for each disk with knot", " At every specified cutting length of 200 m produced by peeling two disks (a disk without knots was peeled first followed by a disk with knots), the peeling was stopped and the amount of wear on the clearance face of the peeling tools was measured under an optical video microscope. The 1 3 illustration of wear measurement on the clearance face of the cutting tools is depicted in a previous paper (Darmawan et al. 2008). The worn edges were also investigated under SEM and optical profilometer to characterize the wear patterns. Peeling of the disks was continued up to a total cutting length of about 2 km. At every 200 m of the cutting length, X-axis force component (parallel force) was also recorded, as depicted in Fig. 3b. Measurement of the parallel force was made with a load cell attached on the tool holder of the microlathe in such way that the vertical pressures working on the tool are detected by the load cell. The load cell was connected to a strain amplifier. Further, GP-IB board was used to record the force during cutting and Lab View software was used to display the force on the personal computer. A laser profilometer measurement system (WYKO NT1100) was used to measure both the roughness on the face of veneer and the roughness on the cutting edges of the pelling tool" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003785_j.actaastro.2009.03.018-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003785_j.actaastro.2009.03.018-Figure1-1.png", "caption": "Fig. 1. Geometrical representation of (Z\u0302mn 1 , Z\u0302mn 2 , Z\u0302mn 3 ) from (X\u0302m 1 , X\u0302n 2 ).", "texts": [ " In order to make A\u0303mn orthonormalized, we regenerate (X\u0302m 1 , X\u0302n 2 ) with contribution weights into (Y\u0302 mn 1 , Y\u0302 mn 2 ) such as Y\u0302 mn 1 = (X\u0302m 1 + ( 1 \u2212 1)(X\u0302m 1 \u00b7 X\u0302n 2 )X\u0302 n 2 )/ \u2016X\u0302m 1 + ( 1 \u2212 1)(X\u0302m 1 \u00b7 X\u0302n 2 )X\u0302 n 2\u20162 Y\u0302 mn 2 = (X\u0302 n 2 + ( 2 \u2212 1)(X\u0302m 1 \u00b7 X\u0302n 2 )X\u0302 m 1 )/ \u2016X\u0302n 2 + ( 2 \u2212 1)(X\u0302m 1 \u00b7 X\u0302n 2 )X\u0302 m 1 \u20162 (5) for m, n \u2208 {1, 2} where s , s \u2208 {1, 2} is a set of nonnegative weights satisfying 1 + 2 = 1. The weight s corresponding to the level of contribution to construct Y\u0302 mn s , can be adjusted according to the reliability of s-th component of measurement vector. From (Y\u0302 mn 1 , Y\u0302 mn 2 ) we compute the intermediate vectors (P\u0302mn, Q\u0302mn) at right angles such as P\u0302mn = (Y\u0302 mn 1 + Y\u0302 mn 2 )/\u2016Y\u0302 mn 1 + Y\u0302 mn 2 \u20162 Q\u0302mn = (Y\u0302 mn 1 \u2212 Y\u0302 mn 2 )/\u2016Y\u0302 mn 1 \u2212 Y\u0302 mn 2 \u20162 (6) for m, n \u2208 {1, 2} and using the geometrical property as shown in Fig. 1 the corresponding attitude matrix candidates are obtained as Amn = [Z\u0302mn 1 ...Z\u0302mn 2 ...Z\u0302mn 3 ] (7) for m, n \u2208 {1, 2} with Z\u0302mn 1 = (P\u0302mn + Q\u0302mn)/ \u221a 2, Z\u0302mn 2 = (P\u0302mn \u2212 Q\u0302mn)/ \u221a 2, and Z\u0302mn 3 = Z\u0302mn 1 \u00d7 Z\u0302mn 2 . For the determination of the optimal solution among {Amn}m,n\u2208{1,2}, we define a cost function to be minimized as J = min m,n\u2208{1,2} { 1 2 2\u2211 i=1 \u2225\u2225\u2225\u2225 [ wi1 wi2 ] \u2212 [(A\u22121 mnV\u0302i )1 (A\u22121 mnV\u0302i )2 ]\u2225\u2225\u2225\u2225 2 } (8) where for a notational convenience the j-th component of a vector x\u0302 is denoted by (x\u0302) j " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000558_romoco.2002.1177105-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000558_romoco.2002.1177105-Figure6-1.png", "caption": "Figure 6", "texts": [ " At fig. 5 we present simple example for desired formation with nine target points and nine robots. The initial positions of robots cause that planned trajectories are not crossed, but when dimensions of robots are sufficiently big there can Occur collision of robots 1 and 2 with robot 9. In accordance with previously described method robots 1 and 2 suspends its motion when they may violate forbidden area of robot 9. Robot 9 has highest priority and has right of way before all other robots. At fig. 6 wepresent similar example. In this case all robots are positioned at one side of the desired formation. At first robots I., 2 and 3 are assigned to the target points A, B and C. Then robots 4,s and 6 are assigned to the robots D, E and F. Finally robots 7.8 and 9 are assigned to the target points G, H and 1. The succession of motion of robots is reverse: robot 9 with highest priority moves first, then robots 8, 7 and so on; point B. When we lay some additional condition for shapes of trajectories we can assure that formation building will be executed without bypass maneuvers" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003315_09544062jmes711-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003315_09544062jmes711-Figure7-1.png", "caption": "Fig. 7 Maximum deformation shape strain contour plots for (a) slight downward response, (b) stiff response, and (c) soft response A", "texts": [ " Figure 5 gives details of both model and experimental comparisons for each impact scenario. Quantitative data for both FE model and experimentation concerning the two-dimensional asymmetric distorted shape at maximum deformation are given in Fig. 6. The data presented in Figs 5 and 6 reveal material anisotropy to have a significant effect on ball impact distortions. In addition to the seven distorted shapes that occur at maximum deformation, material anisotropy was also shown to affect postimpact ball characteristics. This is shown in Fig. 7(a), where the downward distortion results in the onset of clockwise rotation throughout the rebound phase. This can be largely attributed to the downward distortion displacing the centre of mass downwards giving rise to a coupling between the resultant force vector and the centre of mass vector giving rise to the onset of postimpact ball rotation. The data provided in Figs 5 and 6 shows the FE model to give agreement within 5 per cent of experimental deformation data at maximum deformation point", " Figure 5 also shows good agreement between the model and experimental data for deformations that occur at the end of impact where a distinct tear drop shape is apparent. The deformations here were also predetermined by preimpact ball orientation. For example there were greater levels of elongation of the ball at the end of impact for the soft response A, when compared with the stiff response. The good agreement between the FE model and experimental data enabled further evaluation of the complex deformation behaviour of the ball. Ball deformation behaviour was found to be significantly affected by both panel material anisotropy and stitching. Figure 7 depicts the distribution of strains within the panels at maximum deformation for the slight downward, stiff, and soft response A. The preimpact ball orientation is shown alongside, with the panel yarn directions in view. The intersection of the ball surface with a plane shown by the dotted line, forms a great circle which increases as the ball approaches maximum deformation throughout the impact. Figure 7 shows that the panels that are situated within close proximity with this plane have a profound effect on ball deformation. This is exemplified in Fig. 7(a), which depicts a slight downward response where it is shown that the warp and weft directions in panels A, B, C, JMES711 \u00a9 IMechE 2007 Proc. IMechE Vol. 221 Part C: J. Mechanical Engineering Science at UQ Library on June 22, 2015pic.sagepub.comDownloaded from and D are orientated at a non-zero angle with respect to the plane of hoop strain. Panel E exhibits low levels of deformation due to its orientation, which results in strain being distributed among the neighbouring panels. Panel D for example is positioned at a greater distance from the plane of hoop strain, however, exhibits high levels of strain than panel E. Figure 7(b) depicts the stiff response which can primarily be attributed to the yarn directions in panels A, B, C, and D being orientated coincident with the plane of hoop strain. Figure 7(c) depicts the soft response A impact that exhibits high levels of deformation due to all of the panels in view orientated such that their yarn directions are non-zero with the plane of hoop strain. The stitching seam was also found to have a significant influence on the distortions that occurred at maximum deformation. If a particular impact orientation resulted in the position of the seam being within close proximity of the plate, the stiffer material definition would prevent deformation, while deformation would take place within the adjoining panel" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000217_imtc.1998.679759-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000217_imtc.1998.679759-Figure5-1.png", "caption": "Fig 5", "texts": [ " The connection between the bendable portion and the last section of flexible tubing is watertight. A. Bendable portion The bendable portion is a 3D pneumatic actuator with three degrees of freedom - stretch, yaw and pitch. It is flexible and bendable to any angle. Actuator is formed from an elastomer material, preferably - silicone rubber which has an expansion ratio range from 300% to 400%. Further, actu,ator has one through channel for inserting fiber bundlles (or video camera) and the sensor imager, and three pressure chambers radially distributed as showri on Figure 5 (on 120 degrees to each other). Pressure in each chamber is controlled 21 1 independently through flexible tubes which are connected to electro-pneumatic transducers. A fluid applying tube is hermetically fit to the inside wall of each chamber and is sealed with a pressure resistant seal. Electro-pneumatic transducers use a current generated by an 80522-based 8 bit microcontroller instrument and transform it to an adequate pressure signal. A radial expansion restraint encircles the whole length of the actuator to prevent a deformation in a radial direction and it is, preferably, nylon fiber" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003806_icelmach.2010.5608274-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003806_icelmach.2010.5608274-Figure7-1.png", "caption": "Fig. 7. The equipotential lines of the vector potential correspond to time 0.2 s. One flux tube contains a flux per unit length of 0.001 Wb/m. (left) Magnitude of magnetic flux density at time 0.2 s (right)", "texts": [ " It gives time of displacement of one element equal to about 3 10-5 s at synchronous speed, comparable with the average time step of computation. The gap region division is fundamental for avoiding erroneous oscillation generations of the field due to meshing. The machine was running at synchronous speed and feed with sinusoidal voltage. The time-stepping analysis was run over 10 periods of the supply voltage up the steady state was reached. After this time several snapshots are taken for next voltage period. Fig. 7 show the magnetic field of the motor at time 0.2 s. The number of samples was chosen according to following discrete Fourier transform (DFT) analysis. 80 samples were used. It is important that the values of air gap division angle and angle between samples are not the same or were an integer multiple of. Using the calculated at samples values of x and y components of magnetic flux density in each element the DFT analysis was performed on the flux density components waveform in order to consider the contributions of the higher harmonics" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003096_1774674.1774705-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003096_1774674.1774705-Figure1-1.png", "caption": "Figure 1. Local sensor-based surveying along n parallel transects of length m.", "texts": [ " V ariants of the latter have been proposed ba sed on di stribution of m easurement sa mples within the cells of a t essellated gr id representation of the survey region [4]. H ere, w e a pply a b asic ge ometric m easure c omprising a combination of su ch att ributes. It is re ferred to as the quality of performance, QoP, defined as a ratio of area covered to distance traveled [9 ]. A pplying th is m etric to th e r ecent field t est r esult mentioned a bove w ould yi eld a Q oP of 24 ba sed on t he s urvey region area and to tal t raverse distance. In general, the QoP for a local sensor-based survey al ong pa rallel t ransects (Fig. 1) is computed as Q p = m(n 1) p [mn + (n 1) p] (1 ) where m is the tr ansect len gth, n i s the n umber of transects traversed, an d p i s the separation di stance bet ween adjacent transects and i s assumed h ere to b e comparable to the survey sensor footprint. The num erator a nd d enominator of Eq. ( 1) respectively r epresent the a rea surveyed an d to tal d istance traversed during the survey. In t he n ext sec tion w e di scuss m obile surveying us ing i n-situ remote se nsing a nd apply t he sa me metric to a rea c overage performance o f several ty pes o f re mote sensor-based su rvey trajectories" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002091_aim.2003.1225147-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002091_aim.2003.1225147-Figure1-1.png", "caption": "Figure 1: Parallel-wire system (1.R.type)", "texts": [ "EYWORDS: Orthogonalization, Convergence, ,Parallel, Wire, Control, Stability INTRODUCTION The parallel wire-driven robot system is a kind of parallel mechanism[l, 2, 3, 4, 5 , 6, 71. This system utilizes extremely light flexible wires instead of heavy rigid links as shown in Figure 1 and 2. The mass of moving part would be extremely small, because the m a s of wires can be negligible in comparison with the rigid links. Therefore, relatively small motors are able to generate high acceleration and high speed. However, wire can not push but can pull an object, then the driving principle is deferent from usual serial-link robot and parallel-link robot. Such parallel-wire driven robots have been already proposed so far. Higuchi et al. investigated the mechanism of the parallel-wire drive system and showed some experimental results using a twc-dimensional robot[l]. Osumi et al. developed a crane to move heavy objects . by using the parallel-wire mechanismj21. Kawamura et al. developed a high-speed robot using seven wires for &7803-7759-1/03/$17.00 @ 2003 IEEE 509 six degrees of freedom[%]. The parallel-wire driven system is classified into two types based on the drive principle. One is the incompletely restrained type (I.R. type) as shown in Figure 1, and the ot,her is the completely restrained type (C.R. type) as shown in Figure 2. Distinction between the types is to apply external force as drive means actively or not. The former actively utilizes external force to o p erate, such BS the gravity. The latter u t i l i s only wire tension. Generally speaking, the I.R. type can easily obtain larger work space, and can operate with fewer wires than the C.R. type[6, 71. However, it might be difficult to suppress the vibration problem, because the LR" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003661_54002-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003661_54002-Figure2-1.png", "caption": "Fig. 2: A buckle made of the superposition of two wrinkles symmetrical displayed with respect to the (0z)-axis. The slope breakdown at x= b1 has been labelled \u03b8.", "texts": [ " Accordingly with these experimental observations and previous studies [15,16], the folding of the film at the boundary between the two buckles is residual and is assumed to result from microscopic plastic deformation mechanisms in the film, such as the formation of lowangle tilt boundaries, see for example [17\u201320]. Despite the fact that two-dimensional buckles are observed, the superposition of only two (one-dimensional) wrinkles leading to a symmetrical structure with respect to (0z) vertical axis has been modelled in this letter for sake of simplicity (see fig. 2 for axes). It is believed that relevant information concerning the superposition of non-symmetric wrinkles and blisters may be derived from this simplified analysis. 54002-p1 In the hypothesis where the Young modulus of the substrate (Es = 150GPa) is about two times greater than the one (Ef = 80GPa) of the film of thickness h, the elastic effects of the substrate can be neglected such that it may be assimilated to a rigid support [21,22]. The initial state of stress in the planar film is chosen as follows: \u03c30xx = \u03c3 0 yy = \u2212\u03c30, where \u03c30 is a positive constant. Once the buckling has occurred, the total stress tensor in the film yields \u03c3totij = \u03c3 0 ij +\u03c3ij where \u03c3ij is the stress variation due to the buckling. It is assumed that this stress \u03c3totij is constant in each buckle. The components ui, vi and wi of the displacement variation from the reference state are defined along the x, y and z directions, respectively, with i= 1, 2 depending on the wrinkle to be considered (see fig. 2). The wrinkle (1) lies in the area limited by x\u2208 [\u2212b1, b1] while the wrinkle (2) is defined for x\u2208 [\u2212b2, \u2212b1] and x\u2208 [b1, b2]. In the case of one-dimensional wrinkles, the vector field (ui, vi, wi) only depends on the x variable, vi being zero. The component wi of the displacement field of the wrinkles satisfies, within the framework of the non-linear FvK\u2019s theory of thin plates, the following equation [9]: d4wi dx4 +\u03b12 d2wi dx2 = 0, (1) with \u03b1= \u221a h(\u03c30\u2212\u03c3xx)/D. The bending stiffness D of the film is defined as follows: D=Efh 3/{12(1\u2212 \u03bd2f )} with \u03bdf its Poisson\u2019s ratio. The non-zero ui component of the displacement of each wrinkle can be determined from the equations [9] \u2202ui \u2202x + 1 2 ( \u2202wi \u2202x )2 = 1\u2212 \u03bd2f Ef \u03c3xx, \u03c3yy = \u03bdf \u03c3xx. (2) Since the final buckling structure considered in fig. 2 is assumed to be symmetric with respect to the (0z) vertical axis, only half of the structure (x 0) has been investigated. The boundary and continuity conditions to be satisfied by the displacement field write, respectively, u1(0) = u2(b2) =w2(b2) = 0, (3) dw2 dx |x=b2= 0, dw2 dx |x=b1 \u2212dw1 dx |x=b1= \u03b8, (4) and u1(b1) = u2(b1), w1(b1) =w2(b1), (5) with \u03b8 the slope breakdown of the film profile at x= b1 characterizing the border between the two wrinkles. From 54002-p2 A2 = 1 6\u03c02Ef [ 6b2Ef\u03b8 cos ( \u03c0 b1 b2 ) \u2212 6\u03c0b1Ef\u03b8 sin\u22121 ( \u03c0 b1 b2 ) + \u221a 6Ef ( \u22122\u03c04Efh2+3b22 ( Ef\u03b82+8\u03c02(1\u2212 \u03bd2f )\u03c30 ) +3Ef\u03b82 ( b22 cos ( 2\u03c0 b1 b2 ) +2\u03c0K ))] , (11) eq" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002406_0094-114x(74)90016-0-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002406_0094-114x(74)90016-0-Figure1-1.png", "caption": "Figure 1", "texts": [], "surrounding_texts": [ "Now a C - H - C - H - linkage with two pairs of parallel joint axes is known to be mobile [13, 17, 18]. Thus we need not further investigate this case, and can exclude from the following the possibility of parallel joint axes. The C - H - C - H - linkage with two pairs of parallel joint axes is listed as solution no. l in Table I." ] }, { "image_filename": "designv11_32_0003860_j.elecom.2010.04.002-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003860_j.elecom.2010.04.002-Figure1-1.png", "caption": "Fig. 1. (a) Schematic diagram of the integration process", "texts": [ "3 913 UmL\u22121) was purchased from Oriental Yeast (Japan). All other chemicals were of analytical reagent grade and were used without further purification. D-glucose stock solution was prepared with a phosphate buffer (0.1 M, pH 7) and stored overnight to reach the mutarotative equilibrium. Epoxy resin (Alardite 2020) and silver-epoxy resin (Dotite D-753) were obtained from Huntsman (USA) and Fujikura Kasei (Japan), respectively. The fabrication scheme and the structure of our MEA are illustrated in Fig. 1. Firstly, a Pt wire (20 \u03bcm in diameter; Niraco, Japan) was inserted into a silicon tube (i.d. 0.5 mm). The tube was filled half with the epoxy resin (overnight, 55 \u00b0C). The silver-epoxy resin was crammed into the tube from the opposite side (4 h, 55 \u00b0C). The resin was ejected from the silicon tube and is called Pt-embedded rod. A blank rod was also prepared in the same manner without using Pt wire. The Pt-embedded rods and the blank rods were inserted together in a silicon tube (i.d. 3 mm) (Fig. 1a). The Pt-embedded rods were arrayed to keep away from the neighboring ones in a distance between the Pt wires of at least 500 \u03bcm (Fig. 1b). The number of the Pt-embedded rod in the MEA (N) was varied from 1 to 7. In this paper, a single microelectrode is described as MEA with N=1, for simplification in description. After arraying the rods, the space among the rods was filled with the epoxy resin. The rod array was then ejected from the silicon tube and mounted in a glass tube (i.d. 3 mm). The silver-epoxy resin was crammed into the glass tube from the opposite side and a lead wire was inserted in the silver-epoxy resin for the electrical connect with the Pt-embedded rods. The glass tube was filled with the epoxy resin in the back side (Fig. 1c). The surface of the MEA was polished to a flat and mirror finish with sandpaper (#1500) and alumina slurry (0.05 \u03bcm). Cyclic voltammetry and amperometry were carried out in a threeelectrode system on an ALS CHI 611B electrochemical analyzer (BAS Inc.) equipped with a Faraday gage in a laboratory-made electrolysis cell at a total volume of 1.0 mL. The MEA, a Pt wire and an Ag|AgCl|KCl (sat.) were used as the working, counter and reference electrodes, respectively. All potentials in this paper are referred to the reference electrode" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003345_iros.2007.4399234-Figure9-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003345_iros.2007.4399234-Figure9-1.png", "caption": "Fig. 9. Trajectory following. Red bars are speed corrections, blue bars are heading corrections. The size of the UAV is magnified ten times for a better view.", "texts": [ " 7 shows the simulation setting where each UAV is running on a single computer and is communicating through the network. Our system is supported by the LAAS architecture [12], including the functional layer and the execution controller that would run on real UAVs. The flight control of the formation is the combination of a trajectory tracking system [13] in a navigation module that provides speed, heading and altitude setpoints and corrections on position, speed, heading and altitude that come from a formation module. On Fig. 9, the color lines ended by a sphere represent the relative position of the UAVs in the formation, so the four spheres are ideally merged. In this case, the tracking algorithm has properly placed the spheres on the trajectory but the green UAV is too far ahead, so the speed correction (the red bar above) forces it to slow down while the others speed up. In this scenario, there is only one OJ, the yellow UAV. On Fig. 10, we can see that the formation is performing a reconfiguration so that the yellow aircraft is placed between the EW radar and the rest of the formation" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003924_iros.2010.5650335-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003924_iros.2010.5650335-Figure2-1.png", "caption": "Fig. 2. Vehicle schematic for vertical flight mode", "texts": [ " The transformation of the components of the angular velocity generated by a sequence of Euler rotations from the body to the local reference system is written as follows: H (\u03a6) = 1 t\u03b8s\u03c6 t\u03b8c\u03c6 0 c\u03c6 \u2212s\u03c6 0 s\u03c6/c\u03b8 c\u03c6/c\u03b8 (3) where s, c and t are used to denote the sin, cos and the tan respectively. The term Jb in (2) represents the inertia matrix. Since the X-4 prototype is symmetrical in the xz-plane and the xyplane, the products of inertia Jxy , Jyz and Jxz vanish. Then Jb and its inverse can be written by Jb = Jx 0 0 0 Jy 0 0 0 Jz (4) The aerodynamics and thrust moments can be denoted by M b = [ \u2113 m n ]T , and are shown in Figure 2. Then differentiating (1) we get \u03a6\u0308 = H\u0307 (\u03a6)\u03c9bb/e +H (\u03a6) \u03c9\u0307bb/e (5) Introducing the RHS of (2) into (5), \u03a6\u0308 = H\u0307 (\u03a6)\u03c9bb/e +H (\u03a6) ( Jb )\u22121 [ Mb \u2212 \u2126bb/eJ b\u03c9bb/e ] (6) It is proposed that Mb , \u2126bb/eJ b\u03c9bb/e + JbH (\u03a6)\u22121 [ \u03c4\u0303 \u2212 H\u0307 (\u03a6)\u03c9bb/e ] (7) where \u03c4\u0303 = [ \u03c4\u0303\u03c6 \u03c4\u0303\u03b8 \u03c4\u0303\u03c8 ]T . Then (5) can be rewritten as \u03c6\u0308 = \u03c4\u0303\u03c6 (8) \u03b8\u0308 = \u03c4\u0303\u03b8 (9) \u03c8\u0308 = \u03c4\u0303\u03c8 (10) Newton\u2019s second law is used to obtain the equations of translational motion in the inertial frame of reference as p\u0308nCM/T = Cn/b Fb m + gn (11) where the position of CM in the North-East-Down (NED) coordinate system with respect to Fe, is given by pnCM/T = [ x y z ]T " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001194_iecon.1999.816428-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001194_iecon.1999.816428-Figure1-1.png", "caption": "Fig. 1. A ball-and-heam system.", "texts": [ " Section I1 presents the fuzzy plant model of a ball-and-beam system. Based on this model, we design a fuzzy controller which will be presented in Section 111. In section IV, the system stability of the fuzzy controlled ball-and-beam system will be analyzed. The stability condition and the membership functions of the fuzzy controller will be derived. In section V, simulation results will be given to verify the analysis results. In section 6, a conclusion will be drawn. 11. Fuzzy MODELOF A BALL-AND-BEAM SYSTEM A ball and beam system is shown in Fig. 1 [4]. Its dynamic equations are given as follows, XI (0 = X , ( t ) i, (0 = B(xl (Ox4 (t)' + g sin(+ i 3 ( t ) = x4(0 i, ( t ) =U@) (1) where xl(t) is the position of the ball measured from the centre of the beam, xz(t) is the velocity of the ball, x3(t) is the angle of the beam with respect to the horizontal axis, x4(t) is the angular velocity of the beam with respect to the horizontal axis; B = MRz =0.7143, J, =2x10\"kgm2 is the J , + MR' moment of inertia of the ball about the centre of the ball, M = 0" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001538_j.jmatprotec.2003.11.035-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001538_j.jmatprotec.2003.11.035-Figure2-1.png", "caption": "Fig. 2. Shape and dimensions (mm) of the seal strip used in this investigation.", "texts": [ " The table gives also the performance index \u03b3 = \u2211 Bi\u03b1i, where B is the scaled property, \u03b1 the weighting factor, and i is summed over all the n relevant properties. As indicated in Table 3, the performance index obtained for different materials leads to AISI 304, 316, 321 and 430 stainless steels as potential materials for labyrinth seal strips. However, when the resistance to intergranular corrosion, availability and cost are considered, AISI 321 comes out as the optimum material. In fact, the working interval of this steel is 427\u2013871 \u25e6C and with high Ti levels it has the best corrosion resistance among the selected materials [8]. Fig. 2 shows a drawing of one of the seals. In practice, depending on the position of the seal strip in the turbine, the different dimensions and radii shown in the drawing are modified. Consequently, the manufacturing process should be flexible and precise enough so that during the fabrication it is possible to reach the required tolerances. It should be also low cost, low scrap and rapid in order to be competitive. With these objectives, various manufacturing processes were analyzed [9,10] and finally a combination of roll forming and three-roll bending was selected as the optimum fabrication method" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001487_j.mechmachtheory.2004.05.004-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001487_j.mechmachtheory.2004.05.004-Figure4-1.png", "caption": "Fig. 4. A point-line displacement.", "texts": [ " (9), one may find that all point-lines associated with the same line can be expressed as a linear function of h: A\u00f0h\u00de \u00bc A\u00f00\u00de \u00fe hu \u00f0 1 < h < 1\u00de; \u00f014\u00de where A\u00f00\u00de \u00bc \u00f0a1; a2; a3; a01; a02; a03\u00de represents a point of the Klein Quadric, and u \u00bc \u00f00; 0; 0; a1; a2; a3\u00de represents a point of T5. The geometric interpretation of Eq. (14) is a hyperline through point A\u00f00\u00de along the direction of vector u (Fig. 3). Therefore, we have the following property. Property 3. All point-lines associated with the same oriented line of R3 can be mapped to points of the same hyperline of T5. Consider two positions A\u0302, B\u0302 (dual vectors) of a point-line as shown in Fig. 4. The unit line vectors a _ and b _ are coaxial with A\u0302 and B\u0302, respectively. Taking any point on the common perpendicular of A\u0302 and B\u0302 as the reference point, the representations of A\u0302 and B\u0302 read A\u0302 \u00bc exp\u00f0ehA\u00dea _ ; \u00f015\u00de B\u0302 \u00bc exp\u00f0ehB\u00deb _ : \u00f016\u00de The inner, cross, and geometric products of A\u0302 and B\u0302 are as follows: A\u0302 B\u0302 \u00bc exp\u00bde\u00f0hA \u00fe hB\u00de \u00f0a _ b _ \u00de; \u00f017\u00de A\u0302 B\u0302 \u00bc exp\u00bde\u00f0hA \u00fe hB\u00de \u00f0a _ b _ \u00de; \u00f018\u00de A\u0302B\u0302 \u00bc exp\u00bde\u00f0hA \u00fe hB\u00de \u00f0a _ b _ \u00de: \u00f019\u00de As dual vectors, A\u0302 and B\u0302 have the following relationship [23]: A\u0302B\u0302 \u00bc A\u0302 B\u0302\u00fe A\u0302 B\u0302: \u00f020\u00de The dot and cross products of the two unit line vectors a _ and b _ are [30]: a _ b _ \u00bc cos h\u0302; \u00f021\u00de a _ b _ \u00bc s _ sin h\u0302; \u00f022\u00de where h\u0302 \u00bc h \u00fe es is the dual angle subtended by the two point-line axes, and s _ is the unit line vector along the common perpendicular referred to as the common-normal axis", " The inverse of Q can be calculated as the inverse of a dual quaternion, Q 1 \u00bc Q QQ \u00bc exp\u00bde\u00f0Dh\u00de \u00f0cos h\u0302 s _ sin h\u0302\u00de fexp\u00bde\u00f0Dh\u00de \u00f0cos h\u0302 \u00fe s _ sin h\u0302\u00degfexp\u00bde\u00f0Dh\u00de \u00f0cos h\u0302 s _ sin h\u0302\u00deg \u00bc cos h\u0302 s _ sin h\u0302 exp\u00bde\u00f0Dh\u00de \u00f0cos2 h\u0302 \u00f0 s_ s_\u00de sin2 h\u0302\u00de \u00bc exp\u00bd e\u00f0Dh\u00de \u00f0cos h\u0302 s _ sin h\u0302\u00de: \u00f036\u00de Q 1 is also a point-line operator, and its operation on B\u0302 yields A\u0302: A\u0302 \u00bc Q 1B\u0302: \u00f037\u00de According to Eq. (36), the common-normal axis of Q 1 is s_, which is coaxial with s _ but in the opposite direction. Because the reference point is assumed on the common-normal axis, and after the screw displacement q, the reference point remains on the common-normal axis, the endpoint offsets hA and hB at both point-line positions are measured from the common-normal axis (Fig. 4). If the reference point is not on the common-normal axis, for the point-line displacement operation to be valid, the reference point should also be transformed by the screw displacement q. Let pA be the reference point for A\u0302, the reference point pB for B\u0302 can be calculated by [23] pB \u00bc gpAg \u00fe t; \u00f038\u00de where g \u00bc cos h 2 \u00fe s sin h 2 ; \u00f039\u00de t \u00bc s0 sin h \u00fe s s0\u00f01 cos h\u00de \u00fe ss: \u00f040\u00de Note that s and s0 are respectively the direction-cosine vector and moment vector of the commonnormal axis. Eq. (32) shows that a point-line operator, which is the product of a screw operator and a translation operator, is determined by s _ , h\u0302 and Dh" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003519_s0001924000051204-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003519_s0001924000051204-Figure2-1.png", "caption": "Figure 2. Idealisation of lubrication system.", "texts": [ " This determines the complete pressure distribution p. We may now proceed to the calculation of the load carrying capacity. Denoting by m the normal to the Pressure p Prescribed S e c t i o n A - A We detail in the present section one finite element formulation for the case when the two surfaces are plane and hence v and m constant vectors. Our analysis pre sumes triangular TRIM and TRic-like elements, but it is equally possible to develop a theory for quadrilateral ele ments. We show a characteristic net in Fig. 2 together with a typical TRIC 10 element. The interpolation matrix may be found in Appendix II, eqns. (19) to (21); see also Fig. 1 of this reference. The corresponding set p r of nodal values is built up from the pressures at the nodal points. For a TRIC 10 element the reader is referred to Fig. 2 from which he will deduce Pi={Pi Pi Pio}. \u2022 \u2022 (IV.23) When either of the quantities h, /j,, dh/dt and q vary within a single element, the matrix 0 in Figure 3(a), the infinity manifold N can be easily checked to be the singular surface obtained by rotation of the figure eight shown in Figure 3(b) about the axis, together with a disjoint point. In these coordinates, the system has six critical points on N, indeed (0, 0, 0, 0), (0, 0, It, 0), (0, +x/2U-(0o), +0o, 0), where 0o = +arcsin 2x/~. The first one corresponds to the isolated point, while the second one is the singular point in the figure eight. The remaining points are contained in the two-di~nensional part of N, as we can see in Figure 4. From the Hill regions in Figure 2, we also see that in the case h < 0, solutions are bounded away from the origin so that the origin manifold is empty. If h = 0, approach to the origin is only on the region x < 0, although the positive x-axis is the remaining part of the line of equilibrium points. The manifold at the origin Co and its flow are diffeomorphic to N and this agrees with the general theory (Section 4). If h > 0, the approach to the origin can take place in any direction. Passing to configuration coordinates r, X, Y, where r = x~-2-+y 2, X = x/r, Y = y/r, the energy relation becomes l /2(pl 2 + p2) = otr3Xy2q_ h, so that Ch = {(r, X, Y, Pl, p2) :p2 + p2 = 2h, X 2 + y2 = 1}, (14) which topologically is a torus S 1 \u00d7 S ~ as expected. It has two closed curves S~ of equilibrium points defined by p~ = + 2x/2hX, p2 = \u00b1x/2-hY. All nonequilibrium solutions on Ch come out from one of the curves and end up in the other, after some spiraling. We can now describe the energy levels Eh with their added boundaries. In the case h = 0, we just have/~0 = Co \u00d7 [0, 1] and the flow is projectable on Co, with four homothetic solutions. The cases h > 0 and h < 0 are described in Figure 4. In case h > 0, the drawing in Figure 4 has to be identified at the two ends. Thus, Eh is topologically a solid torus where the interior of a set N is deleted in its interior. The manifold at infinity N shows its six equilibrium points. Even though Ch has two closed curves of equilibrium points (at the top and at the bottom), there are six couples of homothetic solutions from the central configurations. In two couples, the solutions just coincide, while the other couples are separated by equilibrium points, as shown in Figure 4. In the case h < 0, Eh is the interior of N when it is described in 3-space. That is, it is topologically two disjoint 3-balls Eh = B 3 \u00d7 {0, 1}. There are six points of equilibrium on N as before, plus two homothetic solutions beginning and ending at equilibrium points. MECHANICAL SYSTEMS WITH HOMOGENEOUS POTENTIALS 271 Broucke [3] has shown that if h < 0, all the solutions eventually escape to infinity. If h = 0, this is also true, except for solutions going asymptotically to the equilibrium point at the origin of the configuration plane" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003357_3-540-32834-3_16-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003357_3-540-32834-3_16-Figure7-1.png", "caption": "Figure 7. Task message propagation. Arrows on the links indicate messages in transit and arrows parallel to links indicate the \u201cchild-of\u201d relationship. Double circles indicate the roots of partial TSTs.", "texts": [ " Each node must decide on two issues: 1) what task to select and propagate, and 2) how to be a part of a TST. Initially, nodes that have competing tasks propagate their tasks by sending a task message (TM) to their neighbors and designating themselves as the root of a partial TST. Assuming that the recipient of a TM has no tasks for itself and receives only one TM, then it will adopt the received task and create a \u201cchild-of\u201d relationship toward the sender of the TM. The recipient will in turn propagate the received task by sending a new TM to the rest of its neighbors. To illustrate this idea, Figure 7 shows an example in which nodes P1 and P6 are the initiators of tasks t1 and t6 respectively and the rest of the nodes are non-initiator nodes. Node P2 and P3 are the recipients of TM(t1) sent by P1, and therefore have selected task t1. Similarly, P4 and P5 are the recipients of TM(t6) sent by P6, and therefore have selected task t6. In this situation, parallel arrows show the \u201cchild-of\u201d relationships that the nodes have created. Based on the above assumption, no message has been sent through the link l14", " To resolve the conflict, the recipient node deletes all of its previous \u201cchild-of\u201d relationships, makes a choice between its previous task and the received task (using its task selection function), propagates a newRoot message (NRM) containing the newly selected task to all of its neighbors, and then promotes itself as a new root for the selected task. The role of NRM is to merge partial TSTs and create a new root for the resulting TST. Therefore, the recipient of a NRM adopts the received task, creates a new \u201cchildof\u201d relationship towards the sender of the NRM, becomes a non-root node (if previously a root), and propagates a new NRM containing the received task to the rest of its children. Figure 8 shows the result of merging the two partial TSTs in Figure 7 for the situation where P4 has been the node that has received a conflicting TM from P1. As a result, P4 chooses a task between t6 and t1 (say t6 is chosen), promotes itself to be the root of the new TST, and propagates NRM(t6) to P1, P5 and P6, which turns P1 and P6 into non-root nodes. Consequently, P1 will adopt t6 as its new task and propagate a new TM to P2 and P3 for the task switch. As shown in Figure 8, the final result of the task negotiation process is a single TST with a specified root node and a selected task" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002610_0892705707082327-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002610_0892705707082327-Figure2-1.png", "caption": "Figure 2. Schematic for the hot pressing process of KFRTC made from commingled yarns.", "texts": [ " Second, knitted preforms are prepared by knitting the commingled yarns. Finally, KFRTC are produced by hot pressing the knitted preforms. In the hot pressing process, knitted preforms made from commingled yarns are placed between two molding plates. They are then put between the upper and lower heating plates for hot pressing. The thickness of the final composites is controlled by placing a molding frame at a certain thickness around the preforms, which are sandwiched between two molding plates (Figure 2). To obtain composites with lower void content and high quality, it is necessary to control the molding thickness besides the molding temperature and pressure in the hot pressing process of knitted composites due to the meshy structure of the knitted fabric. The molding thickness here refers to the thickness of the composites obtained by hot pressing. To establish control of the thickness of the composites, a theoretically optical molding thickness of the composites is deduced based upon the following assumptions: 1", " Substituting Equations (12) and (13) into Equation (9), one has 100hc \u00bc lPre dlPre nf Ntexf 1000 f \u00fe nm Ntexm 1000 m : \u00f014\u00de Thus, the theoretical molding thickness of the composite hc can be expressed by: hc \u00bc 10 5 lPre dlPre nf Ntexf f \u00fe nm Ntexm m : \u00f015\u00de In Equation (15), lPre can be obtained by the unrolling method, dlPre can be measured according to FZ70002-1991 [12], Ntexf, Ntexm and f, m can be determined according to the GB/T4743-1995 [13] and the pycnometer method [14], and nf and nm are easy to determine. The theoretical molding thickness of the composites hc can be calculated from Equation (15). The actual molding thickness h of the composites produced by the hot pressing process (Figure 2) is dependent on the thickness of the molding frame and is almost equal to it. In the actual hot pressing process, the matrix fiber does not melt in situ, nor does the matrix fiber integrate with the reinforcement in situ (see Assumption (2)). However, the melt matrix flows in the radial and longitudinal directions of the reinforcing fiber, and this flow may cause the loss of matrix from the mixed system and result in voids in the composites. Therefore, if the loss of matrix caused by the flow is taken into account, the actual molding thickness h, which can be taken as equal to the thickness of the molding frame) should be smaller than the theoretical molding thickness hc", " There were seven composite samples in each group. The samples in groups C1, C2, and C3 were, respectively numbered C11, C12, . . . . . . ,C17, C21, C22, . . . . . .C27 and C31, C32 . . . . . .C37. Samples in the same group were produced from the same knitted preforms, i.e., they had the same theoretical molding thickness hc (Table 2), but they had different actual molding thicknesses h, which were controlled by inserting steel molding frame with certain thickness between the upper and lower molding plates during the hot press process (Figure 2). The preforms used for the composite samples of all three groups were knitted with the same kind of glass fiber/polypropylene fiber (GF/PP) commingled yarn, which consisted of two plies of 330 dtex glass fiber (volume density gf\u00bc 2.51 g/cm3) and two plies of 330 dtex polypropylene fiber (volume density pp\u00bc 0.91 g/cm3). However, their loop density and loop length were different from each other. Table 1 gives the loop density and loop length of the knitted preforms used for preparing the three groups of composites" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003368_csse.2008.471-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003368_csse.2008.471-Figure1-1.png", "caption": "Figure 1. The control of maintaining formation", "texts": [ " Through the experiment based on the AmigoBot robot platform, it is proved that the method can meet the problem which can not converge fleetlyin in the course of obstacles avoidence. II. FORMATION METHODS In formation control, it is truth to pay the great amount of computation for the optimization of movement planning. But it may use less amount of computation in feedback control. Moreover, it can combine with the simple high-level movement plan. Here the \u03d5\u2212l control is mainly employed to keep the formation of robots. There is a two-robot system in Figure 1. The aim of \u03d5\u2212l control is to maintain the relative distance l and orientation \u03d5 of the robots. That is to say the robots will be in formation, only if the value of ),( \u03d5l can keep in the desired value ),( ddl \u03d5 . 2,1),,,( =iyx iii \u03b8 represents the pose of each robot, which is the reference point of the robot. And the reference point is on the axis of the robot\u2019s rotation center, and has the distance of id to the rotation center. For convenience, we let ddd == 21 . In the control process, what robot i needs are its local information ),,,,( iiiii vyx \u03c9\u03b8 and the information of its reference robot ))(,,,,( ijvyx jjjjj \u2260\u03c9\u03b8 , where iiv \u03c9, represent the transition and rotation speed of robot i respectively. For the system in Figure 1, let 21 \u03b8\u03b8\u03d5\u03b3 \u2212+= . The dynamic equations of the system are: 978-0-7695-3336-0/08 $25.00 \u00a9 2008 IEEE DOI 10.1109/CSSE.2008.471 1045 \u03d5\u03c9\u03d5\u03b3\u03c9\u03b3 sincossincos 1122 dvdvl +\u2212\u2212= \uff081\uff09 )coscossinsin(1 11221 \u03c9\u03d5\u03c9\u03b3\u03c9\u03b3\u03d5\u03d5 lddvv l \u2212+\u2212\u2212= \uff082\uff09 The aim of the system: )(1 lll d \u2212= \u03b1 \uff083\uff09 )(2 \u03d5\u03d5\u03b1\u03d5 \u2212= d \uff084\uff09 Where 21,\u03b1\u03b1 are positive constants. So from the equations above, the input of robot 2 can be derived that: ]sin cossin)([cos 1 1122 \u03b3\u03c1\u03c9 \u03d5\u03c9\u03d5\u03d5\u03d5\u03b1\u03b3\u03c9 ++ \u2212\u2212\u2212\u2212= l dvl d d \uff085\uff09 \u03b3\u03c9\u03c1 tan22 dv += \uff086\uff09 Where \u03b3 \u03b1\u03d5\u03c9\u03d5\u03c1 cos )(sincos 111 lldv d \u2212+\u2212 = \uff087\uff09 Such giving robot angular velocity, speed, location and direction, the robot turn to move toward the position of the reference robot, and to maintain the formation" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000069_153250002753338418-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000069_153250002753338418-Figure2-1.png", "caption": "Figure 2. Rotating and oscillating elds in the proposed approach.", "texts": [ " Induction machines during normal operations usually show zero sequence phase voltages as a consequence of saturation phenomena. Saturation of stator and rotor iron causes the air-gap ux to assume a attened waveform, as shown in Figure 1, with harmonic content highly dominated by the third harmonic component that depends, through a nonlinear function, on the amplitude of the fundamental air-gap ux. An additional uctuating high-frequency voltage is injected in order to produce a high-frequency oscillating eld, Fh f , along the estimated d axis, as shown in Figure 2. This eld, according to the position of the estimated d axis with respect to the main eld axis Fm , generates a variation of saturation level that modulates the amplitude of the zero sequence high-frequency ux, and consequently of the high-frequency zero sequence voltage. If the estimated d axis is in phase with the correct d axis, the variation of the saturation level is maximum and the amplitude of the high-frequency component of the zero-sequence voltage has a maximum. On the contrary, if the estimated d axis is in quadrature with the correct d axis, the variation of the saturation level is minimum and the amplitude of the high-frequency component of the zero sequence voltage has a minimum" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003035_13506501jet230-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003035_13506501jet230-Figure1-1.png", "caption": "Fig. 1 Schematic diagram of hydrodynamic porous journal bearing under steady-state operating condition", "texts": [ " With the help of steady-state and dynamic film pressure distributions, the stability characteristics in terms of critical mass parameter and whirl ratio have been obtained and compared with the no-slip case and the Newtonian case to reveal the influence of velocity slip and couple stresses, respectively, on the stability of bearings. 2 ANALYSIS 2.1 Lubricant flow equations The porous bearing configuration with a journal rotating at a uniform angular velocity, about its axis is shown schematically in Fig. 1. A porous bush of thickness, H is press-fitted inside a solid housing. JET230 \u00a9 IMechE 2007 Proc. IMechE Vol. 221 Part J: J. Engineering Tribology at The University of Iowa Libraries on June 13, 2015pij.sagepub.comDownloaded from The non-dimensional governing equations for the pressure distributions in the porous bush and in the clearance space between the journal and the bearing with the effect of slip flow of couple stress fluid are represented by the following two equations, respectively, based on the assumption of purely viscous flow of fluid in the porous bush as mentioned in reference [19]", "3 Boundary conditions for film pressures In porous bush p\u0304\u2032 j(\u03b8 , y\u0304, \u00b11) = 0 \u2202p\u0304\u2032 j(\u03b8 , \u22121, z\u0304) \u2202 y\u0304 = 0 \u2202p\u0304\u2032 j(\u03b8 , y\u0304, 0) \u2202 z\u0304 = 0 p\u0304\u2032 j(0, y\u0304, z\u0304) = p\u0304\u2032 j(\u03b82, y\u0304, z\u0304) = 0, \u03b82 \u03b8 2\u03c0 (8a) In bearing clearance p\u0304j(\u03b8 , \u00b11) = 0 \u2202p\u0304j(\u03b8 , 0) \u2202 z\u0304 = 0 p\u0304j(0, z\u0304) = p\u0304j(\u03b82, z\u0304) = 0, \u03b82 \u03b8 2\u03c0 \u2202p\u03040(\u03b82, z\u0304) \u2202\u03b8 = 0 (8b) JET230 \u00a9 IMechE 2007 Proc. IMechE Vol. 221 Part J: J. Engineering Tribology at The University of Iowa Libraries on June 13, 2015pij.sagepub.comDownloaded from where, \u03b82 is the angular coordinate at which the film cavitates. At the film-porous bush interface p\u0304\u2032 j(\u03b8 , 0, z\u0304) = p\u0304j(\u03b8 , z\u0304) (8c) In all cases, j = 0, 1, and 2. j = 0 corresponds to the case for steady-state condition. j = 1 and 2 correspond to the cases for dynamic conditions. 2.4 Stability characteristics Referring to Fig. 1, the non-dimensional equations of motion of the journal, assuming to be rigid and of mass, M per bearing as mentioned in reference [18], can be written as under (\u2212M\u0304\u03bb2W\u0304 + i\u03bbD\u0304rr + S\u0304rr)\u03b51 + (i\u03b50\u03bbD\u0304r\u03c6 + \u03b50D\u0304r\u03c6 + W\u0304 sin \u03c60)\u03c61 = 0 (9a) (i\u03bbD\u0304\u03c6r + S\u0304\u03c6r)\u03b51 + (\u2212M\u0304\u03bb2\u03b50W\u0304 + i\u03bb\u03b50D\u0304\u03c6\u03c6 + \u03b50S\u0304\u03c6\u03c6 + W\u0304 cos \u03c60)\u03c61 = 0 (9b) For a non-trivial solution, the determinant of equations (9a) and (9b) must vanish and thus equating imaginary and real terms of equation obtained from the determinant separately to zero, the following two equations result M\u0304 W\u0304 = 1 \u03bb2(D\u0304rr + D\u0304\u03c6\u03c6) [ (S\u0304rr D\u0304\u03c6\u03c6 + S\u0304\u03c6\u03c6D\u0304rr) \u2212 (S\u0304\u03c6r D\u0304r\u03c6 + S\u0304r\u03c6D\u0304\u03c6r) \u2212 D\u0304\u03c6r W\u0304 sin \u03c60 \u2212 D\u0304rr W\u0304 cos \u03c60 \u03b50 ] (10a) (M\u0304 W\u0304 )2\u03bb4 \u2212 \u03bb2 [ M\u0304 W\u0304 ( S\u0304\u03c6\u03c6 + S\u0304rr + W\u0304 cos \u03c60 \u03b50 ) +(D\u0304rr D\u0304\u03c6\u03c6 \u2212 D\u0304r\u03c6D\u0304\u03c6r) ] + (S\u0304rr S\u0304\u03c6\u03c6 \u2212 S\u0304\u03c6r S\u0304r\u03c6) + S\u0304rr W\u0304 cos \u03c60 \u2212 S\u0304\u03c6r W\u0304 sin \u03c60 \u03b50 = 0 (10b) where, M\u0304 = MC 2/W and \u03bb = \u03c9p/ , S\u0304rr , S\u0304\u03c6r , S\u0304\u03c6\u03c6 , S\u0304r\u03c6 and D\u0304rr , D\u0304\u03c6r , D\u0304\u03c6\u03c6 , D\u0304r\u03c6 are the non-dimensional stiffness and damping coefficients of film as defined in reference [18]" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001592_aim.2003.1225099-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001592_aim.2003.1225099-Figure3-1.png", "caption": "Figure 3: Configuration for the calculation of ERP. T ~ , T~ are ranged data from robot\u2019s position PI, Pz, respectively. w e n these ranged data originated from the same flat wall, ERP R1, R2 are on the intersections of the flat wall and two perpendicular lines through PI, Pa .", "texts": [ " , \u2019 4 IinplementationTo demonstrate that our proposed system can be implemented just by using low cost sensors, we utilized mobile robots equipped with ultrasonic range sensors. Although ultrasonic range sensors only have the single ability to measure distances to closest objects in the sight of I them. Therefore it is possible to determine distance to the object as well as its direction if multiple measurements from different positions are matched, assuming that reference objects are flat walls. In result, one degree of freedom of position and pose of a wall are hopefully measured. 4.1 Landmark measurement As shown in Figure 3, let us consider that a couple of range data TI, TZ are obtained by ultrasonic sensors which are fit- : ted on the left side of the robot when the robot was located at . P ~ ( x l , y ~ ) , Pz(x2,yz). respectively. Ifthese range data were I originated from the same flat wall, then the reflection points on the wall should be on the intersections of the flat wall and two \u2019 perpendicular lines through PI, Pz. Because ultrasonic waves ~ are reflected specularly over the flat wall surface. We call these " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-FigureA.14-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-FigureA.14-1.png", "caption": "Fig. A.14. Typical diagonal measurement set-up", "texts": [ " Diagonal measurements are useful in machine tool acceptance testing or in a periodic maintenance program to assess quickly the condition of a machine. Therefore, linear measurements along the work zone diagonals can provide a quick assessment of the overall positioning accuracy. The HP 10768A diagonal measurement kit is an optical accessory to the HP5529A laser measurement system. A schematic of the accessories is shown in Figure A.12. Figure A.13 shows the typical optics used for a diagonal measurement. A typical set-up for a diagonal measurement is shown in Figure A.14. The accuracy associated with laser measurements are also affected by several factors usually relating to the set-up, optical deformation and also environmental conditions. The main factors will be described. The perpendicular distance between the measurement axis of a machine (the scales) and the actual displacement axis is called the Abbe\u0301 offset. As a result of the Abbe\u0300 offset which is inevitably existent, an Abbe\u0301 error occurs when there is an angular displacement of the moving part during its translation" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003315_09544062jmes711-Figure13-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003315_09544062jmes711-Figure13-1.png", "caption": "Fig. 13 Strain contour plot of soft response B showing top, side, and bottom view", "texts": [ " However, due to the orientation of the panel, small amounts of strain are developed and a flattening of the panel commences within the plane of view. As the gross motion of the ball continues to travel towards the plate an in-plane compressive force is developed. As fabric materials tend to buckle through compressive loading [24], a negative bend curvature is established within the panel. Figure 12 provides further evidence of the formation of a negative bend curvature observed throughout testing which was replicated within the model. Out-of-plane deformation behaviour was also found to be of significant importance in soccer ball impacts. Figure 13 gives details of the soft response B showing side, top, and bottom views. It is shown that greater levels of deformation were apparent in the side view due to the yarn directions forming various angles with respect to the plane of hoop strain. Both the top and bottom views suggested a stiffer ball response due to JMES711 \u00a9 IMechE 2007 Proc. IMechE Vol. 221 Part C: J. Mechanical Engineering Science at UQ Library on June 22, 2015pic.sagepub.comDownloaded from the yarn directions being coincident with that of the plane of hoop strain" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002455_tmag.2005.862760-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002455_tmag.2005.862760-Figure3-1.png", "caption": "Fig. 3. Structure of \u201c \u201d type armature.", "texts": [ " This paper puts forward a new high-response moving-iron electromagnetic actuator; both the theoretical and experimental analysis are presented, and the actuator is practically applied into a real electronic engraving system to testify its engraving performance. The actuator shown in Fig. 2 consists of permanent magnets, \u201c \u201d type armature, an upper magnetic conductor, a bottom magnetic conductor, a magnetic isolator, a driving coil, and a linking rod that is linked to the engraving needle (not drawn out). The \u201c \u201d type armature, together with the output components, is shown in Fig. 3. The armature is fixed on the magnetic conductor by two cantilever beams, which not only support the armature but also act as high-stiffness springs through their elastic Digital Object Identifier 10.1109/TMAG.2005.862760 distortions. While the actuator works, unlike the conventional armatures, the middle part of the \u201c \u201d type armature does not 0018-9464/$20.00 \u00a9 2006 IEEE move, thus the moving mass of the armature is reduced; moreover, the output components are made of light materials such as aluminum" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000457_978-3-642-55848-1-Figure3.8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000457_978-3-642-55848-1-Figure3.8-1.png", "caption": "Fig. 3.8. The creation of a bond line", "texts": [ " Bonds are simple objects that indicate which port is connected to which. A CBond class is defined with attributes that hold the bond identifying label (id), the starting and the ending component, and the port ids, as well as data necessary for visual represen tation of the bonds. The bond class defines methods necessary for the creation and destruction of bond objects, copying, saving, loading, and drawing. Bonds, as ob jects, are contained in documents. The procedure for the creation of bonds is as follows (Fig. 3.8): 1. Select a component port or a document port. The starting position of the bond line is obtained from the port and corresponds to the position on the port boundary from which the bond will be drawn. 2. The document class is called to create a CBond object. The start-off position of the bond is set. 3. Select the next point in the document drawing area. Check if the point is within the other component port: o If it is not, add a point to the bond object and continue with step 3. o Otherwise, check if it is a port of another component and of the correct type-i" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003394_peds.2007.4487699-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003394_peds.2007.4487699-Figure7-1.png", "caption": "Fig. 7. A 2D linearised cross-sectional view of a RFAPM machine with concentrated Type I stator coils showing all three three-phase coils (with 3 Fig. 8. A 3D view of the concentrated Type II stator coil configuration of coils per 4 poles). RFAPM machine.", "texts": [ " Three adjacent coils for this (say) Type I concentrated coil configuration are graphically depicted in Fig. 6. In order to construct a three-phase machine using concentrated coils, three coils, one for each phase, need to be equally spaced over 2, 4, 8, etc. number of poles. In order to obtain the maximum flux-linkage, the average coil width should strive to 2p mechanical degrees or 7 electrical degrees. Intuitively, thep best results will be obtained with three coils per four poles, as shown in Fig. 7. By substituting (23) into (22) and (22) into (20), equation (20) reduces to AN = 4NBplrnfkA , (24) which is similar to equation (2), with only a different the value of kx, namely Cos ( A)-Cos ( p +AP) 2A P 2 (25) Analytically, the flux-linkage can be calculated as a+ 7-6 A1 jj Q BPl sin (OP) rndOdz (19) and thus for N conductors as N AzAN = 2AI Ajd (20) As the rotor and the stator move relative to one another, the angle a, with a = Wmt, will change. The flux-linkage and thus the induced voltage will vary sinusoidally for a constant mechanical speed, Wi" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002624_physreve.76.046316-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002624_physreve.76.046316-Figure1-1.png", "caption": "FIG. 1. Configuration of two spherical particles and the corresponding coordinates.", "texts": [ " In comparison between the theoretical and corresponding experimental results, the limitation of the quasisteady description of two interacting noncolloidal particles is presented. Consider two spherical particles of radii R1 and R2 with densities 1 and 2, respectively, released in an unbounded fluid of density and viscosity in a gravitational acceleration environment g. The two particles are considered to make planar motion in the vertical y-z symmetric plane in order to simplify the analysis, as shown in Fig. 1. Particle i i=1,2 , with center oi located at 0,yi ,zi and driven by the gravity, settles down in the fluid with a translational velocity ui and an angular velocity i with its rotation axis perpendicular to the y-z plane. On the assumption that the fluid is incompressible and the flow due to tardy particle motion is regarded as a creeping one, the flow is described by its velocity u and hydrodynamic pressure p, satisfying the Stokes equations \u00b7 u = 0, p \u2212 2u = 0, 1 with the no-slip boundary conditions on particle surfaces and the fluid velocity vanishing at infinity, u = ui + ie1 ri on ri = Ri i = 1,2 , 2a u \u2192 0 as r \u2192 , 2b where e is the unit vector along the positive direction of the corresponding axis in numerical order. B. Analytical solution for a two-particle system Two sets of auxiliary coordinates, x ,y ,z and x ,Y ,Z , fixed at two particle centers are introduced for convenience see Fig. 1 , which can be turned into spherical ones by x = r1 sin 1 sin , y = r1 sin 1 cos , z = r1 cos 1, and x = r2 sin 2 sin , Y = r2 sin 2 cos , Z = r2 cos 2. 3 From the general solution given by Lamb, the velocity field u outside an isolated spherical particle translating and rotating in a Stokes flow can be written in the r1 , 1 , coordinates as u = m=0 1 B3\u2212m P1 m cos m r1 2 \u2212 A3\u2212mr1 2 6 P1 m cos m r1 2 + 2A3\u2212me3\u2212m 3 r1 + \u2212 1 m+1Cem+2 P1 m cos m r1 2 , 4a and the hydrodynamic pressure due to the same flow as p = m=0 1 A3\u2212mP1 m cos m r1 2 \u2212 gz + p0, 4b where A, B, and C are constants to be determined by the boundary conditions, p0 is a reference pressure, and P1 m denotes the associated Legendre function P1 m cos 1 " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001744_135065004322842799-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001744_135065004322842799-Figure4-1.png", "caption": "Fig. 4 Distribution of pressure ps used to get to the preloading", "texts": [ " The calculation of the compliance matrix necessary for the elastohydrodynamic (EHD) study is done by taking into account the particularities of this mesh. As an example, 2 mm of pre-load leads to a cell length b \u02c6 0.1 mm; the analysis of the defect periodicity of the lip surface gives a cell width l \u02c6 0:0125 mm; the static Proc. Instn Mech. Engrs Vol. 218 Part J: J. Engineering Tribology J02903 # IMechE 2004 at NORTH CAROLINA STATE UNIV on March 18, 2015pij.sagepub.comDownloaded from pressure \u00aeeld ps that pushes back the lip is given in Fig. 4; and, \u00aenally, a 0.5 mm height for a threedimensional part of the lip h3 is chosen. The elastohydrodynamic problem is solved on a two-dimensional mesh of this cell. The main hypothesis concerns: (a) a perfectly elastic lip seal, (b) a perfectly smooth rotating shaft, (c) a perfectly centred seal (no whipping). After elaboration of the elasticity matrix from the threedimensional\u00b1two-dimensional mesh of the structure (Fig. 3a), the Reynolds equation is solved, coupled, through the elasticity matrix, to the elastic behaviour of the seal, while controlling the cavitation" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002741_imece2007-41351-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002741_imece2007-41351-Figure2-1.png", "caption": "Fig. 2. Illustration of a segment of a five-axis sculptured surface machining toolpath.", "texts": [ " The orthogonal to oblique transformation, along with an orthogonal cutting database are used to obtain cutting force coefficients that consider the effects of flute geometry and chip thickness variation along the axis of the cutter. As shown later in the paper, the simulated cutting forces are shown to be in reasonable agreement with experiements. A five-axis toolpath for sculptured surface machining is composed of a number of small segments connected together in series. In each segment, the translational and angular velocities can be assumed to be constant, with changes occurring at the segment connection nodes or at the end of each NC block, see Fig. 2 3 Copyright \u00a9 2007 by ASME ?url=/data/conferences/imece2007/71496/ on 02/04/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Down To calculate cutting forces along each segment, the depth of cut is divided into a number of differential elements along the axis of the cutter (see Fig. 3). The chip thickness at each differential element depends on the local feedrate, tool geometry and engagement conditions. If the chip thickness, local cutting edge geometry and cutting coefficients for each element are known, the elemental cutting forces can be calculated and then summed to obtain the total forces cutting acting on the cutter", "37 The first three columns of each line give the x,y and z position of the tool tip and the next three columns give the unitvector orientation of the tool axis in the global system. The seventh column gives the feed rate between commands in inverse time feed (G93 command in NC program standards) and the eighth column gives the running estimated elapsed time. If the segment ( i ) is small, the tool tip can be assumed to move from point Pi{ } to point Pi 1+{ } at a constant linear velocity ( fLi ), while rotating from orientation Ti{ } to Ti 1+{ } around the tool tip at a constant angular velocity, \u03c9i (see Fig. 2). The total distance travelled by the tool tip is given by, \u0394di Pi 1+{ } Pi{ }\u2013= (1) The magnitude of the feed rate at the tool tip is constant over tool path segment, i , and can be calculated from the inverse time feed using: fLi \u0394di \u0394ti ------- \u0394di\u0394tif i( )= = (2) Where \u0394ti and \u0394tif i( ) are the time taken and inverse time taken respectively, for the tool to travel tool path segment i . The inverse time feed for segment, i , is one divided by the time taken to travel though toolpath segment i " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003872_tac.1966.1098380-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003872_tac.1966.1098380-Figure3-1.png", "caption": "Fig. 3 . Graphical interpretation of the new criterion.", "texts": [ " The frequency response function GGw) is given by G(jw) = - LL'? (G - aw2) + j ~ ( b - u?) The system is asymptotically stable for all positive linear gains. For a = 2, b = c = 1 , the modified Kyquist plot and Popov line are shown in Fig. 2. The Popov sector is found to be [0, 3 - E ] where E > 0 is arbitrarily small. Using Corollary 4, i t is first noted that G(0) = O . Choose q = - c / b ; then 2 0 for all w. The graphical interpretation of this inequality, for the above numerical values, is shown in Fig. 3. Hence, for all bounded nonlinearities n-ith slope restriction $'> 0 and for all initial states, the response y(t) is bounded on [ O , =) and tends to zero as f--, %I. Actually, for the given numerical example? a stronger result can be obtained using Corollary 1. From inequality (10) with k l = l , H ( w ) = Re j q G C j w ) + w ? { Re GCjw) - k 1 j G(&) 1 2 ) -qw4(1 - w2) + w4(2w? - 1) - w6 (1 - 2 4 2 + - &)? w4[(2 + q - l ) w ? - (1 + q ) ] ( 1 - 2&)' + w ? ( l - w ? ) ? - - Choose q = - 1 ; then H(w) = 0" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002382_pime_proc_1973_187_028_02-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002382_pime_proc_1973_187_028_02-Figure1-1.png", "caption": "Fig. 1. The network of forces acting lining of the brake shoe", "texts": [ " The influence coefficients of the shoe and drum are calculated at these positions and are used in conjunction with the network of forces to set up a matrix equation, which is made to satisfy the equilibrium conditions of the shoe, and is solved with the aid of a computer programme to determine the forces. 2.1 The matrix equation The lining is divided in L elements each of which subtend an angle x at the drum centre. Suppose the lining initially makes non-uniform contact and then full contact with the drum after the brake is actuated. Fig. 1 shows the network of forces acting over the lining of, and the external forces acting on, a leading shoe. H is the abutment point, P the actuating force, R the abutment reaction, and 0 the drum centre. O X is parallel to the direction of P, O Y perpendicular to OX, OC is the bisector of the lining arc AB, angle AOB = 2a and w is the abutment angle. Resolving the pressure and friction forces parallel to and perpendicular to 0s (the bisector of the first element) gives : i = L i = 1 Rh = 2 Qi(cos ( i - 1 ) x - p sin (i-1)x) (1) and i = L i= 1 R, = Z: Q,(sin (i- l ) x + p cos (i- 1)x) (2) on the where i is the element number and Qi is the normal force acting on the element", " 3 EXPERIMENTAL VERIFICATION OF THE THEORY The theory has been assessed experimentally using an inertia dynamometer to measure the torques developed by a two-leading shoe brake over a range of actuating pressures and for different contact geometries. Proc lnstn Mech Engrs 1973 Vol 187 26/73 at University of Bath - The Library on June 5, 2016pme.sagepub.comDownloaded from 3.1 Experimental procedure Three drums of the same nominal stiffness but of different internal diameters, namely 9.002 in, 9.026 in and 9.050 in were used in the investigations on a brake in which the wheel cylinder diameter was 0.875 in, a = 1.125 in, d, = dz = 3-5 in, a = 55\", 7 = 0 and w = 32\" (Fig. 1). A set of linings was bedded to the smallest drum and some control performance lines (plots of torque versus pressure) were then obtained by making brake applications from 550 rev/min to rest with an initial drum temperature of 100\u00b0C. The linings were then rebedded to the drum. A series of performance lines was then obtained on each of the larger drums and, to ensure that the lining curvatures were the same at the start of each investigation, the linings were rebedded to the smallest drum and a control performance line was measured to check for possible variations in the lining friction", "comDownloaded from APPENDIX 2 S H O E F A C T O R E Q U A T I O N S O F THE C O N V E N T I O N A L T H E O R Y The shoe factor equations for the floating shoe under the different contact conditions are as follows : Leading shoe, complete contact pOZ sin w(C, +&) r(Cd1+p2)-pOZ(cos ( w - ~ ) + p sin (w-7 ) ) ) S = . . (20) where C, = (b cot w + a ) cos 7 + dl sin 71 C, = dl cos 7-(b cot w + a ) sin 7 C, = a sin w+& cos w 4r sin a 2a+sin 2a 02 = Leading shoe, crown contact The contact position depends on the coefficient of friction and if + is the angular contact position (measured in an anti-clockwise direction from O X in Fig. 1) the equations relating p, + and the shoe factor are : n sin (,-+)-sin + (n cos (w-+)+cos 9 - n , sin w ) P = p n sin w (sin ++p cos +-pnl sin w ) and S = where n = d , and n1 = r ( a sin w + d , cos w ) (a sin w + d , cos w) Leading shoe, heel and toe contact The shoe factors for heel and toe contact can be calculated from equation (20) with 02 equal to rjcos a. Trailing shoe If the direction of drum rotation is reversed, the shoe becomes trailing and the corresponding expressions are obtained by changing the sign of p in all the above equations", " Although lining pressures are by no means the most important part of the wide subject of brakes, yet they do have much interest. In the early \u201920s it was common practice, when thinking of shoe brakes, to assume that the resultant friction force acted at a point on the surface of the lining, at 90\u201d to the shoe fulcrum. My main interest was to arrive at the forces at work to enable more precise calculations of the stress in brake mechanical parts to proceed with accuracy. Thus from the shoe-lining pressure law, the friction force at all lining angles were integrated, somewhat as illustrated in Fig. 1, in order to arrive at the resultant single force, which acts not at drum radius, but at a greater radius averaging 1.10R. These results were included in a wide ranging paper on \u2018Automobile brakes\u2019 (8). The two-shoe brake unit with non-floating cam operation was commonly used in the early 1920s. Clearly one shoe operated with servo action and the other with antiservo, yet each shoe became worn out at the same time. This would not be the case with a \u2018floating cam\u2019 operation used to increase the brake power" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001068_bf02487718-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001068_bf02487718-Figure3-1.png", "caption": "Fig . 3 R e l a t i o n s h i p b e t w e e n two b o d y - f i x e d c o o r d i n a t e s", "texts": [ " Introduce the type coefficient vj, which is equal to zero when Oj is a rotational joint or equal to 1 when Oj is a sliding joint. Take the sliding distance zj or rotational angle Oj as generalized coordinates qi, qj =vjz j + (1 -- vj)O, ( / '=1 . . . . n) (34) In order to stylize the calculation process, the body-fixed coordinates__e O) and e (0 are defined as follows e (j) : 3 is alongthe sliding or rotating axis of O j, e (0 is 0rthogonal to e~ ) and e(~ ), the distance and angle between e3 ~ and e(~ ) are aj and a~, the distance between e(~ ) and e(t j) before sliding is bj (see Fig.3). Thus the submatrices of .~(ij) has a general formi ~(ij) = c ( 1 - - Vj)qj - - s(1 - vj)qj 0 c~js (1 -- vj)qj c~jc (1 - - Vj)qj -- SO~j SO~jS(1 Vj)qj S ~ f ( 1 - - vj)qj C~j (35) B (i j) = (bj -~- vj~qj)cGgj 0 (bj + vf]j)s~j ctj 0 aj } A--(ij) I where c, s are the abbreviations of cos,-sin. The screw-transformation matrix between two arbitrary bodies in system can be derived from (35) and (8). Since e(~ ) is along kj or p j, the elements of ~j are equal to zero except the 3-rd or 6-th element, _~j = [0 0 Vj 0 0 (] -- Yj)'] (36) Consequently _k ~\" is equal to the reformed matrix ~ , the submatrices of which ~--ij are replaced by its # r th subrows, where /~ = 3(9 - v~)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003571_978-3-642-01237-2_13-Figure13.10-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003571_978-3-642-01237-2_13-Figure13.10-1.png", "caption": "Fig. 13.10 Scheme of Layer Object Manufacturing process", "texts": [ " Christoph Over The term laminated object manufacturing (LOM) which has been primarily used by the developer and manufacturer \u201cHelisys\u201d did displace the broader term layer laminate manufacturing (LLM). C. Over (B) Inno-shape c/o C.F.K. GmbH, 65830 Kriftel, Germany e-mail: over@inno-shape.de LOM describes an additive manufacturing technique where parts are built up layer by layer. The material is coated with glue and pressed together with a preheated roll. Its temperature depends on the layer material and its thickness. After pressing, the layers are cut by a CO2 laser according to the layer outline (Fig. 13.10). Up to four layers can be cut simultaneously. Thereby building time will be increased but accuracy will be decreased since chamfers are reproduced by steps. The thinnest a layer can be is up to 0.25 mm. A wide range of materials can be processed, and the following itemization shows one of the most widely used (Fig. 13.11): \u2022 plastics; \u2022 ceramics; \u2022 paper coated with PE; \u2022 fiber-glass-reinforced composites. When the building process is finished, the part is taken out of the machine and excrescent material is taken off" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002572_j.jhazmat.2007.08.080-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002572_j.jhazmat.2007.08.080-Figure6-1.png", "caption": "Fig. 6. Mass balance of Hg2+ of the reactor.", "texts": [ " However, from the beginning of the treatment, the cells kept growing and propagating as they accumulated Hg2+, so the concentration of the cells was varying all the time before the process came to the stable phase. The varying concentration of the cells made the model complicated. Considering the difficulty to simultaneously simulate the changing situation of cell propagation and Hg2+ removal, we assumed that the average concentration of the cells before its stable phase could be employed for the development of the model. The mass balance of Hg2+ of the reactor was demonstrated n Fig. 6. Apparently from time t to t + dt, Hg2+ amount pumped nto the reactor (Hgin) should be the sum of Hg2+ amount accu- rdous H w c a H w ( b c a H w t F F C w w p o c F c i c p m c a c c t t a o a 4 H a o c t f d n p A l s c i p m t p X. Deng et al. / Journal of Haza From Fig. 6: gin = F inCin dt (4) here Fin is the flow rate of influent (L/h) and Cin is the Hg2+ oncentration of influent (mg/L). Hgac included two parts, Hg2+ in the solution in the reactor nd Hg2+ accumulated by the cells that still stayed in the reactor: gac = MV ( dq dt ) dt + V ( dCR dt ) dt (5) here M is the average concentration of the cells in the solution g/L), V the solution volume in the reactor (L), q the Hg2+ uptake y the cells (mg/g) is calculated by Eq. (1), and CR is the Hg2+ oncentration in the reactor (mg/L)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003281_s0022112006004009-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003281_s0022112006004009-Figure4-1.png", "caption": "Figure 4. (a) Sketch of the three-dimensional problem. (b) An equilibrium drop shape at the end of stage (i), if the fibre axis were oriented parallel to the centreline of the pad. Here and hereinafter the fibre itself is not shown. (c) The fibre is displaced from its equilibrium position and initially rotated by the angle \u03d5 = \u03d50 about the axis passing through its centre-of-mass parallel to the x-axis (top view). The contact lines are supposed to be motionless (relative to the fibre) when the fibre starts moving. The fibre is horizontal.", "texts": [ " As we have seen in the experiment, this is a relatively short stage, which allows us to consider all the contact lines to be effectively arrested. Consider a solder drop of volume V on a metal pad of wetted half-length a. A long cylindrical coated fibre of half-length l0 and radius R0 is placed into the drop parallel to the pad plane (but not to its centreline) so that the centre-of-mass of the fibre is located at the x-axis which passes through the drop centre-of-mass. Suppose that the fibre can move only parallel to the horizontal plane y, z containing the pad (see figure 4a) with the y-axis directed along the pad axis. It is assumed that the solder had already spread over the pad and the coated fibre and as a result, the drop could possess an elongated shape (along the fibre and the pad) similar to the one shown in figure 4(b). Then this would be an equilibrium state of the fibre\u2013drop system if the fibre were oriented parallel to the pad axis. Initially, however, the fibre is displaced from it. The centre-of-mass of the fibre can be displaced parallel to the plane y, z, while it is rotated by an angle \u03d50 about the x-axis (see figure 4c). After that, the drop\u2013fibre system evolves mostly under the action of capillary and viscous forces. The system tends to have a minimal solder surface area for a fixed volume V , and then the fibre moves, while all the contact lines on the pad and fibre are arrested at the positions reached at the end of the stage (i). We shall examine the time evolution of the drop and the corresponding motion of the fibre. Let us estimate the characteristic Reynolds number for this problem. We take the solder density \u03c1 \u223c 10 g cm\u22123, the viscosity \u00b5 \u223c 10 g cm\u22121 s\u22121, the characteristic length scale of the drop d0 0", " The kinematic boundary condition at the surface reads dr i dt = u(r i), (7) where r i is the position vector of the ith material point at the surface at time t . Since all the contact lines are assumed to be arrested, the boundary conditions at the pad and the fibre surface express the no-slip condition and read u = 0, r \u2208 pad surface, (8) u = U(r), r \u2208 fibre surface, (9) where U(r) is the velocity distribution over the fibre surface, determined by its motion as a rigid body. In fact, we assume that the shape of the drop base corresponds to the complicated configuration ABCDE shown in figure 4(a), i.e. some preliminary drop spreading over the borders AC and DE of the pad is allowed for, and points similar to B are located on the substrate outside the pad, as happens in reality even on hydrophobic substrates (Gau et al. 1999) and in the present experiments (cf. figures 2a and 3). The fibre position is determined by the coordinates of its centre-of-mass rcm = (xcm, ycm, zcm) (in our case xcm = const), and two angles: the angle between the pad and the fibre centrelines \u03d5; and the angle of the fibre rotation about its own axis \u03c8 (see figure 4c). The velocity of the centre-of-mass of the fibre ucm and the fibre angular speed \u03c9 can be represented as ucm = (0, Vy, Vz), \u03c9 = (\u03c9\u03d5, \u03c9\u03c8 cos \u03d5, \u03c9\u03c8 sin\u03d5), (10) where \u03c9\u03d5 is the angular speed of the fibre rotation about the x-axis, and \u03c9\u03c8 is the angular speed of rotation about the axis of the fibre. The equations of motion of the fibre read m dVy dt = Fy, (11) m dVz dt = Fz, (12) Ix d\u03c9\u03d5 dt = Mx, (13) I0 d\u03c9\u03c8 dt = My cos \u03d5 + Mz sin\u03d5, (14) dycm dt = Vy, (15) dzcm dt = Vz, (16) d\u03d5 dt = \u03c9\u03d5, (17) d\u03c8 dt = \u03c9\u03c8, (18) where Fy , Fz are the components of the force exerted on the fibre by the drop, Mx , My , Mz are the components of the moment of force relative to the centre-of-mass of the fibre exerted by the drop on the fibre, Ix is the moment of inertia of the fibre relative to the axis, going through its centre-of-mass and parallel to the x-axis, I0 is the moment of inertia of the fibre relative to its own axis", " Using the boundary condition (4), we find\u222b pad+substrate f dS + \u222b fibre f dS + \u03c3 \u222b \u0393\u0303 \u03ban dS = 0, (21)\u222b pad+substrate r\u0303 \u00d7 f dS + \u222b fibre r\u0303 \u00d7 f dS + \u03c3 \u222b \u0393\u0303 \u03ba r\u0303 \u00d7 n dS = 0, (22) where \u0393\u0303 is the drop free surface and f denotes tractions at the surfaces. The third terms in (21) and (22) can be expressed as\u222b \u0393\u0303 \u03ban dS = \u222e CL1 t dl + \u222e CL2 t dl + \u222e CLp t dl, (23)\u222b \u0393\u0303 \u03ba r\u0303 \u00d7 n dS = \u222e CL1 r\u0303 \u00d7 t dl + \u222e CL2 r\u0303 \u00d7 t dl + \u222e CLp r\u0303 \u00d7 t dl, (24) where CL1 and CL2 are the contact lines between the liquid and the fibre, CLp is the contact line between the liquid and the pad and substrate. Also t = \u03c4 \u00d7 n, where \u03c4 is the unit tangent vector to a contact line, and n is the unit outer normal vector to the drop surface (see figure 4a). Substituting (23) and (24) into (21) and (22), respectively, and denoting the total traction acting on the fibre from the drop by F, and the total moment of force acting on the fibre from the drop by M , we obtain F = \u2212 \u222b fibre f dS \u2212 \u03c3 (\u222e CL1 t dl + \u222e CL2 t dl ) = \u222b pad+substrate f dS + \u03c3 \u222e CLp t dl, (25) M = \u2212 \u222b fibre r\u0303 \u00d7 f dS \u2212 \u03c3 (\u222e CL1 r\u0303 \u00d7 t dl + \u222e CL2 r\u0303 \u00d7 t dl ) = \u222b pad+substrate r\u0303 \u00d7 f dS + \u03c3 \u222e CLp r\u0303 \u00d7 t dl. (26) The expressions (25) and (26) mean that, for the inertialess drop, the force and the moment of force acting on the fibre from the drop are equal, with the opposite sign to those acting on the pad and substrate", " Since a sufficiently strong macroscopic flow and the whole system shape are only slightly affected by the contact line motion, we shall use, for simplicity, the no-slip boundary conditions (8) and (9) at the contact lines, as though they were fixed. Actually, the stationary value of the contact angle \u03b1s can be restored only at the very end, after the macroscopic bulk motion has faded. Note that it does not mean that the contact line motion does not play any role in the fibre alignment. The droplet shape elongated along the fibre and required for its alignment (see figure 4b) can result only from the spreading stage (i). Note also that because the geometry of the surface near the contact lines CL1 and CL2 is complicated, we might not have a sufficient number of nodes per unit length on them (see figure 4c). As a result, significant errors in the line integrals along CL1 and CL2 in (25) and (26) can emerge. Therefore, it is much more convenient to calculate the values of F and M using the right-hand sides of the equations (25) and (26), because the geometrical configuration near the contact line CLp is much simpler (we also suppose that CLp does not move). The initial conditions should be specified, determining the initial positions of the free surface and the fibre, as well as its angular velocity r i(0) = r0 i , \u03d5(0) = \u03d50, \u03c8(0) = 0, ycm(0) = y0 cm, zcm(0) = z0 cm, (31) \u03c9(0) = \u03c90, Vy(0) = V 0 y , Vz(0) = V 0 z , (32) where r0 i is the initial position vector (t = 0) of the ith node at the free surface", " The comparison of the results obtained by this method with the results obtained by another iterative method (Rallison 1984) yields the maximum relative error \u223c5 % for the surfaces characteristic of the present problem. This is a good result for the sufficiently rough grids used here. After the velocity at the free surface u and values of F and M are found from (33) and (4), (8), (9) at each time step, the system (7), (11)\u2013(18) is integrated to follow the time evolution of the free surface and the fibre motion. The initial shape of the liquid surface with the fibre inserted in the drop was built in the following manner. The straight contact lines CD and AE in figure 4(a) corresponded to the drop spreading at the end of stage (i) in the experiment. Between the straight contact lines in figure 4(a) a three-dimensional drop configuration with embedded fibre corresponding to the symmetric drop shape shown in figure 4(b) (the fibre is parallel to the pad) and the grid on its surface were constructed using the software system for generating three-dimensional grids and meshes, GRIDGEN. The drop in figure 4(b) is symmetric relative to planes y =0 and z = 0 (cf. figure 4a). To construct more complicated initial shapes existing in the experiments (similar to the one shown in figure 4c), the symmetric mesh of figure 4(b) obtained by GRIDGEN was used as an input for the code, where some constant values of \u03c9\u03d5 , Vy , Vz were set in the boundary condition (9), (10), (19) to introduce a uniform displacement and rotation of the fibre, which are kept virtually constant by some applied force and moment of force acting on the fibre (during this preparatory stage). Then, equations (7), (15)\u2013(17), (33) were solved to determine the corresponding evolution of the drop surface up to the time when the desired deviations \u03d50, y0 cm and z0 cm were obtained. Then the shape obtained (see, for example, figure 4c) was used as an initial condition for the problem under consideration. Introduce the following dimensionless variables r \u2032 = r a0 , t \u2032 = t T0 , \u03c9\u2032 = T0\u03c9, u\u2032 = u V0 , p\u2032 = a0p \u03c3 , \u03ba \u2032 = \u03baa0, (35) where the length scale a0 is the radius of a hemisphere that contained the same volume as the drop, the velocity scale V0 = \u03c3/\u00b5 and the time scale T0 = \u00b5a0/\u03c3 . The dimensionless dynamic boundary condition at the free surface (4) takes the form f = \u03ban, (36) Here and hereinafter, the primes over the dimensionless parameters are dropped for brevity", " After the initial stage of the process, the second component, M2 < 0, begins to play the main role in the fibre alignment (see figure 8), while the component M1 becomes positive owing to the action of the viscous dissipative forces. The approximate equality M2 \u2212M1 is realized for t 1 (see figure 8). The three-dimensional calculations were also conducted for more complicated initial conditions, when the centre-of-mass of the fibre has been displaced from the point (xcm, 0, 0) by the method described at the end of \u00a7 4 (see figure 4c). The initial fibre position corresponded to the following initial values of the centre-of-mass coordinates and the angle between the fibre and the pad centreline y0 cm = z0 cm = 0.2, \u03d50 = 0.3 (17.2 \u25e6). (53) The system of equations (11)\u2013(18) was solved to find the evolution of the fibre-solder system for the case of \u03b2\u0303 = 1. The corresponding time dependences for ycm(t), zcm(t), \u03d5(t) and \u03c8(t) are shown in figure 9. From this figure, we see that the curves ycm(t), zcm(t), \u03d5(t) tend to zero, which means that the fibre returns to the centred position over the pad", " The angle \u03b8 between the fibre and the pad plane tends to zero. This means that the alignment process takes place in this case also, and the fibre tends to become parallel to the pad. Numerical calculations show that the asymptotic law of the time dependence \u03b8(t) is exponential and similar to that in (52). The experiments showed that the alignment process takes place for any initial conditions. For example, we can set the initial condition in the following manner: rotate the fibre from the position shown in figure 4(b) to some angle \u03d5 and then hold it up to the time moment when the liquid motion is stopped owing to viscous dissipation. In that case, the mean curvature tends to a constant value \u03ba0, the pressure \u2013 to \u03c3\u03ba0 and then M1 = 0 if the contact lines do not change their position. Numerical calculations show that also in this case M2 < 0, and the drop aligns the fibre near the pad centreline. The three-dimensional calculations are involved and one is tempted to ask whether a simplified two-dimensional model can capture some important features" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002457_cdc.2005.1582362-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002457_cdc.2005.1582362-Figure5-1.png", "caption": "Fig. 5. Concept for \u201d\u0303 to converge to the target point.", "texts": [ " We call this area \u2126. Observing the structure of (17) leads to the fact that the reachable area of \u2206\u03b7\u0303 is obtained by rotating the area \u2126 through \u03d5 about \u2206\u03c8axis. Therefore, the geometric interpretation of (16) is that \u03d5 is determined such that \u2016\u2206\u03b1\u2032 o\u2016- axis coincides \u2212 \u03b1o \u2016\u03b1o\u2016 as seen in the right figure of Fig. 4. By using \u03d5 satisfying (16), the determination problem of (\u03b81, \u03b82, \u03d5) for the convergence of \u2016\u03b7\u0303 + \u2206\u03b7\u0303\u2016 is reduced to that of (\u03b81, \u03b82) since \u2016\u2206\u03b1\u2032 o\u2016 and \u2206\u03c8 are functions of \u03b81 and \u03b82. Figure 5 shows the concept for \u03b7\u0303 to converge to the target point by using the reachable area \u2126. The areas surrounded by dashed lines are the reachable areas \u2126 at each iteration. As in Fig. 5, \u03b7\u0303 can converges to the target point by shifting to points on the reachable areas \u2126 iteratively. To do so, precise analysis of the reachable area \u2126 is necessary. In the following, the properties of the reachable area \u2126 at the plane (\u2016\u2206\u03b1\u2032 o\u2016,\u2206\u03c8) are investigated. For the reachable area \u2126, the following lemma holds. Lemma 3: Consider the reachable area \u2126 at the plane (\u2016\u2206\u03b1\u2032 o\u2016,\u2206\u03c8) given by (6) and (8). Then, \u2126 is symmetry with respect to the \u2016\u2206\u03b1\u2032 o\u2016-axis. Proof: It is easily checked that \u2016\u2206\u03b1\u2032 o(\u03b81, \u03b82)\u2016 is invariant with respcect to (\u03b81, \u03b82) such that the sign of \u2206\u03c8(\u03b81, \u03b82) change" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001536_imece2004-61961-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001536_imece2004-61961-Figure1-1.png", "caption": "Figure 1. CRUISE MISSILE WITH VARIABLE SPAN MORPHING WING", "texts": [ "org/ on 02/03/2016 Ter b wingspan \u03b2 sideslip angle b0 span of single wing CL lift coefficient Cl roll moment coefficient Cl\u03b4w roll moment stability derivative d center of lift relative to missile center of mass \u03b4 control surface deflection \u03b5 actuator time constant \u03c8 yaw angle FB body reference frame (e1,e2,e3) T Fext externally applied force in body frame FI inertial reference frame (i, j,k)T I inertia matrix M missile mass matrix Mext externally applied moment in body fram (L,M,N)T m\u0304 extending wing mass mb missile body mass mT total mass mT = mb + m\u0304 \u2126 angular velocity in body coordinates (p,q,r)T \u03c6 roll angle q dynamic pressure R rotation matrix rp position of movable mass in body coordinates S reference area \u03b8 pitch angle u control input U airspeed v velocity in body coordinates (u,v,w)T Copyright c\u00a9 2004 by ASME ms of Use: http://www.asme.org/about-asme/terms-of-use Do VT total velocity vector y\u0304e percent wing extension A variable-span morphing wing for a cruise missile, as shown in Fig. 1, is designed to change its wingspan for various flight conditions to increase range. As a result of increasing the wingspan, the aspect ratio and wing area increase and the spanwise lift distribution decreases for the same lift. Thus, the drag of the morphing wing decreases and, consequently, the range of the aerial vehicle is increased. This symmetric wing extension for increased range and endurance has been recently investigated in [1\u20133]. Alternatively, if the wings of a cruise missile are antisymmetrically changed - one wing is extended and the other wing is contracted - or only one wing is extended, a lift differential exists between the wings producing a roll moment about the longitudinal axis of the missile" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003789_13506501jet718-Figure12-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003789_13506501jet718-Figure12-1.png", "caption": "Fig. 12 Result of numerical integration of the equations motion for \u03c9 = 6000 and d\u0304 = 0.5: (a) orbits in the xy-plane; (b) phase diagram; (c) Poincar\u00e9 map; and (d) spectrum plot", "texts": [ "5 for which the critical rotational speed increased by 1320 r/min in comparison with the cylindrical bearing, for the discussed turbine Therefore, in the following discussion, attention is focused on the dynamic responses of the rotor\u2013 bearing system with an elliptical bearing of d\u0304 = 0.5. JET718 Proc. IMechE Vol. 224 Part J: J. Engineering Tribology Figure 11 shows the three-dimensional spectrum plot of the LP rotor\u2013bearing system for d\u0304 = 0.50. It can be observed from Figs 10(d) and 11 that the dynamical responses of the system is synchronous when the rotational speed is less than 5880 r/min. At the rotational speed \u03c9 = 5880 r/min, bifurcation takes place. Figure 12 shows the response at rotational speed \u03c9 = 6000 r/min by the whirl orbit, the diagram, the Poincar\u00e9 map, and the spectrum plot. Figure 12(d) shows that the dynamic response of the rotor\u2013bearing system consists of a 1/3 sub-harmonic resonance and a 2/3 sub-harmonic resonance. Figure 11 shows that the 1/3 sub-harmonic resonance is near the first critical speed. The whirl orbit, the phase diagram, and the Poincar\u00e9 map given in Figs 13(a), (b), and (c) suggest that the response is a quasi-periodic motion. With an increase in rotational speed, the 1/2 sub-harmonic resonance appears, and at rotational speed \u03c9 = 7890 r/min the 2/3 sub-harmonic resonance disappears" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002242_bf00534484-Figure14-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002242_bf00534484-Figure14-1.png", "caption": "Fig. 14. Schematic show of stress and plastic strain increment vectors on instantaneous yield surface", "texts": [ " 0a~--~ ' d~ > o . (21) In order to determine the unknown increment d)~ above, we assume between the stress increments daq and de~. the following relation' d~ dePi j : 2 H ' dsPq d~ p . (22) 3 For uniaxial stress state the above equation is reduced to H ' - - dall de~ ' (23) where H ' is the plastic tangent modulus in uniaxial tension or compression. Moreover, equation (22) means ([15], [20]) tha t we assume the same relation as in uniaxial stress state between ] and d~ = V 3 l d e P [ as shown in Fig. 14. Here dat is the projection of the stress increment da I vector d a on the plastic strain increment vector d e c From (21) and (22) we obtain ~F ~amn\" damn 2 ~F ~F ~24) - - H t - - _ _ 3 ~3at:~ ~akl i . e . , ~F - - ' d a m n ~amn ~F (25) - - H t . . . . 3 Oakt ~am Ing. Arch. Bd. 44, H. 4 (!975) 2t34 M. Tanaka eL al. : On Hardening Theory of Plasticity Next let us consider the expression for the instantaneous movement do~q of the center of the yield surface. According to Ziegler's kinematic hardening theory [lol we assume d~ii = d# " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003167_gt2008-50257-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003167_gt2008-50257-Figure1-1.png", "caption": "FIG. 1 BRUSH SEAL", "texts": [ "org/about-asme/terms-of-use S = source component in momentum equation [Pa/m] T = temperature [K] u = velocity [m/s] x = axial direction [mm] \u03b5 = porosity [-] \u03b8 = circumferential direction [mm] \u00b5 = dynamic viscosity [Pa\u00b7s] \u03c1 = density [kg/m 3 ] 0/1/2 = chamber index (0 \u2013 prechamber) b = bristle n, z = directions normal to bristle s = static; bristle lengthwise direction t = total BSS = bristle pack upstream of two teeth CFD = computational fluid dynamics SSB = bristle pack downstream of two teeth SSS = conventional three-tooth labyrinth Especially in the development of turbomachinery for power generation, it is a main aim to increase the efficiency of the turbines. This can be effectively accomplished by minimizing leakage losses. The potential of such improvements is evident for large steam turbines, where sealing losses are typically in the order of 0.5 % of the total power output of the turbine or up to 40 % of total losses occurring in the turbine. Brush seals can reduce these leakages up to 80 % compared to conventional labyrinth seals [1]. Fig. 1 shows a common assembly of a brush seal. The bristle pack is composed of bristles with a diameter of 0.07 to 0.15 mm. The bristle pack used in this investigation has an axial 2 Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 01/06/2018 width of nearly 2 mm and a free radial clearance in its unpressurized condition. Typically 100-200 bristles per mm in circumferential direction are fixed between the backing plate and the front plate of the seal at a lay angle of 45\u00b0 relative to the radial direction (for lay angle definition see also Fig", " According to the porous model the basic characteristic of the bristle pack is the porosity \u03b5 as defined by the following equation: \u03d5 \u2212= cosb4 nd\u03c0 1\u03b5 b b 2 (4) The bristle pack width is a single unknown in equation (4), for it depends on the pressure drop through the brush seal. A shortened front plate as used in this investigation should make this dependence more important. A realistic value of the bristle pack width is fenced between the manufacturing data and a theoretical value for the closest packing of the bristles (limit for highest pressures). Another parameter strongly affecting the brush seal performance is the free radial clearance s between bristle pack and the rotor (see Fig. 1). Its value is constrained by the initial cold clearance and a remaining clearance in operation even if the blow-down effect is active for the 5 ded From: http://proceedings.asmedigitalcollection.asme.org/ on 01/06/2018 pressurized seal. Thus there are two parameters in the brush seal model that can vary during the operation \u2013 free clearance and bristle pack width. The calibration procedure for the numerical model with experimental data can therefore be based on variation of either the free clearance or the bristle pack width or both parameters" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003249_1.2821385-Figure12-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003249_1.2821385-Figure12-1.png", "caption": "Fig. 12 Closed-loop manipulators \u201eCLMs\u2026 used for data generation. \u201ea\u2026 Four-bar CLM with pendant link, \u201eb\u2026 revolving four bar CLM, and \u201ec\u2026 five-bar CLM.", "texts": [ " For curve, the centroid and the two extremal critical points are computed while reading data from the file. Thus, the bulk of the input data need not be loaded into the data structure. In the following, a variety of data are considered to illustrate the capabilities of the proposed methodology and are presented in the order of increasing complexity from the point of view of workspace analysis. The prototypical two-DOF manipulators used for generating the data are a simple dyad and the ones shown in Fig. 12. The marks in the figures represent the centroids of the curves. 6.1 Full Rotatability. Figure 13 illustrates the cases for a simple dyad with different link lengths and scan resolutions. It demonstrates that our method is not very sensitive to the number of input points used to represent the workspace, although the smoothness of the boundary depends on the number of representative curves. Figure 14 demonstrates that the algorithm can pick up small holes in the workspace, which are not perceptually prominent in the sampled-point representation of the workspace. Both Figs. 14 a and 14 d are generated by a manipulator like the one in Fig. 12 a . The workspace is equivalent to sweeping a circle over a coupler curve. Whereas in the first case, the whole inner envelope Fig. 14 b is discarded as internal singularities, in the second case with a longer pendant link, a small part of the singularity loci Fig. 14 e is recognized to be lying on the inner boundary producing a hole Fig. 14 f . Most existing numerical techniques for workspace boundary determination will fail to detect the small Transactions of the ASME x?url=/data/journals/jmdedb/27868/ on 01/29/2017 Terms of Use: http://www", " Figures 16 b and 16 c especially ilustrate the consistency and fidelity of the boundary singularity valuation in the present method, which does not actually use any inematic information of the manipulator. Figure 17 illustrates the ependence of the result on the order of input scanning. In Fig. 7 a , even though the perceptual boundaries are well defined, the ig. 13 Workspace of a dyad with different sample densities. a\u2026 First link longer, \u201eb\u2026 boundary curves, \u201ec\u2026 second link onger, and \u201ed\u2026 boundary curves. ig. 14 Workspaces of manipulators of the type in Fig. 12\u201ea\u2026. a\u2026 Workspace, \u201eb\u2026 envelopes, \u201ec\u2026 no hole, \u201ed\u2026 workspace, \u201ee\u2026 nvelope, and \u201ef\u2026 small hole. ig. 15 Workspace generated through sweeping of noncircuar curves from a manipulator as in Fig. 12\u201eb\u2026. \u201ea\u2026 Workspace, b\u2026 boundaries, and \u201ec\u2026 same at high resolution. ournal of Mechanical Design om: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess.ash computed boundaries are not so smooth in Fig. 17 b . The location of the centroids in Fig. 17 b indicates that the points of the underlying coupler curve that swept the circle are unevenly distributed; the lower segment has got only four or five points of the total of 50 points. The corresponding portions on the boundary, therefore, also have only that many number of points", " 18, the point to observe is the correctness and robustness of the part of the end curves being augmented to the envelope curves and consolidation of the boundary curves. In FEBRUARY 2008, Vol. 130 / 022306-7 x?url=/data/journals/jmdedb/27868/ on 01/29/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use c n v w l a t w a w fi s b s t e t i o r m p p s c a r t c t t t o fi p F W 0 Downloaded Fr 6.3 Complex Envelope Curves. Figure 19 illustrates the ases with general shapes of the envelope curves, such as combiations of simple, self-intersecting, and mutually intersecting enelope curves. The data pertain to a manipulator as in Fig. 12 a , here the coupler curve of the four-bar CLM directly gives the ocus of the centroids. The two coupler curves, one \u201cfigure eight\u201d nd the other a \u201ccardioid\u201d with an inner loop, were selected and hree different small, medium, large lengths of the pendant link ere used to generate the six workspaces presented in Fig. 19. For ll these combinations, the workspace singularities and boundaries ere appropriately determined by our program. Note that in the rst case figure eight , the outer boundary is produced from the egments picked up from both the envelopes" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure3.9-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure3.9-1.png", "caption": "Fig. 3.9. Negative inverse describing function of the modified relay", "texts": [ " Under the relay feedback, the amplitude and oscillating frequency of the limit cycle is thus given approximately by the solution to Gp(j\u03c9) = \u2212 1 NER(a) , (3.12) i.e., the intersection of the Gp(j\u03c9) and the negative inverse DF of the equivalent relay. The complex equation at Equation (3.12) will generate the following two real equations: |Gp(j\u03c9)| = \u2223\u2223\u2223\u2223 1 NER(a) \u2223\u2223\u2223\u2223 , argGp(j\u03c9) + arg(NER(a)) = \u2212\u03c0. Clearly, two unknown parameters can be obtained from the solution of these equations. The negative inverse DF of the equivalent relay is approximately a ray to the origin in the third quadrant of the complex plane, if h2 > f1 as shown in Figure 3.9. The angle at which this ray intersects the real axis depends on the relative relay amplitude of h1 and h2. In this way, a sustained limit cycle can be induced from servo-mechanical systems, similar to the more conventional single relay set-up for industrial processes. Note that the choice of h1 = 0 and h2 > f1 will lead to a double integrator phenomenon, where no sustained oscillation can be obtained from relay feedback. By varying h1 and/or h2, two relay experiments can be conducted, thus deriving equations from which the unknowns Tp, f1 and f2 can be computed, assuming the gain Kp is known or estimated from other tests" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003188_j.mechmachtheory.2007.07.001-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003188_j.mechmachtheory.2007.07.001-Figure2-1.png", "caption": "Fig. 2. Surface of revolution.", "texts": [ " Therefore, parametric curves Cm and Cn form a set of lines of curvature, and their normal curvatures must be two principal curvatures of moulding surface, and correspond to two principal directions. This property simplifies the discussion on moulding surface. According to the shape of the generator and the directrix, three typical moulding surfaces are described as follows: (1) Surface of revolution. It is generated by rotating a generator Cm around a fixed axis that is simultaneously coplanar with the generator, as shown in Fig. 2. Here, the directrix Cp is a circle whose center lies on the fixed axis and, meanwhile, the fixed axis is also its axis of curvature. (2) Developable surface. It is generated by moving a straight generator Cm, as shown in Fig. 3. According to the well-known result of differential geometry, developable surface can be further classified into (general) cylinder, (general) cone and tangent surface of space curve. The surface normals at all points of the same straight generator Cm are coplanar and parallel, thus this surface possess a same tangent plane at all points of the same generator" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002001_1.3453240-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002001_1.3453240-Figure8-1.png", "caption": "Fig. 8 Plots of Ii versus 6 for \u20ac = 0.5, Co = 0.2, 12t1>/lc3 = 1.0 and various values of a", "texts": [ " As observed from Fig. 6 and 7, it is seen that the results obtained in [7] may also apply, approximately, for porous bearings provided E and Co are substituted by E* and C~, respectively. However, the comparison becomes increasingly poorer beyond E* = 0.15 as seen from Fig. 7. Nevertheless the approximate solution is good provided the values of E* and C~ are small. Journal of Lubrication Technology Finally graphs of normalized pressure p for an oil having a pres sure-dependent viscosity3 11 = 110eCiP are given in Fig. 8 for E = 0.5, Co = 0.2, and a = 6Ci110URt/c2 = 0,0.2,0.4 and 0.6. A typical comparison of the exact pressure distributions in porous, flexible bearings is made in Fig. 9 with the approximate distributions obtained from the non porous solution. Referring to the variable viscosity results given in Fig. 8 and 9, it is seen that the larger the value of a, the larger will be the normalized pressure. A comparison made between the exact solution for porous bearings with the approximate one obtained from the impervious 3 For a pressure-dependent viscosity oil with a = 0.0008 cm2/kg, N = 1800 rpm, viscosity ~ = 5 X 10-6 Rey. for SAE 30 oil at 140\u00b0F, Rl = 1 in (2.54 em), c = 10-3 in (2.54 X 10-3 em), the constant a is about 0.3. OCTOBER 1977 / 453 Downloaded From: http://tribology.asmedigitalcollection" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001767_s00158-003-0344-1-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001767_s00158-003-0344-1-Figure2-1.png", "caption": "Fig. 2 Initial position of, and deployed, inflatable knee bolster", "texts": [ " This evaluator is the percentage improvement of the performance (the fitness value) of the best-so-far design generated by GA (PGA) compared to that of the base design value (PBASE) if there is one. Assume the lower the better; the equation is defined as follows: Performance improvement = (PBASE\u2212PGA) PBASE \u00b7100(%) (1) In the next section, the three GA strategies will be applied to solve three problems in IKB design. 3 Optimal design of inflatable knee bolster (IKB) 3.1 What is an IKB? An IKB is an inflatable airbag cushion deployed in the knee area, in conjunction with frontal airbags, to reduce potential lower-leg injuries. Figure 2 shows pictures of an IKB at its initial position and after deployment. Because IKB is a new occupant restraint technology, it was necessary to conduct a study to evaluate its potential benefits and disadvantages to occupant safety performances. Therefore, the goal of the following case studies was to assess whether IKB can help to improve the New Car Assessment Program (NCAP) star rating either by a component optimal design or by a system optimal design (for instance combining IKB with another restraint system), using the efficient GA method" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001578_acc.2004.1383649-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001578_acc.2004.1383649-Figure2-1.png", "caption": "Fig. 2. Steerable Nips System", "texts": [ " The remainder of this paper is organized as follows. Section I1 will describe the nonholonomic constraints, kinematic model, and dynamic model of the steerable nips mechanism. The control strategy is derived in section 111. Simulation results will be shown in section IV. Finally, conclusions and some comments regarding the control performance are stated in section V. 11. KINEMATIC AND DYNAMIC MODEL OF THE STEERABLE NIPS MECHANISM The steerable nips is illustrated in Figs. 2 - 3. The steerable nips moves a sheet on a flat surface. Figure 2 represents an initial sheet position once the two nips are in contact with the sheet. Figure 3 represents a sheet position while it is being tracked. The left comer of the sheet, point C, will be used to track the position of the sheet. The angular orientation of the sheet is 4. Note that while the paper buckles, point C remains on the flat surface since the buckle occurs only between points 1 and 2. For this reason point C does not move perpendicular to the sheet. 4n2 It is assumed that when the sheet buckles, the sheet is still transversally stiff so rotation is possible" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003998_09544062jmes1329-Figure9-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003998_09544062jmes1329-Figure9-1.png", "caption": "Fig. 9 All forces acting on the collet\u2013spindle interface", "texts": [ " 8, four slots cut into the collet of the high-speed gas spindle system allow the collet to expand when a drill bit is inserted. This study disregarded the area of these slots when calculating the contact area of the collet\u2013spindle interface. By disregarding the slot area, the actual contact area can then be obtained using equation (6), which is derived from equations (4) and (5) A = \u03c0(D + d)L 2 cos \u03b1 \u2212 mlL cos \u03b1 (6) where A (mm2) is the true contact area of the collet\u2013 spindle interface, L (mm) the axial length of the cone, m the number of slots, and l (mm) the width of each slot. Figure 9 shows the contact interface between the collet and the spindle on a high-speed gas spindle system. The normal force N that acts on the conical surface of the collet can be derived by using equation (7) and the true contact area. From the free body diagram of the whole collet\u2013spindle assembly, one can see the three external forces in equilibrium as the normal force N acts on the taper surface, the axial cutting force Fa, and the drawbar force F as exerted by the disc springs. Hence, by substituting equation (7) into force equilibrium equation (8), one can represent the relationship among all of the forces acting on the collet as equation (9)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001933_05698190590948232-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001933_05698190590948232-Figure5-1.png", "caption": "Fig. 5\u2014Structure drawing of the latest face-to-face double seal: 1, inner primary ring; 2, rotating seat; 3, outside primary ring; 4, spring; 5, oil-grade ring; and 6, retainer.", "texts": [], "surrounding_texts": [ "Figure 10 is the relationship of oil temperature rise determined by the difference of sealing-oil outlet and inlet temperatures versus the test speed. Generally, the temperature rise is rather low, for example, 8.2\u25e6C at 10,000 r/min." ] }, { "image_filename": "designv11_32_0000457_978-3-642-55848-1-Figure9.42-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000457_978-3-642-55848-1-Figure9.42-1.png", "caption": "Fig. 9.42. Motion of the body in space", "texts": [ " Likewise, the effort junctions on the right give the moment at the right port of the force at the left port by multiplying it by the rcp'x matrix. The ratios of the transformers are the material coordinates of a body point corre sponding to the port with respect to the mass centre. Thus, they are parameters that depend on the geometry of the rigid body and don't change with its motion. 9.5.3 Rigid Body Dynamics To complete the model, we need a dynamic equation goveming rigid body motion. The simplest form of such an equation is given with respect to axes translating with the body mass centre (Fig. 9.42). We assume that the base frame is an inertial frame. The translational part ofthe motion can be described by p = mIVC} dp =F dt (9.96) Here, m is the body mass and F is the resultant of the forces reduced to the mass centre. We represent the dynamics of body translation in the Base (Fig. 9.43a) by the eM component that describes the motion of the mass centre of the body. This last component (Fig. 9.43b) consists of effort junctions corresponding to the x, y and z components of the body mass centre velocity with respect to the base frame" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003122_j.sna.2008.11.029-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003122_j.sna.2008.11.029-Figure2-1.png", "caption": "Fig. 2. Exploded view for previous design of shot-put sensor.", "texts": [ " The EMG recorder ombined with motion video and force measurement will allow a uantitative examination of the internal and external factors govrning human motions, particularly for effective sampling of the lectric signals from human upper limb such as biceps and triceps tc. The kinematics, kinetics and physiology data recorded by cam- eras, shot-put sensor and SAFMS-T, and EMG device), respectively will be transferred to the laptop for further analysis. The digitalshot sensor is the primary equipment that will be expatiated in the following section. Then multi-target and multi-parameter athlete biomechanics information can be acquired via data fusion (Fig. 2). 3. The digital-shot sensor 3.1. An early version of force sensor As the most crucial portion of the digital-shot, the quality of the force sensor has direct influence upon the performance of system. In the previous work, a strain gauge sensor for male shot-putter was designed and fabricated [11]. However, the force sensor could not endure severe violent collisions felling to the ground. Some design drawbacks have been found in practical applications: (1) The structure was complex for designing, which directly induced the expensive machining cost" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002856_robot.2007.363559-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002856_robot.2007.363559-Figure2-1.png", "caption": "Fig. 2. 3D rendering of the remote scene", "texts": [ " This subsystem handles the forces that have to be fed back to the operator as well as the integration of position information with the motion restrictions. In addition to the main control loop, a video stream provides video feedback from cameras located at the Remote Robotic Cell, whose zoom and orientation can be remotely actuated. A 3D visualizer provides the operator with information concerning the position and orientation of the robot end-effector, this visualizer is aimed to reduce the traffic in the network produced by the video feedback which is a high-bandwidth consumer. The visualizer with a 3D scene is depicted in figure 2. The Force Guidance Module fulfills two different functions: 1) The definition by the operator of a motion restriction rs; 2) The computation of the restriction force fr that must be exerted to maintain the position of the end-effector inside the currently selected motion restriction rs, as well as of the viscous force fv that prevents the velocity of the end-effector from becoming too large for the robot to follow. The restriction force fr and viscous force fv are combined with the master force fm of the wave variable method to generate the total force ft, which is fed to the operator via a haptic device" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003122_j.sna.2008.11.029-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003122_j.sna.2008.11.029-Figure7-1.png", "caption": "Fig. 7. Strain distribution of", "texts": [ "3 and 2.7 \u00d7 103 kg/m3. The compensated mass with the diameter of 26 mm is fabricated by yellow brass, whose density is 8.5 \u00d7 103 kg/m3. SOLID45 is used for the three-dimensional modelling of solid structures in which the threedimensional solid-continuum eight-node element is adopted. The theory of elastic mechanics can be used to the constitutive behavior of the sensor. When the acceleration is only applied to the z-direction, the strain distribution of elastic membrane in the x-direction is shown in Fig. 7. The magnitude of the applied acceleration is 10 m/s2. From this figure, it can be observed that the two edges of the membrane generate the maximal strain. As the piezoresitors will be installed in the place where the maximal deformations occur, the two external sides and the two inner sides along x-axis can be chosen as the location of the four pieces of piezoresitors where high sensitivity can be obtained. elasti 4 n e e t t f A I s m d a i o r a v w F t a v a v T C .3. Static calibration The static calibration for the shot-put sensor is difficult and on-standard as its unique structure" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002219_cdc.2006.377706-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002219_cdc.2006.377706-Figure2-1.png", "caption": "Fig. 2. Sketch of the sets \u2126\u2032 q \u2282 \u2126q , for q = 1, 2 in the (r, x3) plane, for x3 > 0", "texts": [ " (11) It is known that the necessary condition [4] for the sta- bilization by means of a continuous feedback or robust stabilization by locally bounded feedback [21] does not hold for this system. Let us check that we can prove the existence of a hybrid stabilizing feedback by applying Theorem 4.1. Let us denote f(x, u) the right-hand side of the system (11), where x = (x1, x2, x3) and u = (u1, u2). We use the notation: r = \u221a x2 1 + x2 2. We consider a simplified version of the hybrid controller of [11] (see also [9]) and we define a patchy control Lyapunov function as a collection of two patches. These patches \u2126\u2032 q \u2282 \u2126q, for q = 1, 2 are sketched in Figure 2 in the (r, x3) plane (they are surfaces of revolution around the x3 axis and symmetric with respect to (0, r) axis). To define the first one, let us consider the following sets \u2126\u2032 1 = {x = 0, r2 < 1 + \u03c1 2 |x3|} , \u21261 = {x = 0, r2 < \u03c1|x3|} , and the function V1 : R 3 \u2192 R, defined by V1(x) = (\u03c1 + 1) \u221a|x3| \u2212 x1, for all x \u2208 R 3, where \u03c1 > 1 will be prescribed below. Observe first that V1 is a smooth function on a (relative to R 3 \\ {0}) neighborhood of \u21261. Now let us define the second patch, and let us consider the following sets \u2126\u2032 2 = {x = 0, r2 > 3 + \u03c1 4 |x3|} , \u21262 = {x = 0, r2 > |x3|} , and the function V2(x) = 1 2 (r2 + x2 3)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003133_02678290601020104-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003133_02678290601020104-Figure3-1.png", "caption": "Figure 3. Schematic drawing of the set-up for polarized FTIR spectroscopy measurements of free-standing LCE films.", "texts": [ " The films have the dimensions of about 2 mm (width) and 3\u20134 mm (length), and their in thickness is approximately 1 mm. The film thickness is not uniform, and the number of layers varies in the film plane. Polarized Fourier transform infrared (FTIR) spectroscopy is performed with an FTS-6000 FTIR (Bio-Rad) spectrometer in combination with an IR microscope (UMA500 Bio-Rad). The size of the region chosen for the measurement is 2506250 mm2. The polarized IR beam propagates perpendicular to the film surface and to the smectic layers, see figure 3. The dependence of the IR spectra on the polarizer angle Q is measured in 9u steps from 0u to 180u. IR spectra are recorded with a spectral resolution of 4 cm21. The films are uniaxially stretched in discrete steps and measurements are repeated after each step. The average in-plane strain is determined from the distance of the two fixed edges of the film. The temperature of the samples is controlled by a Linkam heating stage THMS 600. A typical IR spectrum is represented in figure 4. The assignment of the particular absorption lines to individual bond types in the molecule was achieved using standard methods [17]" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003919_s10846-010-9488-6-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003919_s10846-010-9488-6-Figure2-1.png", "caption": "Fig. 2 Small flying robot TDL30 (lower side of OAV)", "texts": [], "surrounding_texts": [ "3.1 Attitude Feedback Closed-Loop System\u2019s Dynamics The attitude controller is designed by using a general PD control method. The angular rates and the angles from an AHRS are used for feedback states in a PD control algorithm. We acquired the P and D gain to stabilize the attitude of the vehicle by trial and error. The final inputs to control vanes are then mixed in a mixing system. Figure 3 shows the block diagram of the attitude feedback closedloop system. The attitude model is represented by Eq. 1 Ix\u0308 = Maero (1) Maero is aerodynamic moments due to control vanes, pitching, rolling and yawing moment. And the equation of a feedback system comprehension represented by Eq. 2 with the PD gains. The P gain is KP and the D gain is KD. Ix\u0308 = \u2212KDx\u0307 \u2212 KPx + Maero (2) We represent Eqs. 2 to 3 then the KD and the KP are regarded as a damping coefficient and a spring coefficient of a mass-damper-spring 2nd order system. Ix\u0308 + cx\u0307 + kx = u (3) Therefore, if we find c and k stabilize the system for step inputs, the system will be stable. The inertia of moment (I) were led from the transfer function G(s) with comparison of simulation data and experimental data. G (s) = 1/ I s2 + c/ Is + k/ I (4) We inputted several step signals to the feedback closed-loop systems of rolling and pitching. Figures 4 and 5 are roll and step input responses of its rate. Figures 6 and 7 are pitch and step responses of its rate. All these data are compared with simulations on time domain. Figures 4, 6 and 7 show the similar results in comparison to experiments and simulations. However, Fig. 5 shows different results after 0.4 s, owing to the unbalanced trim. The block diagram of the simulation is shown in Fig. 8. The dynamics of the servo motor driving control vane is considered a 2nd order system [4] and represented in Eq. 5. Gs (s) = \u03c92 n s2 + 2\u03b6\u03c9ns + \u03c92 n (5) Then, \u03c9n and \u03b6 are derived from the experiment\u2019s results. The same structure was applied to the pitching and rolling systems, respectively. Figure 9 shows the frequency response of the pitch close-loop system, which is an important factor(the cut-off frequency is 0.7 Hz) in designing a hovering controller. Fig. 6 Pitch step input responses (pitching rate) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 \u201350 \u201340 \u201330 \u201320 \u201310 0 10 t[sec] q[ de gr ee /s ec ] Pitch step responses ex1 ex2 ex3 ex4 ex5 sim Fig. 7 Pitch step input responses (pitching angle) 2 Pitch step responses 3.2 Lateral and Longitudinal Transition Model and Hovering Control The transition model is determined in Eq. 6 [5]. In the equation, Lc, Lk, Mc and Mk are damping and spring coefficients respectively which were acquired previously. Therefore, Eq. 6 includes the attitude closed-loop systems. Lv and Mu are assumed 0 in hovering condition. \u03b4ail and \u03b4ele are rolling and pitching inputs. d dt \u23a1 \u23a2 \u23a2\u23a2\u23a2 \u23a2\u23a2 \u23a3 p q \u03c6 \u03b8 u v \u23a4 \u23a5 \u23a5\u23a5\u23a5 \u23a5\u23a5 \u23a6 = \u23a1 \u23a2 \u23a2\u23a2\u23a2 \u23a2\u23a2 \u23a3 Lc 0 Lk 0 Mc 0 1 0 0 0 1 0 0 0 0 0 0 g 0 0 Lv Mk Mu 0 0 0 0 0 0 0 \u2212g Xu 0 0 0 Yv \u23a4 \u23a5 \u23a5\u23a5\u23a5 \u23a5\u23a5 \u23a6 \u23a1 \u23a2 \u23a2\u23a2\u23a2 \u23a2\u23a2 \u23a3 p q \u03c6 \u03b8 u v \u23a4 \u23a5 \u23a5\u23a5\u23a5 \u23a5\u23a5 \u23a6 + \u23a1 \u23a2 \u23a2\u23a2\u23a2 \u23a2\u23a2 \u23a3 1 0 0 0 1 0 0 0 0 0 0 0 \u23a4 \u23a5 \u23a5\u23a5\u23a5 \u23a5\u23a5 \u23a6 [ \u03b4ail \u03b4ele ] (6) We designed a controller as SISO (Single Input Single Output) systems. Then Eq. 6 was decomposed to Eqs. 7 and 8. d dt \u23a1 \u23a2 \u23a2 \u23a3 p \u03c6 v y \u23a4 \u23a5 \u23a5 \u23a6 = \u23a1 \u23a2 \u23a2 \u23a3 Lc Lk 1 0 0 g 0 0 Lv 0 0 0 Yv 0 1 0 \u23a4 \u23a5 \u23a5 \u23a6 \u23a1 \u23a2 \u23a2 \u23a3 p \u03c6 v y \u23a4 \u23a5 \u23a5 \u23a6 + \u23a1 \u23a2 \u23a2 \u23a3 1 0 0 0 \u23a4 \u23a5 \u23a5 \u23a6 \u03b4ail (7) d dt \u23a1 \u23a2 \u23a2 \u23a3 q \u03b8 u x \u23a4 \u23a5 \u23a5 \u23a6 = \u23a1 \u23a2 \u23a2 \u23a3 Mc Mk 1 0 0 \u2212g 0 0 Mu 0 0 0 Xu 0 1 0 \u23a4 \u23a5 \u23a5 \u23a6 \u23a1 \u23a2 \u23a2 \u23a3 q \u03b8 u x \u23a4 \u23a5 \u23a5 \u23a6 + \u23a1 \u23a2 \u23a2 \u23a3 1 0 0 0 \u23a4 \u23a5 \u23a5 \u23a6 \u03b4ele (8) The defined SISO systems is used to design a LQI(Linear Quadratic Integrator) method. The system is represented by the following equation. x\u0307 (t) = Ax(t) + Bu(t) y = Cx(t) e\u0307 (t) = e(t) \u2212 y(t) e (t) = \u222bt 0 r(t) \u2212 y(t) dt (9) The extended state-space system, which is involved with error e\u0307 (t), is described by d dt [ x(t) e(t) ] = [ A 0 \u2212C 0 ] [ x(t) e(t) ] + [ B 0 0 1 ] [ u(t) r(t) ] (10) The LQR cost function J is the sum of the steady-state mean-square weighted state xe = [x(t) e(t)]T and the steady-state mean-square weighted input vector ur (t) = [u(t) r(t)]T . J = \u222b\u221e 0 [ xT e (t) Qxe (t) + uT r (t) Rur(t) ] dt The feedback gain F is found as the solution (P) of the algebraic Riccati equation. The optimal feedback control input is shown in the following equation. u (t) = \u2212Fxe (t) F = R\u22121 BT P (11) An identity observer is represented by the follow equation. \u02d9\u0302x = Ax\u0302 + Bu + K ( y \u2212 Cx\u0302 ) (12) Table 2 Specifications of UPS Name Tx node Rx node Server Actual image Weight 17 [g] 11 [g] 31 [g] Size 40 \u00d7 45 \u00d7 39 [mm] 40 \u00d7 45 \u00d7 18 [mm] 60 \u00d7 50 \u00d7 75 [mm] Where x\u0302 is an estimated state of x and the Kalman filter gain K is described by Eq. 13. K = X + CT V\u22121 (13) K consists of a solution of the algebraic Riccati equation (X) and noise power spectrum density (V). Equation 14 shows the state space matrix of the hovering controller with the Kalman filter. d dt [ x\u0302 (t) e (t) ] = [ A \u2212 BF1 \u2212 KC \u2212BF2 0 0 ] [ x\u0302 (t) e (t) ] + [ K 0 \u22121 1 ] [ y (t) r (t) ] u (t) = [\u2212F1 \u2212F2 ] [ x\u0302 (t) e (t) ] (14) 4 Hovering Experiments Results 4.1 Experimental Setup There are several systems for a position reference, such as the motion capture system and the laser tracker, if it is not possible to use the GPS (Global Positioning System). However, these systems have high costs and are complicated due to size and communication. For those reasons, we used an ultrasonic positioning system for the position reference in previous development [6]. The UPS (Ultrasonic Positioning System) is useful for reasons that they have a low cost, are of a small size and are easy to experimental setup. Figure 10 shows the system integration and Table 2 shows the specification of the UPS. The ultrasonic transmitter (Tx) is implemented in the SFR and sends the ultrasonic signal every 50 ms. 0.5 Estimated position of observer The server node (Sx) receives sequentially the distance from the eight receiver node (Rx). The distance from the SFR to the Rx node is calculated by time of flight of an ultrasonic signal. A PC receives the distances from the Sx node and calculates the 3D position of the SFR. Then the 3D position will be sent to the SFR as a current 3D position reference in a local coordinate system. The control loop is running 50 Hz and the position reference is update 20 Hz. The precision of the UPS is the 2 cm RMS (Root Mean Square). The experiment real image is shown in Fig. 11. 4.2 Experiment Results The experimental results of the hovering control with the LQI position controller are shown in Figs. 12, 13 and 14. Figure 12 is X\u2013Y position references of the UPS and Fig. 13 is estimated positions of the Kalman filter in the hovering control. Figure 14 shows the comparison between the UPS and the Kalman filter in time domain. It is confirmed that the error of the UPS was reduced and filtered. The precision of hovering are shown in Figs. 15 and 16. Lateral (Y direction of local coordinate system) precision of the hovering control is 0.097 m RMS (Root Mean Square) and longitudinal (X direction of local coordinate system) precision of the hovering control is 0.110 m RMS." ] }, { "image_filename": "designv11_32_0000925_0266-352x(90)90029-u-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000925_0266-352x(90)90029-u-Figure7-1.png", "caption": "FIGURE 7. False contact cases.", "texts": [ " Its axes are normal and tangent to the boundary of the strained body but not to the rigid one because the penalty technique induces some discrepancy between the contact surfaces. The main advantages of the triad expression at the integration points is in addition to the formulation elegance its uniqueness on the contrary to the nodal triad definition. At each integration point, after computing the locai triad one must determine if there is any contact and which tool segment is affected. Especially numerical experiments have shown that some false contact can occur. For algorithms robustness it is important to exclude these false contacts. The figure 7 shows two examples of false contacts (at points B) which are avoided by the code. First the normal to the element intersects the tool segment out of its active range i.e. outside of the extreme nodes. The second described case is more complex. We want to describe the whole tool as one alone boundary. Therefore each integration point candidate to contact has very large choice of tool segments and its normal could sometimes intersect the boundary at the opposite of the body. These false contacts are detected by comparing the two internal normais (one for each body): their scalar product is negative for true contact: if e~ \u2022 nA > 0 then contact exist" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003279_1.3046132-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003279_1.3046132-Figure4-1.png", "caption": "Fig. 4 Dimension measurements of cured samples after laser heating", "texts": [ " In fact acetone is a solvent for the uncured coating resin nd was used to demonstrate the effectiveness of resin removal uring heating. It is important to remark, however, that the test onditions differ from those of the laser because in this case the emperature does not depend on the interaction time. 3.2 Analysis of Cured Samples. The shape of the cured sand ppeared elliptical, showing the effect of the elliptical spot on the urface and in depth. This is visible in Fig. 2 and is schematically epicted in Fig. 4. In Fig. 5 the weight of the treated sand is eported against the interaction time. Increasing time at a given ower, a higher treated sand weight was reached, as expected. The lope in the weight increment at higher powers is steeper. Very ifferent results were obtained at similar values for the input en- ig. 2 \u201ea\u2026 Surface appearance after laser heating. \u201eb\u2026 A scheatic image of the interaction area. ig. 3 Heating tests performed in an oven over long time peiods at different temperatures ournal of Manufacturing Science and Engineering om: http://manufacturingscience" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000358_nme.1620300308-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000358_nme.1620300308-Figure5-1.png", "caption": "Figure 5. Geometric interpretation of the secant stiffness method", "texts": [ " The final stress is given by In this method the final stress state claculated using the direct method is forced back to the (9) where R, = a and 0 < p < 1 is a constant, which renders the final stress state S, to satisfy the following consistency condition: $I = Sf.Sf - R 2 = 0 (10) Figure 4 shows the method geometrically. The method was first introduced by Marcal' and is widely used in structural analysis. 3.2. The secant stiffness method contact stress S,: In this method an intermediate stress state Si is first computed using the trial stress S, and the si = 4(S, + S,) (1 1) The final stress state is given by s, = S, - - 2G (Si - Ae)Si R? where Ri = ,/- Figure 5 illustrates the method geometrically. Rice and TracyZ have proved that equation (12) yields a final stress state which happens to lie on the yield surface. This can be easily seen from Figure 5. This method has generally replaced the first method. 496 w. wu In this method the stress state returns directly from the trial stress vector S, to the yield surface. S, = S, + 2GAe (1 3) s, = AS, (14) where 0 < A < 1 is a constant, which renders the final stress state S, to satisfy the following consistency condition: Sp*Sp = R 2 (15) This method was first proposed by Wilkins4 and is widely used in computations of hydrodynamics. The method seems to be quite simple at first sight; however, the accuracy has been proved to be better than the first two methods" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure7.12-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure7.12-1.png", "caption": "Fig. 7.12. Coupling of Tetrahedron-structure to box-structure by six members", "texts": [], "surrounding_texts": [ "Thus far, the approach to obtain the tetrahedron space-structure from the triangle plane-structure, the pyramid from the tetrahedron, and the box from the tetrahedron has been illustrated. The next aspect of the design is to combine some of these structures. The structures can be treated as being coupled together as rigid bodies, and a rigid body in space has six degrees of freedom, i.e., the structure is capable of translations in the x, y and z directions, and rotation about the x, y and z axes. Therefore, six members are needed providing six reactive forces to exactly constrain the structure in space. Figure 7.11 shows a typical gantry configuration, which is used extensively in many coordinate-measuring machines (CMM). However, one of the members is bearing a bending load, which has been shown earlier to be very detrimental 7.1 Mechanical Design to Minimise Vibration 205 to the stiffness of the structure. There are alternative structure configurations as shown in Figures 7.12 and 7.13, although some redesign maybe needed if such a configuration is utilized. If the ground is perceived as another rigid body in which the spacestructure is to be coupled, then the design of the supports for a space-structure is similar to those of coupling two space-structures together, i.e., six reactive forces are needed to exactly constrain the space-structure. Some ways to arrange the six supporting members constraining a space-structure are suggested in Figure 7.14. Examples of physical supports offering one, two or three reactive forces are shown in Figure 7.15. This method of design, known as kinematical design, requires the use of point contact at the interfaces. Unfortunately, this method has some disadvantages, namely: \u2022 Load carrying limitation \u2022 Stiffness may be too low for application 206 7 Vibration Monitoring and Control \u2022 Low damping There are, however, ways to overcome the disadvantages which are via the semi-kinematical approach. This approach is a modification of the kinematical approach, and it targets to overcome the limitations of pure kinematical design. The direct way is to replace all point contact with a small area, as shown in Figure 7.16. Doing so decreases the contact stress, but increases the stiffness and load carrying capacity. However, the area contact should be kept to a reasonably small area. This section has only illustrated some fundamental concepts in designing rigid and statically determinate machine structures. Interested readers may refer to (Blanding, 1999) for more details on designing machine using the exact constraints principles. 7.2 Adaptive Notch Filter 207" ] }, { "image_filename": "designv11_32_0001197_iros.1998.724648-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001197_iros.1998.724648-Figure5-1.png", "caption": "Figure 5: Example 2", "texts": [ " Different criteria may have physical meaning and it is always difficult to propose a [\u2018natural\u201d criteria for this problem. Another optimization process that proved useful is the following: first, determine (xf , y f ) by minimizing (yf)\u2019 for q,f E Si. Then, determine 19\u2019 solving the scalar optimization problem: Roughly speaking, this optimization process tends to minimize the projection of q,f along the direction normal to the nonholonomic distribution [7] in the initial configuration. Example 2: (Fig. 5) qo = ( O , O , O , 4, g) and xf = (3.48,3.87,0.9). The final configuration is then gf = (3,2,0.17, - 0.17, -0.5) and the local planner is the barycentric one. References 7 Conclusion We have reported strategies for realizing operational Point To Point Tasks with nonholonomic mobile manipulators. Our approach is first based on a generalized space planner constructed with different classes of parameterized paths. Then, dealing with redundancy of the global mechanical system, an approach based on optimizing the path of the nonholonomic mobile base is developed and illustrated, for simplicity purposes, on a four degrees of freedom planar system" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003122_j.sna.2008.11.029-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003122_j.sna.2008.11.029-Figure1-1.png", "caption": "Fig. 1. The shot-put athlete biomechanical information acquisition system.", "texts": [ " System description In the context of human motion, there are several subsystems hich comprise the larger system that connects a signal originating n the central nervous system to the human body [10]. In order to nalysis complicated movements and to find dominating factors, it eems necessary to acquire abundant reliable biomechanics inforation form the human body. In the field of shot throwing, the raditional methods focus on the acquisition of kinematics data, hich has a great gulf fixed in practical application. Therefore, to onstruct the information acquisition platform which can collect otion signals of a skilled shot-putter is fundamental. Fig. 1 shows the human body motion biomechanics integrated nformation acquisition system developed by the State Key Laboatory of Robot Sensing System, Institute of Intelligent Machines, hinese Academy of Sciences. The overall system consists of a senor embedded digital-shot, a six-axis force/torque measuring plate AFMS-T, an EMG signal remote measuring device and two highpeed cameras based vision system etc. These devices will work ogether to detect the integrated information form the shot-putter n real time when an athlete executes a series of movement from reparation to throwing" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000364_robot.1988.12028-Figure18-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000364_robot.1988.12028-Figure18-1.png", "caption": "Figure 18: Translation Region with Friction.", "texts": [ " One should note that the conditions for stable manipulation and translational lift-off are very closely related to the requirements discussed by Nguyen [13] for force closure grasps of frictionless objects. The primary difference is that one of the rigid contact constraints has been replaced by the weight of the object . Contact friction affects the location and size of the translation region. In constructing T, we use the graphical method described in Section 2.4, but instead of using the contact normals of f l and f5, we use the appropriate edges of the friction cones at t h e c0n tac t s . l . The edges are chosen so that the friction force will oppose the planned motion of the object. In Figure 18. the object is to be pushed up the finger on the right. Therefore we use the edges of the friction cones rotated counter-clockwise from the contact normals. The translation region is now defined by those points on the object's perimeter whose entire friction cones pass between the boundaries of the translation window. It is also required that the geometry of the grasp is such that no two friction cones \"see one another,\" since then the grasp would jam [13]. The effects of friction are discussed in detail elsewhere 1191" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003443_6.2007-6784-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003443_6.2007-6784-Figure7-1.png", "caption": "Figure 7. Gap estimates and between the nominal and shell trajectories in the pitch plane z\u0394 nz\u0394", "texts": [], "surrounding_texts": [ "The guidance method proposed aims to track the nominal trajectory that should be followed by the gunnery shell to hit the target. The nominal trajectory is defined as the ballistic trajectory together with the effect of a nominal wind. This tracking of the nominal trajectory is realized by comparing the shell position and the desired position given from the nominal trajectory. This comparison is accomplished along the y and z axes of the flat earth reference frame to be able to correct the altitude and drift separately. Also, this comparison is based on the shell position along the x-axis of the flat earth reference frame rather than on the elapsed flight time. This choice is more appropriate from a tracking point of view, because the nominal trajectory is easier to follow, in this case, for a guided shell with a muzzle velocity different from the nominal one. The concept consists of storing the nominal trajectory in the CCF computer at launch, and only at a discrete number of points. So, the nominal trajectory between these points is computed during the flight using a piecewise cubic spline interpolation between successive known positions of the nominal trajectory, as shown in Fig. 6 for a launch elevation angle of 45\u00b0. Some tests carried out to implement the nominal trajectory with a polynomial fit have produced poor results. The polynomial order to obtain an accurate solution is high, which leads to ill-conditioned polynomial. Another issue with the polynomial method comes from the target position that cannot be implemented in the polynomial. As a result, it is not possible to have a polynomial which generates a nominal trajectory without a miss distance error. The selected approach based on piecewise cubic spline interpolation is better from this point of view. In fact, the target position can be used as the last known position of the nominal trajectory, which forces the interpolated nominal trajectory to pass through the target. It is important to point out that in the proposed guidance method, the general firing tables providing impact data for a given shell under different muzzle velocities, angles of launch and wind conditions keep their utility. Also, with this guidance method, there is no need to predict the impact point during the flight. Thus, this approach requires lower computing power than methods based on a recursive prediction of the remaining flight trajectory. Finally, by following a nominal desired trajectory that is in fact the ballistic one, this method generates low guidance corrections, which maintains a low drag and a better airspeed; of course, assuming small disturbances over the projectile flight. 12 American Institute of Aeronautics and Astronautics In the proposed guidance method, it is possible to estimate the gap between the nominal and actual shell trajectories using the nonlinear estimates and y\u0394 z\u0394 , which represent the differences between the nominal and shell positions along the y and z axes in the flat earth reference frame. However, to obtain better estimations, the nominal trajectory attitude can be used to compute the linear trajectory gap estimates ny\u0394 and , shown in Fig. nz\u0394 7 for the pitch plane, as: ( ) ( )nn nn zz yy \u03b8 \u03c8 cos cos \u0394=\u0394 \u0394=\u0394 (11) The architecture of the proposed guidance algorithm, with the trajectory gap estimates of Eq. (11), is shown in Fig. 8. This is a classical series guidance and control architecture, where the control loop (inner loop) set points and are the variables manipulated by the guidance loop. The guidance loop output variables are the shell positions and along the y and z axes of the flat earth reference frame. * nq * nr y z 13 American Institute of Aeronautics and Astronautics B. Input-Output Pairing To select a suitable input-output pairing, temporal simulations were performed for the range of Mach numbers at which the projectile is expected to fly. The pairing with and with appeared clearly the best over the Mach numbers studied. Here, a frequency analysis with the GRDG y * nr z * nq L was not realized, but should be interesting because the small input-output interaction observed at high airspeed increases greatly when the Mach number decrease, most particularly under Mach 1." ] }, { "image_filename": "designv11_32_0001466_tmag.1982.1061888-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001466_tmag.1982.1061888-Figure5-1.png", "caption": "Fig. 5 - Depic t ion of the I1 Conductor", "texts": [], "surrounding_texts": [ "342\nI t e r a t i o n Formula for Magnet ic Charge Strength Determination\nAn i t e r a t i v e s o l u t i o n p r o c e d u r e similar t o t h o s e employed by t h e writers e lsewhere i s adap ted fo r so lv - ing (16) [12 ,13 ,14 ,15] :\nwhere k i s t h e number o f t h e i t e r a t i o n . When Q=P, t h e in tegrand of (17) is set e q u a l t o z e r o . I t can be shown t h a t t h e l i m i t o f the in tegrand of (17) is ze ro when Q approaches P . I n add i t ion (17 ) can be shown t o be uniformly convergent by mathematical induct ion. S p a c e l i m i t a t i o n p r o h i b i t s p r e s e n t a t i o n h e r e o f t h e d e t a i l e d p r o o f s .\nSOLUTION PROCEDURES\nd e v e l o p e d f o r c a l c u l a t i n g t h e magnet ic f i e l d i n t h e end A comprehensive computer program package has been r eg ion and the e l ec t romagne t i c fo rces on t h e end windings . Its execut ion i s i n t h r e e s t e p s . F i r s t , t h e end-region boundary descr ipt ion and the end-winding l o c a t i o n s are entered and processed. Second, a magn e t i c c h a r g e d i s t r i b u t i o n on the boundary is ca l cu la t ed . Th i rd , t he in s t an taneous 3-D f l u x p a t t e r n a n d f o r c e d i s t r i b u t i o n are c a l c u l q t e d .\nGeometry I n p u t s\nThe s u r f a c e S shown i n F i g . 1, on which the magn e t i c c h a r g e s a r e t o b e d i s t r i b u t e d , is d i v i d e d i n t o small pa t ches , each w i th cons t an t cha rge s t r eng th . On each pa tch a r e p r e s e n t a t i v e p o i n t i s chosen where the boundary condi t ion w i l l be enforced . The pa tch area a c t s as a w e i g h t i n g f a c t o r i n t h e c a l c u l a t i o n , a n d t h e sur face normal a t t h e r e p r e s e n t a t i v e p o i n t d e f i n e s t h e p a t c h o r i e n t a t i o n . The axisymmetr ic boundary surface i s d i v i d e d i n t o s e c t o r s c o r r e s p o n d i n g t o t h e number of s l o t s i n t h e a r m a t u r e . S u r f a c e - p a t c h g e n e r a t i o n i s c o n d u c t e d i n d e t a i l f o r o n l y o n e o f t h e s e s e c t o r s . P a t c h e s f o r t h e r e m a i n i n g s e c t o r s are then genera ted s i m p l y b y r o t a t i n g t h e b a s i c set. I n t h i s p a p e r on ly the e f f ec t o f t he a rma tu re end wind ing cu r ren t s is cons i d e r e d . S i n c e a l l the windings a re assumed to have t h e same shape, only one winding, called \"#l conductor\", is input for conductor geometry genera t ion . The conduc to r i s r ep resen ted by t h e l i n e a r c u r r e n t - f i l a m e n t s a long i t s c e n t e r l i n e . The complete model of surface pa tches and conductor loca t ions is checked v isua l ly through a 3-D g r a p h i c a l c a p a b i l i t y .\nMagnet ic Charge Calculat ions\nThe magnet ic charge d is t r ibu t ion on the magnet ized boundary i n r e s p o n s e t o a l l the a rmature end winding c u r r e n t s i s o b t a i n e d b y s u p e r p o s i n g t h e d i s t r i b u t i o n o f c h a r g e t h a t a r i s e i n r e s p o n s e t o e a c h s e p a r a t e cond u c t o r c u r r e n t . Each o f t h e s e d i s t r i b u t i o n s i s obt a i n e d b y r o t a t i n g a n d s c a l i n g t h e s o - c a l l e d \" b a s i c so lu t ion\" , which i s t h e c a l c u l a t e d d i s t r i b u t i o n a r i s i n g i n r e s p o n s e t o ill c o n d u c t o r c a r r y i n g u n i t y c u r r e n t . T h i s b a s i c s o l u t i o n is ob ta ined by s o l v i n g t h e i t e r a - t ion formula (17) . Thg ngrmal f lux induced by armature elld wind ing cu r ren t s , H j *Np i n (17) , is obtained from (.?).\nFie ld and Force Calcu la t ions ___- The e l e c t r o m a g n e t i c f i e l d i n t h e e n d r e g i o n i s ob ta ined by summing t h e e f f e c t s o f a l l t h e c u r r e n t car ry ing conductors and the boundary magnet ic charges . The n o r m a l f i e l d i n t e n s i t i e s on the boundary pa tches a r e c a l c u l a t e d d i r e c t l y by (10) . The electromagnefi_c f o r c e s a c t i n g on the conduc to r s a re ob ta ined f rom JxB. A pos tp rocesso r has been des igned to d i sp l ay the 3-D\nf i e l d and f o r c e r e s u l t s i n s e v e r a l d i f f e r e n t ways f o r a number of s p e c i f i e d v i e w i n g c r o s s s e c t i o n s .\nNUMERICAL RESULTS\nTest-Case Generator Description\nA Westinghouse-manufactured generator, which i s a two-pole 3 -phase tu rb ine-genera tor a ted a t 850 NVA a t 24 kV, was s e l e c t e d f o r t h i s t e s t ca l cu la - t i on . F igu re 3 shows t h e 4 2 computer-generated a rma tu re co i l w ind ings o f co i l p i t ch 1 7 / 2 1 and 13 ,650 end-region boundary patches. Each coil consists of 69 l i n e s e g m e n t s f o r t h e p a r t o u t s i d e of t he i ronboundary . A s i n d i c a t e d i n t h e s o l u t i o n p r o c e d u r e s , t h e a x i s y m - metr ic boundary i s d i v i d e d i n t o 42 s e c t o r s and only 325 pa tches in one sec to r a re ac tua l ly gene ra t ed and s t o r e d . z\nF igu re 4 is a p l o t o f t h e mmf wave of armature r e a c t i o n f o r t h e c a l c u l a t e d i n s t a n t o f time when t h e\nc u r r e n t i n p h a s e A ( a b s e c t o r number 1) has a maximum p o s i t i v e v a l u e . The d i s c r e t e c o n d u c t o r c u r r e n t d a t a show seven s lo t s pe r phase , and the re is a p h a s e d i f - f e r e n c e i n mmf between top and bottom conductors of a g i v e n s l o t e q u i v a l e n t t o a f o u r - s l o t s h i f t . T h e s e", "343\nt h e i n i t i a l v a l u e f o r M(P). Twen ty - s ix i t e r a t ionswere n e c e s s a r y t o o b t a i n t h e f i n a l c o n v e r g e d s o l u t i o n w i t h i n 1% t o l e r a n c e f o r c h a n g e s b e t w e e n s u c c e s s i v e i t e r a t i o n s o v e r t h e s i g n i f i c a n t p a r t s o f t h e b o u n d a r y . The f i e l d i n t e n s i t y d i s t r i b u t i o n s f o r t h e 81 conduc tor are shown i n F i g s . 6 and 7 f o r r a d i a l i h d t r a n s - ve r se v i ewing p l anes a t '3 = 225' and i = 1.917 f t , r e s p e c t i v e l y . The c a l c u l a t i o n p o i n t s are a t t h e c e n t e r s\n.................... .................... .................... 1 d::::::::::::::::: . . . . . . . . . . . . . . . . .\n. . . . . . . . . . . . . . . . . . , ( ( , . 1 . . . . . . . . . . . . . . . . . ( I ( . . . . . . . . . . . . . . . . . . ,...... ........... ......,- .......... .(,,.,....... ......... .. 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -\n0 . (ROTOR) R(sT,rroRP = 225aQ0\n0. 1.50 3. 4.50 6.\nS o l u t i o h a t a Transverse Cross Sect ion\nf in i t e -d imens ion conduc to r , where th i s ca l cu la t ion may no t be phys i ca l ly mean ingfu l . The f i e i d c a l c u l a t i o n , however, i s e x a c t when t h e c a l c u l a t i n g p o i n t i s r i g h t a t t h e c e n t e r o f t h e c o n d u c t o r , d u e t o t h e s i n g u l a r i t y f r e e f o r m u l a (5) u s e d f o r t h e a c t u a l c a l c u l a t i o n .\nInstantaneous Armature Reaction\nAny i n s t a n t a n e o u s f l u x f i e l d o f t h e a r m a t u r e r eac t ion can be ob ta ined from t h e b a s i c s o l u t i o n . F o r t h e i n s t a n t o f time shown i n F i g . 4 , t h e c a l c u l a t e d f i e l d i n t e n s i t y d i s t r i b u t i o n s are shown i n F i g s . 8 and 9. The symbols are similar t o t h o s e u s e d i n F i g s . 6 and 7 e x c e p t t h a t t h e c o n d u c t o r c r o s s i n g p o i n t s a r e\n.................... .................... .................... .................... .................... .................... ........................ ........................\nh W LI N v ( ? -\nC v)\n.-(\n0 = 225.0\" (ROTOR) (STATOR)", "344\ni n b o t h f i g u r e s . T h i s d e m o n s t r a t e s t h e e s s e n t i a l advantage of the present model , as opposed t o t h e conven t iona l cu r ren t - shee t app roach dep ic t ed i n Fig. 4 , i f c a l c u l a t i o n r e g i o n o f i n t e r e s t is c l o s e t o , o r r i g h t o n , t h e c o n d u c t o r b a s k e t s .\n1 - 4 . -3. - 2 . -1. 0. 1. 2. 3 . 4 . 5 .\nR e a c t i o n a t a Transverse Cross Sec t ion\nF i e l d i n t e n s i t y f o r a s p e c i f i c se t o f p o i n t s a l o n g t h e p e r i p h e r a l d i r e c t i o n i n t h e c e n t e r of t h e a i r gap a t z = 0.5 f t i s c a l c u l a t e d . F i g u r e 10 shows a t r a n s - v e r s e c u t ( F i g . 10A) and t h e a s s o c i a t e d r a d i a l componen t o f f l ux ve r sus 0 (F ig . 10B). The s o l i d l i n e i n\nfrom the fundamental harmonic with the same ampl i tude and zeros . This checks w i th t he des ign behav io r o f a synchronous generator . Figure 11 shows the f lux a long the pe r iphe ra l boundary pa t ches . A s i g n i f i c a n t k i n k e x i s t s a t t h e p h a s e c e n t e r l i n e f o r p o i n t s o f p a t c h 1/64, because the pa tch i s a l i g n e d w i t h t h e n e a r b y cond u c t o r . F o r t h e o t h e r p a t c h e s , e i t h e r p e r p e n d i c u l a r t o o r f a r away f r o m t h e c o n d u c t o r s , t h i s phenomenon d o e s n o t e x i s t . G e n e r a l l y , t h e phenomenon w i l l be s een i n a p l o t o f t h e r a d i a l f l u x component a s a func t ion o f 8 f o r any f i e l d p o i n t c l o s e t o a conductor . The f o r c e s a c t i n g on t h e c o n d u c t o r s a r e r e p r e s e n t e d i n F i g s . 1 2 and 13. F igu re 1 2 shows x,y,z-components and t o t a l f o r c e s e x e r t e d on fou r conduc to r s . The r e s u l t s i n - d i c a t e t h a t l a r g e r f o r c e s e x i s t n e a r t o b o t h e n d s o f the conductors and phase center l ine regions. These\nFx FZ\nA F Y\n0 Total F\n+u( IS THE SECTOR NO. OF THE TOP-LAYER CONDUCTOR\nc a l c u l a t e d f o r c e s are due to the sca led-down cur ren t va lues used (F ig . 4 ) ; s c a l i n g b a c k up, 1 x 10-5 l b / f t i n F i g s . 1 2 and 13 would become 87 .1 l b / i n f o r a c t u a l cu r ren t va lues . Hence fo r t he fou r p lo t t ed conduc to r s t h e a c t u a l maximum f o r c e a t t h a t i n s t a n t i s about 900 l b / i n . F i g u r e 13 is a three-component force plot on a l l t h e c o n d u c t o r s a t a t r a n s v e r s e c r o s s s e c t i o n ( cons t an t 2). The d i s c o n t i n u i t i e s i n t h e d i s t r i b u t i o n s" ] }, { "image_filename": "designv11_32_0001251_icit.2002.1189888-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001251_icit.2002.1189888-Figure4-1.png", "caption": "Figure 4: v-shape path", "texts": [ " This step will create point P(xb, .I{) at the intersection point on local x-axis. r2 is the distance from T to P(Figure 5). After a summit of the v-shape, S ( x t , A) and orientation e;, are located, two different paths on which WL is able to move can be demonstrated depend on the following two criteria: 1. rl 5 rz, then, the symmetrical clothoids, 0-S, and A section S-T' will be defined (see Section 3.). 188 IEEE ICIT'02, Bangkok, THAILAND 2 between T' and T will be tilled with a line, seginent(Figure 4). demonstrated as follows: The svmmetrical clothoid. 0-S will be defined. A section _ I , between S and 2 will be filled with a line segment, where will be ri > rz, then, the symmetrical clothoid, 0--S will be = r2/2, consequently, the symmehical c]othoid, Z-T defined. However, a section between S and 2 will he tilled with a line segment. then the svmmetrical 6), - , clothoid, Z-T will be defined subsequently. Case3: erruck = 0 Case2: x; 5 0 and O,'Fuck # 0 Algorithm for locating the summit ofv-shape S(xf,,A) and orientation 9; can he concluded as follows: 1" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000975_app.1988.070350315-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000975_app.1988.070350315-Figure4-1.png", "caption": "Fig. 4. Dependence of the amount of immobilized enzymes on the electrophoretic mobility of latex particles at pH 9.5 (AA) GO; (0.) PO; (AO) electrophoretic mobility (EPM) of particle having no enzymes; (A c-- , -+ 0, +--) EPM shift caused by enzyme immobilization; charged amount: GO 154 mg, PO 44 mg/g particle.", "texts": [ " The unusual dependence for PO seems to be explained in terms of the electrostatic interaction between an enzyme molecule and a particle. Namely, the fact that the electrophoretic mobility of PO-bearing particles became mostly constant regardless of that of particles before combining enzymes, as Effect of NH, density on the amount and the relative activity of immobilized peroxidase. (0) amount of immobilized PO; (0) percentage of activity of immobilized PO to that of the same amount of free PO; charged PO: 44 mg/g particle. 748 KAWAGUCHI, KOIWAI, AND OHTSUKA shown by closed symbols in Figure 4, would indicate that the difference in surface potential between enzyme and particle can be a factor in determining the extent of immobilization. The result obtained in GO immobilizing system, shown in Figures 2 and 4, supports the above speculation. Activity of Separately Immobilized Enzymes Relative activity in Figures 2 and 3 measures the percentage of activity of immobilized enzymes against that of the same amount of free enzymes. According to the results shown in the figures, the activity of immobilized enzymes increases with increasing amount of immobilized enzymes" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003802_tpas.1967.291730-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003802_tpas.1967.291730-Figure2-1.png", "caption": "Fig. 2. Range of designs considered: from 115 kV to new 230 kV.", "texts": [ "-2] -[51 The application of METIFOR to the analysis of the Otter Tail Power Company uprating not only provided a quantitative measure of the expected performance of alternate line designs and enabled the accurate definition of minimum electrical design requirements, but the results of the study also provided a basis for planning the structural designi modifications which became necessary. Design Alternates Several proposed uprated designs were evaluated during the METIFOR analysis. The range of designs considered is illustrated in Fig. 2 which compares the unmodified 115- kV structure with a new-construction 230-kV design contemplated before completion of the METIFOR study. Nine design alternates considered in the final uprating study are described in Table I. 540 LARSON ET AL.: TRANSMISSION LINE UPRATING Conductor Selection The first step in the design studies was conductor selection. Choice of conductor influences the wind swing characteristics of the line and thus the flashover strength of air gaps during winds. Conductor diameter and weight are also basic to structural considerations of mechanical loading anid ground clearance requirements", " The METIFOR swing angle calculation incorporates some very conservative assumptions, and it is doubtful whether the large swing angles at which flashovers were registered will ever be experienced. Based on these arguments, the required investment for additional design margin above the design selected was not felt to be justified by any corresponding increase in reliability. The basic tangent structure in the original 115-kV transmission lines in the Otter Tail Power Company system is illustrated in Fig. 2. The most common pole sizes are 60 and 65 feet, class 2 and 3. The spans average about 660 feet. Pole spacing is 13 feet. Conductor size is 266.S kemil ACSR 26/7. In the sixth edition of the National Electric Safety Code ground clearance requirements were reduced so that 230- kV conductors can now be at about the same level as that required for 115-kV conductors under the fifth edition. This simplified the structure modifications and reduced the cost significantly. Conversion Modifications The converted tangent structure design is shown in Fig", " These string lengths were ir-creased in order to minimize leakage current problems and maintenance at these structures. Full-Scale Mechanical Tests Full-scale mechanical tests were performed oni the converted tangent structure to determine the strength of the individual members and the assembled structure. The uplift anchors were also tested. These tests demonstrated that: 1) The structure can support a vertical load of 15 000 pounds without noticeable deformation. The maximum vertical strength is far in excess of that figure. 2) The transverse strength of the structure is about 15 000 pounds, with the poles being the weak members. 3) The power-installed screw anchors performed very satisfactorily as uplift attachments, but the following factors should be noted: a) There must be sufficient bearing surface at the bottom of the pole to derive maximum benefit from these anchors. b) Anchors should be installed so that they do not place a torque on the poles during a loading condition. This can be accomplished by installing two anchors on each pole, one on each side", " The calculated lightning trip-out rate for the uprated design with complete bonding was less than 2.0 (app.oximately 1.8). The corresponding permanent outage rate (unsuccessful reclosures) would be less than 0.06. Mr. Lokay indicates that other calculating methods would show the lightning performance of an 8-insulator design to be about 4-5 tripouts per 100 miles per year. The calculations performed for the uprating study confirm this estimate of the trip-out rate for the 230-kV structure as originally planned (Fig. 2), but by limiting the modifications to the original structure, the predicted trip-out rates were reduced to the values shown in the paper. These lightning calculations were based on an isokeraunic level of 30. A review of the Otter Tail Power Company operating records for the past six years shows a lightning trip-out rate of about 0.5 per 100 miles per year for the 115-kV system. This indicates that the predicted tripout rates should be conservative. With regard to Mr. Stewart's question concerning the radio noise performance of the uprated line, the noise level is equally a function of the generating characteristics of the conductor configuration and the propagation characteristics of the line, including the attenuation factors for the three modal components, in addition to the surface gradient" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003806_icelmach.2010.5608274-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003806_icelmach.2010.5608274-Figure8-1.png", "caption": "Fig. 8. Magnitude of the first harmonic of magnetic flux density.", "texts": [ " This method is very helpful, when the machine is running supplied from PWM inverter, but the separation loss is necessary, which is difficult. However, additional advantage of the previous method is to separate the harmonic and place of their impact. Designers can easily determine the source of the various harmonics using years of experience, their contribution to the overall losses and localization of losses caused by. To highlight the impact of motion of the rotor, the calculations were done with and without of rotor movement. At next Fig. 8-13 the distribution of calculated flux density harmonics magnitude were shown. Another problem with which we meet calculating core losses is rotational losses. At low and medium flux density values the rotational losses may be several times higher than the alternating flux density losses. They are two possible solution of this problem. The first one presented in [17]-[19] use correction coefficients for hysteresis and excess losses, the second use correction for the total losses computed for pure alternating flux [20]-[22]" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002839_tmag.2007.891390-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002839_tmag.2007.891390-Figure3-1.png", "caption": "Fig. 3. Yoke, lateral view (dimensions in millimeters).", "texts": [], "surrounding_texts": [ "The rotational single sheet tester (RSST) (Figs. 2 and 3) is the most employed device for the measurement of the magnetic properties and the power losses in electrical sheets under 2-D magnetic flux. With this device, one can determine the performance of a material under rotational flux and analyze the magnetization process. The workbench used in this paper is composed of a magnetic yoke, inverters, feedback controllers, magnetic field and induction sensors, signal amplifiers as well as boards for signal generation and data acquisition based on personal computers. The yoke of the RSST was crafted by the overlapping of silicon steel sheets. Its geometry and dimensions are presented in Figs. 2 and 3. The and directions excitation are obtained by two coils sets. These coils are fed by two independent frequency inverters. Each PWM voltage inverter is controlled by a closed loop that imposes the magnetic induction waveform in the sample. The sliding mode control is used here [7]. This type of control is inherently predictive, robust and appropriate for nonlinear loads. It gives excellent results on this application, revealing efficiency for a large range of induction and frequency variation. The magnetic inductions and fields in the sample are evaluated by a set of sensor coils. To evaluate the magnetic induction, two perpendicular coils are used. These coils ( -coils) involve the sample and furnish the induction components along and directions. In the other hand, the magnetic field components TABLE I PARAMETERS FOR THE ANISOTROPIC MATERIAL Fig. 4. Measured field locus\u2014model input. are measured using two perpendicular -coils also perpendicularly wounded on a common nonmagnetic material thin plate and placed over the sample [7], [8]." ] }, { "image_filename": "designv11_32_0002918_bfb0110389-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002918_bfb0110389-Figure7-1.png", "caption": "Fig. 7. Basic idea of an IPC for grasping tasks.", "texts": [ " This is the case in both [15] and [16]. The IPC will therefore be characterized by the following differential equations: OtIc T1 x = ( J ( x ) - + (is) W1 = gT(x) + B(x) T1 (19) where J(x) is skew symmetric, R(x) positive semi-definite, T1,. 9 9 Tn are a set of interaction twists and WI , . . 9 I~V,~ a set of the dual interaction wrenches. It has been shown in [15] tha t the feed-through term B(x) is needed in telemanipulation to adapt the impedance of the line. An example of an IPC for the control of a robotic hand is reported in Fig. 7. The shown springs and the spherical object shown in the middle and called the virtual object are virtual and implemented by means of control in the IPC. The supervisor, by means of twists inputs T 1 , . . . , Tn, T~ can change the rest length of the springs and the virtual position xv. This schema has been also test experimentally and it has given very satisfactory results [16]. I n t r i n s i c P a s s i v i t y The most important feature of such a controller is that , in the case in which the supervisor would not supply power to the IPC by setting for example T1 = T2 " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002269_j.engfracmech.2006.04.002-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002269_j.engfracmech.2006.04.002-Figure3-1.png", "caption": "Fig. 3. 3D contact pressure plotted in one meshing instant: (a) pinion; (b) gear.", "texts": [ " This approach makes possible to carry out very accurate contact analysis and stress calculation employing a relative coarse mesh; in particular, unlike the usual solvers based only on the Finite Element Method, a locally refined mesh around the contact region is not required. This latter characteristic is very advantageous when, as it happens in the present study, the researcher is interested in studying the whole meshing cycle trying to capture the contact zone which travels fast over the two mating bodies. Fig. 3 reports the contact pressure 3D plots computed for the pinion and for the driven gear in one meshing instant [21]; it is evident that the load is shared between more than one tooth pair and that the pressure distribution shows a typical sharp and oblong shape. These pictures make also clear that such complex loading conditions could not be reproduced by the Hertz theory which, on the contrary, is widely employed to solve successfully contact problem in spur gear. The second step of the procedure requires the calculation of the displacement field which is induced under the tooth surface by the previously obtained contact pressure distribution; with this aim, it is convenient to schematize the tooth as a half-space. This assumption can be considered realistic for the tooth of the driven member. In fact, unlike the pinion, the cutting process usually adopted for manufacturing this member [23] produces a simpler tooth geometry allowing to neglect the curvature along the tooth profile (this evidence is easily noted\u2014see Fig. 3\u2014by comparing the transverse tooth profile of two members). For these reasons, the following discussion is referred to the gear member; future developments of this work will be aimed to assess the extension of that assumption also to the driving member. According to these considerations, Fig. 4 shows from different points of view the contact pressure distribution computed in one meshing instant applied to the two dimensions geometric development of the gear tooth convex surface; x-axis and y-axis are the measures of the curvilinear coordinate respectively along the face width and along the profile of the tooth" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003382_scored.2007.4451443-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003382_scored.2007.4451443-Figure1-1.png", "caption": "Fig. 1. Vertical Active Magnetic Bearing System", "texts": [ " In order to synthesize the proposed sliding surface with the controller, a vertical shaft AMB system model for the application of turbo molecular pump system is re-derived based on the work done in [8]. A. R. Husain, Student Member, IEEE, M. N. Ahmad and A. H. Mohd. Yatim, Senior Member, IEEE Sliding Mode Control with Linear Quadratic Hyperplane Design: An application to an Active Magnetic Bearing System S The 5 th Student Conference on Research and Development \u2013SCOReD 2007 11-12 December 2007, Malaysia 1-4244-1470-9/07/$25.00 \u00a92007 IEEE. The gyroscopic effect that causes the coupling between two axes of motions (pitch and yaw) is also considered. Fig. 1 illustrates the five degree-of-freedom (DOF) vertical magnetic bearing in which the vertical axis (z-axis) is assumed to be decoupled from the system and hence controlled separately. The top part of the rotor of the system in Fig. 1 is controlled actively by the magnetic bearing, labeled as AMB, in which the coil currents are the inputs. The bottom part of the rotor however is levitated to the center of the system by using two sets of permanent magnets labeled as PMB. The rotation of rotor around the z-axis is supplied by external driving mechanism and considered a time-varying parameter. Fig. 2 illustrates the free-body diagram of the rotor which shows the total forces produced by the AMB and PMB of the system. Based on the principle of flight dynamics [11], the equations of motion of the rotor-magnetic bearing system is as follows: )cos(2 tlmffxm unxxg bu \u03c9\u03c9++= bu xbxuzar fLfLJJ \u2212+\u2212= \u03b1\u03c9\u03b2 )sin(2 tlmffym unyyg bu \u03c9\u03c9++= bu ybyuzar fLfLJJ +\u2212= \u03b2\u03c9\u03b1 The terms )cos(2 tlmun \u03c9\u03c9 and )sin(2 tlmun \u03c9\u03c9 are the imbalances due the difference between rotor geometric center and mass center" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003722_j.jmatprotec.2009.01.018-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003722_j.jmatprotec.2009.01.018-Figure2-1.png", "caption": "Fig. 2. 3D modeling of Kaplan turbine blade.", "texts": [ " Conventionally, the pattern drawing is used to repreent surfaces of blade in the runner\u2019s design, which is not able to eet the requirements for establishing digital models in the digtal design and manufacturing of hydro turbine\u2019s blades (Lai and ang, 1997; Lai, 2001). For the exact geometrical modeling of a lade, the pattern drawing has to be transformed to the point sets long the intersection curves between blade and stream surfaces ith the special developed software (Lai and Wang, 1997), and then he NURBS representation is used as a unified digital model for the urfaces geometrical design of a blade. In order to implement NC achining on a gentry machine, a blade is usually subdivided into ore than 10 sculptured surfaces (Lai, 2000, 2001). Fig. 2 shows typical large Kaplan turbine blade, which consists of a flange ith sphere surface and surfaces of face, back, inlet, outlet, hub and hroud with skirts. As shown in Fig. 3, a typical large Francis turine blade can be subdivided into the surfaces of face, back, crown, and, inlet, outlet, weld preps between crown and blade, and weld reps between band and blade. How to establish the 3D model of hese kinds of blade had been presented in the reference (Lai et al., 002). . Localization and machined error evaluation by hree-dimensional digitized measure ", " The function of the developed software for simulation machining of large hydro turbine blades includes: (1) tool path simulation and verification for cutting; (2) machine processing simulation and verification for collision. Fig. 7 shows a snapshot during machine processing simulation of a large Kaplan blade. 8. Examples for digital manufacture of large blades The above-mentioned digital manufacture techniques have been used in manufacturing of both the large Francis and Kaplan hydro turbine blades by us. As an example, 5-axis machining of a large Kaplan blade is shown in Fig. 8, and its 3D model is shown in Fig. 2. This blade is for Gaobazhou Hydro Power Station in China and its diameter of runner is \u00d85800 mm (hereafter is called Example No. 1). Another example is 5-axis machining of a large Francis blade with runner diameter of \u00d810000 mm (hereafter is called Example No. 2) shown in Fig. 9, and its 3D model is shown in Fig. 3. This blade is for Table 1 The detail machining information for two examples. Example No. 1 Example No. 2 Machine specification X-travel:15.5 m, Y-travel: 6.9 m, Z-travel:1.6 m, W-travel:4 m, C-axis: \u00b1180\u25e6 , A-axis: \u00b195\u25e6 Kind of blade Kaplan (feature: small curvature) Francis (feature: large curvature) Area (m2) \u223c15 \u223c40 Cutting depth (mm) Rough machining 5\u20138 mm with \u00d8250 mm face milling cutter 5\u201310 mm with \u00d8200 mm face milling cutter Semi-finishing 3 mm with \u00d8200 mm face milling cutter 3 mm with \u00d8160 mm face milling cutter Finishing 2 mm with \u00d8200 mm face milling cutter 2 mm with \u00d8160 mm face milling cutter Total machining time (h) 30 Max" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000051_6.2003-5522-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000051_6.2003-5522-Figure3-1.png", "caption": "Figure 3: Georgia Institute of Technology UAV", "texts": [ " Although the trajectories are nearly identical, this does not imply that the simplified formulation can be used in place of the tangent plane formulation with negligible effect on the guided solution when the full 6 American Institute of Aeronautics and Astronautics aircraft dynamics are taken into account. This can only be assessed using a higher fidelity simulation of the aircraft motion. Aircraft specification To test the optimization routines more accurately, it has been decided to use a Georgia Tech UAV that is under construction, depicted in Figure 3. This UAV has a wingspan of 170 inches with a center chord of 17.25 inches. The span of the horizontal tail is 43.2 inches while the overall length of the aircraft is 128.3 inches. This vehicle has an empty weight of about 50 pounds and can carry up to 50 pounds in payload and fuel. The maximum endurance of this aircraft is approximately 3 hours. In addition, it has a 20 horsepower, 2 stroke, air cooled engine. The velocity range of this UAV is assumed to be 60 feet per second to 200 feet per second" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003258_msf.534-536.461-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003258_msf.534-536.461-Figure2-1.png", "caption": "Figure 2: Jaw implants and artificial knee joint. Laser sintered of biocompatible CobaltChrome MP1 alloy in EOSINT M270.", "texts": [ "1 x 10-6 m/mK to meet the such of ceramic. The properties of the laser sintered dental alloy meets the stringent requirements of standard ISO 16744:2003 of base metal materials for fixed dental restorations. In addition to CoCrMo -based implant materials, biomedical Ti alloys are currently in pilot testing phase at selected EOSINT M270 customers. The benefit of the process is that individual biomedical implants or dental restorations can be manufactured directly from 3-dimensional scanned data. Figure 2 presents biomedical implants manufactured of CobaltChrome MP1 by EOSINT M270. In dental application area dental restorations and bridges can be manufactured from data received from dental scanner. After laser sintering the restorations and bridges will be shot-peened, snapped off the support and finished by ceramic coating. Figure 3 presents 198 dental unique restorations on building platform and final restorations after coating with ceramic. As the DMLS material selection widens it is expected that the number of suitable applications will continue to expand" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000937_a:1004155000693-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000937_a:1004155000693-Figure1-1.png", "caption": "Fig. 1. Schematic representation of substrate, sample holder and magnet arrangement to induce a uniaxial magnetic anisotropy in the electrodeposited \u00aelms plated with the IrRDE. N and S are respectively the north and the south poles of the magnets.", "texts": [ " These experiments were carried out with the rRCE using a \u00aexed pulse on-time and varying pulse o - time. Subsequent experiments were carried out with the IrRDE. The experimental series 2 of Table 2 at \u00aexed duty cycle was aimed at obtaining alloys of constant composition for di erent applied pulse parameters in order to observe their e ect on the structure sensitive coercive \u00aeeld strength. Series 3 was similar except that a magnetic \u00aeeld was applied during plating and that the rotation rate was lower. Two magnets were embedded in the sample holder and positioned under the silicium wafer (Figure 1) to induce a uniaxial magnetic anisot- ropy in the electrodeposits. The assembly was held together using silver conducting paste to guarantee a good electrical contact of the doped silicium substrate with the sample holder. 3.5. Characterization of deposits The current e ciency was determined by gravimetry using the larger surface area rRCE. A precision balance (Sartorius model 2004 MP6, Instrumenten Gesellschaft AG) was used to measure the weight gain to better than 1.0% for \u00aelms thicker than 1 lm" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003150_icca.2007.4376412-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003150_icca.2007.4376412-Figure1-1.png", "caption": "Figure 1. Schematic of an elastic robot", "texts": [ " It should be point out that the assumption of C being of the special form of (Ip 0) is not crucial for we get the result of Theorem 2. That is, we can obtain the similar conclusion to Theorem 2 for general form of C [11]. The gain matrix is computed by (15) and this implies that we must solve the Riccati equation in order to design reduced-order adaptive observer. In full-order observer design, we only need to find matrix K such that the Riccati equation has symmetric positive definite solution. IV. SIMULATION In this section, we will apply the reduced-order adaptive observer to a real model. Figure 1 shows the schematic of a laboratory model of a single-link flexible joint robot. The corresponding state-space mode is Om =Ct)m k mgh rk l=- (01 -OM)--) +ui(l JlW 0 k(1 m gh i(1 with Jm being inertia of the motor; J1 the inertia of the link; 0m the angular rotation of the motor; 01 the angular position of the link; CO)m the angular velocity of the motor; and ()1 the angular velocity of the link. The dynamic system is nonlinear and of the form of {x = Ax + Bf(x) + Fg(x)u ly =Cx where x = (X1 x2 x3 X4 ) = (O Wn 01 01)T and 0 - 48" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003815_000143459-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003815_000143459-Figure8-1.png", "caption": "Fig. 8. Explanation see text.", "texts": [ "6 X 100 gt - 160 kg E quilib rium in D requires th a t the re su ltan t o f th e load , g 3 and th e p a te lla r p ressure passes th ro u g h D, this is 360 kg. T he re su lta n t th ro u g h A (300 kg) and the force in g2 (30 kg) can be found in analogy w ith the m ethod described u n d er m odel 2. The p a ram e te rs and stress in m odel 3 are listed in tab le I I I . A p p aren tly , th e tensile force in g3 causes a rise of the in te n s ity of stress in th e p roxim al p a r t of th e tib ia (from 20.13 to 41.31 kg /cm 2) bu t it decreases th e stress in th e d ista l p a r t from 29.96 to 4.34 kg/cm 2. M odel 4 (fig. 8) In th is m odel, th e tensile force in g 3 is increased to 150 kg (active co n trac tio n of th e m. gastrocnem ius, its line of action coincides w ith th a t of th e superficial flexor). T he re su lta n t o f g 3 and th e load passes caudal to E and th is would cause s tre tch in g of th e hock jo in t w hich Table I I I r (cm) u (cm) F (cm2) N (kg) Od (kg/cm2) A 7.2 0 168.70 200 1.18 B 9.9 6 307.75 200 0.93 B 8.4 4.2 221.55 297 1.34 K 3.3 1.2 34.19 297 3.95 K 3.3 1.8 34.19 319 11.03 C 3.3 0 34" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002455_tmag.2005.862760-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002455_tmag.2005.862760-Figure1-1.png", "caption": "Fig. 1. Schematic of the engraving system.", "texts": [ " The results show that the actuator has a displacement of 65 m, hysteresis of less than 5.5%, and amplitude cutoff frequency of 3.1 kHz. We tested the actuator on a real engraving system and confirmed its characteristics by the engraving results. Index Terms\u2014Dynamic measurement, electromagnetic actuator, electronic engraving system, full-bridge magnetic circuit, high response, type armature. I. INTRODUCTION OWING to its low processing cost, high product quality, and environmental protection, the electronic engraving system shown in Fig. 1 is widely used in gravure printing. When the cylinder rotates, an engraving diamond needle driven by an electromechanical converter will engrave the cylinder, and the engraving cell\u2019s size and depth changes proportionally to the image density. As a key component of the engraving system, the electromechanical converter is required to have a displacement of more than 60 m, driving force of more than 20 N, and amplitude cutoff frequency of higher than 2 kHz. Nowadays, electromagnetic actuators have been successfully employed to convert electrical signals into mechanical movements in many applications due to their high level of driving force, rugged structure, and compact volume; however, the conventional high-response electromagnetic actuators such as solenoid or energy-stored actuator, are only suitable for ON\u2013OFF applications [1]\u2013[3], and the microelectromagnetic systems (MEMS) actuator could not provide sufficient driving force [4], [5]; therefore, they do not meet the demands of continuous control of the engraving system" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000507_s0167-8922(08)70996-9-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000507_s0167-8922(08)70996-9-Figure1-1.png", "caption": "Fig . 1 . The R 3 t e s t r i g used f o r t e s t i n g s p h e r i c a l r o l l e r b e a r i n g s .", "texts": [ " The test bearings were loaded using hydraulic cylinders and lubricated from a circulating oil system with high performance oil filtering. On both test rigs, the temperatures of the inlet and the oulet oil and of the test bearing inner and outer ring were measured using thermocouples. The electrical capacitance of the test bearings was measured from the bearing outer ring to the inner ring using a Lubcheck instrument (Ref. 1). The Lubcheck and thermocouple signals were taken f rom the rotating shaft using a slipring. A cross-section of one of the test positions of the R3 test rig is shown in Fig. 1, in which the thermocouple positions are also indicated. The tests were conducted using pure radial loads up to 26 kN for the deep groove ball bearings and up to 140 kN for the spherical roller bearings. Half of the ring circumference was therefore loaded. 3 ELECTRICAL CAPACITANCE CALCULATION A computer program was developed to calculate the electrical bearing capacitance as a function of bearing geometry and operating conditions. In this program, the ring/rolling element contacts were considered as a set of series and parallel capacitors as shown in Fig", " 5 shows the measured and the calculated capacitances of a 22220 CC spherical roller bearing as a function of shaft speed at two test loads: 50 kN and 140 kN. The test bearings were lubricated with Shell Turbo T68 oil, with an inlet temperature of 49\u00b0C and a flow rate of 2.2 l/min. The test bearing temperature was first stabilised at an outer ring temperature of 58\u00b0C at a shaft speed of 1500 rpm. At the test load of 140 kN,the \"bulk\" inner ring temperature was measured to be 20\u00b0C higher (for thermocouple positions, see Fig. 1). These temperatures were used as effective temperature for the film thickness calculations. Then, similar to the experiments with the 6309 bearings, a speed sweep was made from 0 to 2500 rpm in less than one minute. Here, the stray capacitance and the unloaded zone capacitance are less than 10% of the total bearing capacitance. here excellent agreement was found between measured and calculated capacitances. At a shaft speed of 2500 rpm, the calculated film thickness of the most heavily loaded inner ring/ roller contact (HCI, see Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001869_00207170500036159-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001869_00207170500036159-Figure1-1.png", "caption": "Figure 1. State trajectories for system (\u2014) and -approximate observer ( ).", "texts": [ " , u\u00f0 p\u00de with p < n 1 (Zeitz 1989, 1998). Of course, this map must then be injective for any admissible input, a condition sometimes called uniform observability for any input (Gauthier et al. 1991). Example 1 (continued): The -approximate observer proposed in (24)\u2013(25) for system (5) is given by _\u0302z \u00bc z\u03022 3z\u03021z\u0302 2=3 2 \" # \u00fe 1 2 2 \" # y z\u03021\u00bd , x\u0302 \u00bc z\u03021 z\u03021=32 \" # : \u00f038\u00de The construction of the extension qIn is immediate, since qn\u00f0R n \u00de \u00bc R n and therefore qIn \u00bc q 1 n . The results of this observer are shown in figure 1, where the simulations correspond to x0 \u00bc \u00bd1, 1 T, i.e. q2\u00f0x0\u00de \u00bc \u00bd1, 1 T, while z\u03020 \u00bc \u00bd1, 0 T. The gain is \u00bc 5. Note that for these initial conditions, the observability normal form (7) has no unique solutions. Note also how every time x2\u00f0t\u00de is close to zero, the error increases. Recall that at x2\u00bc 0, i.e. z2\u00bc 0, the transformed system (7) fails to be locally Lipschitz. D ow nl oa de d by [ N or th C ar ol in a St at e U ni ve rs ity ] at 0 1: 31 2 6 Se pt em be r 20 12 A methodology for the design of practical observers for systems whose observability map of order n is injective with a uniformly continuous inverse has been proposed" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002134_1.5060506-Figure21-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002134_1.5060506-Figure21-1.png", "caption": "Figure 21. Non-planar filling paths", "texts": [ " Page 317 Laser Materials Processing Conference ICALEO\u00ae 2005 Congress Proceedings For tool path generation the STL model of the buffer layer is sliced by a rational B\u00e9zier surface, which is generated by extrusion of a rational B\u00e9zier curve representing the planed cladding layers. A rational function is necessary for surface representation because the base material is cylindrical. Fig. 20 shows the buffer layer of the oil drilling tool sliced with a cylindrical B\u00e9zier surface. The results of the slicing procedure are the outer and inner contour curves. Fig. 21 shows the non-planar deposition paths for the buffer layer inside the outer and inner contour curves. Nonplanar slicing enables the fabrication of arbitrarily shaped layers on existing tool surfaces, as shown in Fig. 22. Non-planar deposition paths can be generated by nonplanar slicing planes, as mentioned before, or by direct slicing using so called \u201cdrive-surfaces\u201d [4]. A drive surface is used to drive the laser along the current tool path. The tool path is defined as the intersection curve between drive-surface and part surface" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003122_j.sna.2008.11.029-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003122_j.sna.2008.11.029-Figure4-1.png", "caption": "Fig. 4. Installation of the overall digital-shot: (a) schematic; (b) fabricated.", "texts": [ " The sensor and the mechanial shell of the shot are designed and fabricated respectively. The echanical structure of the digital-shot mainly includes the upper hell and the lower shell. The upper shell, connected with the lower ne via four screw joints, is designed to fix the supplying power. esides of the tri-dimensional accelerometer circuits, the analogigital conversion and storing circuits are installed in the body of the ower shell, which is attached with the power lamp and its switch, he sampling lamp and its switch, the synchronizing module, etc. Fig. 4 depicts the schematic drawing and assembling of digitalshot, where the different ports in the lower shell are labelled amply as shown in Fig. 4a. The mechanical structure of the digitalshot mainly includes the upper shell and the lower shell mounted together by screw joints. The upper shell is mainly for housing the power supply. The tri-dimensional accelerometer circuits, the analog\u2013digital conversion, storing circuits and a synchronizing module are all installed inside the body of the lower shell. A power indicating light, a sampling indicating light and their switches, are mounted on the shot surface (as shown in Fig. 4b). The three axes acceleration sensor is installed underneath the data sampling and processing circuits and locates at the centre of the ball. While being thrown, the force applied by the athlete will induce piezoresistive strains. The 3D strain signals will then be converted into raw voltage signals propositional to 3D accelerations Ax, Ay and Az, respectively. The synchronizing port is designed to synchronize the kinematic data obtained by two high-speed vidicons. The electricizing port supplies the power for the drive of signal processing circuits, analog PCB and the sensor" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002269_j.engfracmech.2006.04.002-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002269_j.engfracmech.2006.04.002-Figure5-1.png", "caption": "Fig. 5. Scheme for computing the displacement field.", "texts": [ " 4 shows from different points of view the contact pressure distribution computed in one meshing instant applied to the two dimensions geometric development of the gear tooth convex surface; x-axis and y-axis are the measures of the curvilinear coordinate respectively along the face width and along the profile of the tooth. Doing this way, the loading condition is being reduced to a pressure distribution applied to the free plane of a half-space. This representation allows to straightforwardly obtain the displacement field under the tooth surface. With this aim, the contact pressure distribution is firstly schematized as a set of finite number of point forces normal to the free surface of the half-space. Then, according to the Boussinesq theory [24,25] and employing the scheme reported in Fig. 5, the displacement components induced by each of those point loadings are analytically computed; the reference frame (r, h, z) is cylindrical and has the origin in the point of loading application. Omitting the analytical calculations, the following relations allow to obtain the state of stress under the tooth surface: rr \u00bc P 2p \u00f01 2m\u00de 1 r2 z r2 \u00f0r2 \u00fe z2\u00de 1=2 3r2z\u00f0r2 \u00fe z2\u00de 5=2 \u00f01\u00de rz \u00bc 3P 2p z3\u00f0r2 \u00fe z2\u00de 5=2 \u00f02\u00de rh \u00bc P 2p \u00f01 2m\u00de 1 r2 \u00fe z r2 \u00f0r2 \u00fe z2\u00de 1=2 \u00fe z\u00f0r2 \u00fe z2\u00de 3=2 \u00f03\u00de srz \u00bc 3 P 2p rz2\u00f0r2 \u00fe z2\u00de 5=2 \u00f04\u00de Then, the terms u and w, which are the components of the displacement respectively along r and z axes, can be computed: u \u00bc \u00f01 2m\u00de\u00f01\u00fe m\u00de 2pEr z\u00f0r2 \u00fe z2\u00de 1=2 1\u00fe 1 1 2t r2z\u00f0r2 \u00fe z2\u00de 3=2 \u00f05\u00de w \u00bc P 2pE \u00f01\u00fe t\u00dez2\u00f0r2 \u00fe z2\u00de 3=2 \u00fe 2\u00f01 t2\u00de\u00f0r2 \u00fe z2\u00de 1=2 h i \u00f06\u00de These terms can be also expressed in a rectangular reference frame (x, y, z) by using the following relation: ux \u00bc u\u00f0r; z\u00de cos h \u00f07\u00de uy \u00bc u\u00f0r; z\u00de sin h \u00f08\u00de uz \u00bc w\u00f0r; z\u00de \u00f09\u00de Repeating these calculations for each point loading Pi and by adding each contribute, the displacement field everywhere in the half-space is known: ux;tot \u00bc Xn i\u00bc1 ux;i uy;tot \u00bc Xn i\u00bc1 uy;i uz;tot \u00bc Xn i\u00bc1 uz;i \u00f010\u00de In this paper, friction between the mating surfaces has been neglected" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002297_bf02482627-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002297_bf02482627-Figure7-1.png", "caption": "Fig. 7. S k e t c h of t e s t a r r a n g e m e n t , inc l ined sp in ax is", "texts": [ " Plate dis tance 2h = 1 toni, bubble d iameter 2a = 20 ram, angula r velocity ~ = 2 S - 1 a) 2a ~ 2 0 m m , Q ~ 1, 5 s -1, At ~ 3 s b) 2 a ~ 2 0 m m , Q ~ 2 s -1, At = 3 s c) 2a ~ 26 ram, \u2022 ~ 2, 7 s -1, At ~ 2 s At ~ t ime interval between flashes Ing. Arch. Bd. 45, H. 5]6 (1976) recognized tha t the larger bubbles display a distinct deformation of their contour, even if the angular speed is relatively small. Near the center of rotat ion the bubbles are almost circular again. I t was observed fur ther tha t the onset of the bubble motion drags on with increasing angular velocity. Fig. 7 depicts the experimental set up schematically with the spin axis inclined toward the vertical about an angle of 2~ say. This corresponds to an effective gravi ty g = go sin of the order g ~ 4 . 1 o - ~ g o , with go as the terrestrial value of the gravitat ional acceleration. As pointed out previously, the bubble follows a circular pa th of radius R 0 (given by (9)) relative to the rotat ing plates. Photographs of bubble orbits, taken by a camera moving with the plates, are shown in Fig. 8. One sees tha t the centers of the circles are displaced in relation to the Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003696_jmes_jour_1968_010_054_02-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003696_jmes_jour_1968_010_054_02-Figure1-1.png", "caption": "Fig. 1", "texts": [ " Equations for velocities and accelerations can be derived from the kinematic equations. These derived equations are linear and can readily be solved once the kinematic equations have been solved. Unfortunately the kinematic equations themselves are non-linear. Solutions in closed form of these equations were given for the slider-crank and 4-bar linkage, using methods that do not seem capable of extension to more complex mechanisms. The present note describes a method that is generally applicable. The method is illustrated by the analysis of the mechanism shown in Fig. 1. The notation used in the figure is a special case, restricted to pivoted linkages, of the general notation given previously (I). Link lengths are denoted by the letter a and variable angles by 6, with distinguishing subscripts. The two fixed angles are denoted by A and B. The link a12 is rotated through a gear train from the input shaft and the link a15 drives the output shaft through another gear train. The constants p , q, Y and s define the gear ratios and shaft settings. All angles are measured as exterior angles of the closed polygons formed by the links" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000836_1.1565647-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000836_1.1565647-Figure1-1.png", "caption": "Fig. 1. A pattern of shock waves for the efflux of a plane overexpanded jet of the ideal gas from a profiled nozzle.", "texts": [ "onsider the efflux of a nonviscous perfect gas at a supersonic velocity (M0 > 1) from a planar profiled nozzle (Fig. 1) in an overexpanded noncalculated (n < 1) regime. As a result, a normal shock wave 1 appears at the nozzle edge, the intensity of which J1 = 1/n = p\u221e/pA is characterized by the static pressure difference between atmosphere (p\u221e) and the nozzle edge (pA). Once the shock wave intensity J1 and the Mach number M0 are known, one can determine the angle \u03b21(M0, J1) of the flow rotation at the shock and the Mach number M1(M0, J1) behind the shock (see, e.g., [1]). In the case of a strongly overexpanded jet (J1 \u2208 [Jc(M0), J\u2217(M0)], where Jc(M0) is the intensity of the stationary Mach configuration [2] and J\u2217(M0) is the intensity corresponding to the Mach number of unity behind the shock), the shock wave can be irregularly reflected from the symmetry axis, with the formation of a triple shock wave configuration at point T (Fig. 1). The jet is supersonic behind the reflected shock wave 2 and subsonic behind the Mach disk 3. Using the dynamic compatibility conditions on the tangential discontinuity \u03c4 originating from point T [2] for the given shock wave intensity J1 and the initial Mach number M0, it is possible to find the angles \u03b22 and \u03b23 of the flow rotation on these shocks and to determine the corresponding intensities J2 and J3. For the shock waves depicted in Fig. 1, the angles \u03b21 and \u03b23 are negative, while \u03b22 is positive. When the shock wave 2 reaches the jet boundary AB, a centered rarefaction wave 4 is formed at point B. Incident upon the tangential discontinuity \u03c4, the latter wave leads to a bending of this discontinuity. This paper presents an approximate analytical model of flow in the region behind the shock waves originating from point T. The model is constructed based on several assumptions. First, we assume that the J1J2 J3, \u03b21 M0 J1,( )= \u03b22 M1 J2,( )+ \u03b23 M0 J3,( )= 1063-7850/03/2903- $24", " This allows us to relate the ordinate y(x) of the tangential discontinuity \u03c4, the Mach number M3(x), and the static pressure p3(x) in the transverse cross section to the analogous quantities yT , M3T , and p3T at the triple point [2]: (1) Here, \u03b5 = (\u03b3 \u2013 1)/(\u03b3 + 1), \u03b3 is the adiabatic index, p3T = p1J3, p1 is the static pressure in the flow in front of the shock wave 1, and M3T(M0, J3) is the Mach number behind the shock wave 3. The second assumption is that the subsonic flow accelerates to become supersonic behind the Mach disk 3, the transition taking pace at the critical cross section CC' corresponding to a minimum of the y(x) function (Fig. 1). According to the third assumption, the flow behind the shock wave 2 is vortexless and the first family characteristics in the TBD y x( ) yT ---------- M3T M3 x( ) -------------- \u00b5 M3 x( )( ) \u00b5 M3T( ) ----------------------- 1/2\u03b5 ,= p3 x( ) p3T ------------ \u00b5 M3T( ) M3 x( ) ------------------ 1 \u03b5+( )/2\u03b5 ,= \u00b5 M( ) 1 \u03b5 M2 1\u2013( ).+= 003 MAIK \u201cNauka/Interperiodica\u201d region are linear. Therefore, the flow in this region represents a simple Prandtl\u2013Meyer wave. The angle \u03d12 of the current lines relative to the abscissa axis, the static pressure p2, and Mach number M2 are related to the corresponding parameters \u03d12T = \u03b23, p2T, and M2T at the point T by the following relations [2]: (2) Here, p2T = p1J1J2, M2T(M1, J2) is the Mach number behind jump 2", " The first two assumptions are traditional, being frequently involved in the numerical calculations of flows in supersonic overexpanded jets by the method of characteristics [3, 4]. Justification of the third assumption is provided by an analysis of the results of calculations presented below. Using the first and third assumptions, together with the conditions of equal static pressures and (p3 = p2, p3T = p2T) and the slopes of the current lines (\u03d12 = \u03d13, \u03d12T = \u03d13T) on both sides of the tangential discontinuity \u03c4, it is possible to determine the shape of the TD region of \u03c4 (Fig. 1) upon solving the ordinary differential equation (3) with relations (1) and (2). In addition, using the third assumption with a solution of the problem of interaction between the shock wave and a weak discontinuity, it is possible to determine the shape of the curvilinear shock wave TB (see [5]). This interaction gives rise to the discontinuity \u2206K of the shock wave curvature, the value of which is proportional to the discontinuity \u2206N of the current line curvature on the weak discontinuity: (4) The coefficient of proportionality \u03a6(M, J) depends on the Mach number M in front of the shock wave and the shock wave intensity J at the point of interaction [2]. Recently [5], it was demonstrated that, under the above assumptions, formula (4) leads to the following relationship between the curvature Ks2 of shock wave 2 and the shock wave intensity J2, the Mach number M1 of the flow in front of the shock wave, and the curvature K\u03d1 of the current line behind the shock wave: (5) Here, Ks2 refers to an arbitrary point H of shock wave 2, and K\u03d1 , to the point of intersection of the characteristic H1H of the first family with the shock wave (Fig. 1). \u03d12 = \u03b23 \u03c9 M2T( ) \u03c9 M2( ), p2 p2T -------\u2013+ = \u00b5 M2T( ) \u00b5 M2( ) ---------------- 1 \u03b5+( )/2\u03b5 , \u03c9 M( ) 1 \u03b5 ------ \u03b5 M2 1\u2013( )arctan M2 1\u2013 .arctan\u2013= y' x( ) \u03d1tan= \u2206K \u03a6 M J,( )\u2206N .= Ks2 \u03a6 M1 J2,( )K\u03d1.= T The latter curvature can be expressed through the curvature K\u03c4 of the tangential discontinuity at the point H1: (6) where xH1 and xH are abscissas of the points H1 and H, \u03d1 is the slope of the current line relative to the abscissa axis, M(\u03d1) is the Mach number of the H1H characteristic, and \u03b1 = 1/M). As can be readily shown, Eqs. (5) and (6) can be reduced to an ordinary differential equation of the first order with respect to the function y(x) describing the shape of the curvilinear shock wave 2. The integration has to be performed over the interval [xT, xB], with the upper limit being determined from the condition yB \u2013 yA = (xB \u2013 xA) (Fig. 1). The first characteristic BD of the centered shock wave 4 is simultaneously the characteristic of the second family of the simple wave TBD. Therefore, this characteristic obeys the relation which determines, together with Eqs. (1)\u2013(3), the coordinates of point D at which the characteristic BD intersects the tangential discontinuity \u03c4. In addition, the characteristic BD represents a weak discontinuity for the curvature of the current lines. In particular, point D features a break in the curvature of the tangential discontinuity \u03c4. This leads to a change in the curvature sign, whereby the tangential discontinuity to the right of point D is convex (Fig. 1). The results of numerical calculations [3, 4] showed that the angle \u03b24 of flow rotation in the centered wave BDF does not exceed several degrees. Therefore, \u03b24 can be used as a small parameter for solving the problems of interactions between the simple waves TBD and BDF and between the wave BDF and the tangential discontinuity \u03c4 using the method described in [6]. Using this approach, it is easy to obtain an ordinary differential equation describing in the first approximation the shape of the tangential discontinuity \u03c4 in the region from point D to a point at which the velocity on the lower side of \u03c4 reaches the critical value (M3 = 1). Using the above relations, it is possible to calculate the flow in the case when the height yT of the Mach disk 3 is given together with M0 and J1 (Fig. 1). The Mach disk height is determined by iterations, whereby M0, J1, and a certain yT value are set in each step. Then, the shapes of the shock wave 2 and the tangential discontinuity \u03c4 are determined using the algorithm described above. In this way, the tangential discontinuity \u03c4 is constructed until one of the conditions \u03d1\u03c4 = 0 or M3 = 1 is fulfilled. In the former case, the height yT is too large, and in the latter case, it is too small. Taking K\u03d1 \u03c7 \u03d1( ) xH xc\u2013 ----------------,= xc = xH1 \u03c7 \u03d1( ) K\u03c4 --------- , \u03c7 \u03d1( )\u2013 = 1 \u03b5\u2013( ) M2 \u03d1( ) 1\u2013( ) \u03d1 \u03b1+( )cos M3 \u03d1( ) ------------------------------------------------------------------ ,\u2013 (arcsin \u03b21tan \u03c9 M2D( ) \u03d12D+ \u03c9 M2B( ) \u03d12B,+= ECHNICAL PHYSICS LETTERS Vol" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002278_09544097jrrt75-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002278_09544097jrrt75-Figure1-1.png", "caption": "Fig. 1 The UIC double-link suspension for two-axle wagons. (a) Side view; (b) close-up of double links; (c) view of links and bearings: (1), carbody, (2) wheelset, (3) leaf spring, (4) axle guard, (5) end bearing, (6) link, (7) intermediate bearing, and (8) link pin", "texts": [ " Another reason is that the characteristics vary with maintenance status of the link suspension and possibly also with climate conditions. The link suspension is still a very common suspension design for freight wagons in western and central Europe today and is used on bogie wagons as well as on two-axle wagons [1\u20133]. Even though the principal design has existed for more than 100 years, its physical characteristics are still not yet fully understood. The main components in the link suspension system are the leaf spring, links, and bearings, as shown in Fig. 1. The carbody or bogie frame is connected to the leaf spring via the suspension links. The system allows vertical, lateral, and longitudinal relativemotions between the axlebox and the carbody or bogie frame. During lateral motions, the links roll/ slide over the bearings, whereas longitudinal motions are accommodated by rolling/sliding between the end bearings and link pins. In this article, the lateral characteristics of link suspension systems are investigated. Results from stationary vehicle tests and laboratory component tests are presented and discussed", "0, 3.0, 4.0, 5.0 Hz; amplitude: 1, 2, 5, 8, 10 mm (zero to peak). One test is performed with new components (links and end bearings). Six tests are performed with components worn in service. Wear limits for the components in the suspension are standardized [3]. Proc. IMechE Vol. 220 Part F: J. Rail and Rapid Transit JRRT75 # IMechE 2006 at UNIV OF PITTSBURGH on March 18, 2015pif.sagepub.comDownloaded from During overhaul of a vehicle, the distance between the link pins is checked, measure L in Fig. 1. Nominal distance for thedouble-link suspension is 289 mmand the components are exchanged if the distance is greater than 302 mm. The components \u2018worn in service\u2019 used in these tests were all on the maintenance limit. In this article, only a limited number of typical test results and phenomena are shown. Several cycles per loop are plotted in the force\u2013 displacement figures in section 3.2. In Fig. 4(a), the load dependence of a typical measured lateral characteristic is shown. In Fig. 4(b), the lateral force is normalized with the load" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002278_09544097jrrt75-Figure9-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002278_09544097jrrt75-Figure9-1.png", "caption": "Fig. 9 Simulation model \u2013 forces and angles. (a) Link, (b) lower end bearing and loading mass, (c) resulting force perpendicular to link", "texts": [ "comDownloaded from where Croll is a factor to compensate for the elastic deformation of the contact surface due to the load, whereas jA2j and jB2j are the respective radii for the actual undeformed surfaces. During normal loading, the end bearing surface is deformed so a radius smaller than the initial one appears, whereas the link surface is deformed to a larger contact radius than the initial. Thus, Croll \u00bc 1 for unloaded and undeformed surfaces. Normal and tangential forces in the contacts between links and bearings are shown in Fig. 9. Vectors Pij are defined reaching from point i to point j. The vectors are defined in components as exemplified Pij \u00bc PijX PijZ , VflexF \u00bc VflexFX VflexFZ , q \u00bc qX qZ , \u20acq \u00bc d2q dt2 (3) For the link, equilibrium equations are written as (inertia forces are neglected) Z: Fj1 sin (wB2)\u00feN1 cos (wB2) Fj2 sin (wD2) N2 cos (wD2) \u00bc 0 (4) X: Fj1 cos (wB2) N1 sin (wB2) Fj2 cos (wD2)\u00feN2 sin (wD2) \u00bc 0 (5) a: { Fj2 cos (wD2)\u00feN2 sin (wD2)} P12Z \u00fe {Fj2 sin (wD2)\u00feN2 cos (wD2)} P12X (6) where P12 is the vector from points 1 to 2 P12 \u00bc B1 \u00fe B2 \u00fe C \u00fe D1 D2 \u00fe VflexC (7) Deformations in the links, end bearings, and contacts represented by VflexF are assumed to be linearly dependent on the perpendicular force Fl" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003745_tpwrd.2010.2068567-Figure15-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003745_tpwrd.2010.2068567-Figure15-1.png", "caption": "Fig. 15. Experimental setup of the load test platform.", "texts": [ " 14, it can be seen that the connection force value is in the range of 0.7\u20131.8 kN, caused by the weight of insulators and connection pressure. The force is not strong enough to make porcelain insulators break in the static loading process. In order to verify the calculation results by experimental results, a series of experiments was conducted. The displacements and force along the insulator string were measured from the experimental platform. The experimental test setup used for the verification is illustrated in Fig. 15. The V-shape insulator string consisting of two insulator strings was suspended in the steel frame. The bottom of the V-shape insulator string was connected with the link plate. In order to simulate the force applied on the V-shape insulators, the horizontal and vertical load were applied through the link plate. Keeping the vertical load constant, the horizontal force was increased gradually and displacements of the link plate were recorded by the laser-range finder simultaneously. The composite and porcelain insulators used in the experiments are presented in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003394_peds.2007.4487699-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003394_peds.2007.4487699-Figure2-1.png", "caption": "Fig. 2. A 3D view of the typical coil configuration of a RFAPM machine with overlapping stator coils.", "texts": [ " For the theoretical analysis, it will therefore be assumed that the air gap flux density of the RFAPM machine 1-4244-0645-5/07/$20.00\u00a92007 IEEE a BP cM Ep h hm hy lp kf k,~ kq qKT fe fg N p PCU Pe Pm q Q rn Rcu Rph vcu w is also sinusoidal and that the peak flux density, BP,, is the same for all three types of machines under consideration. A. RFAPM machine with overlapping coils A three-dimensional view of the typical coil configuration of a RFAPM machine with overlapping stator coils are shown in Fig. 2. A two-dimensional linearised cross-sectional view along the nominal stator radius of only one phase of the overlapping stator coil configuration, with a sinusoidal radial flux density, a coil pitch, Oq, equal to the pole pitch, Op= 2p, a coil position a with respect to the flux density wave and a coil side with of 2A can be represented as shown in Fig. 3. For the analysis we assume that the stator thickness is much smaller than the nominal stator radius, i.e. h < rN allowing us to consider all the turns to be situated on the nominal stator radius", " We will begin our comparative analysis of the different stator coil configurations by comparing the difference in the flux-linkage factor, as express by (3), (25) and (32), for a common 16 pole rotor configuration. In Fig. 10 the different (32) flux-linkage factors are plotted against the stator coil side- width factor, kA, with A Almax (38) From this graph it can be seen that the maximum fluxlinkage of the Type II concentrated coil configuration occurs with the coil side-width at 37% of its maximum possible value, with k,, = 0.966. For the overlapping coil configuration, the coil side-width is usually very close to its maximum possible value, as was shown in Fig. 2, resulting in kA - 1.0 and therefore k,, 0.955. The flux-linkage is only affected by the number of coils and the coil side-width. On the other hand, from (36), the torque factor is also affected by (. Thus, the smaller the end-turn length in comparison with the active stack length, the higher the torque factor would be. The end-turn lengths of all the coil configurations depend on the nominal radius and the number of stator coils, as given by (11), (26) and (33). The overlapping coil configuration's end-turn length is also dependant on the the coil height, while the Type II concentrated coil configuration's end-turn length is again also dependant on the coil side-width angle, A" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002587_ac60299a006-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002587_ac60299a006-Figure1-1.png", "caption": "Figure 1. an activated target Gravity-track sample holder for rapid retrieval of", "texts": [ " The irradiation chamber and the beam current measurement have been previously described (9). The chamber Irradiation. (9) J. F. Lamb, D. M. Lee, and S . S . Markowitz, Proc. 2nd Con/. 011 Practical Aspects of Actrearion Analysis with Charged Particles, Liege, Euratom, Brussels, 1967,1,225 (1968). was operated under a helium gas atmosphere rather than in the accelerator vacuum to minimize time-loss during sample retrieval. The activated samples were transferred to the counting chamber by a gravity-track which is shown in Figure 1. The target is mounted over a 0.75-inch diameter centerhole in an aluminum disk held in place during bombardment by a pin attached to the solenoid. At the end of the bombardment, the solenoid is activated, releasing the pin, and the disk to which the target is affixed rolls down the plastic gravity-track to the shielded NaI detectors. This apparatus allows counting to begin within approximately two seconds after the end of the bombardment. During this two-second delay, very short-lived activities decay away" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000028_auto.2000.48.4.157-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000028_auto.2000.48.4.157-Figure5-1.png", "caption": "Figure 5: The Compass Gait Biped from [4]", "texts": [], "surrounding_texts": [ "The existence of passive gaits in simple bipeds is interesting and may help to explain the e ciency of human locomotion. To date, however, there are few results to indicate that the existence of such gaits is useful for the development of feedback control laws in powered bipeds. In particular, the sensitivity to initial conditions and ground slope must rst be addressed. Later, robustness to external disturbances and parameter uncertainty must be investigated. In this paper we 161 Brought to you by | provisional account Unauthenticated Download Date | 6/25/15 4:44 PM address the sensitivity to ground slope via potential energy shaping control. The sensitivity to initial conditions and robustness to uncertainty and disturbances is addressed via hybrid switching control strategies. In this section we consider the compass gait biped with actuators at the ankle and hip. Since the foot is idealized to a point, we treat the system as though there were a pin joint at the foot/ground interface of the stance leg during the single support phase. The dynamic equations are thus given by (26) with control input u = [uH ; us] T with independent hip torque uH and ankle torque us. Under the assumption of full actuation, we may, of course, apply any number of tracking controllers that provide global trajectory tracking - such as computed torque, backstepping, etc. However, a common conjecture in the bipedal locomotion community is that controllers which exploit the \\natural dynamics\" of the biped will prove to be more energy e cient and will produce more anthropomorphic motion. Although this conjecture has yet to be fully explored, we will adopt its philosophy here and seek controllers based on energy shaping rather than trajectory tracking. As a rst attempt toward developing natural feedback controllers for the compass gait we can easily prove the following result: Theorem: Suppose we are given a vector of initial conditions X = X( 0) = ( ns(0); s(0); _ ns(0); _ s(0)) T (30) such that, with u = 0, a stable passive limit cycle exists corresponding to the ground slope 0 and X lies in it's basin of attraction. For any ground slope, , de ne = 0 and let R de ne a 2-D rotation through the angle . Note that in Cartesian space, R has the usual matrix representation, R = cos( ) sin( ) sin( ) cos( ) while, in the con guration space of the Compass Gait robot, which is the 2-torus, R is represented by the shift operator, R (q) = (q1 ; q2 )T : With a slight abuse of notation we will use R for both representations. Let P = P R and g = @P @q T Then with the feedback control law u = S 1( @P @q @P @q ) = S 1(g(q) g (q)) (31) there is a stable limit cycle corresponding to the slope and, moreover, the point X( ) = ( ns(0) + ; s(0) + ; _ ns(0); _ s(0)) T (32) lies in its basin of attraction. Proof: It is enough to note from Equation ( 27) that the inertia matrix M(q), and hence the Christo el symbols de ning C(q; _q), are rotation invariant, i.e., are a function only of the di erence ns s. Thus with the control law (31), the closed loop system is given by M(q) q + C(q; _q) _q + g (q) =M(q ) q + C(q ; _q) _q + g(q ) (33) = 0 and the result follows from the substitution q ! q. Remarks: 1. We see that the control law u e ectively cancels the gravity torque acting on the robot and produces a \\virtual gravity vector\" that corresponds to the slope 0. In this way the passive limit cycle motion of the compass gait biped is made slope invariant. 2. We note that the total energy E of the system is E = 1 2 _qTM(q) _q + P (q) (34) where P (q) is the Potential Energy due to gravity and 1 2 _qTM(q) _q is the Kinetic Energy. Fur- thermore, the Potential Energy P (q) satis es @P @q T = g(q) (35) By the well-known passivity property of rigid robots we know that _E = _qTSu (36) so that, with u = 0, the total energy is conserved during each step along the stable limit cycle of the unactuated biped. De ning the \\shifted\" energy function E (q; _q) = E(R (q); _q) = 1 2 _qTM(q) _q + P (q) (37) it is easily to see that _E = _qT (Su g(q) + g (q)) (38) so that E is conserved with the control law (31). This observation is the reason that the control law (31) is termed a passivity based control law. 3. The idea of shaping the potential energy in robot manipulators goes back to the work of [13]. In this context we only need to know the initial conditions that results in stable walking for one particular slope and we can achieve stable walking on any slope - uphill, downhill, or on level ground. 162 Brought to you by | provisional account Unauthenticated Download Date | 6/25/15 4:44 PM" ] }, { "image_filename": "designv11_32_0002359_s00332-005-0700-y-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002359_s00332-005-0700-y-Figure3-1.png", "caption": "Fig. 3. A curve in space, tether section.", "texts": [ " For example, the twist vector can be expressed in the director basis in the following way: \u03ba(s) = 3\u2211 i=1 \u03bai di , (7) Stability and Bifurcation Analysis of a Spinning Space Tether 513 where \u03ba1 and \u03ba2 represent the bending curvature of the rod around d1 and d2 respectively, and \u03ba3 represents the twist of the rod around d3. Suppose that the centre line of a rod is a curve in space of length L . Here we assume that this curve is inextensible, so the arc length s can be used as a material coordinate. For every s, we suppose that, after deformation, the cross section of the rod S(s) lies in the normal plane to the curve (see Figure 3). Therefore, the position vector of an arbitrary point of the rod can be expressed as X(s, \u03be1, \u03be2, t) = x(s, t)+ \u03be1d1(s, t)+ \u03be2d2(s, t) = x(s, t)+ r(s, \u03be1, \u03be2, t), (8) where {\u03be1, \u03be2} are the components of position in the cross-section axes {d1(s), d2(s)}. Once the kinematics of a point of the rod has been stated, the next step is to derive the dynamic equations. Besides the assumption that there is no shear deformation, when deriving the Kichhoff equations of the rod element in the next section, we assume that a characteristic radius of the cross section h = \u221a max{\u03be1}2 +max{\u03be2}2 is small compared to the length of the rod ( h L 1), and also that the norm of the twist vector fulfils | \u03ba(s, t) | h \u223c h L [18]", " This set of assumptions allows us to derive a tractable model neglecting higher-order terms in the force and moment balance equations (a differential slice of rod can be considered to be a rigid solid). Such assumptions permit large overall deformations of the rod although the local strains remain small. This point is crucial because, as explained in the introduction, geometric nonlinearity plays an essential role in stabilizing the SET dynamics. The above assumptions effectively consider the rod to be made of a set of infinitesimal slices centred at every s. Hence, a one-dimensional approach can be used. As shown in Figure 3, there is a traction, which is the projection of the stress tensor onto the crosssection plane, due to the interaction of each infinitesimal element of the cross section 514 J. Valverde, J. L. Escalona, J. Dom\u0131\u0301nguez, and A. R. Champneys with the next one. Denoting such a traction by f = f (s, \u03be1, \u03be2, t), the total elastic force exerted in a section S(s) is given by F(s, t) = \u222b S(s) f (s, \u03be1, \u03be2, t) dS, (9) where dS is an infinitesimal area element. The total elastic force vector can be expressed in the director basis as F(s, t) =\u22113 i=1 Fi di ", " Assuming the SET to be made of viscoelastic material [23], the three-dimensional stress-strain relation can be written as \u03c3 = 2G\u03b5+ \u03bbtr(\u03b5)I + 2G\u03b3v\u03b5\u0307+ \u03bb\u03b3d tr(\u03b5\u0307)I, (15) where the over-line represents a tensor quantity (in this case the stress and strain tensors), \u03bb is the Lame\u0301 constant, I is a unitary tensor, tr() is the trace of a tensor, and \u03b3v and \u03b3d are viscoelastic constants. The constant \u03b3v is related to the volumetric (dilatation) stress tensor and \u03b3d is related to the deviatoric stress tensor [23]. The components of the tractions f are the projections of the stress tensor \u03c3 onto the cross-section plane, whose normal is d3. Naming the components of stress tensor as \u03c3i j , where i, j = 1, 2, 3, the traction vector is (see Figure 3) f = (\u03c331, \u03c332, \u03c333) T . (16) Substituting (16) into the expression for the moment, which is given by (10), we obtain M1= \u222b S(s) \u03be2\u03c333 dS, M2= \u222b S(s) \u2212\u03be1\u03c333 dS, M3= \u222b S(s) (\u03be1\u03c332 \u2212 \u03be2\u03c331) dS. (17) Applying Saint Venant\u2019s solution for a rod free of volume forces with applied loads at its ends [22], and assuming that both damping constants are equal (\u03b3v = \u03b3d = \u03b3 ) yields 516 J. Valverde, J. L. Escalona, J. Dom\u0131\u0301nguez, and A. R. Champneys the so-called Kelvin-Voight constitutive laws, \u03c331 = E 1+ \u03bd (\u03b531 + \u03b3 \u03b5\u030731), \u03c332 = E 1+ \u03bd (\u03b532 + \u03b3 \u03b5\u030732), \u03c333 = E(\u03b533 + \u03b3 \u03b5\u030733), (18) where \u03bd is the Poisson\u2019s ratio of the material and 2\u03b531 = \u03ba3 ( \u2202\u03c6 \u2202\u03be1 \u2212 \u03be2 ) , 2\u03b532 = \u03ba3 ( \u2202\u03c6 \u2202\u03be2 + \u03be1 ) , \u03b533 = \u03ba1\u03be2 \u2212 \u03ba2\u03be1, (19) where \u03c6 is the torsion function for the corresponding cross-section [22]" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001695_imc.1990.687358-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001695_imc.1990.687358-Figure4-1.png", "caption": "Figure 4 shows the location of the position sensor and the marks on the robot. The position sensor is fixed just below the ceiling of the laboratory ro6m facing the floor. The specification of the position sensor is shown in Table 1.", "texts": [], "surrounding_texts": [ "In order to reduce experiments of an ronment for the re paper proposes the ient. We construct virtual environmen the environment. E effectiveness of t a collision avoida correction method based on wall recc of ultrasonic sew\nComputer simulat ic ment is the first of a mobile robot motion control of tion, in sensory i it is seldom SUCCE in a real world bj computer simulatic damages of the rot cult to experiment situation. These omous control soft\nIn order to solve development of aul the utilization 01 consists of the rc ronment which is I considered to lie system and the ful\nAfter checking thc puter simulation, realistically usir system is that we easily than by api real situation. WI motion this systeo autonomous control opment . Hffoct lvoness of 1 devolopmont o f thc mobllc robot ngaii of position cstlmr\nlifficulties in carrying out control :tual mobile robot in a real envilization of autonomous control, this itilization of a virtual environi an experiment system using the and controlled the actual robot in the experiment we demonstrated the system through the development of :e algorithm against a wall and a F the position estimation error iition using the range information rs.\n1. Introduction\nwith a robot and a model environtep of autonomous control research LI-[31. Because of the errors in robot, in estimation 01 its locaformation of the robot sensor, etc., sful to Control a mobile robot well jimply using the result of the . Sometimes this leads to the t in experiments and makes it diffiautonomous control in the actual hings make the development of autonw e take a lot of time.\nhis kind of problem and speed up the nomous control technique, we propose a virtual environment system, which 1 robot hardware and a model envit around the robot. This system is etween the full computer simulation actual system.\ncontrol algorithm by the full come can check it further and more this system. The merit of this an refine the control algorithm more ying the algorithm directly to the h the measurement of the robot is useful for the evaluation of algorithm as well as for iLs devel-\nc system Is drmonstrutrd through thr col I ision avoidancc alg'orl thm of I I t ti wall and thc corrrctlon mrthod ion orror using wall rocogiiltlon.\n2. Utilization of virtual environment\nAs shown in Fig.1 the first stage of the development of autonomous control of a mobile robot is computer simulation with a robot model and an environment model built in a computer. Both models and control algorithms are tested in this simulation. At the next stage4after debugging they are applied to the real situation. That is, they are used to control an actual robot in the real world based on the result of the computer simulation. If something is wrong, the models and/or the' algorithms are checked, modified if necessary and applied to the actual situation again. This is a usual way of mobile robot control study. But it is sometimes dangerous because collision of the robot with objects in the real environment is possible if there is a failure in the control.\nThe method to'use the virtual environment lies between these two stages : the full computer Simulation system and the full actual system as shown in Fig.1. In this case where the robot is controlled in the virtual environment model, there is no danger if the models and/or the control algorithms are' Fong, for there are no real obstacles in the environmen ! . After the debugging in this system the algorithms are used in the real environment. Because of the smaller gap between the virtual environment system and the real world, it is easier and less dangerous to control the robot in the real world based on the result of the virtual environment system.\nFigure 2 shows the concept of the experimental system of a mobile robot control using the virtual environment. Here the actual robot is controlled in a free space. A host computer assumes the environment model in the space. By the result of a real-time motion measurement of the robot, the host computer knous the position and the orientation of the robot in the enbironment model. Based on the relation betueen the robot\nComputer simulation\nrobot model\n\\", "virtual environment\nI host computer\nreal-time motion measurement system\nFig.2 A concept of mobile robot control system using the virtual environment.\nand the model environment, the host computer simulates sensory data the robot would obtain with its external sensors, such as ultrasonic and laser range sensors, if the model environment were real. The robot is given the information from the host, analyses it and moves in the environment using the given algorithm. If the robot should fail in moving around and collide with the assumed objects in the model environment, there will be no trouble or no danger. The result of the real-time motion measurement is also used to evaluate the control algorithms quantitatively.\nAfter the test of the algorithms in the virtual environment we can test them more realistically by placing actual objects corresponding to the virtual environment. Compared to the usual way of the study, the utilization of the virtual environment is expected to speed up the development.\nThe real-time motion measurement system, a mobile robot and a host computer are components of the system. It would seem possible to construct the system without the host computer, but because of the limited ability of the computer on board the robot' and for the better manmachine interface with the operator, the proposed system which uses the host computer is better. It i s important to establish communication among the three components of the system. Especially the communication between the host computer and the on board computer should be a wireless link in order not to restrict the motion of the robot and to facilitate the experiments.\n3. Experimental system\nIn order to use the proposed system for the study of autonomous control of a mobile robot we constructed an experimental system. Figure 3 is the outline of the system. The details of the each part are as follows.\n3.1 Real-time notion measurement system\nVision is favorable to measure the position of a robot\nr m real-time mark\ntracking device\nn mobi .le robot\nm a 0 1 EX PC9801RA (host computer) Fig.3 An experimental system of mobile robot control using virtual environment.\nwithout restricting its motion. In order to avoid the time consuming visual processing by software we used a hardware logic to detect the bright spot positions of the marks in the visual plane. A position sensor G120 i s a product of Laboratory of Oh-you Keisoku Kenkyusho Inc., Tokyo..This apparatus can detect spot marks on a plane sixty times of a second at most using a CCD sensor.\nThe principle of the detection is to count x and y coordinates of the pixels which are included in the mark while scanning the plane. After thsscanning the center coordinates of the mark are given by dividing the counted sums by the number of pixels within the mark. By specifying windows it is possible to measure more than one mark at the same time.", "Table 1 Specification\nnumber of tracking output. . . . . . . . . . . . . . . . . . . .p speed.............,.. resolution. communication....\ntf the real-time mark tracking device(G120)\nmarks...2 osition and size of marks ..... 1/60 Isample/secl ............... 256 x 192 [pixel] ......... RS232C. max 19200 BPS\nFig.5 A mobile robot \"MELBOY\".\ncomputer sends commands and send command to system to set a window turn. With this each lamp mark and automatically.\nThe restriction fron sensor is that the the sensor is mounted degrees of freedom, measurement of the\n3.2 Mobile robot\nThe appearance of a front vidw is drawn the robot is the with a caster wheel this mechanism the turning and pivoting-. tires and the caster motor with a harmonic the pulse drive system control the rotatioral angle of the wheel. i s controlled according two drive wheels. Tke the caster wheel anc. head. The resolutior axes i s 1/20000 of t . control boards are motor drive circuit trol the wheels for the computer. The are used to estimate reckoning. Table 2 hardware.\nThe robot has four sensor as external are attached on the of the body. The lar8t the rotary table with range information ir sensor unit is the driving signal of tie 49 kHz sound. By sending the signal signal with a 400 kIz obtained with the minimum measuring shows the timing chc.rt sensors. By driving in turn, range msec from each sensor.\nThe computer on boai*d CPU 80286 and NDP computer has two 1 disk. All the infori of the actuators, si\nlaser transmitter\nto turn on and off each lamp the real-time motion measurement\nand start tracking the mark in sequence it i s possible to identify\nneasure the orientation of the robot\nthe present placement of this neasuring area is not large. But if\non the rotary table with two we can enlarge the area where the robot i s possible.\nmobile robot i s shown in Fig.5. Its in Fig.6. The mobile mechanism of\nto support the body posture. With Iobot i s capable of moving straight,\nThe drive wheels have pneumatic wheel has a solid tire. A DC servo gear drives each main wheel. By using an encoder it is easy to speed as well as the rotatjon\nThe direction of the caster wheel\ncorventional two-wheel-driven type\nto the rotational speed of the same.contro1 systems are used for for the rotary table of the sensor of the rotational control of these revolution. Intelligent motor\nised between the computer and the boards. They make it easy to conthey reduce the processing load of\nthe position of the robot by dead rhows the specification of the robot\nercoder signals of the main wheels\ntltrasonic sensors and a laser range asensorS. Three ultrasonic sensors front, the right and the left sides ultrasonic sensor is mounted on the laser range sensor to get any direction. The ultrasonic I product of Polaroid Co. , U.S.A. The sensor consists of 56 pulses of\nmecuuring the time interval between tnd receiving the reflectional\nclock, range information i s rt!solution of millimeter order. The distance is about 0.3 m. Figure 7\naf driving the four ultrasonic one of the sensors every 100 msec\ninformation can be obtained every 400\nthe robot is the combination of 80287 of 10 MHz. For the storage the FIB 3.5 inch FDDs and a 2 MB RAM tion processing, such as control pling of the sensor data and\nlaser range frnde controller\nsensor head\nmotor controller programmable counteri ultrasonic controller peripheral IO\nfront ultrasonic\nleft ultrasonic\nmotor servo\nDC-E\u20ac converters\n.- Fig.6 A front view of the mobile robot." ] }, { "image_filename": "designv11_32_0001636_1.5060217-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001636_1.5060217-Figure1-1.png", "caption": "Figure 1. Schematic of the laser surface modification process showing the principle components related to energy transport.", "texts": [ " Because of the recent interest in developing numerical techniques to simulate the energy and mass transport phenomena associated with the laser surface modification process, as well as with laser deposition for producing near net shapes, there is a need for an improved understanding of laser absorption with powder layers. This particular research has been directed at the absorption of the laser beam directed onto a powder layer sitting upon the substrate. This is believed to be applicable to preplaced powder processes, as well as processes that rely on ancillary feeding of powder to the interaction zone. Shown in Figure 1 is a schematic of the process that involves a diffuse laser beam presented to a powder layer preplaced onto a substrate. A portion of the laser energy is absorbed within the powder layer and transferred to the substrate. When a laser operating at the infrared wavelength, which constitutes most lasers used for surface modification processes, is directed at a metallic surface, much of the energy is reflected and a fraction of energy is absorbed within a thin layer. In metals, absorption occurs over a very small depth, and the decrease of laser intensity or attenuation that occurs within this layer may be estimated through: ( ) )zkexp(IzI o \u03bb \u03c0 = 4 (1) where is the intensity of the incoming beam, oI ( )zI is the intensity at a depth below the surface at z, k is the attenuation index or extinction coefficient, and \u03bb is the wavelength of the beam" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001170_robot.1997.619321-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001170_robot.1997.619321-Figure4-1.png", "caption": "Fig. 4 The definition of the stabilization constraint", "texts": [ " As the motion of the manipulator becomes unstable, the pseudo-acceleration vector b crosses one of the boundaries of the AP. This implies that it is impossible to realize the motion within the specified torque bounds. The AP must always contain the pseudoacceleration b at its interior to guarantee the feasibility. From the condition, we propose the following inequality constraint to prohibit the vector b from crossing over the polyhedron: where n E 'iRm is a unit vector whose direction is normal to the boundary plane of the polyhedron from b with the minimum distance. As illustrated in Fig. 4, Eq. (15) may constrain b from approaching to the nearest boundary plane. The time derivative vector b is derived from the definition of b in Section 2 as follows: nTB. s 0 (15) . d b = -(xd - j e+ JM-'h) dt Then Eq. (15) is linear for the joint acceleration and can also be written in terms of the joint torques as where C is a 1 x n matrix and d is a scalar defined as g ( r ) = CT - d I 0 (17) It is not so much difficult to compute C and d . The inequality equation (17) is called as stabilization constraint hereafter. We are to add the stabilization constraint to the torque minimization problem (9). However, the stabilization constraint is not required for a stable motion since b continues to remain in the AP. Thus it is desirable to describe the constraint with the following form: where r represents the minimum distance from b to the boundary plane of the AP and E is the threshold value to be specified. The minimum distance r can be easily computed from the AP. We can know from Fig. 4 that r is the isotropic acceleration of the manipulator for a given state. We now consider the torque minimization subject to the stabilization constraint: minimize subject to A r = b (19) ~ g , ( r ) = 11 wrllm C r l d To find the solution of the above problem using the method proposed in Section 3, the inequality constraint is converted to the equality constraint by introducing the slackvariable s as C r + s = d , s > O (20) If we define a new variables vector 7 E%'+' as r = [ r T s IT , the optimization problem (19) can be transformed to the following form, - where ", " The torque at joint 3 retains its upper limit value for a while because the parameter S of the stabilization constraint in Eq. (21) has been activated not to exceed the torque limit at joint 3. This result is similar to that of Li et al.4 although they are obtained through different approaches. In contrast to the above result, the joint torques of the MO method overrun their limits at about t = 0.6 s . Fig. 6 illustrates the action of the stabilization constraint by using the representation of Fig. 4. The SC method restrain b not moving to the boundary of the AP by changing d with 1.he stabilization constraint at t = 0.47 s. For the TO method, the pseudo-acceleration b however continues to move out of the AP. Usually the manipulator has large joint velocities as b has a large magnitude. Lastly, we carry out the simulation for an extreme case that the end-effector moves to the boundary of its workspace. This example was treated by Cheng et al.' and the duration time is T, = 2.378 seconds. With the same 240 7 value E = 15ym2 as the previous simulation, the global motion could not be stabilized" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001825_bf02655218-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001825_bf02655218-Figure1-1.png", "caption": "Fig. 1 Schematic arrangements of single roller quenching method.", "texts": [], "surrounding_texts": [ "Sendai 980 and T. Ojima A. Kuroiwa, Research and Developement Laboratory, TDK Electronics Co. Lid., Ichikawa 272, Japan (Received June 29, 1979) Polycrystalline silicon ribbons were prepared by Roller Quenching Methods. Ribbons were obtained flexible and of virtually continuous length, 20~ m to 200~,L m in thickness, and 1 mm to 50 mm in width. Microscopic observations of etched ribbon surfaces showed that the average grain sizes were 20~ m to 30y~ m. Crosssectional views showed the ribbons to have a columnar grain structure. Unwanted impurities were undetectable by Auger analysis, except very thin oxygenated layer was present on the surface of the ribbons. By means of DC conductivity and Hall measurements of intentionally doped silicon ribbons, it was found that the active carrier concentration of the ribbons was nearly the same as the doped carrier concentration, from 1014/cm3 to 1020/cm3, the resistivity of the ribbons were about one order of magnitude higher than that of silicon single crystals, and the Hall mobility parallel to the ribbon axis and perpendicular to the ribbon plane was l to 150 cm 2.V -I. sec -l and 50 to 700 cm 2.V-I sec-l respectively. A solar cell using the present ribbon was made by means of a CVD silicon 111 0361-5235/80/0100-0111503,00/1 9 1980 A IME deposition method. Satisfactory diode characteristics and a conversion efficiency of about 5 % were obtained. Key words:solar cell, silicon, rapid quenching, silicon r ibb on. Introduction Among various kinds of solar cells, silicon cells attract many investigations because of advantages such as reliability, unlimited supply of the raw materials and so on. For practical use of solar cells, it is necessary to achieve a great reduction in cost and high speed production of cells with long life and high efficiency. The conventional technology, based on cutting large ingots into wafers, is accompanied by severe waste of materials and fabrication time. Efforts have been made to grow silicon ribbons, and the EFG process I, the web-Dendric process 2, the Stepanov process 3, the Ribbon to Ribbon process 4 and the Horizontal Pulling process 5 were proposed. The main attraction of these processes lies in the fact that the direct production of ribbon-shaped crystals from the melt permit significant cost reductions over the usual methods of manufacturing silicon solar cells. When quick roller quenching methods can be used to form molten silicon into thin crystalline ribbons, a large reduction in cost and fabrication time is expected. We have applied the above-mentioned roller quench- ing methods to prepare at high speed long flexible ribbonshaped magnetic materials such as Sendust 6, 7 and high silicon-iron alloys with good magnetic and mechanical characteristics even though these materials are mechanically brittle in their bulk states. We tried to extend these methods to prepare at high speed silicon polycrystalline ribbons with good electronic and mechanical properties, and very brief results of these experiments were reported 8. Flexible polycrystalline 1. heat resisting tube 2. furnace 3~ roller 4 chamber 5. bellows 6. silicon charge 7. silicon ribbon A. inert gas. Fig. Roller quenched silicon ribbon wound on a 34 mm rod, whose thickness is 30~ m and width is 2 ram. f silicon ribbons with thicknesses from 20jgL m to 200jhL m were produced at a very high speed of around 30 m/sec. In this paper we report more fully on the roller quenching method and the resulting ribbon characteristics such as morphology, impurity analysis, electrical properties and preliminary results on the fabrication of the diodes and solar cells. Experiments In these experiments, n- and p-type silicon ribbons were made by direct roller quenching methods. In these methods the molten silicon material was injected between a pair of rapidly rotating rolls or onto the surface of a single roll, and cooled immediately into a long crystalline ribbon. One form of the experimental apparatus is shown in Fig. I. The starting silicon charge 6 was put in a heatresisting tube with a small nozzle l, and melted with a small furnace Z. A stream of the molten silicon charge was ejected onto the surface of the roll 3 through the nozzle by a rapid increase of Ar pressure 4 in the tube. At this moment the molten charge was quenched very rapidly by the roll into a long crystalline silicon ribbon. Some ribbons were prepared in an Ar atmosphere. The thickness and width of the ribbon could be controlled by changing the roll material, the roll size, the speed of rotation, the ejection pressure, and the temperature of the melt. One representative condition which proved satisfactory was as follows : the roll material was copper, roll diameter about 40 cm, rotational speed about 1000 rpm, ejection pressure about 0.5 atmosphere, temperature of the melt about 1500~ tube material quartz, and nozzle diameter 0.5 ram. Auger spectra of silicon ribbons were observed by means of a PHI 545 Auger Electron spectrometer. IDC 0 \"o CD - | 0) -~=. o ~ ~ ~o~ i ~ o o~o ~ m . ,...i N o | w M Z W It 0 0 9 ~ 2 ~ 2 Lt~ conductivity and Hall measurements were made along the ribbon axis and across the thickness. In these measurements ohmic contacts were made using A1 on p-type ribbons and AuSb on n-type ribbons by vacuum deposition and annealing at 550~ and 350~ for 10 minutes respectively. We attempted to form a p-n junction on the p-type ribbon by employing chemical vapor deposition using silane (Sill4) and phosphine (PH3) on p-type silicon ribbons at 1000~ Results and Discussions The roller quenched crystalline silicon ribbons were typically l to i0 rnm wide for the single roll method, and up to 50 mm wide for the pair-of-rolls method in which the width was limited by the roll width. The ribbons were Z0~ m to 200~ m in thickness. The silicon ribbon obtained in one preparation process has constant thickness and width along the growth direction. Figure Z shows these ribbons which were flexible, and it was possible to wind them around a rod 34 mm in diameter when the thickness of ribbon was 30~m. Except for the present roller quenched ribbons, such a small thickness of reported silicon ribbon has not previously been. Measurements of X-ray diffraction pattern on as prepared silicon ribbon showed nearly equal diffraction contribution from (iii) (ZZ0) (311) (400) .... . X-ray source was CuKo~ and referred to ASTM data. This means the rapidly quenched silicon ribbon has no preferred orientation. Microscopic examinations were made on as-prepared ribbons. Before this examination, the surface was mechanically polished, and etched for ten seconds in a mixture of 95 ~ nitric acid 5 ~ hydrofluoric acid. Fig. 3 shows typical grain structure of the silicon ribbon surface and of the cross-section. Grain sizes were measured with the line-intercept-method9 yielding the average grain size of about Z07U. m on the surface. In the crosssection of the ribbon, we observed a colmnar structure perpendicular to the ribbon plane with grains extending through the entire or half of the thickness of the ribbons depending on either the single roll or a pair of rolls methods employed, respectively. Auger Spectroscopy In Fig. 4 (A) are shown the Auger spectra for the free surface of the silicon ribbon prepared by the single roll method in an atmosphere of 3.3x104 Pa argon gas. The 92 eV peak corresponds to elemental Si l0 , and Carbon, 9 peaks are also observed. After argon ion bombardment for one minute at i. 0 kV and i0 mA ion current corresponding to 7 A etching, the 92 eV peak becomes sharp and the oxygen peak fades out as shown in (B). It is noted that the peaks correspond to SiOZII and unwanted impurities were not observed except oxygen contamination in a region about 7 A from the ribbon surface. Fig. 5 shows Auger spectra from the free surface of the silicon ribbon prepared in air by single roller method. The 92 eV peak is entirely missing in (A) but appears after argon ion bombardment for 3 rain at i. 5 kV and I0 mA ion current as shown in (B). Insertion in Fig. 5 shows the depth profile of Si and O from the free surface. This shows about 50 A thickness of the surface layer is oxydized to SiO Z during the rapid quenching process when silicon ribbon is prepared in air atmosphere. Electrical Properties IDC conductivity and Hall measurements of the inten- tionally boron and phosphorous doped silicon ribbons were made. Carrier concentrations of the ribbons were directly determined from these measurements at room temperature. In Fig. 6 are plotted the active carrier concentra- ..r t ~ I z n, M. o 9 \" / t ~ ~ I -- U l Z Q: ttJ t,J o P - t y p e 9 N - t y p e I I 1 I I 1 Id ~ Io ~ ,o '7 ,o\" Io ~ Io ~ CARRIER DENSITY OF CHARGE ( cm -3 ) F i g . 6 A c t i v e c a r r i e r d e n s i t y of the s i l i c o n r i b b o n v e r s u s d e n s i t y of s i l i c o n c h a r g e . 9 9 P-doped ribbon 0 \" B-doped ribbon Solid line shows nribbon = ncharg e. Resistivity of the ribbon versus that of the silicon charge. Solid line shows f ribbon-- ~charge\" O\" p-type ribbon doped with boron Q 9 n-type ribbon doped with phosphorous ,0 s Ir =E -r O ILl IX 10 m 0 0 -I 0 8 0 EPI P - DOPED | B - DOPED , CVD FK)LY P.N N I I I I I o\" ld s lo '~ ld ~ lo '~ 1# 1( DOPING CONCENTRATION (ATOMS/ CM) F i g , Resistivity of the ribbon versus the doping concentration of the charge deduced from the Irvin curve 15 O : B-doped ribbon ..... : CVD films 13 9 :P-doped ribbon EPI : single crystals 13 i i ~, 9 , , t 9 , / _~) o f ;'o \\ / , ' 9 'o / ,' ~ I l l I 9 \\,\\ o =:li ' c= v l , 9 ~ o. I I 9 0 9 0 I I l m TO \"- o z ~ ~.~- ; , = o = ~ ~ o ~ ~ \"~ .. ~ o ' ~ U < ~ . ~ i \" 0 = 9 - :>,~j . ~ 9 . 4--~ ~ o~ 0 ~, tion versus silicon charge dop{ng concentrations. The solid line corresponds to the active carrier concentration of the ribbon when it remains unchanged by the present roller quenching process. From this figure, except for the lower doping region ( /~ 1014/crn 3 ) of n-type ribbons, no large deviation from the solid line was found for both the p- and n-type ribbons. Fig. 7 shows the electrical resistivity of the ribbons, ~) ribbon' as a function of the resistivity of the silicon charge,~) charge\" The solid line shows f ribbon = Jgchar~e. The resistivity of the ribbons are l to l0 times higher than that of silicon charges. It is interesting to plot the electrical resistivities of ribbons ranging from 10-~crn to 10J~crn as a functions of doping density due to the Irvin curve IZ. The results are shown in Fig. 8. These were compared with curves obtained for polycrystalline silicon and epitaxial single crystal silicon grown by chemical vapor deposition 13 In Fig. 9 are shown the data of the Hall mobility measurements of both p- and n-type ribbons and those of single crystals as well as of chemically vapor deposited polycrystalline 14 silicon films as a function of active carrier densities. It is interesting to remark that some of the data on the present ribbons are lying near the curves for single crystals. The Hall mobility perpendicular to the films was 50 to 700 cm 2. V -I- sec -1, as expected from the grain structure. The dip of the Hall mobility parallel to the ribbon surface plotted as a function of active carrier density is found in Fig. 9. Analytical transport properties on the rapid quenched polycrystalline silicon ribbons are under experiments. Diodes and Photo-Voltaic Properties In this work, p-n junctions were formed on p-type ribbons by employing chemical vapor deposition (CVD). The n-type silicon was deposited on p-type ribbons (l&Icm) by the pyrolysis of silane (Sill4) with phosphine (PH3) as a dopant. The horizontal type quartz reaction tube (7x 10x50 cm 3) was used. The ribbons were heated upto 980 Fig. i0 E U E > 9 i i i i i :F VOLTAGE (V) 10 ~ / ~ ,, ,' ~v~l LLMINATED 20 Current-voltage characteristics for rapidly quenched polycrystalline silicon cell illuminated in AM 1 sunlight ( 94 mW/cm 2 ). Current-voltage characteristics of CVD cell on rapidly quenched polycrystalline silicon. ~ by high frequency power supply. The flow rates of the silane (Sill4) and phosphine (PH3) are respectively ix 10 -3 tool/rain, and 0.5x 10 -3 tool. /rain. and unchanged during the growth. Purified hydrogen was used as a carrier gas ( flow rate 20 i/rain ). The deposition time of i. 5 minutes corresponds to 0. 3]II m thickness of n-type deposition layer. The diode~thus obtained were mesaetched by the mixture of 75 ~/0 nitric acid and 25 ~/0 hydrofluoric acid for 30 seconds. The electrodes were made using silver paste. Cells dimention exhibiting the diode characteristics were circular of Z. 3 turn in diameter ( area 4. Z ram2). The current-voltage characteristics of the cell under illumination of an AM l ( 94 mW/cm Z ) are shown in Fig. i0. Open-circuit voltage, short-circuit current density and fill factor were 0. 50 volt, 15 mA/cm 2 and 0.63, respectively, which corresponds to a conversion efficiency of 5 %. Fig. ii shows the current-voltage characteristics of the larger cell ( area 1 cm 2 ) made with the same condition s. Acknowledgements The authors express their reverential thanks to Prof. Dr. T. Takahashi for his most warm encouragements and to Prof. Dr. J. Nishizawa for his helpful advices. References i. K. V. Ravi, H. B. Serrege, H, E. Bates, A. D. Morrison, D. N. Jewett and J. C. Ho, Proc. 12 th IEEE Photovoltaic Specialist Conf. pp. 299 302, May 6-8 (1976), 2. D. Z. Barrett. E. H. Myers D. R. Hamilton and A. I. Bennett, J. Eleetrochem. Soc., if8 952 (1971) 3. S. V Tsvinskii and A. V. Stepanov, Soviet Phisics- Solid State, 7 148 (1965)" ] }, { "image_filename": "designv11_32_0000230_roman.1996.568749-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000230_roman.1996.568749-Figure8-1.png", "caption": "Fig. 8. It was considered that the subject avoided the experimenter at almost constant walking velocity. It is thought that the man's avoidance locus is expressed as expression (3) .", "texts": [ "7 Relationship between velocity and slope per relation of both parameters calculated based on data of Fig. 6 are shown in Fig. 7. Y [\"I 100 L -20 -2ood- Fig. 6 Sample of approximated data Other subject's data were added for comparison. The slope per time and the velocity were not proportioned as shown in Fig. 7. It was considered that the velocity was almost constant. The slope per time did not relate to the velocity. In addition, the relationship between time and the velocity is shown in time Velocity[mm/s] Collstant . . * I O 0 0 0 0 I I I I I I , Time[s] 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Fig.8 Relationship between velocity and time As a result, the avoidance walking locus was drawn in catenary which has k % 3.9 10 and m % -4.482 as the average of these coefficients. The expression substituting these values is shown in expression (5 ) . y = 3 . 9 1 0 ~ 0 ~ h ~ -4.482 ( 5 ) ( 3 . 3 Under the conditions of this experiment, the characteristics of humans passing are as follows. Man always moves almost at a constant velocity. 0 The avoidance locus which is best approximated to the catenary is generated" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003880_j.tcs.2010.03.006-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003880_j.tcs.2010.03.006-Figure1-1.png", "caption": "Fig. 1. (a) Photo of a Kobot. (b) Scaled drawing of a Kobot illustrating the circular body, wheels, placement of the sensors and range for the second sensor. The sensors are placed uniformly at 45\u25e6 intervals. Each square patch in the grayscale blob indicates the output of the sensor averaged over 200 samples. A white plastic stick with a diameter of 2 cm is used as the target. Darker colors denote higher values of sensor measurement. Source: Images are taken from [22].", "texts": [ " The rest of the paper is organized as follows. The experimental platforms used are introduced in Section 2. In Section 3, we describe our flocking behavior. Section 4 presents our experimental framework. The metrics utilized are described in Section 5. Section 6 introduces four factors that influence long-range migration of flocks. The experiments are presented in Section 7, and finally, Section 8 concludes the paper. A Kobot is a CD-sized, differentially driven and power efficient robot platform weighing only 350 g with batteries (Fig. 1(a)). The robot has eight infrared (IR) sensors around its body that can sense nearby robots and obstacles, and is equipped with a digital compass placed on top of a plastic mast. The communication among robots as well as between the robots and a console is carried out through a wireless communication module with a range of approximately 20 m indoors. The infrared short-range sensing sub-system (IRSS) uses modulated infrared signals to measure the range and bearing of other robots in close proximity. It consists of eight IR sensors placed uniformly at 45\u25e6 intervals, as shown in Fig. 1(b), and a main sensor controller. Each sensor is capable of measuring distances up to 20 cm at seven discrete levels at a rate of 18 Hz. The output of the kth sensor is an integer pair (rk, ok). The type of the detected object is denoted with rk \u2208 {0, 1}, where 0 stands for obstacles and 1 stands for robots, which are the neighboring robots in close proximity and sensed by the IRSS. The distance from the object being sensed is represented by ok \u2208 {0, 1, . . . , 7}. The value of ok increases as the distance gets closer such that a nearby object is indicated as ok = 7" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003779_0369-5816(65)90138-9-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003779_0369-5816(65)90138-9-Figure5-1.png", "caption": "Fig. 5. Notation for cylindrical part of shell", "texts": [], "surrounding_texts": [ "and is bounded by the i n t e r s e c t i ons of th i s cy l i n - de r with the plane m x = 0 and the p l anes\n2 n 0 - n x = ~ l . (7)\nThe faces IV and V l ie on the p a r a b o l o i d s\nm x = :~\u00bd [2 - ( 2 n 0 - 1) 2 - ( 2 n 0 - 2 n x - 1) 2] . (8)\nThis y ie ld locus has the o r ig in of coo rd ina t e s as a c en t e r of s y m m e t r y . I t has uniquely d e t e r - mined suppor t ing p lanes at a l l po in ts except those on the p a r a b o l i c a r c s (4) and (5), the s e g - ment CD, and the poin ts obtained f rom these by s y m m e t r y with r e s p e c t to the or igin .\nAn exact y ie ld locus for a sandwich she l l , if M 0 and N O a r e t aken to r e p r e s e n t the y ie ld m o - ment and the y ie ld fo rce of the sandwich she l l , was d e s c r i b e d by Hodge [9] and is shown in fig. 2. If, however , M 0 and N O a r e given the va lues c o r r e spond ing to a so l id she l l , th is po lyhedron r e p r e s e n t s an approx ima t ion to the exact y ie ld locus of fig. 1. The c o r r e spond ing f a c e s of the po lyhedron l ie in the fol lowing p lanes :\nface I n O = 1\nII n O - n x = 1\nH I n x - m x = - 1\nI V 2 n 0 - n x + m x = 2\nV 2 n 0 . n x - m x = 9\n(9)\nface I nO = 1\nII n O - n ~ o = 1\nIII m ~ o = l\ni v n \u00a2 = 1\nOther p l anes can be obtained by s y m m e t r y with r e s p e c t to the or ig in .\nTh is y i e l d su r f ace was f i r s t p r o p o s e d by D ruc ke r and Shield [11] for ro ta t iona l ly s y m m e t - r i c she l l s . I t can a lso be obtained for cy l i nd r i ca ! she l l s by e l imina t ing rn 8 f rom the Hodge \" twomoment l i m i t e d - i n t e r a c t i o n \" su r face [18]; i t i s r e f e r r e d to a s a \"one -momen t l i m i t e d - i n t e r a c - t ion\" y ie ld sur face .\nThis hexagonal p r i s m is much s i m p l e r but is by no means as good a f i t at some points . 1 R e - ducing a l l i t s v e r t i c e s by the f ac to r \u00bd(5~,- 1) p r o d u c e s an i n s c r i b e d y ie ld sur face . A t h r e e - q u a r t e r s i ze p r i s m , however , l i e s within the a c -\nAnother approx ima t ion to the y ie ld su r face i s shown in fig. 3. Th is y ie ld condi t ion i s defined by the fo l lowing eight p l anes :", "E4 AXISYMMETRIC INTERSECTING SHELI.~ OF REVOLUTION 89\ntual y ie ld su r f ace ove r an extended range of v a l - ues of p r a c t i c a l i n t e r e s t for p r e s s u r e v e s s e l s .\n3. APPLICATION OF THE THEORIES TO INTERSECTING SHELLS\nIn o r d e r to be able to make use of the y ie ld loci for i n t e r s ec t i ng she l l s as r e p r e s e n t e d in sec t ion 2, some approx ima t ions to the shel l conf igura t ion mus t be in t roduced. Although the fo l - lowing a rgumen t holds t rue for any she l l of r e v o - lution, we r e s t r i c t o u r s e l v e s to the spec ia l c a se of a r a d i a l out let f rom a s p h e r i c a l she l l subjec t to in te rna l p r e s s u r e as shown in fig. 4.\nF o r the c y l i n d r i c a l p a r t of the she l l , the equat ions of equ i l ib r ium, with the notat ion of f ig. 5, a r e given by:\ndQ NO dMx + - - r = P ' dx - Q ' N x = \u00bdpr \" (10)\nF o r N o = const the in teg ra t ion of eq. (10) y i e ld s to\n(11) M x = \u00bd( , - ~ - ) x ' 2 + A x , B .\nThe constants A and B can be evaluated using any suitable stress distribution, provided this assumed stress field nowhere exceeds any of the chosen yield surfaces of section 2, e.g.\n/\na t x = l , Q = 0 , M x = M c , N o = N c , (12) a t x : 0 , Q : Q ' , M x : M ' c , NO : N c . T where Mc, M c, N c a r e the a p p r o p r i a t e va lues of the m o m e ~ s and t h ru s t on the y ie ld sur face .\nS i m i l a r l y for the s p h e r i c a l p a r t of the she l l , equ i l ib r ium equat ions with the notat ion of fig. 6 become\"\nN 0 sinq~ + Q cosq~= \u00bdPR sinq) ,\ns i n e + N 0 sin~0 + d~(Q s i n g ) = p R s i n ~ , (13) N, dM\u00a2 de sin(p + (Mq) -Mo)cosq ) - Q R sinq) = 0 .\nIn o r d e r to mee t the r e q u i r e m e n t s govern ing the use of the y ie ld su r face , MO must be e l i m i - nated f rom the t h i rd equation. Two poss ib l e ways of achieving th is may be dev i sed by set t ing:\na) M O = 0 , (14)\nb) MO = M~o \u2022 (15)\nIn t roduct ion of the condi t ion (14) in the equ i - l i b r i um equat ions (13) and in tegra t ing l eads to:\nQ = (\u00bdPR -No)cp + C ,\n=R(\u00bdPR .-N0)(1 - \u00a2 cot q)) - CR cot ~o + ~ (16) Mq)\nNq~ = \u00bdPR - (\u00bdPR - NO)(p cot \u00a2 - C cot ~0 .\nS imi l a r l y , by in se r t i ng condit ion (15) in eq. (13) and in tegra t ing , we obtain:", "Q = (\u00bdiPR -No)~o + C ,\nMq~ = [\u00bd(~R -No)q~2 +Cq)]R + D , (17)\nN~o = ~OR - (~PRI \"No) s~ + sin~C\nHere too, the integration is performed under the condition that circumferential membrane forces are constant. By invoking a suitable stress field, the constants C and D may be evaluated thus:\na t q ~ = / 3 , Q=O , Mq~=Ms, N O = N s , (18) at~o = a , Q = Q\" Mq~ ' , = M s , N O = N s \u2022\nwhere Ms, Ms, N s lie on the yield surface. Satisfying force and moment equilibrium at the sphere-cylinder junction leads to an expression for the collapse pressure in terms of the shell geometry. As described in section 1, however, this will establish only a \"lower bound\" on the collapse pressure, provided approprmte inequalities on M~o(Mx) , Nq)(Nx) and NO, depending upon the yield surfaces of section 2, are satisfied. The results thus obtained are restr icted to those shell configurations where the assumed s t ress profile, NO= const, and conditions (14) or (15) can be imposed.\nBy choosing his boundary conditions to satisfy face I of the yield surface of fig. 1 and the set of eq. (16), Lind [19] has been able to establish such a collapse pressure. The complexity of the equations obtained makes it necessary to use a trial and e r ro r procedure. Gill [20], on the other hand, by taking face I of the hexagonal pr ism yield locus of fig. 3, in association with the boundary conditions (12) and (18) and the set of eq. (17), arr ives at a fairly simple expression for the collapse pressure. The solution by Cloud [21] may also be derived as a particular case of Gill 's expression for the collapse load.\nAn upper bound on the collapse pressure can be found by equating the external rate of doing work to the internal rate of energy dissipation for a kinematically admissible pattern of three hinge circles. A velocity field of the form\nU= c[1-cos(E-q)] , W= -csin(~-\u00a2)\nsatisfies these hinge conditions. Here too, the contribution of M 0 to the work equations, in spite of the change of the circumferential curvature, must be neglected. Gill has attempted such a procedure, but instead of minimizing the parameters which locate the positions of the hinge c i r -\ncles in the work equation, has taken them from the so-called lower bound solution.\n4. DISCUSSION\nIn the previously described approximate theories of rotationally symmetric shells, based upon neglecting entirely the circumferential moment M 8 in both the yield condition and equilibrium equations, the solutions are reliable only for those regions of the shell some distance from the axis of revolution. Moreover, the assumption that there is no interaction between meridianal moment M~ and membrane forces NO and N~, makes the approximations more unrealistic. For instance, in the case of the yield surface comprising a circumscribed hexagonal prism, the upper bound (or kinematic t h e o r e m ) c l e a r l y gives an upper bound on the collapse pressure. On the other hand, merely satisfying equilibrium with such a circumscribed yield surface gives an approximate result which cannot be identified either as a lower or an upper bound. Fur thermore, the elimination of M 0 from the equations representing the yield surface, makes it dubious whether the flow rule, following from the identity of plastic potential and yield surface, could be applied to geometrical entities obtained as a r e - sult of operations performed.\nSo long as large factors of safety are used, the approximate solutions described above are satisfactory for design purposes. As the r e - quirements of high pressures and economy of design become more stringent, however, the needs for more exact analyses are pressing. In order to achieve such solutions, consideration must be given to certain .aspects of the problem. It was shown that the yield surface for a cylindrical shell is, in general, non-linear, even though the yield condition may be piecewise linear (Tresca). The same applies to the shell configuration. The ambiguities of the solutions arise from this non-linear characterist ic and one method of recovering a piecewise linear problem is to approximate the uniform shell to an idealized sandwich shell. Another method is by a piecewise linear approximation to the yield surface.\nThe current investigations are concerned with establishing proper bounds to the intersecting shell problem by considering the approaches described above. Comparisons between existing approximate theories should be made in order to guide the designer in choosing appropriate solutions by delineating their ranges of validity." ] }, { "image_filename": "designv11_32_0000161_s0007-8506(07)61130-5-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000161_s0007-8506(07)61130-5-Figure2-1.png", "caption": "FIGURE 2 Example of Conventional System", "texts": [], "surrounding_texts": [ "Keynote Papers\ncation Power Oriented Electronic\nMechatronics and Asks\nJack Dinsdale (1). University of Dundee, Scotland/UK and Kazuo Yamazaki, Toyohashi University of Technology/Japan\nActuators\nThe 1950 decade saw t h e s t a r t o f a m a j o r i n c r e a s e i n t h e use o f e l e c t r o n i c s , and s u b s e q u e n t l y computers, i n t h e c o n t r o l o f machines and i n p a r t i c u l a r o f p r o d u c t i o n mach ine ry . T h i s concep t o f an i n t e r - d i s c i p l i n a r y app roach t o machine t e c h n o l o g y has been termed M e c h a t r o n i c s . r e f e r r i n g t o an i n t e g r a t e d d i s c i p l i n e wh ich s y s t e m a t i c a l l y combines f i n e mechan ica l e n g i n e e r i n g w i t h e l e c t r o n i c s and computer c o n t r o l . K i t h i n t h e 1980 decade, t h e d e s i g n o f i n c r e a s i n g l y complex ne tworks u s i n g s t a n d a r d semiconduc to r d e v i c e s has been augmented by t h e i n t r o d u c t i o n o f t h e A S I C ( A p p l i c a t i o n S p e c i f i c I n t e g r a t e d C i r c u i t ) wh ich enab les c i r c u i t d e s i g n e r s t o c o n f i g u r e indiv-1 ne tworks o n t o b a s i c i n t e g r a t e d c i r c u i t s f o r s p e c i f i c a p p l i c a t i o n s . T h i s paper d i s c u s s e s t h e background t o t h e i n t r o d u c t i o n and development o f b o t h m e c h a t r o n i c s and A S I C S , a c o m b i n a t i o n now r e f e r r e d t o as su e r m e c h a t r o n i c s . g i v i n g examples o f a p p l i c a t i o n s r e l e v a n t t o m a n u f a c t u r i n g techno logy , and i : d rca t i ng l i k e l y moves i n t h e f u t u r e .\nKeywords: M e c h a t r o n i c s . c o n t r o l , s o f t w a r e s e r v o , e n g i n e e r i n g e d u c a t i o n . semiconduc to rs , i n t e g r a t e d c i r c u i t s , semi-custom I C , f u l l - c u s t o m I C . A S I C .\n1. I n t r o d u c t i o n\nInterfaces : Circuit\nThe s u b j e c t f i e l d o f machine systems, r a n g i n g f r o m complex m a n u f a c t u r i n g mach ine ry t o mass-produced consumer p r o d u c t s , i s e x p e r i e n c i n g two f a r - r e a c h i n g r e v o l u t i o n s . The f i r s t m a j o r change i s concerned w i t h t h e t e c h n o l o g i c a l make-up o f machines. U n t i l 40 y e a r s ago mach ine ry was a l m o s t e n t i r e l y mechan ica l i n n a t u r e ( a c c e p t i n g t h e p resence o f e l e c t r i c o r h y d r a u l i c m o t o r s as p r i m e movers ) ; c o n t r o l systems and d i s p l a y s were a l s o mechan ica l i n n a t u r e , f r e q u e n t l y u s i n g i n g e n i o u s mechanisms t o a c h i e v e t h e d e s i r e d r e s u l t s . However. t h e i n c r e a s i n g use o f e l e c t r o n i c s i n i n d u s t r i a l c o n t r o l systems, g r e a t l y a c c e l e r a t e d by t h e i n t r o d u c t i o n o f semiconduc to rs i n t h e 1 9 5 0 ' s , and t h e adven t o f f a s t , r e l i a b l e e l e c t r o n i c d i g i t a l computers i n t h e 196O's/7O1s. have caused machine d e s i g n t o become h i g h l y m u l t i - d i s c i p l i n a r y i n n a t u r e , w i t h mechan ica l e n g i n e e r i n g comb in ing w i t h e l e c t r o n i c s and computer c o n t r o l i n a c l o s e l y i n t e g r a t e d way t o c o n c e i v e and d e v e l o p p r o d u c t s and p rocesses wh ich would n o t have been p o s s i b l e w i t h o u t such a m u l t i - d i s c i p l i n a r y approach. The t e r m c o i n e d f o r t h i s approach t o machine d e s i g n i s m e c h a t r o n i c s , a l t h o u g h i t has t o be s a i d t h a t v e r y few e n g i n e e r s a r e f u l l y aware e i t h e r o f i t s e x i s t e n c e o r i t s s i g n i f i c a n c e .\nThe e v o l u t i o n o f i n c r e a s i n g l y s o p h i s t i c a t e d l e v e l s o f e l e c t r o n i c and computer c o n t r o l has encouraged t h e d e s i g n o f semiconduc to r d e v i c e s ( c h i p s ) o f g r e a t c o m p l e x i t y , i n c l u d i n g p r o c e s s o r s c a p a b l e o f b e i n g programmed w i t h s o f t w a r e wh ich can i t s e l f adap t a u t o m a t i c a l l y t o chang ing l o c a l c o n d i t i o n s , However, t h e l a s t few y e a r s have seen an i n t e r e s t i n g m u t a t i o n o f t h i s t r e n d o f development : r a t h e r t h a n p r o l i f e r a t e g e n e r a l - p u r p o s e d e v i c e s o f e v e r - i n c r e a s i n g c o m p l e x i t y , d e v i c e d e s i g n e r s have p r o v i d e d machine c o n t r o l e n g i n e e r s w i t h a range o f semiconduc to r c h i p s wh ich can be c o n f i g u r e d t o s u i t t h e s p e c i f i c a p p l i c a t i o n i n hand. The d e s i g n o f semiconduc to r c h i p a r c h i t e c t u r e i s a h i g h l y s p e c i a l i s e d a c t i v i t y wh ich wou ld n o t g e n e r a l l y be t a c k l e d by t h o s e concerned w i t h t h e d e s i g n and development o f machine systems o r t h e i r c o n t r o l l e r s . However, t h e A S I C ( A p p l i c a t i o n S p e c i f i c I n t e g r a t e d C i r c u i t ) c h i p a v o i d s t h i s d i f f i c u l t y by p r o v i d i n g a l a r g e number o f b a s i c semic o n d u c t o r e lemen ts : a m p l i f i e r s , ga tes , s w i t c h e s , l o g i c e lemen ts , memories, e t c and i n v i t i n g t h e machine d e s i g n e r t o s p e c i f y t h e \" o v e r l a y \" wh ich w i l l i n t e r - c o n n e c t as many o f t h e s e b a s i c e lemen ts as a r e r e q u i r e d t o p r o v i d e t h e c o n t r o l o r f u n c t i o n s needed.\nMechanical MicroProcessor Based Logic Unit :\nMemory Standard\n- Digital I/O Signal Analog 1/0 Circuit Conditioning - Sensors\nG e n e r a l l y n o t a l l o f t h e e lemen ts w i l l be used i n any g i v e n a p p l i c a t i o n . T h i s app roach a l s o has t h e m a j o r advantages f i r s t l y t h a t t h e i n i t i a l uncus tomised A S I C c h i p i s common t o a l a r g e number o f customers and a p p l i c a t i o n s . hence e n a b l i n g t h e c o s t t o be k e p t l ow ; s e c o n d l y t h a t t h e o v e r l a y can sometimes be des igned such t h a t any f a u l t y e lemen ts i d e n t i f i e d on t e s t w i l l n o t a f f e c t t h e o v e r a l l A S I C per formance; and t h i r d l y t h a t f a r g r e a t e r commerc ia l s e c u r i t y i s a v a i l a b l e t h a n w i t h a r e g u l a r ne twork o f s t a n d a r d g e n e r a l - pu rpose c h i p s - a c o m p e t i t o r can g e n e r a l l y deduce t h e comp le te c i r c u i t d e t a i l s o f a p r i n t e d c i r c u i t c a r d s t u f f e d w i t h g e n e r a l - p u r p o s e c h i p s . whereas an A S I C p r e s e n t s a secu re ne twork wh ich canno t be p i r a t e d because a l l o f t h e i n t e r c o n n e c t i o n d e t a i l l i e s w i t h i n t h e s i l i c o n s t r u c t u r e .\nT h i s Keynote Paper d i s c u s s e s i n some d e t a i l t h e e v o l u t i o n o f b o t h M e c h a t r o n i c s and ASICs and i n d i c a t e s l i k e l y f u t u r e developments i n b o t h t e c h n o l o g i e s .\nSystem\n2 M e c h a t r o n i c s D e f i n i t i o n s\nM e c h a t r o n i c s combines t h e words Mechanics and E l e c t r o n i c s . I t can be d e f i n e d as : \" a c o m b i n a t i o n o f mechan ica l e n g i n e e r i n g , e l e c t r o n i c c o n t r o l and systems e n g i n e e r i n g i n t h e d e s i g n o f p r o d u c t s and p rocesses\" . Examples o f m e c h a t r o n i c systems a r e i n t e l l i g e n t machines such as advanced i n d u s t r i a l r o b o t s , a u t o m a t i c g u i d e d v e h i c l e s ( A G V s ) and compu te r - c o n t r o l l e d m a n u f a c t u r i n g machines. A l s o consumer e l e c t r o n i c s , l i k e t h e compact d i s c , cameras w i t h e l e c t r o n i c f u n c t i o n s and q u a r t z watches a r e p r o d u c t s f o r wh ich a m e c h a t r o n i c d e s i g n i s e s s e n t i a l . Common t o a l l t hese systems i s t h e s t r o n g i n t e r a c t i o n o f a l l t h e d i s c i p l i n e s i n v o l v e d , i n t h e d e s i g n as w e l l as i n t h e p r o d u c t i o n phase. W i t h a m e c h a t r o n i c d e s i g n p r o d u c t s can be r e a l i z e d which, i n each o f t h e d i s c i p l i n e s a lone , may be d i f f i c u l t o r even i m p o s s i b l e t o r e a l i z e . The r e s u l t i s a p r o d u c t w i t h s u p e r i o r s p e c i f i c a t i o n s . The word ' m e c h a t r o n i c s ' was o r i g i n a l l y c o i n e d more t h a n t e n y e a r s ago by t h e Japanese M i n i s t r y f o r Trade and I n d u s t r y ( M I T I ) by wh ich was meant \" t h e a p p l i c a t i o n o f m i c r o e l e c t r o n i c s i n mechan ica l e n g i n e e r i n g \"\nA c c o r d i n g t o I R O A C . t h e I n d u s t r i a l Research and Development A d v i s o r y Commrttee o f t h e Furopean tominuni ty (EC), t h e t e r m M e c h a t r o n i c s r e f e r s t o a s y n e r g i s t i c c o m b i n a t i o n o f p r e c i s i o n mechan ica l e n g i n e e r i n g , e l e c t r o n i c c o n t r o l and systems t h i n k i n g - -\nFIGURE 1 General Configurotion of Mechotronics System Hordwore.\nAnnals of the ClRP Vol. 38/2/1989 627", "i n t h e d e s i g n o f p r o d u c t s and m a n u f a c t u r i n g p r o c e s s e s . I t i s an i n t e r d i s c i p l i n a r y s u b j e c t t h a t d raws on t h e c o n s t i t u e n t d i s c i p l i n e s and i n c l u d e s s u b j e c t s n o t n o r m a l l y a s s o c i a t e d w i t h any one o f t h o s e above\" . The m e c h a t r o n i c s p h i l o s o p h y i s t h u s a m u l t i - d i s c i p l i n a r y d e s i g n a p p r o a c h based on sys tems a n a l y s i s , m o d e l l i n g and c o n t r o l .\nM o s t t y p i c a l mach ines c a n be c o n s t r u c t e d u s i n g f i v e m a j o r f u n c t i o n a l subsys tems[4 ] a s f o l l o w s :\n- Advanced c o n t r o l and i n f o r m a t i o n subsys tems - I n t e r c o n n e c t i o n subsys tems based on p r e d e f i n e d\n- Sensor subsys tems w i t h t h e a b i l i t y t o e x t r a c t\n- A c t u a t o r subsys tems t o t r a n s f o r m e n e r g y s u p p l i e s\n- Mechan isms t o c a r r y o u t t h e work on t h e\nA number o f m a t e r i a l , e n e r g y and i n f o r m a t i o n p r o c e s s e s a r e u s u a l l y p r e s e n t i n a l l m e c h a t r o n i c sys tems ; a t y p i c a l g e n e r a l r e p r e s e n t a t i o n o f a m e c h a t r o n i c s y s t e m i s shown i n f i g u r e 1. I n t h e c a s e o f i n f o r m a t i o n p r o c e s s e s , i n f o r m a t i o n c a n o n l y be s t o r e d o r t r a n s - m i t t e d a s an a t t r i b u t e o f e i t h e r m a t e r i a l ( f o r examp le , p r i n t on p a p e r ) o r e n e r g y ( f o r example , e l e c t r o m a g n e t i c waves ) . M o s t o f t h e s i g n i f i c a n t advances i n m e c h a t r o n i c sys tems have been due t o t h e c o n t i n u o u s d e v e l o p m e n t o f i n f o r m a t i o n p r o c e s s e s r e q u i r i n g e v e r d e c r e a s i n g a s s o c i a t e d masses and e n e r g i e s .\nOne o f t h e m o s t i m p o r t a n t f e a t u r e s o f t h e m e c h a t r o n i c s s y s t e m i s t h e f l e x i b l e c o m b i n a t i o n o f a s i m p l e mechan ism w i t h a s o p h i s t i c a t e d c o n t r o l sys tem. F i g u r e 2 i s an examp le o f a c o n v e n t i o n a l mechan ism f o r c o n t r o l l i n g m u l t i - a x i s m o t i o n [ ~ o J . A g e a r t r a i n i s u s u a l l y emp loyed , w i t h i t s d e s i g n based on a s p e c i f i c a t i o n such as r o t a t i o n a l speed, d i r e c t i o n and t o r q u e . The o u t p u t p e r f o r m a n c e i s d e t e r m i n e d b y t h e m o t o r r a t i n g and t h e p a r a m e t e r s o f a p a r t i c u l a r s e t o f g e a r s . T h i s c o n v e n t i o n a l c o n f i g u r a t i o n i s a c c e p t a b l e i n s i t u a t i o n s when a f i x e d i n p u t / o u t p u t r e l a t i o n s h i p i s r e q u i r e d . However . i n c a s e s where a v a r i a b l e r e l a t i o n s h i p i s d e s i r e d , i t i s n e c e s s a r y t o have a c o n t r o l s y s t e m whose f u n c t i o n i s e q u i v a l e n t t o t h e i n s t a n t a n e o u s g e n e r a t i o n o f a new s e t g e a r t r a i n s . F i g u r e 3 shows an examp le o f a s o l u t i o n t o w h i c h\np r o t o c o l s\nu s e f u l i n f o r m a t i o n\ni n t o u s e f u l work\nd e s i r e d p r o c e s s e s .\nA2 I-\nFIGURE 3 Example of Mechatronics System\nm e c h a t r o n i c s t e c h n o l o g y c a n c o n t r i b u t e . I n s t e a d o f h a v i n g a p h y s i c a l g e a r t r a i n , each a x i s i s e q u i p p e d w i t h a m o t o r w h i c h c a n be d i r e c t l y c o n t r o l l e d b y an e l e c t r o n i c c o n t r o l sys tem. The s y s t e m f e a t u r e s a s i m p l i f i e d mechan ism w h i c h e l i m i n a t e s t h e complex g e a r t r a i n and p r o v i d e s a h i g h e r f l e x i b i l i t y o f m o t i o n c o n t r o l w i t h a n e l e c t r o n i c c o n t r o l sys tem. The c o n t r o l s y s t e m now i s m i c r o p r o c e s s o r based and any r e q u i r e d m o t i o n o f t h e mechan ism c a n be programmed wi;h s o f t w a r e . a m e c h a t r o n i c s c o n t r o l sys tem' ' o r \" m e c h a t r o n i c s c o n t r o l l e r \" . o f t e n r e f e r r e d t o a s an e l e c t r o n i c g e a r b o x \" , has been d e s c r i b e d b y D i n s d a l e e t a1 L8).\n3 M e c h a t r o n i c s Sys tems D e s i g n\nD e s i g n i s a c o m b i n a t i o n o f a r t , s c i e n c e and mathemat i c s , and a s s y s t e m c o m p l e x i t y i n c r e a s e s i t becomes n e c e s s a r y t o i n c r e a s e t h e s c i e n t i f i c i n p u t b y r e s e a r c h i n g new t h e o r i e s and r e l a t i o n s h i p s w h i c h encompass as much as p o s s i b l e o f t h e w h o l e sys tem.\nD e s i g n has been d e f i n e d b y C o n n o l l y [4) as\n\" t h e i n i t i a t i o n o f change i n man made t h i n g s \" .\nand t h e o b j e c t i v e s o f d e s i g n i n g a r e o f t e n l e s s c o n c e r n e d w i t h t h e p r o d u c t i t s e l f and more c o n c e r n e d w i t h t h e changes t h a t m a n u f a c t u r e r s , d i s t r i b u t o r s , u s e r s and s o c i e t y as a w h o l e a r e e x p e c t e d t o make, i n o r d e r t o b e n e f i t f r o m t h e new d e s i g n .\nM o s t m a c h i n e d e s i g n i s e m p i r i c a l , and r e l i e s h e a v i l y on m o d i f y i n g p r e v i o u s mach ines t o a c h i e v e h i g h e r p e r f o r m a n c e .\nT h i s c o n t r o l s y s t e m i s u s u a l l y named\nA p r a c t i c : l embod iment o f t h i s scheme,\nI n new f i e l d s l i k e m e c h a t r o n i c s t h e r e a r e f e w e r ' r u l e s o f thumb ' t o go by , p a r t i c u l a r l y i n e l e c t r o n i c s , and even t h o u g h t h e f i r s t s i n g l e c h i p m i c r o p r o c e s s o r s were i n t r o d u c e d i n 1971. t h e d e s i g n o f m i c r o p r o c e s s o r based sys tems i s s t i l l l a r g e l y based on p r a c t i c a l e x p e r i e n c e .\nAny s y s t e m m u s t p e r f o r m b o t h e f f e c t i v e l y and e f f i c i e n t l y , and c o n s e q u e n t l y compromises m u s t be made be tween :\n- p e r f o r m a n c e and p h y s i c a l p a r a m e t e r s l i k e d e l i v e r y r a t e s , c a p a c i t y , a c c u r a c y , r e p e a t a b i l i t y . p r e c i s i o n , speed, e n e r g y o u t p u t , s i z e , e t c .\n- o p e r a t i o n a l and s u p p o r t f e a t u r e s such a s manmach ine i n t e r f a c e , a v a i l a b i l i t y . d e p e n d a b i l i t y , r e l i a b i l i t y , m a i n t e n a n c e , m o b i l i t y , p o r t a b i l i t y , p r o g r a m m a b i l i t y , e t c\n- economic f a c t o r s s u c h a s i n i t i a l c o s t , o p e r a t i n g c o s t ( i n c l u d i n g e n e r g y c o n s u m p t i o n ) , l i f e c y c l e c o s t , e t c .\nI n t h e d e s i g n s t a g e , e v e r y e f f o r t i s made t o a c h i e v e an op t imum b a l a n c e be tween p e r f o r m a n c e , o p e r a t i o n a l and c o s t f a c t o r s , and i t i s e s s e n t i a l t h a t a d e q u a t e a n a l y s i s i s c a r r i e d o u t a t t h e e a r l y s t a g e s t o m i n i m i z e any u n c e r t a i n t i e s a b o u t t h e s e f a c t o r s . Hence. d e s i g n has a l s o been d e s c r i b e d a s \" t h e a r t o f i n t e l l i g e n t compromise\" .\n4 M e c h a t r o n i c s P e r s p e c t i v e\nW i t h h i n d s i g h t , i t c a n now be r e c o g n i s e d t h a t t h e t e r m M e c h a t r o n i c s a c k n o w l e d g e s a t r e n d i n m u l t i d i s c i p l i n a r y d e s i g n p h i l o s o p h y b e g i n n i n g many y e a r s ago and a c c e l e r a t i n g m a r k e d l y d u r i n g t h e 1980 decade. T h i s t r e d i s w e l l i l l u s t r a t d i n f i g u r e 4 ( a f t e r Yamazaki [ 2 O g and van B r u s s e l (89 w h i c h shows how t h e s t e a d y i n c r e a s e i n mach ine e n g i n e e r i n g t h i s c e n t u r y i n i t i a l l y i n v o k e d o n l y m e c h a n i c a l e l e m e n t s ( t h e t e c h n o l o g i e s o f e l e c t r i c a l and e l e c t r o n i c e n g i n e e r i n g were s t i l l i n t h e i r embryo s t a g e s ) . However , f r o m t h e l a t e 1 9 4 0 ' s t h e m e c h a n i c a l e n g i n e e r i n g scene began t o be s h a r e d b y e l e c t r i c s and e l e c t r o n i c s , a l b e i t h a r d w a r e o n l y , and m a c h i n e s w e r e c o n t r o l l e d a t t h a t t i m e b y h t r d - w i r e d e l e c t r o n i c c o n t r o l l e r s r e p r e s e n t i n g t h e g e n e r a t i o n o f m e c h a t r o n i c s . The compu te r , t h o u g h a l r e a d y i n v e n t e d , was y e t t o become s u f f i c i e n t l y d e v e l o p e d and r e l i a b l e , and i t d i d n o t p l a y any f i r s t\ns i g n i f i c a n t p a r t i n i n d u s t r i a l e n g i n e e r i n g u n t i l t h e e a r l y 1 9 7 0 ' s . when t h e r o l e s p r e v i o u s l y a d o p t e d b y e l e c t r o - m e c h a n i c a l h a r d w a r e began t o be r e p l a c e d by compu te r s o f t w a r e , r e p r e s e n t i n g t h e \"second G e n e r a t i o n o f m e c h a t r o n i c s \" . T h i s t r e n d i s c o n t i n u i n g : w i t h t h e s t e a d y d e v e l o p m e n t o f g e n e r a l - p u r p o s e c o m p u t e r p r o c e s s o r s and s o f t w a r e a t i n c r e a s i n g l y a t t r a c t i v e p r i c e s , t h e r e m a i n i n g a r e a s o f e l e c t r o - m e c h a n i c a l l y p rogrammed c o n t r o l a r e g i v i n g way t o t h e more v e r s a t i l e , a d a p t a b l e and c o s t - e f f e c t i v e f i e l d o f s o f t w a r e c o n t r o l . F i g u r e 4 a l s o shows t h e i n t r o - d u c t i o n o f t h e A S I C ( A p p l i c a t i o n S p e c i f i c I n t e g r a t e d C i r c u i t ) w i t h i n t h e l a s t f e w y e a r s , w h i c h i s p r o v i d i n g a r e t u r n t o t h e c u s t o m i s e d h a r d w a r e , a l b e i t c o m b i n i n g m e c h a n i c a l , e l e c t r i c a l and e l e c t r o n i c e n g i n e e r i n g w i t h b o t h h a r d w a r e and s o f t w a r e a t t r i b u t e s , t h a t t h e o r i g i n a l t r e n d away f r o m d e d i c a t e d , c u s t o m i s e d . m e c h a n i c a l h a r d w a r e s t a r t i n g i n t h e 1 9 5 0 ' s a p p e a r e d t o be f o r s a k i n g , t h e \" t h i r d g e n e r a t i o n o f m e c h a t r o n i c s . I t wou ld , however , be v e r y wrong t o d i s m i s s m e c h a t r o n i c s as a c o n v e n i e n t c a t c h - a l l buzz -word , i n v e n t e d t o a s s i s t e m p i r e b u i l d e r s . L i k e w i s e , i t mus t n o t be assumed t h a t an a s s e m b l y o f m e c h a n i c a l . e l e c t r o n i c and c o m p u t e r s p e c i a l i s t s r e p r e s e n t s m e c h a t r o n i c s . The t r u e m e c h a t r o n i c s e n g i n e e r i s t h a t T h i s l a t e s t t r e n d may,,be d e s c r i b e d as\n628", "r a r e i n d i v i d u a l who has a g e n u i n e i n t e r e s t and a b i l i t y a c r o s s a w i d e r a n g e o f t e c h n o l o g i e s , and who t a k e s a d e l i g h t i n w o r k i n g a c r o s s d i s c i p l i n a r y b o u n d a r i e s t o i d e n t i f y and u s e t h e p a r t i c u l a r b l e n d o f t e c h n o l o g i e s w h i c h w i l l p r o v i d e t h e m o s t economic , e l e g a n t and a p p r o p r i a t e s o l u t i o n t o t h e p r o b l e m i n hand. F u r t h e r more , he i s a h i g h c o m m u n i c a t o r who has t h e knack o f b e i n g a b l e t o e n t h u s e o t h e r s a b o u t t e c h n o l o g i e s o u t s i d e t h e i r own, and hence t o b r e a k down b u i l t - i n r e s i s t a n c e t o t h e use o f a l t e r n a t i v e approaches . W i t h t h e o n g o i n g and i n c r e a s i n g momentum i n m u l t i - d i s c i p l i n a r y t h i n k i n g , c o u p l e d w i t h m a j o r changes i n t h e s t r u c t u r i n g o f d e g r e e c o u r s e s and o t h e r educat i o n a l modu les , i t i s becoming c l e a r t h a t t h e s u b j e c t g r o u p i n g embraced by m e c h a t r o n i c s i s a l r e a d y a m a j o r f o r c e i n t h e d e s i g n and r e a l i s a t i o n o f b o t h p r o d u c t s and p r o c e s s e s .\n5 M e c h a t r o n i c s E d u c a t i o n\nI t i s p r o b a b l y t r u e t h a t t h e m o s t u r g e n t t a s k f o r e d u c a t i o n a l i s t s , e s p e c i a l l y i n Europe and p a r t i c u l a r l y i n t h e UK, i s t o make e n g i n e e r s a t a l l l e v e l s aware o f t h e t e r m m e c h a t r o n i c s . i t s mean ing and i t s s i g n i f i - cance t o s o many a s p e c t s o f i n d u s t r y . A g a i n and a g a i n , compan ies w i l l d i s c u s s a d v e r t i s e m e n t s f o r m e c h a t r o n i c s c o u r s e s as b e i n g o f . a t t h e b e s t , p e r i p h e r a l i n t e r e s t t o them, when i t i s v e r y c l e a r t h a t t h e i r w o r k l i e s d i r e c t l y w i t h i n t h e m a i n s t r e a m o f t h i s s u b j e c t . Ye t i n d u s t r i a l i s t s who have been p e r s u a d e d (somet imes a g a i n s t t h e i r w i l l ) t o a t t e n d c o u r s e s o r become i n v o l v e d w i t h t h e s u b j e c t i n o t h e r ways, w i l l f r e q u e n t l y e x c l a i m a f t e r w a r d s t h a t p r e v i o u s l y t h e y were unaware o f t h e r e l e v a n c e o f t h e s u b j e c t t o t h e i r b u s i n e s s and even t o t h e i r c o m m e r c i a l s u r v i v a l . I t c a n be a r g u e d r u e f u l l y t h a t t h e c o i n i n g o f t h e t e r m m e c h a t r o n i c s has been a m i x e d b l e s s i n g , d e t r a c t i n g a s i t does f r o m t h e u n d o u b t e d i m p o r t a n c e i n t h e l a t e 2 0 t h c e n t u r y o f t h e c o m b i n a t i o n o f s u b j e c t s w h i c h i t r e p r e s e n t s and w h i c h a r e w e l l u n d e r s t o o d , a t l e a s t as i n d i v i d u a l s u b j e c t s .\nI n many c o u n t r i e s , Eu rope i n p a r t i c u l a r , t h e t r a d i - t i o n a l e t h o s o f e n g i n e e r i n g e d u c a t i o n and i n s t i t u t i o n s has been one o f t h e n a r r o w s p e c i a l i z a t i o n . C o n s i d e r t h e UK: t h e f i r s t p r o f e s s i o n a l e n g i n e e r i n g i n s t i t u - t i o n t o be f o r m e d was t h e I n s t i t u t i o n o f C i v i l E n g i n e e r s , f o u n d e d i n 1818. T h i s was f o l l o w e d i n 1847 b y t h e I n s t i t u t i o n o f M e c h a n i c a l E n g i n e e r s , e s t a b l i s h e d b y George S tephenson when he was d e n i e d e n t r y t o t h e C i v i l s on t h e g r o u n d s o f h i s n o t w o r k i n g i n t h e f i e l d o f c i v i l e n g i n e e r i n g . These were f o l l o w e d i n 1871 b y t h e I n s t i t u t i o n o f E l e c t r i c a l E n g i n e e r s and, s u b s e q u e n t l y , b y a p l e t h o r a o f b o d i e s , each s p e c i a l i s i n g i n a n a r r o w l y - d e f i n e d b r a n c h o f e n g i n e e r i n g . The e n g i n e e r i n g d e p a r t m e n t s i n u n i v e r s i - t i e s have f o l l o w e d a s i m i l a r e v o l u t i o n a r y r o u t e ; a l t h o u g h many were c o n c e i v e d i n i t i a l l y as d e p a r t m e n t s o f e n g i n e e r i n g , w i t h o n l y a f e w n o t a b l e e x c e p t i o n s t h e y have d e v e l o p e d i n t o s p e c i a l i s t d e p a r t m e n t s o f c i v i l e n g i n e e r i n g , m e c h a n i c a l e n g i n e e r i n g , e l e c t r o n i c s . c o m p u t e r s c i e n c e and many o t h e r s . F u r t h e r m o r e , e v e n t h o s e d e p a r t m e n t s w h i c h have m a i n t a i n e d t h e b r o a d e t h o s o f g e n e r a l e n g i n e e r i n g p r o m o t e f i n a l y e a r s p e c i a l i s a t i o n . s p e c i a l i s t s u b - g r o u p s . e t c . A g a i n s t t h i s b a c k g r o u n d t h e g e n e r a l s i t u a t i o n t o d a y i s t h a t a new r e s e a r c h t o p i c , b r a n c h o f t e c h n o l o g y , o r i n n o v a t o r y s u b j e c t w i l l p r o b a b l y o r i g i n a t e as t h e p r o v i n c e o f a s m a l l g r o u p ( s o m e t i m e s a s i n g l e i n d i v i d u a l ) w i t h i n a l a r g e r d e p a r t m e n t , g r a d u a l l y i n c r e a s i n g i n s i z e and r e s o u r c e s u n t i l i t c a n j u s t i f y t h e f o r m a t i o n o f a new s p e c i a l i s e d d e p a r t m e n t w h i c h t h e n s p l i t s o f f f r o m t h e p a r e n t g r o u p .\nThe w h o l e c o n c e p t o f m e c h a t r o n i c s i s d i f f e r e n t : i n s t e a d o f a new s p e c i a l i s e d s u b j e c t a r e a d e v e l o p i n g o u t o f a n e x i s t i n g d i s c i p l i n e , m e c h a t r o n i c s i s d r a w i n g t o g e t h e r e l e m e n t s o f e x i s t i n g s u b j e c t a r e a s . M e c h a t r o n i c s . t h e r e f o r e , c a n n o t be r e g a r d e d as a new s p e c i a l i s a t i o n b u t r a t h e r a s an i n t e g r a t i n g d i s c i p l i n e w h i c h opposes t h e t r a d i t i o n a l s t y l e o f academic d e v e l o p m e n t d e s c r i b e d above. N e v e r t h e l e s s , a t l e a s t i n t h e UK, t h e p r e s e n t d e m o g r a p h i c s i t u a t i o n w h i c h i s e x p e c t e d t o r e s u l t i n a 30% r e d u c t i o n i n u n i v e r s i t y s t u d e n t numbers be tween 1985 and 1995. a s a r e s u l t o f changes i n t h e b i r t h r a t e some 20 y e a r s ago, may w e l l f o r c e some e s t a b l i s h e d s p e c i a l i s t d e p a r t m e n t s o f m e c h a n i c a l e n g i n e e r i n g , e l e c t r o n i c s . c o m p u t e r s c i e n c e and o t h e r d i s c i p l i n e s t o merge t o g e t h e r i n o r d e r t o m a i n t a i n a v i a b l e n u c l e u s o f s t u d e n t s . I n t h i s event , and p r o v i d e d t h a t t h e t u t o r s and o t h e r s t a f f , , c o n c e r n e d a r e p r e p a r e d and a b l e t o \" t h i n k m e c h a t r o n i c s , 1 . e . t o seek p o s i t i v e l y f o r ways i n w h i c h t h e i r s u b j e c t s c a n b e s t be i n t e g r a t e d , t h e s e merged d e p a r t m e n t s c o u l d do c o n s i d e r a b l y worse t h a n a d d r e s s t h e b r o a d s u b j e c t o f m e c h a t r o n i c s . b o t h i n name and f u n c t i o n .\nS i n c e t h e e a r l y 1 9 8 0 ' s u n i v e r s i t i e s i n a number o f c o u n t r i e s have s t a r t e d t o i n t r o d u c e c o u r s e s and o t h e r a c t i v i t i e s i n t h e s u b j e c t . The f o l l o w i n g p a r a g r a p h s\nd e s c r i b e i n i t i a t i v e s known t o t h e a u t h o r s o f t h i s p a p e r .\nJapan\nPerhaps i n e v i t a b l y , t h e g r e a t e s t c o n c e n t r a t i o n o f work i n m e c h a t r o n i c s t o d a t e has stemmed f r o m t h e n a t i o n w h i c h c o i n e d t h e word . N e v e r t h e l e s s , o n l y one u n i v e r s i t y , T o y o h a s h i U n i v e r s i t y o f T e c h n o l o g y . has r e p o r t e d a r e g u l a r ME c o u r s e \" M e c h a t r o n i c s E n g i n e e r i n g \" w h i c h was e s t a b l i s h e d i n 1983. M o s t o t h e r e n g i n e e r - i n g d e p a r t m e n t s o f Japanese u n i v e r s i t i e s l a y c l a i m t o t e a c h i n g e l e m e n t s o f m e c h a t r o n i c s w i t h i n t h e i r c o u r s e s and a l s o t o c o n d u c t i n g r e s e a r c h i n t h i s f i e l d . C u r r e n t r e s e a r c h i s r e p o r t e d a t Tokyo I n s t i t u t e o f T e c h n o l o g y on t h e dynamic b e h a v i o u r o f i n f o r m a t i o n p r o c e s s i n g d e v i c e s , d e v e l o p m e n t o f a p r e c i s i o n x - y s t a g e , bonded s t r u c t u r e s f o r i n f o r m a t i o n p r o c e s s i n g d e v i c e s and s l i c i n g t e c h n o l o g y f o r s i l i c o n w a f e r s . A t Kobe U n i v e r s i t y , r e s e a r c h i s b e i n g c o n d u c t e d i n c o m p u t e r c o n t r o l o f r o b o t s , and dynamic and t h e r m a l sys tems , and a l s o t h e d e v e l o p m e n t o f v a r i o u s s e n s o r s and image p r o c e s s i n g . I n t e r e s t i n g l y , t h e v i e w o f Japanese e d u c a t i o n a l i s t s i s t h a t t h e m e c h a t r o n i c s e n g i n e e r i s e s s e n t i a l l y a m e c h a n i c a l e n g i n e e r whose e d u c a t i o n has been b r o a d e n e d t o i n c l u d e a good handson know ledge and a b i l i t y i n m i c r o p r o c e s s o r h a r d w a r e and s o f t w a r e , e l e c t r o n i c s , a c t u a t o r s and c o n t r o l .\nThe Japanese have a l s o i n s t i t u t e d m e e t i n g s d e d i c a t e d t o t h e p r o m o t i o n o f m e c h a t r o n i c s . The I n t e r n a t i o n a l C o n f e r e n c e on Advanced M e c h a t r o n i c s , h e l d i n Tokyo i n May 1989, c o v e r e d t h e w i d e s p e c t r u m f r o m f i n e mechan isms t o e l e c t r i c a l d e v i c e s , a l b e i t f r o m a w i d e r v i e w p o i n t t h a n t h a t a d o p t e d b y t h e I n t e r n a t i o n a l P r e c i s i o n E n g i n e e r i n g Semina rs o r g a n i s e d b y C r a n f i e l d I n s t i t u t e o f T e c h n o l o g y (UK) w i t h m e e t i n g s h e l d a t C r a n f i e l d ( 1 9 8 1 ) G a i t h e r s b u r g ( 1 9 8 3 ) I n t e r l a k e n ( 1 9 8 5 ) C r a n f i e l d ( 1 9 8 7 ) and s h o r t l y M o n t e r e y ( 1 9 8 9 ) . These l a t t e r m e e t i n g s have p r o v i d e d a c o m p r e h e n s i v e expose o f t h e p r e c i s i o n a s p e c t s o f m e c h a t r o n i c s , a l t h o u g h n o t s p e c i f i c a l l y i n v o k i n p t h i s te rm.\nUSA\nM e r c h a n t has commented r e c e n t l y t h a t a l t h o u g h many N. A m e r i c a n u n i v e r s i t i e s a r e w o r k i n g i n t h i s f i e l d , t h e r e a p p e a r t o be no c o u r s e s a t any l e v e l s p e c i f i c a l l y t i t l e d \" m e c h a t r o n i c s \" ; i n f a c t t h e d e s i g n a t i o n m e c h a t r o n i c s i s a l m o s t n e v e r used.\nEu rope\nSecond t o Japan, Eu rope a p p e a r s t o have embraced t h e s u b j e c t o f m e c h a t r o n i c s m o s t a c t i v e l y , w i t h p r o f e s s o r s ' c h a i r s , u n i v e r s i t y c o u r s e s a t a l l l e v e l s , r e s e a r c h programmes and i n d u s t r i a l s h o r t c o u r s e s ( c o n t i n u i n g e d u c a t i o n ) much i n e v i d e n c e . One o f t h e f i r s t u n i v e r s i t i e s t o t a c k l e t h e s u b j e c t was t h e K a t h o l i e k e U n i v e r s i t e i t Leuven (KUL B e l g i u m ) . P e t e r s and van B r u s s e l have d e s c r i b e d a o n e - y e a r p o s t g r a d u a t e c o u r s e o n t h e s u b j e c t w h i c h s t a r t e d i n 1986. T h i s was s o : u c c e s s f u l t h a t f r o m O c t o b e r 1989 an o p t i o n M e c h a t r o n i c s i n E l e c t r o - m e c h a n i c a l E n g i n e e r i n g \" w i l l commence i n t h e t h i r d y e a r o f t h e f i r s t - d e g r e e programme i n M e c h a n i c a l E n g i n e e r i n g , f o l l o w i n g two y e a r s o f b a s i c s c i e n c e . T h i s o p t i o n w i l l e x t e n d l a t e r t o t h e f o u r t h and f i f t h y e a r s . Worke rs a t KUL a r e a l s o v e r y a c t i v e i n m e c h a t r o n i c s r e s e a r c h . However, i t i s p o i n t e d o u t t h a t w h i l e many i n d u s t r i a l i s t s a r e n o t y e t f a m i l i a r w i t h t h e te rm. many compan ies have a l r e a d y i n t e g r a t e d i t i n t o t h e i r d e s i g n and m a n u f a c t u r i n g a c t i v i t i e s .\nA t t h e U n i v e r s i t y o f Twente , t h e N e t h e r l a n d s , Heuve lman has r e p o r t e d t h a t a l t h o u g h many c o u r s e s c a n be c o n s i d e r e d as c o n t r i b u t i n g t o t h e o v e r a l l m e c h a t r o n i c s s y l l a b u s , t h e r e i s no s i n g l e d e s i g n a t e d c o u r s e as such. The u n i v e r s i t y i s a c t i v e l y p u r s u i n g r e s e a r c h . i n c l u d i n g p a r a l l e l p r o c e s s i n g w i t h t r a n s - p u t e r s , f a s t l i n e a r m o t o r s . v i s i o n sys tems and d e s i g n m e t h o d o l o g y f o r m e c h a t r o n i c s sys tems a s a p p l i e d t o f a s t m a n i p u l a t o r s and l a s e r beam m a c h i n i n g . I m p o r t a n t l y . t h e U n i v e r s i t y o f Twente has r e c e i v e d ( 1 9 8 9 ) g o v e r n m e n t f u n d i n g f o r r e s e a r c h i n m e c h a t r o n i c s w h i c h h a s l e d t o t h e e t t a b l i s h m e n t o f t h e \" M e c h a t r o n i c s R e s e a r c h C e n t r e Twen te (MRCT) w h i c h w i l l c o - o r d i n a t e t h e m e c h a t r o n i c s a c t i v i t i e s o f t h e d e p a r t m e n t s o f E l e c t r i c a l E n g i n e e r i n g , M e c h a n i c a l E n g i n e e r i n g , A p p l i e d M a t h e m a t i c s and I n f o r m a t i c s .\nI n Denmark t h e D a n i s h T e c h n i c a l U n i v e r s i t y a g a i n o p e r a t e s c o u r s e s c o n t r i b u t i n g t o t h e s u b j e c t and a l s o p r e s e n t s a number o f s h o r t c o u r s e s f o r i n d u s t r y .\nRWTH Aachen. W Germany, is e s p e c i a l l y c o n c e r n e d w i t h a p p l i c a t i o n s o f m e c h a t r o n i c s t o p r o d u c t i o n e n g i n e e r i n g , c o n c e n t r a t i n g o n s t r a t e g i e s and components f o r C I M . d a t a d r i v e n m a n u f a c t u r i n g , and c e t i n a s p e c t s o f a u t o m a t e d d e s i g n and c a l c u l a t i o n \u20ac3 f i e l d o f m e c h a t r o n i c s has been c a r r i e b o u t s i n c e 1980\n-\n-\nNark i n t h e\n629" ] }, { "image_filename": "designv11_32_0003206_jst.28-Figure17-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003206_jst.28-Figure17-1.png", "caption": "Figure 17. Single-element model of a cricket ball. m, ball mass. y, displacement. k, spring stiffness. a, spring power. c, damping coefficient.", "texts": [ " The mean speed for the cricket ball just before hitting the transducer was obtained by a frame-tracking function. A set of continuous active images is shown in Figure 16a. The image playback tool is shown in Figure 16b. The reference scaling setup tool (Figure 16c) and a velocity calculation diagram (Figure 16d) are also shown. In this research, two mathematical models have been developed incorporating the experimentally determined cricket ball behavior. The first model, termed here as the single-element model, consists of a single non-linear spring-damper unit (Figure 17). The second, \u2018three-element model\u2019 (Figure 18) is a more complicated spring-damper system, in which three Maxwell units are connected in parallel. For better accuracy, both models\u2019 parameters have been identified as functions of impact speed. The single element model is a Maxwell unit with a motion equation and is described as follows. Fy \u00bc kya \u00fe c _y \u00f017\u00de Normally, k, a and c can be obtained by solving the differential equation in relation to impact speed. In this article, a more efficient method is proposed, which employs a genetic algorithm (GA) to determine the model parameters" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003997_1.4002089-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003997_1.4002089-Figure3-1.png", "caption": "Fig. 3 Parametrization of rail", "texts": [ " sing these parameters, the location of the contact point on wheel an be, respectively, defined in the body coordinate systems using he two surface parameters s1 wk and s2 wk as u\u0304wk s1 wk,s2 wk = x\u0304wk s1 wk,s2 wk y\u0304wk s1 wk,s2 wk z\u0304wk s1 wk,s2 wk T 3 he tangents to the wheel surface at the contact point are defined n the body coordinate system as t\u03041 wk = u\u0304wk s1 wk , t\u03042 wk = u\u0304wk s2 wk 4 nd the normal vector as n\u0304wk = t\u03041 wk t\u03042 wk 5 Similarly, the geometry of the rail surface can be described sing the two surface parameters s1 rk and s2 rk, as shown in Fig. 3. he global position vector of an arbitrary point on the surface of ail r can be written as rrk = Rrk + Arku\u0304rk 6 here Rrk defines the location of the origin of the rail profile oordinate system in the global coordinate system and is given as unction of the arc-length surface parameter s1 rk, Ark defines the rientation of the profile coordinate system that is also function of he arc-length surface parameter s1 rk, and u\u0304rk is the position vector f the contact point defined with respect to the profile coordinate ystem and is expressed using the rail surface parameters s1 rk and 2 rk" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure4.13-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure4.13-1.png", "caption": "Fig. 4.13. XY Table-Configuration II", "texts": [ " Real-time experiments are carried out on two configurations of X-Y table. Both set-ups use a 2.5 \u03bcm resolution digital encoders installed on the x and y motors. The specifications for the motors are listed in Table 4.3. One table is configured to a moving gantry type, with two motors driving the load along the x direction. Figure 4.12 shows a photograph of the table. The other table is a more conventional one with one motor each along the x and y direction, the photograph of which is as shown in Figure 4.13. 4.3 Experiments 109 For this second configuration, the control task in the experiment is to execute an XY diagonal as straightly and precisely as possible. Such requirements on precise diagonal motion are essential for the calibration of machine geometrical properties. Clearly, in this application, a tight co-ordination between the X and Y motors is as important as the requirement for the moving gantry stage. Experimental results are shown in Figure 4.14. A maximum tracking error of 15 \u03bcm is registered for the individual control loop with a position inter-axis offset of as much as 16 \u03bcm" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002382_pime_proc_1973_187_028_02-Figure15-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002382_pime_proc_1973_187_028_02-Figure15-1.png", "caption": "Fig. 15. The simplified system of forces acting on the brake shoe", "texts": [ " Thus, if i represents the position of an element at which the deflection is to be calculated and j the position of an element on which the unit force acts the expression for the influence coefficients are as follows: where Ad is the equivalent flexural rigidity of the drum, 0 = (i- I)x and B = (j- 1)x. If I is greater than ~ / 2 then n-l8-/31 must be substituted for l8-/3l in this equation. The shoe Let a line force Q and an associated frictional force pQ act on the shoe at M which is a point on the neutral axis (see Fig. 15). The basic equations relating the shoe deflections at a point W to the position and magnitude of Q are: 20 15 10 5 60 -300 I b f 60 -540 I b f 3 0 0 - 5 4 0 I b f --- ----- 40 40 30 20 10 30 and -Qrn(sin(/3-8>-p(1-cos (13-8))) -y < B < 13 where u1 and u, are the outward radial deflections, 0 = (i- 1/2)x, ,!? = ( j - lj2)x and r, and A, are respectively the radius of the neutral axis and flexural rigidity of the shoe. The relationship between P and Q can be found if it is assumed that the shoe is pivoted at H (in order to make the problem tractable) so that on taking moments about H: +(a-pd,) sin (S-" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000952_21.105084-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000952_21.105084-Figure1-1.png", "caption": "Fig. 1. Two robots in a serial connection.", "texts": [ " I N T R O D U ~ I O N OORDINATION of two or more robots can in- C crease complexity and range of automation tasks performed by robots. When in coordinations, multiple robots are connected together in one form or another. Two kinds of connections are possible. The first is called parallel connection in which two or more robots hold a single object and sit on a common ground. The second is called serial connection in which the base of one robot is held by the end-effector of the other, and only the latter robot has its base sitting on the ground. A typical serial connection is shown in Fig. 1. Note that in Fig. 1, we call the robot whose base is held by the other robot the first robot, and the one whose base sits on the ground the second robot. In the past few years, a great number of studies have been conducted on the parallel connection [ 1]-[51. The serial connection, however, has received much less attention. Multilimbed robots as the one shown in Fig. 2 have recently been developed for use in factory automation [6]. The main feature of multilimbed robots is that an arm is installed on a legged mainbody", " The authors are with the Department of Electrical Engineering, Ohio State University, Columbus, OH 43210. IEEE Log Number 9035164. tion. If we consider the mainbody as an end-effector and the feet as a base, the combination of the mainbody and feet can be considered as a robotic system which is fixed on the ground. The arm, on the other hand, is held by the mainbody. As a result, we end up with the base of the first robot (the arm) held by the end-effector of the second robot (the mainbody), thus a serial connection as shown in Fig. 1. Since the mainbody of multilimbed robots has both transitional and rotational capability along and about all the three Cartesian axes, a multilimbed robot is more capable than an ordinary arm which is mounted either on the ground or on a wheeled platform whose motion is restrained on a two-dimensional plane. The following three advantages are obvious for a multilimbed robot. 1) The workspace is enlarged. For an ordinary arm, the workspace is limited by the range of the arm motion with respect to its base" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001144_978-3-642-83410-3_7-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001144_978-3-642-83410-3_7-Figure1-1.png", "caption": "Fig. 1. A sensorized platform for the detection of contact force.", "texts": [ " The platform can be static, or it can incorporate actuators in order to cooperate with the robot in performing insertion operations. A static platform of the first kind has been proposed by Watson and Drake (1975) for assembly operations. The platform incorporates sensors which detect the horizontal and vertical components of the resultant force acting on the platform, from which the point of application of the resultant can be calculated. In a typical peg-in-hole assembly operation, schematically depicted in Fig. 1, the platform carries the recipient part while the robot gripper holds the part to be inserted. In this, as in many other similar situations, possible insertion strategies involve force feedback accommodation procedures, conSisting of commanding motions of the manipulator in certain directions, with the constraint that given force threshold values are not exceeded (Coiffet 1983). In a second interesting approach described by a group of Japanese investigators (Kasai et al. 1981), the platform has the twofold function of sensing forces and commanding accommodation movements" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001138_nme.235-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001138_nme.235-Figure1-1.png", "caption": "Figure 1. Schematic of the geometry of a half-space with an embedded cavity subjected to loading at the surface: (a) top view (the surface of the half-space is divided by loading area S1 and the remaining in 0 and \u03c6\u03b5 is the so called \u201cbell\u201d function, which belong to the C\u221e class over the whole real axis but is nonzero in the interval (\u2212\u03b5, \u03b5) and it is equal to: \u03c6\u03b5(\u03b6) , C\u03b5e ( 1( \u03b6 \u03b5 ) 2 \u2212 1 ) if |\u03b6| < \u03b5 0 otherwise C\u03b5 is a real number such that: C\u22121 \u03b5 = \u222b \u03b5 0 e 1( x \u03b5 ) 2 \u22121 dx By construction the function \u03c8\u03b5 belongs to the C\u221e class because it is an integral function of a C\u221e integrand, and moreover satisfies \u03c8\u03b5(x) = \u22121 \u2200x < \u2212\u03b5 and \u03c8\u03b5(x) = 1 \u2200x > \u03b5. Hence it coincides with the sign function outside the interval [\u2212\u03b5, \u03b5]. With reference to fig.3, some symbols relative to the nonsmooth function will be described below. For any input w\u0303 of the uncertain nonsmooth block, the corresponding output u\u0303 = F (w\u0303) is not unique but, in view of Assumption (2.1), belongs to a suitable interval [u1, u2]. The extremal values u1 and u2 can be easily computed considering the worst cases of the uncertain parameters describing such nonlinearity. In other words, two \u2019worst-case\u2019 functions, f(\u00b7), f(\u00b7) can be determined. They are limiting functions containing that the \u201dtrue\u201d nonlinear function, whichever the uncertainty is" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003662_s12239-009-0025-1-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003662_s12239-009-0025-1-Figure3-1.png", "caption": "Figure 3. Definition of coupled vectors and .x y", "texts": [ " Thus, the tracking error function can be rearranged as Equation (5) by neglecting the last equation in Equation (4): . (5) As shown in Equation (5), tracking error functions have two controllable variables, \u03b2 and \u03c5, which are coupled as nonlinear functions. In particular, since \u03b2 has a nonlinear relation to the steering angle, as shown in Equation (2), it may be difficult to linearize the state space equations. In order to solve this difficulty, in this study, two coupled vectors and are introduced to linearize the equations, as shown in Figure 3. By introducing and , Equation (5) can be rearranged as Equation (6). These simplified equations constitute the linear formula for and , which facilitates the application of a predictive control law. (6) where =\u03c5\u00b7cos\u03b2, =\u03c5\u00b7sin\u03b2 Most model-based predictive controllers employ a linear model of mobile robot kinematics to predict future system outputs. The predictive controller comprises feed-forward and feedback components. The feed-forward control vector formulates nonlinear error functions, and the feedback control input is calculated from the linearized state equations" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001902_j.ymssp.2004.12.004-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001902_j.ymssp.2004.12.004-Figure8-1.png", "caption": "Fig. 8. The distribution of the signal with varying time\u2013frequency\u2013amplitude.", "texts": [ " It can be seen that the adaptive modelling method can track the two combined frequency components quite well, and the resolution of the time and frequency are reasonably good. The next transient signal to be simulated is a time\u2013frequency and time\u2013amplitude-varying signal and it is expressed as u\u00f0t\u00de \u00bc 0:5 sin\u00f0p 28t2\u00de \u00fe 0:5\u00bd1\u00fe 0:2 sin\u00f02p 6t\u00de sin\u00f02p 88t\u00de: (16) Two frequency components exist in the signal: one has the frequency changing quickly with time and the other has a constant frequency but the amplitude changes periodically. The time\u2013frequency\u2013amplitude distributions are shown in Fig. 8. From the figure it can be seen that the signal characteristics with both varying time\u2013frequency and varying time\u2013amplitude distributions are extracted by the adaptive modelling approach. A general analytical solution for the transient vibration response of the constant linear chirp excitation is not possible and numerical techniques must be used. The transient vibration response of the chirp signal through a 2 dof system and a typical error of the adaptive modelling are shown in Fig. 9. From the figure, it can be seen that the transient vibration responses are frequency- and amplitude-varying chirp signals" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003579_s00107-009-0324-2-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003579_s00107-009-0324-2-Figure1-1.png", "caption": "Fig. 1 Schematic diagram of laser melting on the surfaces of the AISI M2 Abb. 1 Schematische Darstellung des Laserschmelzens an AISI-M2Oberfla\u0308chen", "texts": [ " Prior to laser melting all M2 samples were cleaned. The laser melting was carried out at LABOMAP ENSAM Cluny using a continuous wave of CO2 laser with generated beam power up to 4000 Watt. The surfaces of the M2 samples were scanned by the laser beam at a laser power of 2800 Watt and a scanning speed of 600 mm/min (Table 2). The laser beam, which is producing energy density redistribution, was positioned above the surface of the M2 samples in such a way that a laser spot of 4 mm in diameter was produced on the sample surface (Fig. 1a). Laser scanning on the surface of the M2 samples was in parallel direction to the width of the sample under helium atmosphere in order to protect against oxidation. End groove with a depth of 2 mm and width of 20 mm was prepared in the L2 substrates. M2 powders, whose composition is indicated in Table 1, were used to build multiple clad layers on the groove of the substrate. Numerical controlled coaxial laser cladding system was applied in this experiment (Fig. 2a). The laser used in this study was a continuous wave diode type with an output power of up to 3 kW" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003315_09544062jmes711-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003315_09544062jmes711-Figure8-1.png", "caption": "Fig. 8 Strain contour plot of soft response A distortion showing a top, side, and bottom view", "texts": [ " The stitching seam was also found to have a significant influence on the distortions that occurred at maximum deformation. If a particular impact orientation resulted in the position of the seam being within close proximity of the plate, the stiffer material definition would prevent deformation, while deformation would take place within the adjoining panel. The experimental and FE model data provided evidence for the skeletal-like behaviour of the seam. An example of this is shown in the soft response A as depicted in Fig. 8. Upon inspection of the side view, the upper surface shows a slight lump adjacent to a flat region, Proc. IMechE Vol. 221 Part C: J. Mechanical Engineering Science JMES711 \u00a9 IMechE 2007 at UQ Library on June 22, 2015pic.sagepub.comDownloaded from which can be attributed to a hexagonal panel undergoing high levels of strain, followed by a stitching seam preventing straining as shown in the top view. The lower surface of the side view reveals a flat portion followed by high levels of deformation, which may be attributed to a seam followed by a pentagonal panel undergoing high levels of deformation as shown in the bottom view" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003253_20070625-5-fr-2916.00091-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003253_20070625-5-fr-2916.00091-Figure2-1.png", "caption": "Fig. 2. The reference frames I\u2295, Ee and Eh c", "texts": [ ", 1998) including authors\u2019 papers. The paper suggests new results on guidance and nonlinear robust gyromoment attitude control of the agile SC. Let us introduce the inertial reference frame (IRF) I\u2295 (O\u2295XI eY I eZ I e), the geodesic Greenwich reference frame (GRF) Ee (O\u2295XeYeZe) which is rotated with respect to the IRF by angular rate vector \u03c9\u2295 \u2261 \u03c9e and the geodesic horizon reference frame (HRF) Eh e (C Xh cYh c Zh c ) with origin in a point C and ellipsoidal geodesic coordinates altitude Hc, longitude Lc and latitude Bc, fig. 2. There are standard defined the SC body reference frame (BRF) B (Oxyz) with origin in the SC mass center O, the orbit reference frame (ORF) O (Oxoyozo), the optical telescope (sensor) reference frame (SRF) S (Oxsyszs) and the image field reference frame (FRF) F (Oix iyizi) with origin in center Oi of the telescope focal plane yiOiz i. The BRF attitude with respect to the IRF is defined by quaternion \u039bb I \u2261 \u039b = (\u03bb0,\u03bb),\u03bb = (\u03bb1, \u03bb2, \u03bb3), and with respect to the ORF \u2014 by the column \u03c6 = {\u03c6i, i = 1 : 3} of Euler-Krylov angles \u03c6i in the sequence 31\u20322\u2032\u2032", " This problem consists in determination of quaternion \u039b(t) by the SC BRF B attitude with respect to the IRF I\u2295, vectors of angular rate \u03c9(t) = {\u03c9i(t)}, angular acceleration \u03b5(t) = {\u03b5i(t)} = \u03c9\u0307(t) and its derivative \u03b5\u0307(t) = \u2217 \u03b5(t) + \u03c9(t) \u00d7 \u03b5(t) in the form of explicit functions, proceed from principle requirement: optical image of the Earth given part must to move by desired way at focal plane yiOiz i of the telescope. Solution is based on a vector composition of all elemental motions in the GRF Ee with regard to initial coordinates, the scan azimuth, the Sun zenith angle and a current observation perspective, using next reference frames: the HRF Eh e , the SRF S and the FRF F . Vectors r(t) and v(t) are presented in the GRF Ee : re = Te I rI; ve = Te I(vI \u2212 [\u03c9\u2295i3\u00d7]rI), where Te I =[\u03c1e(t)] 3; \u03c1e(t) = \u03c10 e +\u03c9\u2295(t\u2212t0), see fig. 2, and vectors \u03c9s e and vs e are defined as \u03c9s e =Ts b(\u03c9 \u2212 \u039b\u0303 b I \u03c9\u2295i3 \u039bb I); vs e =\u039b\u0303 s e ve \u039bs e, where \u039bs e = \u039bI e \u039bb I \u039bs b; \u039b\u0307 s e = \u039bs e \u03c9s e/2 and constant matrix Ts b represents the telescope fixation on the SC body. The observation oblique range D(t) is analytically calculated as D(t) = |rc e \u2212 re(t)|. If matrix Cs h \u2261 C\u0303 =\u2016 c\u0303ij \u2016 defines the SRF S orientation with respect to the HRF Eh e , then for any point M(y\u0303i, z\u0303i) at the telescope focal plane yiOiz i the components V\u0303 i y (y\u0303i, z\u0303i) and V\u0303 i z (y\u0303i, z\u0303i) of vector by a normed image motion velocity are appeared as:[ V\u0303 i y V\u0303 i z ] \u2261 [ \u02d9\u0303yi \u02d9\u0303zi ] = [ y\u0303i 1 0 z\u0303i 0 1 ] qiv\u0303s e1 \u2212 y\u0303i \u03c9s e3 + z\u0303i \u03c9s e2 qiv\u0303s e2 \u2212 \u03c9s e3 \u2212 z\u0303i \u03c9s e1 qiv\u0303s e3 + \u03c9s e2 + y\u0303i \u03c9s e1 " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000131_s0167-6911(01)00130-x-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000131_s0167-6911(01)00130-x-Figure1-1.png", "caption": "Fig. 1. Scheme of the system.", "texts": [ " A system x\u0307 = f(x; u); y = h(x; u); with input u and output y is a passive system if there exists a continuously di?erentiable positive semi-de>nite function V (x) such that @V @x (x)f(x; u)6 uTy: 3. The arguments of the functions will be omitted whenever no confusion can arise from the context. The system under consideration is composed of a four-way electrohydraulic servovalve, a linear cylinder and a mass m. The servovalve acts on the cylinder which carries the mass. The control input u is the servovalve voltage. The scheme of Fig. 1 represents this system. In order to take into account the physical characteristics of the particular system we are interested in, we introduce the following main assumptions: (i) the servovalve is symmetrical and its dynamics are negligible, (ii) the pressures are homogeneous in each cylinder chamber, (iii) the cylinder has no leakage Mows and no dry friction, (iv) the temperature is constant. Under the previous assumptions, the system model is deduced from the three following laws: (i) the pressure evolution law of each cylinder chamber, (ii) the volumetric Mow rates Qp(Pp; u) and Qn(Pn; u) provided by the servovalve ports, (iii) the mechanical equation of the moving part" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002817_tmag.2006.892268-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002817_tmag.2006.892268-Figure2-1.png", "caption": "Fig. 2. SPT head model used for optimizing finite-difference cell size. (a) Whole schematic model. (b) Main pole.", "texts": [ " Specifically, the calculation procedures of magnetostatic fields in this model can be reduced to 50 6 56 times from 50 6 300 times if the numbers of layers in the -direction are assumed to be 50 for the head and 6 for the medium. The finite-difference cell size is critical in LLG calculations; if the cell size is too coarse, it is impossible to simulate the magnetization process or magnetization pattern, while excessively fine cells only lead to a waste of computer memory and calculation time. It was generally thought that 10-nm cells were fine enough. We have used the model shown in Fig. 2 to confirm the cell size. An excitation field in the yoke was used instead of a coil current to reduce the memory usage. The maximum excitation field of 6.28 kOe in the yoke was determined by changing the magnitude prior to the calculations. The material characteristics used for the calculations are shown in Table I. In Fig. 3, the dynamic response of the recording fields is compared on the intermediate plane, while the quasi-static (t 1.2-ns) field distributions in the recording layer are compared in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003219_gt2007-27984-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003219_gt2007-27984-Figure2-1.png", "caption": "Figure 2. Incipient Bearing Fault Signatures Difficult to Extract", "texts": [ " Although bearing characteristic frequencies are easily calculated, they are not always easily detected by conventional frequency domain analysis techniques. Vibration amplitudes at these frequencies due to incipient faults (and sometimes more developed faults) are often indistinguishable from background noise or obscured by much higher amplitude vibration from other sources including 2 ownloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/04/2016 Te engine rotors, blade passing, and gear mesh in a running engine. This difficulty is illustrated in Figure 2. Vibro-acoustic data sources provide some of the most reliable quantitative indicators of bearing, gear, and rotating component fatigue that is available (1). These indicators are typically spread throughout the vibro-acoustic regime. The vibration monitoring software developed as part of the SBIR Phase I/II program discussed herein applies advanced high frequency incipient fault detection and diagnostic algorithms on high frequency vibration monitoring sensor data collected from bearings and accessory gearboxes in gas turbine engines" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002817_tmag.2006.892268-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002817_tmag.2006.892268-Figure5-1.png", "caption": "Fig. 5. SPT head model used for micromagnetic calculations. (a) Whole schematic model. (b) Main pole.", "texts": [ " However, this means that a higher coercivity medium with higher anisotropy energy has to be introduced to maintain medium thermal stability. Write heads with higher moment materials can generate higher fields; however, the latest write heads are already using materials with a moment close to 24 kG, the theoretical upper limit. Therefore, optimizing the write head structure, especially the pole-tip region, is one of the most important themes in regards to obtaining a large recording field. The SPT write head model shown in Fig. 5 was considered. This model has a main pole thickness (MPT) and a width (MPW) in the range 100\u2013180 nm and a throat height (TH) of 0\u2013100 nm. Cubic cells of 20 nm per side were used in the whole analyzed region. In order to simulate the pole-tip area precisely, both the overall height and width of the SPT head have been reduced. The material characteristics shown in Table I and the excitation field shown in Fig. 3 were used. In Fig. 6, the calculated recording fields in the recording layer at quasisteady state (t 1" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002073_s00366-005-0008-4-Figure14-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002073_s00366-005-0008-4-Figure14-1.png", "caption": "Fig. 14 Single frame of fourbar animation for the second branch", "texts": [ " This third argument, TRACE_ON, is a macro used to specify tracing of the coupler point. Note that the member function animation() contains a single integer argument. This number refers to the branch number of the fourbar linkage. Depending on its type, a fourbar linkage may have up to four branches. Since the fourbar defined in the problem statement is a Grashof crank-rocker, it has only two branches. Figure 12 shows one frame of animation for the first branch of the fourbar mechanism, whereas Fig. 13 is an overlay of all the frames of animation. Likewise, Fig. 14 is one frame of animation of the second branch, and Fig. 15 shows all of the animation frames. An object-based mechanism toolkit has been developed. The toolkit consists of animation program QuickAnimationTM and a collection of classes for design and analysis of commonly used planar mechanisms. Written in Ch, a C/C++ interpreter, the Ch Mechanism Toolkit is useful for solving practical engineering problems in design and analysis of mechanisms. It can compute the angular positions, velocities, and accelerations of the individual links of mechanisms such as the fourbar, slidercrank, geared-fivebar mechanisms, sixbar linkages, and cam-follower systems" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001900_1.1850943-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001900_1.1850943-Figure8-1.png", "caption": "Fig. 8 Rotation of reaction forces", "texts": [ " 7 si , j ,k ,m ,n 1 2 d cos 4R2 d2 sin2 i , j ,k ,m ,n (28) It follows that the corrective reaction force at this point is calculated using ci , j ,k ,m ,n B k ,k min si , j ,k ,m ,n , Ci , j ,k ,m ,n old k ,k B R\u0302i , j ,k ,m ,n old (29) where the negative sign indicates the correction force acts in the direction to reduce the magnitude of the reaction force. Finally, the total reaction force at bi , j ,k is computed by summing the contributions due to all the scanned target bristles Ri , j ,k bristles m n Ci , j ,k ,m ,n (30) It should be noted that the computed reaction force may not lie normal to the bristle surfaces due to other 3D bristle deflections occuring within the bristle pack . In order to reduce this error, the reaction force must be realigned normal to the bristle surface, but with its magnitude kept constant as shown in Fig. 8. The net effect of this rotation is to displace the point bi , j ,k by an amount ci , j ,k ,m ,n , where Ci , j ,k ,m ,n Ci , j ,k ,m ,n new Ci , j ,k ,m ,n old 2 Ci , j ,k ,m ,n old (31) Fig. 7 Free bristle-point movement in a \u00c4const plane 586 \u00d5 Vol. 127, JULY 2005 ded From: http://gasturbinespower.asmedigitalcollection.asme.org/ on 01/29/ Since this quantity can be quite large, the rotation is relaxed by setting Ci , j ,k ,m ,n new Ci , j ,k ,m ,n old rotate Ci , j ,k ,m ,n new Ci , j ,k ,m ,n old (32) In this way, the reaction force is \u2018\u2018nudged\u2019\u2019 in the right direction, and the overall stability of the iterations is conserved" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003518_s0001924000052763-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003518_s0001924000052763-Figure3-1.png", "caption": "Figure 3. Local component sub-beams in a SHEBA element.", "texts": [ " Using the standard relations PH = K / j p i i \u00b0, P i 2 = K L 2 p i , 2 \u2022 \u2022 ( 2 5 ) we find from eqns. (2), (3) and (6) P11 = Erfllm-1KivoJn~1m\u00a3NO (26) which, in conjunction with the first of eqns. (24), becomes where Analogously P11=flLm-1N = ihN h = \\ha hp hy J = 2ftLm~1 PL 2=flLm-M = ihM (27) (28) (27a) Eqns. (27) and (27a) may be interpreted structurally as a representation of the shell by component local sub-beams \u00ab. f3, J, which carry the loads ihaNa, ihaMa, etc. There fore, the local a sub-beam is to be understood to have the length ma, the width \\ha and height t {see Fig. 3). The triangular local sub-element is then represented in the adirection by an a sub-beam. For the evaluation of the geometrical stiffness we also require the natural load vector PL3. From the theoretical and computational point of view it is most convenient to establish PL3 by considering the equilibrium on each com ponent sub-beam. We can then apply the standard beam theory as in ref. 3. Since P13 is effectively associated with the shear forces hQ in the sub-beams, we may write for a typical fi component ^ ( ^ G H ) = - ^ d P ^ dsu (29) which may also be deduced from Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001072_pen.760271502-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001072_pen.760271502-Figure2-1.png", "caption": "Fig. 2. Helmet shell side view. Fig. 4. Suspension straps, side view.", "texts": [], "surrounding_texts": [ "Of the six impact locations specified by the American National Standards Institute/American Society for Testing and Materials (ANSI/ ASTM F 429-75), the crown site was loaded because it provided the configuration from which an easy comparison could be made between experimental and analytical results. - -Z RESTRAINT 2 Fig. 1 . Helmet shell, boundary conditions. L. Vetter, R . Vanderby, and L. J . Broutman 300 250 H 200 W 0 a 150 100 50 In a test of an actual helmet, a set of forcedeflection curves were generated. The test was done using an Instron testing machine with the helmet mounted on a rigid headform. The test setup was similar to that shown in Fig. 5. The results of these tests are shown in Fig. 6. The curves in Fig. 6 are numbered 1, 2, and 3, corresponding to the first, second, and third loading, respectively, of the helmet. Each test was run within 1 min of the previous test. It is interesting to note that each succeeding compression of the helmet resulted in a stiffer force-def lection curve than the preceding loading. This was no doubt due to the time-dependent recovery properties of the foam rubber. The computer model did not attempt to duplicate this behavior, but rather attempted to duplicate the average behavior of the actual helmet. Figure 6 also shows the computer model results superimposed over the experimental curves for comparison purposes. The curve from the computer model is very close to the curve from the second loading of the actual helmet. The greatest discrepancy occurs at the greater displacements. This implies that at the larger displacements, the actual helmet may be - - - - - - FLAT PLATE YpjJ 47; )-\"ELMET LOAD CELL Fig. 5. Helmet load deflection test. 3 50 I 2 3 LOADINGS OF ACTUAL HELMET _-_ COMPUTER MODEL \"0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 DEFLECTION, inches Fig. 6. Force-deflection curve of computer model superimposed over experimental results. stiffer than the computer model. The computer model curves are still between the curves of the first and second helmet loading. Figure 6 establishes sufficient correlation between the computer model and the actual helmet tests to justify the use of this model in further studies in which certain parameters are varied. As these parameters are varied, comparisons will be made with both the basic computer model results and the actual helmet test results." ] }, { "image_filename": "designv11_32_0002657_0041-2678(73)90005-5-Figure12-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002657_0041-2678(73)90005-5-Figure12-1.png", "caption": "Figs 12 and 13 show horizontal and vertical single-bearing grease relief mountings. Ref 2 gives details of vertical double-bearing mountings and includes a list of the advantages of grease relief systems. It also records comments of general design interest.", "texts": [], "surrounding_texts": [ "H_\nI\nU L\nFig 8 Angle packing Fig 9 Angle packing\nThe diametral running clearance e mm, Fig 3, can be based on the expression:\n-0 .00 e = 0.250 + 0.0025 C +0.08\nwhere C is the shaft diameter in mm and the plus and minus figures indicate the limits of manufacture.\nIf the long shaft seals take up too much room, plenty of labyrinth running clearance glands are illustrated in bearing manufacturers' catalogues. These provide a tortuous path which dirt particles must travel if they are to reach the interior of the mounting. All running clearances should be filled with grease on assembly.\nThese complicated seals are necessary only to keep dirt out and not to keep the grease in. If grease leaks from a mounting it usually means that either the grease is liquefying and is not the correct lubricant for the job or there is too much of it in the mounting.\nRunning the bearing With the mounting grease charged and closed the bearing is ready for starting up. If it is possible the shaft should be rotated a few times by hand to check that it is free from tight spots and undue stiffness. To keep a check during the starting period it is useful to record the temperature of the mounting and plot it against time. Fig 10 shows four examples of the plots which can be obtained.\nPlot AB The rate of heat generation is too high and temperature quickly rises to the limit. Running must be stopped immediately. Reasons for this unsatisfactory behaviour can be one or more of the following:\n1 The mounting is grossly overpacked. 2 The grease does not channel. 3 The speed is too high.\n4 The proportional volumes, bearing packing to the spaces left in the covers, is incorrect. 5 The shaft seal may be fouling.\nPlot AC The temperature again exceeds the limit and running must be stopped. The rate of heat generation is less than with plot AB and the plot does show signs of levelling off but finally turns upwards and passes the limit. The remarks for plot AB again apply although it is unlikely to be Item 5 at fault.\nWith a plot such asAC, 'nursing' may be tried to get the bearing running properly. With this artifice the bearing is allowed to cool to ambient temperature and then restarted. If the bearing fails to get under way after two or at the most three attempts, nursing should be abandoned.\nPlot AD The rate of heat generation has been reduced further and the temperature levels off. This may be a satisfactory start if the level is not too high. If the heat generated is solely due to the grease and the bearing i.e. no heat is being supplied fr~tn an outside source, a useful limiting level is 60\u00b0C. It may be advantageous to try nursing or removing a small quantity of the grease if the level is too high.\n26 TRIBOLOGY February 1973", "Plot AE This is the ideal start. The temperature rises to a peak, turns over and then falls to a low level. No action is required and the bearing can run on.\nIt has been advocated so far that a bearing should always be charged full of grease. For a fully packed ball bearing of any type a satisfactory starting curve, such as plot AE should be obtainable, even at the maximum permissible speed of the bearing. With a fully packed high speed roller bearing, particularly those above 75 mm bore, a plot like AE cannot always be obtained. A roller bearing does not channel so readily as a ball bearing. If a roller bearing cannot be run in slower than the running speed, the packing of the bearing should be reduced, as with the half-pack in Fig 11.\nRe lub r i ca t ion Facilities for relubrication must be designed carefully. To be efficient, either the injected new grease or some of the grease already in the mounting, displaced by the injection, must pass into the bearing. It is of little value injecting into an open space - the point of injection should be positioned where there is already a full packing. Further, grease cannot be added bit by bit with time unless there is some opening where the surplus can escape. If there is not an outlet the mounting will eventually become choked, temperature will rise and driving power will be wasted. Escape plugs and pipes are of little value. To move grease through such apertures requires considerable pressure - the grease is more likely to squirt out of the shaft seal. There are three answers to this problem:\n1 Remove cover and clear grease out of it. If the cover is a large one about a quarter to a third of the lower region can be made detachable and this part only need be removed.\n2 Make the cover large enough to cope with the addition of the sum total of the injects over the maintenance period. The cover here and in 1 wilt be the one not containing the injected point. 3 Adopt a mounting with a grease relief system, generally referred to as a grease valve mounting.\nSince the publication of Ref 2, set ups 3 and 5 have been tested with horizontal shafts. They both proved to be efficient up to DN = 275 000, the maximum value tested; where D is the bearing bore in mm and N is the speed in rev/min. Concluding remarks Grease is an engineering component. It is just as much a part of a machine as any other of its vital components. In\nTRIBOLOGY February 1973 27", "Sco v e n g e ~ _ _ ~\nproper manner in which it will be used as is afforded to the other components.\nLubricating rolling bearings with grease is an art. Many wrinkles exist, generally learned from experience. This article has described some of them. Enclosure covers should be properly proport ioned and the quantities of grease required accurately dispensed and carefully charged into their correct spaces. In this way a greased rolling bearing will give a satisfactory service.\nReferences 1 Harris, J. H. 'The lubrication of rolling bearings', Shell-Mex\nand BP Ltd, London (1972)" ] }, { "image_filename": "designv11_32_0001696_icnsc.2005.1461309-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001696_icnsc.2005.1461309-Figure8-1.png", "caption": "Fig. 8. Goal circle decision on set 2 Internal tangential line between circle T and c, : pl", "texts": [], "surrounding_texts": [ "( x + R)2 + y 2 = R 2 . Take the derivative:\n(@ / dx) = ( R + x) I y > 0, range in left start circle: y > 0 and x > -R , range expressed with anglea and by conditions: 0 5 d 5 (Z / 2) : (arc length)\nAlso, right start circle: (X - R)\u2019 f y 2 = RZ Take the derivative: (4 / dc) = ( R - X ) / y < 0 Range in left start circle: y < 0 and x < R Range expressed with angle p and by conditions:\n(3n / 2 j 5 p I 2n : (arc length)\nAsa result, when-eo < xG I - R I a < p :. Left start circle is selected Theorem 1-2 Select the right for 0 5 xG < R and\nif X , satisfies the xG = ~ ( 1 - cos e) , eG 2 (n / 2) - e, Select tbe left for 0 I x, < R and\nif xG sutisfies thexi = R(l- COSO), E ( @ ) e ( x / 2 ) - O7\nThe relationship behveen goal point xG and its heading\nangle 8, , in figure 6 can be expressed as below.\nx, = R(1- cos 8). If\u2018we find a circle which passes a point G and is tangential to y-axis, the slope of the path p is always W . HG = (n/ 2) - 8 , Right goal circle:\n( x - C, (XI) + (y - C, ( y ) ) \u201d = R * , Left goal circle:\nC,(x,y) = ((x, + R c o s ( ( I F / ~ ) + B)),(yc - Rsin(-(a/2) + 0))\nC , (x ,y ) = ((x, -Rcos( (w/2)+8) ) , (yG +Rsin(-(lr/2)+8))\nTherefore, (X - R)* + ( y - R sin8)2 = R 2 , take the\nderivative: dy / & = ( .R - x) / ( y - R sin 0) , If y\u2018 = R sin 8 , (dy / &) = conclude a theorem as below. Theorem 1-3 \u2019 .\n(x - c, (x>)\u2019 + (Y - c, (Y))\u2019 = R 2\nWith a similar way, we can\nSelect the left for - R < XG 5 0 and i fx , satisfies rhex, =-R(l+cosO), 0, 5 - ( ~ / 2 ) + 0 .\nSelect the right for - R C xG I 0 and ifxc satisfies rhex, = - q i + COS e) and 0, -(K / 2) + 0 Stage 2: To decide a goal circIe with respect to $y / & A ( x , y ) . A point in the selected start circle either left or\nright is named A(x, U) and still goal point is G(x, y , 8) . If dY / = (44 - G W ) U ( x ) - G(x) = 0, I\nBoth left and right goal circles can be selected, for the external and internal tangential lines are same. Theorem 1-4 Select the left for (dy / & ) A ~ x , y l < tan 8, ,\nto C, ( x , y ) = Length from A(x, y ) to C, ( x , y) Also, ar; lengths from a and p are zero. Therefore, either left or right circle can be selected. When tan e,> (dy / &) A ( x , y ) . The slope of the path from\nA(x, y ) to Left Goal Circle is less than (dy / & ) A ( x , y j . The\nslope of the path from A(x, y ) to Right Goal Circle is\ngreater than (dy / &) a ( x , y ) . If the arc length comes fioma\nin Left Goal Circle and p in Right Goal Circle,\nLeft Goal Circle (K / 2) - 6, I a 5 n - 8, : (arc length)\nRight Goal Circle 2R - 0, I p I (51c / 2) - 6, : (arc-\nlength) As a result, Set 2, Stage 1: To decide a circle in the starting point with respect to Goal Point (x, , y,, e,-) Set 2 is same as set 1 except the range of goal heading angle.\n< p :. Left Goak Circle is selected\n(xs,ys,es) =(o, O, ~ / 2 ) . - = 4 xG <\nyc > 0, -X I e, < U", "Theorem 2-1 Select the right for 2R I xG < 00 Select the left for - 00 < xG I -2R Proof : If (x, , y,) = (2R, y,) , Left goal circle:\n(X - R)\u2019 f (y - YG)\u2019 = R 2 This is same as the right start\ncircle: (X - R)2 + (U}\u2019 = R 2 . The slope of external tangential line between these two circles is dy / dx = 00\nTherefore, if xG > 2R , ( d y / d x ) > 0 . In a same way,\nIfx, = -2R , right goal circle:\n( X + R ) 2 =R2Leftstart\ncircle: ( x + R)\u2019 + y2 = R 2 Therefore, 4 / dx = DQ .\nIfx, < -2R, &I& < 0 Theorem 2-2 Select the left for R I xG < 2R and if xG satisfies the xG = 2R - R COS 8 and (-0 - (XI 2)) < e, c (-0 + (7r12)).\nSelect the right for R I xG < 2R and\nif xF satisfies the xG = 2R - R COS 0 and\n( - e - ( X / 2 ) ) > 0 , , ( - 0 + ( n / 2 ) ) < ~ , Proof: The basic concept is same as theorem 1-2 and 1-3 except R becomes 2R. When xG = 2R - R cos 8, there are two angles; the first one makes the slope of a left goal circle (4 /dx) = w ; the other make that of the right goal\nInternal tangential line between circle T and C, : p 2 pl = p 2 , There exist two internal tangential lines between circle T and c, , One: pl ,the other: p 3 , pl = p 3 As a result, pl = p 2 and pl = p3 Therefore, p 2 = p3 Set 3, Stage 1 and Stage 2, Theorem 3 Set 3 is exactly same as set 2, if xG - > X: and xS - > x;. Therefore, by translation and rotation mentioned in 6-3, (x,,ys,&) = @ Y O Y ( ~ / W - > cxb?Y;,a (XG,YG,eG) - > ( X ; . , Y ; . , ~ ; ) = ~ o , o , w Then, we take the same steps; state 1 and 2 in set 2. Set 4, Stage 1-1, Theorem 4-1 Right start circle is selected for 2R < xG < 00 Left start circle is selected for - w < X , < 2R Proof: rfx, = 2R , Left goal circle:\n( X - R ) 2 -k ( y - y c ) 2 = R 2 , Right goal circle:\n( ~ - 3 3 R ) ~ + ( y - ~ ~ ) ~ = R2,1ei?startcircIe: circle L@ /& = 00 , The former is with right starting circle; the latter with left starting circle. ( x + ~ 1 2 + $ = ~2 , right Start circle:\n(x - 8)2 f y z = RZ. When the slope between two . Theorem 2-3 Select the left for 0 5 xG < R and if\n- (IT / 2) < e, and 0 > 0, . Select the right for\n0 5 xG < R and if - (z/2) > 8 ,and-n < 0,.\nto (4 Proof: In the range of- R C xG < R , there always exist two signs of slope dy / ch ; one is positive, the other is\nnegative, for when xG = R and if 8, = 0 orec = x , dy / & = same in this range.\ncircles 4 / d~ = 00 , it is independent on the yc and\nthe xG of left goal circie = The xG Right start circle Then, two paths from right start circle to either left or right goal circles are same, Also, shorter external paths in from\nheading angle 8,, Ifx, = 2R - R COS 0 and when\nQ, < -(n/ 2) and x, > R, Then, by the proof on stage 2 in set 2 ,right start circle is selected .Also, when OG > -(n/ 2) and X, > R . Right start circle is setected Stage 2\u201d1, Theorem 4-2 Select the left for ( d y / a ! ~ ) ~ ( ~ , ~ ) < tan(0, + n)\nStage 2: To decide a circle in the goal point with respect each start circle to goal circles are same. By the rotation of R ( r , y ) and (xG 7 Y G\n. Also, the lengths of two paths are always\nTheorem 2-4 Select the left for (& / A) ajx,y) < talI(6, + X) . Select the right for (+/ Proof > tan(8, + X I .\nSelect the right for ( d y / d ~ ) , , , , ~ , > tan(eG -t X) Proof: Proof is same as stage 2 in set 2 Stage 1-2 The decision in starting point is same as on stage 2 in set 2. Stage 2-2, Theorem 4-3", "Select the right for - 2 K < XG C 2R and\nii-nce, <-(n/2). Select the left\u2019for - 2R < xG < 2R and\ni f - ( ~ / 2 ) < 6, < 0. Proof : In the range of0 < xG < 2 R , we can not decide a\ncircle in starting point with respect to change of heading angle of goal point 8, , If 0, = -(n / 2) Left goal circle:\n(x - xG + (y - yG)\u2019 = R 2 Right goal circle:\n(x - (x, - 2R))\u2019 + ( y - y c ) 2 = R z Left start circle:\n(x + R)\u2019 f y2 = R 2 Right start circle: (X - R ) 2 + JJ* = R 2 . External tangential lines between .\nlei? start circle and left goal circle:, 4 / dx = yG /(-R + x,;) External tangential lines between right start circle and right goal circle: dy / dt = yc / ( -R + xG ) These two are same in slope and length. The difference is in the intemal tangential lines; in detail, internal tangential line between right start circle and left goal circle is getting shorter when 0 < xG \u20ac 2R . But as long as two external fangential lines are same, we can not decide a circle in starting point. Instead of it, 6, decides a\ncircle in goal point. When - f l C 6, < -(Kt 2) The center of right goal circle c, (x, v) : C, (x, y ) - COS(-@ + ( X / 2)) . The center of lee goal circle C - L(x, y ) : C, [x, y) + cos(-@ + ( X I 2)) When - (W / 2) < 0, <: 0 . The center of right goal\ncircleC-R(x,y): C,(x,y> +\u2019cos(-O+(n/2)) The center of left goal circle c - L(x, y ) : c, (X,y) - COS(-@ + (X / 2)) As a result,\nWhen- W < 0, < -(a 12) , right goal circle is selected.\nWhen - (n / 2) < 8, < 0 , left goal circle is selected.\n2\n~\nV. SIMULATION This rapid and efficient algorithm was implemented as\nsimulation in Windows environment.\n__--I-\nFig. 9. In the simulation results, red circles represent the starting circles; blue, goal circles. Dashed lines are optimal paths generated by the algorithm in each case. When the optimal path is generated, a text sentence shows at the bottom of each point; in detail, \u201cright circle is selected\u201c, \u2018\u2018left circle is selected\u201d.\nVI. CONCLUSION An intelligent and rapid decision maker of the shortest\npath is implemented under simple conditions. The suggested algorithm is very easy and suitable for quick decisions in highly complicated systems. First, we analyze the geometrical characteristics of lines and arcs. Based on the known optimal sets, we compare current situation or case with one of them. We divide the problem into two stages 1 and 2; the former is related to relative shifting of goal point and decides one of the circles in starting point, the latter is about heading angle of goal point, which is compared with a reference angle.\nREFERENCES\n14 L E. Dubins, \u201cOn Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents,\u201d American Joumal of Mathematics, vol. 79,\n[Z] S . A. Eonoff, \u201cPath-planning for unmanned air vehicle,\u201d in AFRL Technical Report, 1999. [3] S. A. Bortoff, \u201cPath planning for UAVs,\u201d in Proc. American Control Conf., (Chicago, IL), pp. 364-348,2000. [4] P. R. Chandler, S. Rasmussen, and M. Pachter, \u201cUAV cooperative path planning,\u201d In Proc. AlAA Guidance, Navigation, and Control Conf., (Denver, CO), pp- AlAA-2000-4370,2000. T. A. Mclain, P.R. Chandler,\u2019and M. Pachter, \u201cA decomposition strategy for optimal coordination of unmanned vehicles,\u201d in Proc. Of American Control Conf., (Chicago, L), pp. 349.373,2000. T. W. McLain, and R. W. Beard, \u2018Trajectory planning for coordinate rendezvous of unmanned air vehicles,\u201d in Proc. AIAA Guidance, Navigation, and Control Conf., (Denver, CO), pp. AIM-2000-4369, 2000. Guang Yang, and Vikram Kapila, \u201cOptimal Path Planning for Unmanned Air Vehicles with Kinematic and Tactical Constraints,\u201d in Proc. 41\u201c IEEE Con$ on Decision and Control. pp ,1301-1306, 2002. [8] Christopher T. Cunningham and Randy S. Roberts, \u201cAn Adaptive Path Planning Algorithm for Cooperating Unmanned Air Vehicles,\u201d in Proc. IEEEIni. Con$ on Robotics onddutomation, pp. 3981-3986, 2001. loannis K. Nikolos, Kimon P. Valavanis, and Nikos C. Tsourvelooudis, and Anatgyros N. Kostaras, \u201cEvolutionary Algorithm Based OfflineiOnline Path Planner for UAV Navigation,\u201d E E E Trans. on Systems, Man, and Cybernetics-Part B: Cybernetics,\np p . 497-516, 1957.\n[SI\n[6]\n[7]\n[9]\nvol. 2, pp. I-I5,2003. [ IO1 J.A. Reeds and LA. Shepp, \u201cOptimal paths for a car that goes both\nforwards and backwards,\u201d Pacific Joumal of Mathematics, 145(2), 1990.\n[ I 13 H. J. Sussmann, and G. Tang. \u201cShortest paths for the Reeds-Shepp Car : a worked out example of the use of geometric techniques in nonlinear optimal control,\u201d in Research Report SYCON-91-10, Rutgers University, New Brunswick, NJ, 1991, [12] I.-D. Boissonnat, A. C-er-em, and J. Leblond, \u201cShortest paths of bounded cunjature in the plane,\u201d Int:Proc. 9th IEEE Conf. Robot. Autom., 1992.\n\u2018report 97438,1998. [13] Jean Paul Laumond \u201cRobot Motion Planning and ControP\u2019 LAAS" ] }, { "image_filename": "designv11_32_0002269_j.engfracmech.2006.04.002-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002269_j.engfracmech.2006.04.002-Figure8-1.png", "caption": "Fig. 8. Definition of the main parameters of the analysis: (a) crack position on the tooth surface; (b) calculation points along the crack front.", "texts": [ " Making a conservative assumption, in the analysis friction between crack faces has been neglected. The attention has been focused on the most critical zone of the tooth that is the region just under the contact pressure computed in the 25th meshing step; this area is also in proximity of the pitch line which, as known, is a preferential place for pitting/spalling formation. Considering this loading case, it is useful to place a reference frame having the origin in the point of maximum pressure and the x and y axes parallel to the axes of the pseudo-contact ellipse (Fig. 8a). Table 2 summarizes the crack positions which have been analyzed: referring to the crack center, the crack has been moved along the x-axis and the y-axis; moreover, being the aim of the authors to study the spalling formation, the crack is placed always on a plane parallel to the free surface to a depth where the tangential stresses due to the loading step 25th are maximum (z = 0.25 mm). In Fig. 8a, the crack in the four extreme positions (corresponding to an eccentricity on x-axis equal to \u00b11.0 mm and on y-axis equal to \u00b110 mm) is reported; it also evident that all the crack positions are analyzed considering the meshing steps from the 19th through 31st; in fact, it has been verified that, for such crack positions, all the remaining loading steps have no significant influence on the SIFs value. Finally, it is convenient to define four points on the crack front (Fig. 8b): points A and B are aligned with the x-axis; points C and D are aligned with the y-axis. These points are the ones considered for the stress intensity factors calculation. Once the calculation grid over the gear tooth surface is set up, it is possible to compute the stress intensity factors allowing to map the criticality of the defects. Observing the results obtained for all the analyzed cases, it is easy to note that everywhere in the tooth the stress intensity factor for Mode I is null; this is due to the compressive nature of the load" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003335_isie.2007.4374794-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003335_isie.2007.4374794-Figure5-1.png", "caption": "Fig. 5 Phasor diagram for the fundamental component of the current waveforms in Fig.4", "texts": [ " These two switching states are switching states 2 and 5 where the current in phase U has to find its return path through phase W and vice versa. This is due to the fact that both machine phases are connected to the same inverter leg. Such a constraint reduces the waveforms of Fig. 1 to that given in Fig. 4 after removing the time portions where the switching states 2 and 5 has to take place. controlled current/frequency source of Fig. 3. Using Fourier analysis for the current waveforms of Fig. 4 it can be easily proved that the phasors for the fundamental component of these currents will be given by the phasor diagram of Fig. 5, which is a form of unbalanced three phase operation. The amplitude of the currents in both of phase U and phase W is 2 DI \u03c0 while that of phase V is 2 3 DI \u03c0 . The operation of the three phase unsymmetrical system is usually analysed by means of the decomposition to symmetrical components [7]. As the neutral of the machine is isolated then the sum of the instantaneous machine currents should be equal to zero, and this leads according to the symmetrical components to the absence of the zero-sequence component of the current", " The amplitude of the current per phase for the positive sequence set will be given as: 1 peak 4 3 D U I I \u03c0 + \u22c5 = \u22c5 (5) The amplitude of the current per phase for the negative sequence is: 1 peak 2 3 D U I I \u03c0 \u2212 \u22c5 = \u22c5 (6) It is clear from (5) and (6) that the forward rotating field will dominate as the positive sequence current amplitude is twice that of the negative sequence current. At starting the slip for both of the positive sequence (s) and negative sequence (2-s) will be equal to unity. So the torque in (2) for both positive and negative sequence currents will be proportional to the square of the RMS value of the current. Accordingly if the starting torque produced by the unbalanced currents of Fig. 5 is related to that of the balanced currents of Fig. 1, the ratio will be given as: 2 2 2 2 2 2( ) ( ) 3 3 33.5% 6( ) D D e D I I M I \u03c0 \u03c0 \u03c0 \u2212 \u22c5 \u22c5= \u2245 (7) Two facts apply for the induction motor when fed from constant current source; primarily is the low starting torque as the rotor current at starting is high which reduces the magnetizing current (stator current is constant), thus reducing the flux of the motor. The other noticeable fact is that the machine with rated current will be saturated in the stable region of operation (negative slope region of the torque speed curve)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002804_978-3-540-73011-8_58-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002804_978-3-540-73011-8_58-Figure6-1.png", "caption": "Fig. 6. Example 2", "texts": [], "surrounding_texts": [ "From the above results, we can apply the B-spline quaternion interpolation curve to produce the sweep motion and sweep solid. By adapting the construction method Interpolating Solid Orientations with a 2C -Continuous B-spline Quaternion Curve 613 designed by [9] for B-spline quaternion curves, the C2-continuity is guaranteed which is useful in the construction of the sweep surface/solid. Example 1: given a sequence of object orientations shown as the Figure 4(a). We get the sweep solid as shown in Figure 4(b): (sweeping with cubic B-spline quaternion curve): Example 2: given a sequence of object orientations as Figure5 (a), we get the result shown as (b): (sweeping with cubic B-spline quaternion curve): 614 W. Ge, Z. Huang, and G. Wang" ] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-FigureA.7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-FigureA.7-1.png", "caption": "Fig. A.7. Optics and accessories for squareness measurements (horizontal plane)", "texts": [ " A milling machine with a horizontal spindle and a bed which moves perpendicularly to the spindle is an example of a machine with two perpendicular axes. A CMM with a probe that moves vertically and mounted on a bridge which moves horizontally is another example. The main cause of a squareness deviation is probably the constraints during the manufacture or assembly of the machine to fix two axes exactly perpendicular to each other. The squareness measurement will be useful to allow the small angular difference to be measured and compensated for. The optics required for squareness measurements are given in Figure A.7. The main procedure for squareness measurement on a horizontal plane is to carry out a measurement along the first axis as shown in Figure A.8 using an optical square, and subsequently to carry out a measurement along the second axis according to the set-up in Figure A.9. The second axis measurement is simply a horizontal straightness measurement along the axis on which the reflector was earlier mounted during the first measurement. Figure 5.9 illustrates the concept of obtaining the squareness error from the two straightness measurements" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002817_tmag.2006.892268-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002817_tmag.2006.892268-Figure8-1.png", "caption": "Fig. 8. Main pole-tip region of the trailing shield head model. (a) Side view. (b) ABS view.", "texts": [ " In other words, if the throat height of the main pole is zero, the magnetization in the pole-tip area is not directed into the medium plane. Note that this result is different from that of conventional finite-element analysis, in which a zero throat height gives the largest recording field strength [3]. In perpendicular recording, a trailing shield [10], [11], which is placed behind the main pole, is used to obtain a high recording field gradient, which leads to sharper transitions in the medium and, finally, to a higher linear density recording. In Fig. 8, an SPT head model with the trailing shield is shown. As shown in Figs. 9 and 10, a steeper field at the trailing side is obtained as the main pole-trailing shield distance becomes smaller at the cost of reducing the maximum head field strength. The tendency shown is quite similar to the results from FEM calculations [3] except for the unsaturated regions [11], such as the return yokes. This paper described the micromagnetic simulation of an SPT head for perpendicular magnetic recording. An LLG calculation that treated the whole magnetic material micromagnetically was performed" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000592_icpst.1998.729039-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000592_icpst.1998.729039-Figure1-1.png", "caption": "Fig. 1 - Outline of the model (zoomed)", "texts": [ "K)] (7) The outside undisturbed fluid temperature was made equal to 3 13K. In the air gap the undisturbed fluid temperature was calculated iteratively. The outside fluid velocity was measured ( 5 d s ) and in the air gap it was assumed equal to half of the linear rotor speed. The finite element model was solved for balanced and unbalanced power supply situations considering 33% and full nominal mechanical torque. The unbalanced situations consisted of a 3-phase voltage system with one or two phases voltages reduced by 27%. In fig. 1 and 2 are presented respectively the outline of the model and the finite element mesh (1293 nodes and 2564 elements). -621 - IV. RESULTS In tables I, I1 and I11 are presented the rotor and stator hot spot temperatures (in Kelvin) for the balanced and unbalanced power supply situations. All the errors are referred to the experimental data values obtained in the laboratory tests. The unbalanced full load situations were not tested in order to avoid destroying the motor. In fig. 3 and 4 are presented the isothermal lines obtained with the finite element method corresponding to the balanced nominal conditions and to the 2-phases unbalanced power supply situation, with the equipotencials spaced by 1 K" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000299_robot.2001.932795-Figure12-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000299_robot.2001.932795-Figure12-1.png", "caption": "Figure 12. Photo of LCD panel display based RP system.", "texts": [ " From the experimental results, we can conclude that the proposed adaptive slicing can reduce almost 50 percent number of layers than uniform slicing method without reducing the model accuracy. B. Design and Implementation of Experimental Prototype for The Layered Manufacturing System In order to demonstrate that the proposed approach to adaptive slicing is more efficient than uniform thickness slicing methods, we can implement this algorithm on an LCD panel display based rapid prototyping system which we developed. The structure of the LCD panel display based rapid prototyping system is described in this section. As shown in Figure 12, the major configuration of this platform includes LCD photo-mask, optical system, z-axis elevator, resin supply system, and PC based control system. The Krypton point light source is located on the focus of the parabolic reflector; the parallel light can be generated through the reflection of parabolic reflector. Through the mirror refection, we can generate the parallel light passing through the LCD photo-mask to cure the photopolymer. The CAD model is generated layer-by-layer and attached to a platform that rises as each successive layer is attached to the bottom-most face" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001531_bf02128323-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001531_bf02128323-Figure1-1.png", "caption": "Fig. 1. Four bar Hnkage: scheme and symbols.", "texts": [ " The starting matrix H \u00b0 must be a positive definite symmetric matrix (for example, the identity matrix). It is possible to demonstrate that, if the function F(x) is quadratic, positive def'mite form the matrix H will approach the exact Hessian in so many steps as the number of design variables n. 3. CRANK-ROCKER MECHANISM SYNTHESIS. The above mentioned method is here used to synthetize a crank-rocker mechanism. Our tastk is to define the link lengths a, b , c and the phase angles c~, ~, which specify the starting positions o f bars a and c (fig. 1), in such a way that the output angle 0(~), generated by the motion o f the mechanism, approaches, as close as possible, the given desired angle 0(~). In the same time, the output angular velocity and acceleration o f the rocker, which are dependent on those o f the crank, are restricted within a certain region. The output angle in its non-dimensional form with respect to the frame length can be expressed (fig. 1) as function of the design variable vector x and of the independent variable ~b as follows: 0 = 0 ( x , ~ ) = 7r--~/-- 8 +/3 (3.1) where x = (a, b , c , c~, ~) and a is the crank R 2 = 12 + a 2 -- 2al cos (~b - - \u00a2~) (3.2) R 2 _ a 2 + 12 3' = + arcos (3 .3) 2R l DECEMBER 1981 21 ] | ! 0 + DESIRED FUNCTION 0 ( ~ 1 A OBTAINED FUNCTION O(~ ) I I I I I I I i I 2 3 4 5 ~ k et~k)-et~ k) VHAX=.50 A - . 1 6 2 5 6 6 B = . 9 2 3 2 1 9 C = . 3 4 3 5 4 6 ALFA- .034720 BETA=.123738 1 Fig. 2. Structural error as difference between desired and obtained functions" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000457_978-3-642-55848-1-Figure9.11-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000457_978-3-642-55848-1-Figure9.11-1.png", "caption": "Fig. 9.11. Quick return mechanism", "texts": [ " It describes the balance of moments as implied by Eq. (9.28). The LinRot component describes the transformation between the linear and angular quantities. The corre sponding transformation matrix, as given by Eq. (9.24), needs information on the joint rotation angle and of the position coordinate of the joint. The angle of rota tion is found from the integrator, which integrates the angular velocity taken from the corresponding junction. 340 9 Multibody Dynamics We apply the modelling approach described to the quick-return mechanism of Fig. 9.11. The mechanism is relatively simple, but it contains all the elements that we have discussed so far - the bodies and the rotational and prismatic joints. More complex problems are analysed in the sections that follow. The mechanism consists of a crank that rotates about a joint at 0 1 with angular velocity 0)0. The end of the crank is connected by a revolute joint at O2 to a block that can slide along another member, which, in tum, can rotate about the joint at O. This simple mechanism generates an oscillatory motion of the driven member with different forward and return times", " The system level model of the mechanism is shown in Fig. 9.12. Components Crank and Body are created using the body model of Figs. 9.2 and 9.3. To that end the components are copied from the library and inserted into the document. Some minor adjustments are necessary. Thus, the default name Body for crank component is changed to Crank, but is retained in the other member component. 2 Weights of the bodies are not included in the model. Thus the SE components of Fig. 9.3 are removed. The members are connected by joints at 0 and 01 in Fig. 9.11 to the ground represented here as Base. It is defined later. There are three revolute joints. Hence we create corresponding component models corresponding to Figs. 9.6 and 9.8 by copying from the library. The names 2 In order to change the name the component is disconnected from the bond lines both out side and inside. After the name has been changed, the bonds are redrawn. 9.2 The Modelling of a Rigid Multibody System in a Plane 341 are changed however to correspond to the symbols used in the scheme of the mechanism in Fig. 9.11, i.e. 0, 01 and 02. Similarly the prismatic joint compo nent JointT is taken from the library and inserted into the system level document (Fig. 9.12). All of the joints are frictionless. Thus, in joints 0 and 02 the resistive element R of Fig. 9.8 is disconnected and deleted. Also, the flow junctions are discon nected and deleted too. Because there is no moment transferred to nearby bodies, the corresponding bonds to the body angular velocity junctions are removed (including the corresponding ports at the junctions), as in Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001144_978-3-642-83410-3_7-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001144_978-3-642-83410-3_7-Figure2-1.png", "caption": "Fig. 2. Contact resolving fingertip sensor.", "texts": [ " Although it might be possible in some circumstances to calculate the location of the contact points from the joint positions, a fingertip sensor like the one proposed by Salisbury and developed by Brock and Chiu (1985) provides a more direct and reliable solution to the problem of determining the location and the orientation of a contact. A diagram of the fingertip sensor, which basically consists of a hemispherical cover supported by a structure that permits sensing of all three components of the applied force and all three components of the applied moment resolved at the origin of the sensing system, is depicted in Fig. 2. With the already mentioned assumption of contact occurring at a single point with friction, and with the additional assumptions that the shape of the fingertip contact surface is known and is convex, and that the contact exerts a force directed into the surface, the fingertip sensor (which incorporates small semiconductor strain gauges on metal flexures to measure the forces and the moments about the origin of the fingertip) is capable of reading the magnitude and direction of the resultant contact force as well as the location of the contact" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002856_robot.2007.363559-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002856_robot.2007.363559-Figure8-1.png", "caption": "Fig. 8. Line restriction over a rail", "texts": [ " The Graphic User Interface has been developed with Trolltech\u2019s QT library. The 3D visualizer is implemented using the COIN 3D libraries with the Flex++ and Bison parsers. In order to validate the proposed approach an experimental test was remotely performed using the teleoperation framework with the passive position drift free scheme. It consists on moving the robot end-effector along a rail with a line restriction. The proposed test has the following characteristics: a) The motion of the robot end-effector is restricted to a line in the x1 axis as shown in figure 8. b) The forces coming from the remote robotic cell fm provide information about the interaction of the end effector with the environment. c) The position commands xm correspond to the master position reflected on the restricted line, namely xr. d) Packets have been transmitted using TCP/IPv6 sockets with the scheme of a classical client-server application, providing higher IPv6 QoS to control commands than the video transmission. e) In order to illustrate the test the orientation and the torques have been omitted" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000184_pime_proc_1986_200_140_02-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000184_pime_proc_1986_200_140_02-Figure4-1.png", "caption": "Fig. 4 Forces in a narrow bearing during articulation", "texts": [ " The equations for quasi-static equilibrium may be written : pin : --F, sin t,h1 + G, cos - F , cos $, - GI sin $, + Po = 0 = 0 M o - Glrbi = 0 bush : R , sin A - P , sin 0 + F , sin $, - G , cos $, = 0 M O - G1rbi = 0 Stick or slip conditions can theoretically exist at the pin-bush interface, This depends upon the magnitude of the frictional angle of repose $, compared with the articulation angle 8. The algebraic solution of the above equilibrium equations can be written : 1. For tan 0 < p,. Under these conditions the frictional force is large enough to ensure pin stiction: F1 - = cos 0 PO 2. For tan 0 2 pl.. Under these conditions the frictional force is insuficlent for stiction and pin slip occurs: For both these conditions, the following apply : _ - P , Po sin(4 + a) sin(4 + a - 0) R , sin 9 P o sin(4 + a) _ - 2.2 Narrow end forward (3) (4) The schematic in Fig. 4 shows the corresponding forces and motion involved in this type of chain bearing articulation. As before, the sprocket tooth force is transmitted to the bush, which in this case is press-fitted into the succeeding link Lo. This link remains effectively horizontal and under tension Po throughout articulation. The pin in contact with the bush is press-fitted into the preceding link L, which makes an angle of 6 with the succeeding link Lo. in this case, as the sprocket turns, two points of contact in the bearing experience relative motion, that is at the pin-bush interface and the rollerbush interface" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002001_1.3453240-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002001_1.3453240-Figure4-1.png", "caption": "Fig. 4 Pressure distribution for a long, porous bearing for various values of Co. E = 0.5, 12<1>IIc3 = 1.0, ,., = constant", "texts": [], "surrounding_texts": [ "H. D. Conway Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, N. Y. he Lubrication Flexible Jouraa a Long, Porous, earing Solutions are obtained for the pressure distributions in porous, flexible long bearings. The oil is assumed to have a viscosity which is either (a) constant or (b) varying with pressure according to the law JJ = i]0e aP. Finally, a method is given whereby the pressure distribu tions in porous, flexible bearings can be found approximately from the corresponding values for non-porous bearings. The limits of validity of the approximation are investi gated. I n t r o d u c t i o n Porous material bearings are very commonly used, particularly for lightly loaded applications. An important reason for their popu larity is that they require no external lubrication and consequently they can be used in inaccessible locations. One of the very first theoretical studies of porous bearings was that of Morgan and Cameron [l] .1 This analytical work was further in vestigated and extended by Cameron, Morgan and Stainsby [2]. The latter research indicated that porous metal bearings will run under fully hydrodynamic conditions below a certain critical load provided there is a sufficient supply of oil. Above this critical load, the eccen tricity ratio approaches unity, inferring that the shaft touches the inner surface of the bearing and consequently hydrodynamic lubri cation ceases. The analysis of porous metal bearings was further extended by the researches of Rouleau [3], Sneck [4], Murti [5], and Cusano [6]. Rou leau [3] gave the analysis of narrow, press-fitted porous metal bearings by assuming that the thickness of the bearing was small. Sneck [4] compared the performances of porous and nonporous bearings at moderate eccentricity ratios. Both Murti [5] and Cusano [6] showed that solutions for the pressure distributions in porous, rigid journal bearings could be obtained in cylindrical coordinates, and relaxed the assumption of small bearing thickness. All the above journal bearing investigations were based on the as sumption that the bearing shell is rigid. The effects of bearing flexi bility on the oil film thickness and hence on the lubrication of the journal itself were ignored. Recently the effects of flexibility on lu brication for long and short impervious bearings were studied by Conway and Lee [7], [8]. In impervious bearings there is no normal component of the oil velocity across the interface of the oil film and the bearing shell. 1 Numbers in brackets designate References at end of paper. Contributed by the Lubrication Division for publication in the JOURNAL OF LUBRICATION TECHNOLOGY. Manuscript received by the Lubrication Division, November 10,1976; revised manuscript received April 18,1977. However, this is not the case in porous bearings. The effect of both bearing porosity and flexibility has recently been investigated by the authors for short bearings [9]. As an alternative approach, the investigation is extended here to the case of long porous bearings. The bearing material is again as sumed to be both porous and flexible. This is considered appropriate because although porous bearings are usually lightly loaded, they are also flexible, with a modulus very much lower than that of the solid metal [10]. The stress-strain curve for a typical porous metal is given by Cameron in [10]. This curve is linear up to the quite large stress of 104 psi (6.9 X 107 Pa) with a small effective modulus of about 1.2 X 106 psi (8.27 X 109 Pa). We would expect similar behavior in porous ma terial bearings. The peripheral length of bearings is usually much larger than their thickness, and the bearing shell can frequently be considered as a thin tube surrounded by a relatively rigid housing. It follows that the re sponse of the bearing can be modelled as a Winkler foundation [7], where in the latter is replaced, analytically, by a series of springs which can deflect independently of one another. To consider the validity of such a foundation model, the following simple experiment was performed. A large, thin, flat slab of porous material was compressed by a flat indenter of width equal to the slab thickness. It was observed that the comparison of the slab was largely confined to the material directly under the indenter, the material at short distances away being virtually unaffected. This indictes that the Winkler model is a reasonable one, provided the bearing shell thickness is not too thick. Since the thickness of the bearing shell is already assumed small in adopting the Winkler model, it is in keeping to assume that the pressure gradient in the shell is linear across the material of the bearing, and is zero at the outer surface of the bearing shell. This greatly simplifies the analysis. The shaft and housing are both assumed rigid and their deforma tions are ignored. These are reasonable assumptions in conventional design. Other assumptions which are used to analyze the long, porous bearing may be stated as follows: (1) The lubricant is Newtonian and is incompressible. Journal of Lubrication Technology OCTOBER 1977 / 449 Copyright \u00a9 1977 by ASME i li of , , w. c. l l 01 ll l i l n l lutions tained essure tributions us, l xible i gs. T sumed e cosity ich ther stant ying th press rding e 1) 1)o aP. a ly, thod en reby ssure distrib s rous, l xible ings und roximately cor espon l es -porous i gs. its lidity f e roximation invest . t t . 1 .1 r . ll i iti l t i iti l l i t r i ffi i nt l f il. t i riti l l , t tri it r ti r it , i f rri t t t ft t t i er s rface f t e eari a c se e tl r a ic l ri cation ceases. r , itt t t i it ti . t ti l ti t i t i ti i , i i j l ri l t i i li ri l r i t , r l t ti f ll ri t i . t lf t i ti l t i i i t i , . t 1 r. , , 1 l i i l t t l . . i r is li t t it l r str l04 7 l i 6 9 l ~odel t tl it f ll t . ~ n d t i t i i t ll t . i i i t t i l r l i r l , r i t ri ll t ic ess is t t t ic . tl i li i t l i . t f l : t Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/26/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use (2) The problem is an isothermal one. (3) End leakage for the bearing is ignored. (4) The pressure p is zero at a point denoted by 0 = o. Also p = dp/dO = 0 at 0 = 'Y > 180 degrees. These are so-called Reynolds' conditions. (5) The flow in the oil film satisfies Reynolds' equation appropriately modified for the porosity of the shell. (6) The oil flow in the porous shell is governed by Darcy's law. (7) The permeability is constant. (8) The pressure is continuous across the porous bearing. (9) The normal component of the velocity across the porous boundary is continuous. Analysis (a) Constant Viscosity Oil. Assume that the flow in the porous shell in Fig. 1 is governed by Darcy's law if> of> ql = --- 71 0/ where if> is the permeability, 71 is the viscosity and f> is the pressure in the porous medium. Denote qx, qy, and qz as the respective flows in the x, y, and z directions of the medium. Then continuity of flow in the latter gives a a a - (qx ) + - (qy) + - (qz) = 0 ox oy oz or to the peripheral length of the bearing, it is reasonable to express the pressure gradient across the matrix in Cartesian coordinates. In ad dition it is also reasonable to assume that of>/oy is linear across the porous matrix ofthe bearing shell. Finally of>/oy is zero at the outer surface of the shell, since there is no radial flow of oil there. These ~ (_!. Of\u00bb + ~ (_!. Of\u00bb + ~ (_!. Of\u00bb = 0 ~ 71~ ~ 71~ ~ 71~ (1) assumptions can be expressed as Since the axial pressure gradients in a long, porous bearing are much smaller than the circumferential ones, the term involving the former is neglected. Also if> and 71 are assumed to be constants, so that equa tion (1) reduces to the two-dimensional Laplace equation. The well known Reynolds' equation for a thin film [1) is given as ~ (h 3 OP) + ~ (h 3 OP) = 6U (dh) + 12(Vh - Vol ox 71 ox OZ 71 OZ dx (2) (3) Under steady load, V h = 0 at y = h, the surface of the shaft. In addi tion Vo is the oil velocity into the porous shell at the inner bearing surface y = o. From Darcy's law Vo can be written in the form Thus equation (3) becomes ~ (h 3 OP) + ~ (h 3 OP) = 6U(dh/dx) + 12!. of> I ox 71 ox OZ 71 OZ 71 oy y=o (4) Since op/oz is neglected compared with op/ox for a long bearing, equation (4) reduces to ~ (h 3 OP) = 6U (dh) + 12!.. of> I ox 710 ox dx 710 oy y=o where 71 = 710 for a constant viscosity oil. Since the thickness of the bearing shell is usually small compared C~ = Co/(1 + 12if>t/c 3 ) of> of> I -=w(y+t)and- =0 oy oy y=-t (5) where w = w(x) and Vo = - !. of> I = - !. wt 71 oy y=o 71 From equation (5) and (2), we obtain 02f> 02f> -=--=-w ox 2 oy2 Since the pressure is continuous at the interface of the oil and the bearing shell, it follows that f> I y=o = P and equation (4) becomes a (h 3 OP) U (dh) if>t 02p (6) ox 710 ox = 6 dx - 12 710 ox 2 or d [h 3 dP] (dh) if>t d 2 p dO 710 dO = 6UR 1 dO - 12 710 d0 2 since dx = RldO. Taking into account the radial compression of the bearing shell and using the Winkler foundation hypothesis, the equation of the oil film thickness is written as (7) h = c(1 + \u20ac cosO) + pt(1 - vij)/E (7) where Vo = a quantity between Poisson's ratio v (tangential stress = 0) and [2v2/(I- v\u00bb)1/2 (tangential strain = 0) [7). Substituting (7) into E = e/c c = radial clearance in bearing e = eccentricity h = film thickness E = modulus of elasticity of bearing R 1 = inner radius of the bearing E* = d(1 + 12if>t/c 3 ) v = Poisson's ratio of the bearing p = pressure in the oil film f> = pressure in the porous medium p = pc 2/6 U7IoR 1 t = thickness of bearing shell Co = 6U7IoRlt(1 - vij)/Ec 3 450 / OCTOBER 1977 R2 = radius of the shaft U = peripheral velocity of shaft a = constant in 71 = 710e cxP a = 6a7l0URdc2 'Y = value of 0 where p = dp/dO = 0 Vo = a quantity between v (tangential stress = 0) and [2v2/(I- v\u00bb)1/2 (tangential strain = 0) 71 = viscosity if> = permeability Transactions of the ASME Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/26/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use (6) !!.- [(h 3 + 12<1>t) d P ] = 6T/oUR1 [-e sinll + t(I- vg) dP / E ] dll dll dll and integrating the above equation from 'Y to II dp = 6T/oURde(cosll- cos')') + pt(I - vg)/E) dll [h 3 + 12<1>t) (8) We next introduce a nondimensional parameter p = pc 2/6UT/oRl and equation (8) reduces to p(lI) = f O [E(COS~ - cos')') + CopW) d~ (9a) Jy [(1 + E cos~ + COp(~))3 + 12<1>t/c3) where Co = 6T/oUR 1t(I - vg)/Ec 3. Since from the Reynolds' conditions 56 (dp/dll)dll = 0, it follows that Sa y [E(COS~ - cos')') + CopW) d ~=O o [(1 + E cos~ + COp(~))3 + 12<1>t/c 3) By adding (9a) and (9b), we finally obtain p(lI) = f O [E(COS~ - cos')')+ CopW) d~ Jo [(1 + E cos~ + COp(~))3 + 12<1>t/c 3) (9b) (10) Equation (10) gives the formal solution for the pressure distribution in a long, porous bearing. In order to compute the integral in (10), a trial value of')' is first assumed. Then values of E, CO and 12<1>t/c 3 are selected and p(lI) found from (10). The restraint equation (9b) is then checked to see if it is satisfied. If it is not, another value of')' is assumed and the procedure repeated until it is. For small values of E and Co, (10) can be expressed in the approxi mate form -() So\u00b0 [E(COS~ - cos')') + CopW) d p II \"\" ~ o [(1 + 3E cos~ + 3CopW) + 12<1>t/c 3) Two new parameters E* and C~ are now introduced such that E* = E/(I + 12<1>t/c3), C~ = Co/(I + 12<1>t/c 3) and the approximate form of the pressure is written as p(lI) '\" f O [E*(COS~ - cos')') + C~pW) d~ (11) Jo [1 + 3E* cos~ + 3C~pW) Equation (11) is seen to have the same form as the corresponding one for impervious bearing. It follows that the results obtained by Conway and Lee [7) for impervious bearings will also apply, approximately, for porous bearings provided that E and Co in [7) are redefined as E* and C~ respectively. The validity of this approximation will be in vestigated. As mentioned above, equation (10) can be solved numer ically for an assumed value of ,)\" and the trapezoidal method used to obtain non-uniform step sizes required for accurate representation. Thus equation (10) is written as p(O) = 0 () ; _---\"[....:E(.:..co_s~IIJ'-\u00b7 -_c_os_')'c.,:)_+_C.::!op;....(:.,.IIJi,:.\u00b7).!..)o.t.,j_ P II; = L j=l [(1 + E cosllj + Cop(lIj))3 + 12<1>t/c 3) If error\"\" 0 for an assumed')' = liN and if p(n)(IIN) = p(n)( ')') = 0, then the iteration is assumed complete and the test satisfied. (b) Variable Viscosity Oil. In this analysis the viscosity is assumed to vary with pressure according to the equation T/ = T/oe cxp where C/ is a constant. Continuity of flow in the bearing matrix gives \u00b0 \u00b0 - (qx) + - (qy) = 0 ox oy which leads to [ -C/ (OP)2 + 02p ] + [-a (OP)2 + 02p ] = 0 (12) ox ox 2 oy oy2 As before, the thickness of the shell is small compared to the periphery of the bearing, and op! oy is assumed linear across the matrix and zero at y = -to Then op 02p -= w(y + t) and-= w oy oy2 (13) where w = w(x). Again, at the interface of the oil film and the bearing shell, the pressure is continuous and p = p !y=o. Substituting (13) into (12), we have w(I - C/wt 2) = - -- C/ -[ 02p (OP)2] ox 2 ox (14) In practice C/wt 2 is a small quantity, typical values of C/ being 0.00124 cm2/kg at 25\u00b0C and 0.0006 cm2/kg at 100\u00b0C [11). Thus it is reasonable to expect that awt 2 \u00ab 1. This has the effect of greatly simplifying the analysis. Hence equation (14) can be written in the approximate form w \"\" _ [02P _ a (OP)2] ox 2 ox (15) Since Reynolds' equation allowing for the presence of the porous medium is ~ [h 3 OP] _ 6U (dh) + 12 ~ op I ox T/ ox dx 1] oy y=O Substituting (15) into (16), we have !!.- [(h 3 + 12<1>t) dP] = 6U (dh) dx T/ T/ dx dx where T/ = T/Oe cxP\u2022 The oil film thickness is and h = c(I + E cosll) + pt(I - vg)/E dh dp - = -e sinll + t(I - vg)/E dll dll Substituting (18) into (17) gives dp 6T/oUR1[E(cosll- cos')') + pt(l - vg)/E) -= eap dll [h 3 + 12<1>t) (16) (17) (18) (19) i= 1,2, ... ,N-I Introduce the non-dimensional pressure p = pc 2/6UT/oRl and (19) reduces to where N = number of subintervals and and O. = {(t::.llj + t::.llj+l)/2 J t::.11;/2 j = I,2,(i - 1) j = i N ')' = L t::.llj j=l For the iteration procedure, (10) is expressed as ; [E(cosll\u00b7 - cos')') + Cop(n-l)(II'))o' p(n)(II;) = L J J J j=l [(1 + E cosllj + Cop(n-l)(lIj))3 + 12<1>t/c3) Here n denotes the number of iterations required to satisfy the con vergence test as follows. Set error = r;a~2,,, N_l!p(n)(II;) - p(n-l)(II;j!. Journal of Lubrication Technology p(lI) = f O [E(COS~ - cos,),) + CopW) eapd~ J'Y [(1 + E cos~ + COpW)3 + 12<1>t/c3) (20) where Co = 6UT/oRlt(1 - vg)/Ec 3 and a = 6C/T/oURdc 2 Since 56 (dp/dll)dll = 0, it follows that Sa y --!..::[ E..:..:( c...:.o.:..:s~,--.....:...co~s..!..')':....) _+_C-\"o!....p..:..:(~\"\") '---- -d eCXP ~ = 0 o [(1 + E cos~ + CopW)3 + 12<1>t/c3) (21) Equation (20) can then be expressed as -(II) SaO [E(COS~ - cos')') + CopW) -p = ecxPd~ o [(1 + E cos~ + CopW)3 + 12<1>t/c 3) (22) Equation (22) gives the formal solution for the pressure distribution in a long, porous bearing for an oil having a variable viscosity T/ = OCTOBER 1977 / 451 Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/26/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use ,.,oe\"p. The computation of the integral in (22) is similar to that in (10). Values of E, CO, IX and 12<1>t/c3 are selected and a trial value of)' is assumed. We then find j5 from (22) and check to see if equation (21) is satisfied. If it is not, another value of)' is assumed and the process repeated. Similarly the approximate solution for an oil having pressure dependent viscosity can also be obtained by introducing E* = e!(1 + 12<1>t/c 3) and C~ = Co/(l + 12<1>t/c3) such that -(0) 50 0 [E*(COS~ - cos),) + C~j5W] -d p = e\"P ~ \u00b0 [1 + 3E* cos~ + 3C~j5W] (23) It follows once again that the impervious results obtained by Conway and Lee [7] for the pressure-dependent viscosity case will also apply, approximately, to the porous bearings provided E* and C~ replace E and Co, respectively. Results and Calculations Before performing a numerical analysis, a value of the nondimen sional term 12<1>t/c3 is required, the permeability being assumed constant. Various porous metal bearings have permeabilities ranging from 15 X 10-12 in2 (100 X 10-12 cm2) to about 300 X 10-12 in2 (2000 X 10-12 cm2) [10]. Thus for a bearing material having = 1500 X 10-12 cm2, t = 0.508 cm and c = 2.54 X 10-3 cm, 12<1>t/c3 is about 0.54. Thus values of 12<1>t/c 3 = 0.25 and 1.0 were used in the calcula tions. Graphs of normalized pressure j5 = pc 2/6Uwfi 1 were plotted using the numerical scheme previously outlined. Typical plots for constant viscosity oil and 12<1>t/c3 = 0.25 and 1.0 are given in Fig. 2, 3, 4, and 5 for values of eccentricity ratio E = e/c of 0.5 and 0.75, respectively, and with various values2 of Co = 6U,.,oR1t(1 - va)/Ec 3. It is observed that, for fixed values of eccentricity ratio, the normalized pressures p reduce with increasing values of 12<1>t/c3 from 0.25 to 1.0, particu larly for the smaller Co values. It is also observed that, for fixed values of Co, the normalized pressures increase with increasing values of E from 0.5 to 0.75, particularly for smaller values of 12<1>t/c3. It was already concluded by Conway and Lee [7] that the normal ized pressures for non-porous long bearings are quite sensitive to 2 For a rotational speed N = 1500 rpm, t = 0.2 in (0.50S em), ~o = 3.3 X 10-6 Rey. for SAE 30 oil at 160\u00b0F, Rl = 1 in (2.54 em), E = 106 psi (6.S9 X 109 Pal, \"0 = 0.3, c = 10-3 in (2.54 X 10-3 em), the constant Co is about 0.57. 452 / OCTOBER 1977 variations in the value of the parameter Co. As observed from Fig. 2, 3, 4, and 5, a similar behavior is found for both porous and impervious bearings, especially for larger values of eccentricity ratio. It is also seen that, for fixed values.of E and Co, the normalized pressures for a porous bearing are smaller than those for a corresponding nonporous one. The reductions in the normalized pressure increase with increase in the value of the permeability. Transactions of the ASME Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/26/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use Typical plots for E = 0.2 and 0.3, 12t1>t/c 3 = 1.0 and for various values of Co are given in Fig. 6 and 7 in order to compare the exact results for porous with the approximate ones obtained from the im pervious solution. As observed from Fig. 6 and 7, it is seen that the results obtained in [7] may also apply, approximately, for porous bearings provided E and Co are substituted by E* and C~, respectively. However, the comparison becomes increasingly poorer beyond E* = 0.15 as seen from Fig. 7. Nevertheless the approximate solution is good provided the values of E* and C~ are small. Journal of Lubrication Technology Finally graphs of normalized pressure p for an oil having a pres sure-dependent viscosity3 11 = 110eCiP are given in Fig. 8 for E = 0.5, Co = 0.2, and a = 6Ci110URt/c2 = 0,0.2,0.4 and 0.6. A typical comparison of the exact pressure distributions in porous, flexible bearings is made in Fig. 9 with the approximate distributions obtained from the non porous solution. Referring to the variable viscosity results given in Fig. 8 and 9, it is seen that the larger the value of a, the larger will be the normalized pressure. A comparison made between the exact solution for porous bearings with the approximate one obtained from the impervious 3 For a pressure-dependent viscosity oil with a = 0.0008 cm2/kg, N = 1800 rpm, viscosity ~ = 5 X 10-6 Rey. for SAE 30 oil at 140\u00b0F, Rl = 1 in (2.54 em), c = 10-3 in (2.54 X 10-3 em), the constant a is about 0.3. OCTOBER 1977 / 453 Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/26/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use solution shows good agreement for small values of f* and C~, even for an oil having variable viscosity. Finally it is concluded that the effects of flexibility for porous bearings are more significant than those for impervious ones, par ticularly for bearing materials having high porosity. Based on the normalized pressure curves shown in the above figures, it is also 454 j OCTOBER 1977 concluded that the effects of deformation should not be ignored for Co> 0.5 for constant viscosity oils and for a > 0.3 for variable viscosity oils with Co = 0.2. For large values of Co, the effects of variable vis cosity will be more pronounced. References 1 Morgan, V. 1'., and A. Cameron, \"Mechanism of Lubrication in Porous Metal Bearings,\" Institution of Mechanical Engineers-Proceedings, 1957, pp. 151-157. 2 Cameron, A., V. T. Morgan and A. E. Stainsby, \"Critical Conditions for Hydrodynamic Lubrication of Porous Metal Bearings,\" Institution of Me chanical Engineers-Proceedings, Vol. 176, No. 28, 1962, pp. 761-770. 3 Rouleau, W. 1'., \"Hydrodynamic Lubrication of Narrow Press-Fitted Porous Metal Bearings,\" Journal of Basic Engineering, TRANS. AS ME, Vol. 85,1963, pp. 123-128. 4 Sneck, H. ,I., \"A Mathematical Analog for Determination of Porous Metal Bearing Performance Characteristics,\" JOURNAL OF LUBRICATION TECHNOLOGY, TRANS. ASME, Series F, Vol. 89, 1967. 5 Murti, P. R. K., \"Pressure Distribution in Narrow Porous Bearin!!s,\" JOURNAL OF LUBRICATION TECHNOLOGY, TRANS. ASME, Serie~ F, Vol. 93, 1972, pp. 512-513. 6 Cusano, C., \"Lubrication of Porous Journal Bearings,\" JOURNAL OF LUBRICATION TECHNOLOGY, TRANS. ASME, Vol. 94, 1972, pp. 69- 73. 7 Conway, H. D. and H. C. Lee, \"The Analysis of the Lubrication of a Flexible Journal Bearing,\" JOURNAL OF LUBRICATION TECHNOLOGY, TRANS. ASME, Oct. 1975, pp. 599-604. 8 Conway, H. D. and H. C. Lee, \"The Lubrication of Short, Flexible Journal Bearin\"s,\" to appear in JOURNAL OF LUBRICATION TECH NOLOGY, TRANS. ASME. 9 Mak, W. C., and H. D. Conway, \"Analysis of a Short, Porous, Flexible ,Journal Bearing,\" to appear in the International Journal of Mechanical Sci ences. 10 Cameron, A., The Principles of Lubrication, Wiley 1967, pp. 543- 559. 11 Tipei, N., Theory of Lubrication, Stanford University Press, 1962, pp. 30-31. Transactions of the ASME Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/26/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use" ] }, { "image_filename": "designv11_32_0001991_ip-nbt:20050003-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001991_ip-nbt:20050003-Figure3-1.png", "caption": "Fig. 3 Schematic representation of cyt c modified with Ada fixed on electrode surface modified with CD", "texts": [ " On the other hand, a silver electrode was modified by the formation of an SAM of perthiolated b-CD (b-CDSH) [32]. The defect sites present in the monolayer were not covered (sealed) to avoid a reduction of the active electrode surface. On the other hand, no spacer arm was introduced between b-CD and the thiol groups, so that the charge transfer resistance was not increased [33]. Adamantane-modified cytochrome c (Cyt c-Ada) was then supramolecularly fixed on the modified electrode surface through the inclusion of one or more Ada units into the CD cavities, as schematically represented in Fig. 3. The voltammetric response was a quasi-reversible wave with E1=2B0.18V (against Ag/AgCl), which was very stable and reproducible. The intensity of this signal was not affected by immersion of the electrode in a buffer solution. Overnight immersion in a solution containing 1-adamantanol made this signal disappear. These observations indicate that Cyt c-Ada was strongly fixed to the electrode surface through the inclusion of more than one Ada unit into the CD cavities, that is, through a multivalent supramolecular association [25]" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-FigureA.2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-FigureA.2-1.png", "caption": "Fig. A.2. Optics and accessories for angular measurements", "texts": [ " An angular measurement is concerned with the measurement of the angular displacement (tilt) of the moving part (on which the angular reflector is mounted) from the ideal position. This angular displacement may vary with the linear travel distance of the moving part. The primary causes of an angular deviation include the physical guide imperfections and possibly cogging related effects. The optics and accessories used for the angular measurement are rather similar to those used for linear measurements. A breakdown of these devices and accessories is given in Figure A.2. The set-up for pitch and yaw measurements are given respectively in Figure A.3 and Figure A.4. A closed-up view of the traverse path of the laser beams is given in Figure 5.7 which illustrate that the angular measurement is comprised of two linear measurements at a precisely known separation. Roll measurement is addressed separately in the next section as this measurement will typically require a level-sensitive device to be used. The objective of a straightness measurement is to determine whether the moving part is moving along a straight path" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000457_978-3-642-55848-1-Figure1.3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000457_978-3-642-55848-1-Figure1.3-1.png", "caption": "Fig. 1.3. A simple electro-mechanical actuator", "texts": [ "2 The General Modelling Approach 5 It is, of course, also of interest to study the influence of the system on its envi ronment, e.g. the current drawn by a system from an external source. In the case in which the system can change its environment in a way that there is a 'backwards' influence on its own behaviour, the system should, in most cases, be enlarged to include this part of its environment. It is often useful to decompose a system into components. For example, the simple actuator illustrated in Fig. 1.3 consists of an electric motor driven by a con troller. The motor shaft is connected to a nut. The shaft rotation is transformed by the nut into a translation of an actuator shaft, which moves a load. The position in formation of the load is fed back via a sensor to the controller. Every part of such a system, i.e. the electronic drive unit, motor, shaft, etc., may be modelled as a separate component. The complete model of the drive thus may be depicted as a system of interconnected components. Decomposition of the complete system into its components generally simplifies the modelling task and gives a sharper insight into the system's structure", "selModelica Chapter 2 Bond Graph Modelling Overview The bond graph physical modelling analogy provides a powerful approach to modelling engineering systems in which the power exchange mechanism is impor tant, as is the case in mechatronics. In this chapter we give an overview of the bond graph modelling technique. The intention is not to cover bond graph theory in detail, for there are many good references that do this well, e.g. [1,2]. The pur pose is to introduce the reader to the basic concepts and methods that will be used to develop a general, systematic, object-oriented modelling approach in Chapter 3. Many engineering systems consist of components, e.g. electric motors, gears, shafts, transistors etc. (Fig. 1.3). Simulation models of such components can be represented as objects in the computer memory and depicted on the screen by their name, i.e. any word description chosen to describe the component (Fig. 2.1). The component name is useful for reference to the model, but what is more im portant is to represent how the component is connected to other components. When we look at a component, the internals of its design are usually hidden (e.g. by its housing). What are seen instead are the locations at which it connects to other components" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002589_3.50382-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002589_3.50382-Figure1-1.png", "caption": "Fig, 1 Positive directions for *//, 0, a and (p.", "texts": [ " of the nonrotating blade Radius of the disk (r) Length of the blade (L) where D = Et3/l2(l - t = thickness of the blade; ju = Poisson's ratio The results are presented for an uncambered blade, with aspect ratio (L/b) = 2, thickness ratio (b/t) = 16 and ju = 0.3. The examination of the pseudo-static deformations reveals that the blade undergoes a torsional deformation, in addition to a small longitudinal deformation. The total torsional deformation of the blade is given by = 4>x + yz, where 0yz is deformation due to the components Fy1 and Fzl9 and x is deformation due to Fxlf The positive direction of \\l/9 $ and 9 are shown in Fig. 1. Variation of $x with \\l/ is shown in Fig. 2. Deformation ^js observed to be given by the empirical relationship 0yz ~ \u2014 (Q2 sin 2 0, the state is defined as \u2018\u20180\u2019\u2019, as shown in Fig. 2(a). In contrast, in the case of s < 0, the state is defined as \u2018\u20181\u2019\u2019, as shown in Fig. 2(b). The rotation angle of polarization is expressed by an azimuthal angle , which is the azimuth of the polarization ellipse with respect to the Ex axis. In the case of the binary coding, the boundary of the two states is set to 45 in azimuth. Namely, if the azimuthal angle is less than 45 , the horizontal component becomes larger than the vertical component and the state becomes \u2018\u20180\u2019\u2019. In contrast, the state becomes \u2018\u20181\u2019\u2019 when the azimuthal angle is larger than 45 Here, state \u2018\u20180\u2019\u2019 is assumed as the initial state" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002400_j.mechmachtheory.2006.01.005-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002400_j.mechmachtheory.2006.01.005-Figure1-1.png", "caption": "Fig. 1. Support and drive configuration of a conventional (left) and a pouch (right) belt conveyor.", "texts": [ " After the application of a correction factor to account for the interaction between adjacent elements, which is initially not modelled, experimental results show that the model generates a satisfactory match and that belt speed has little effect on traction in the feasible speed range. 2006 Elsevier Ltd. All rights reserved. Keywords: Rolling contact; Traction; Viscoelasticity; Maxwell model; Pouch belt conveyor; Curved belt surface Traditionally belt conveyors for transporting bulk material have a drive station at the head and/or tail of the system where the belt is wrapped around a drive pulley, see Fig. 1. It is a well proven drive configuration for belt conveyor systems with a single or dual drive stations. However, problems arise when more than two drive stations are desired. Due to the fact that the drive pulley cannot be placed at any arbitrary location along the carrying strand of the belt without interfering with the bulk material flow on the belt, it cannot take full advantage of the benefits a distributed drive system has to offer. An alternative drive method, which offers greater layout flexibility in a multiple drives system, is to implement drive wheels that directly press onto the belt\u2019s surface to generate the desired traction force" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000361_amc.2002.1026960-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000361_amc.2002.1026960-Figure3-1.png", "caption": "Fig. 3 Desired Path", "texts": [ " And by the computed input torque the acceleration of each link becomes equal to the desired acceleration, Therefore, a relationship between a desired path and joint angles must be found. The desired path is decided as following. (1) A position of COM tracks a circle of which a center is on the y axis. 43 8 ( 2 ) A position of a heel of a swing-leg tracks a circle, of which a center is on the y axis. At the same time, a center angle of a heel increases in proportion to one of COM. At first, a coordinate system, of which the origin is at the toe of support-leg, is set (Fig. 3). And a COM (xcOMrrLd, yCOMer,,,) at next landing is selected. A desired trajectory circle is determined as follows: its circumference is through two points, landing point of COM ( x c o M ~ 7 r d , yCOMrrrd) and starting point of COM (zcOMYtart, ycOMbtori), and its center is on the y axis (Fig. 3). The radius ~b~~ and central angle sCOM is expressed as Eq. (2)(3). Where xcOM and yCoM are expressed by Eq. (4)(5). ( 5 ) A desired trajectory circle of a heel of a swing-leg is decided as same way from landing point ( x R e u L d , y5e ,Ld) , starting point ( xgy tnT t , ygsti,,.t) , and its center on the y axis. The radius rg and a central angle s, are expressed as Eq. (6)(7). Where ( x g , y 5 ) is the position of a heel of a swing-leg, which is expressed by Eq. (8) and Eq. (9). This xCOMPlLd is equal to xsend, because the COM goes to just overhead point of a heel when a swing-leg lands" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000364_robot.1988.12028-Figure13-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000364_robot.1988.12028-Figure13-1.png", "caption": "Figure 13: Liftability Regions for Two-Point Grasp.", "texts": [ " is the only element of the most important window, the translat ion window, TW (see Figure 12). Third, the regions J , B3, B4, and T are defined by considering the possible contact normals of the points in region 11. Each point whose normal intersects 4 3 and P3 or J3 belongs to the liftability region B3 or J, respectively. Similarly, if the normal intersects Q4 and P4 or 54, the point belongs to B4 or J, respectively. Any point whose normal passes through TW and P3 or 53 belongs to T or J respectively. Figure 13 shows the liftability regions for the object. Notice that for the two-point initial grasp considered, T is only one orientation of contact against the vertex and thus is unusable. Including another contact in region, I, allows T to grow. The line of action of the new contact force, f5, defines four new points of interest, 915. 453, 954, and 9sg (see Figure 14). The translation window now becomes the closed line segment lying between q l g and qsg. As before, the windows Q3 and 4 4 lie above and below TW" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002242_bf00534484-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002242_bf00534484-Figure2-1.png", "caption": "Fig. 2o. Comparion between theoretical and Fig. 21. Comparion between theoretical and experimental results experimental results", "texts": [ " An appreciable difference is found between the cases of tensile and torsional prestrains. The functions best-fi t ted to the experimental results are as follows : For the case of tensile prestrain A = 2 48o ~1 . . . . s~, / ( = o.784 q- o.152 ~ - - o.oo434 ~ , (17) Ing. Arch. Bd. 44, H. 4 (1975) M. Tanaka et at. : On Hardening Theory of Plasticity 259 2,0\" 1,0 ~jo.O-O o ~ \\ '5 q / , 1,0 2,0 o' , , /o 'o Fig'. t. Subsequent yield surfaces determined as best-f i t ted to measured data[173 )1 2~0 6~ 16~\" o L / ~ - ~ / , - 0 1:0 2,0 0\"~/no Fig. 2. Subsequent yield surfaces determined as best-f i t ted to measured da ta [17] 2,0 1~0' / / . / / y.x.~ _ , .oj__.,\" I 1,0 2,0 O'x/6o Fig. 3. Subsequent yield surfaces determined as best-f i t ted to measured da ta [177 Ing. Arch. Bd, 44, H. 4 (2975) 18 ' 260 M. Tanaka et al. : On Hardening Theory of Plasticity and for the case of to rs iona l p re s t r a in A ---- 5 727 ~/-~.o8~, K ---- o.717 + o.12o ~ - - 0.o0493 ~ . (18) I n Figs. 8 and 9, the solid lines ind ica te the resul ts o b t a i n e d f rom (17) and (18) respec t ive ly " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001728_1.1844992-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001728_1.1844992-Figure2-1.png", "caption": "FIG. 2. Setup consisting of two V-grooved guideways between which two balls roll. One guideway is fixed, while the other is actuated with a linear actuator.", "texts": [ " At the end of this section the results of the different setups are compared and discussed. Figures 2 and 3 show the setup considered in this subsection. It consists of two V-grooved rails between which two balls roll. One rail is fixed, while the other is actuated in the sliding direction by a linear exciter sBr\u00fcel & Kj\u00e6r 4810d. The force on the guideway is measured by a force sensor sKistler-GEPA 9031d. The relative displacement between the two guideways is measured by an eddy-current displacement sensor sBently type 3300d. As Fig. 2 shows, there is also a possibility to vary the preload on the guideway. Rails of different geometry sV-angled can be mounted and different balls ssize and materiald can be inserted between the rails. In this way, the influence of these variables on the hysteretic friction can be measured and classified. These influences are, however, out of the scope of this paper, as our intention is only to validate the dynamical behavior described in Part I of this paper, and will be subject of a separated communication, see Ref" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000309_apec.2001.912472-Figure11-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000309_apec.2001.912472-Figure11-1.png", "caption": "Figure 11 shows the dynamic response of a completely sensorless DTC drive where the initial rotor position has been determined using the method described in the previous sections. These results are similar to what are obtained when the initial rotor position is taken from an encoder.", "texts": [], "surrounding_texts": [ "The error is found to be within the range of -7\" to +7O mechanical which is quite acceptable for the DTC\nE s t i m a t i o n e r r o r ( m e c h . d e g . )\n882", "It is observed fiom figure 4 and figure 7 that the estimated rotor position exists only over the range 0 to 180 \" even though the actual rotor position exists all over the range 0 to 360\". As Ii(r) is periodic, the measured position is also periodic of 180\". The rotor position can be uniquely determined if the polarity can completely be discriminated. The polarity discrimination method is discussed in the following section.\nB. Identification of magnetic polarity of the rotor\nThe initial rotor position has been estimated with the procedure described above, but it has not yet been confirmed whether the estimated position corresponds to the N pole or S pole of the rotor magnets. A method to identify the polarity of the magnet is described in this section, which utilizes the effect of magnetic saliency .\nFigure 9(a) is a diagram of a 4-pole IPMSM with one of the north poles aligned with the stator coil shown. Solid arrows represent the flux fiom the rotor magnet that links the coil. A dashed arrow represents the flux fiom current in the coil. Figure 9(b) shows the rotor rotated to the position where one of the south poles is aligned with the coil. When a north pole is aligned with the coil, the current in the coil increases the flux linked by the coil (figure 9.a), increases stator saturation and slightly decreases the inductance which was present with no stator current. When a south pole is aligned with the coil, the current in the coil decreases the flux linked by the coil (figure 9.b), decreases stator saturation, and slightly increases the inductance that was present with no stator current. Since the inductance of the coil is different for north and south poles, the stator current will be different due to the variation of inductances.\nA rectangular ac voltage (40 volts, 50 Hz) is applied to the motor without a dc component to examine the effect of magnetic saliency. When N pole is aligned with the coil i.e er= 09 the mmf of the positive current is superimposed in additive direction to the mmf of the rotor magnet. Then the magnetic saturation makes the amplitude of positive\ncurrent larger than that of negative current. Figure lO(a) shows result of phase current when the rotor angle was set at e,= 0\" and the rectangular ac voltage was applied to the motor in the direction of a-phase. It is observed that the amplitude of positive current is larger than that of negative current. Figure IO@) shows the results for 8,=18@. In this case the mmf of the positive armature currents superimposed in subtractive direction to the mmf of the rotor magnet. It is observed that the amplitude of positive current is smaller than that of negative current. From the amplitudes of the currents in the two cases, the magnetic polarity of the rotor position can be determined.\n883", "controlled IPMSM drive (Experimental).\nVI. CONCLUSIONS\nThis paper presents a new method to determine the initial rotor position of an IPMSM based on the application of a high frequency voltage vector to the motor. The method has the advantage of insensitivity to variations of stator resistance R, and q-axis inductance L,. The magnet polarity of the rotor at its initial position is also identified using the effect of saliency. Error in initial rotor position estimation is within the range of -7 to +7 mechanical degrees, well within the limits required by the DTC controller of an Interior Permanent Magnet Synchronous Motor.\nTable I Parameters of IPMSM\nI Number of pole pairs P 1 2 I I t Stator resistance R I 19.4R I\n0.447 Wb 0.3885 H\n-axis inductance 0.4755 H Phasevolta e Phase current 1.4A Base speed ua 1500 rpm\nREFERENCES M. F. Rahman, L. Zhong, W. Y. Hu, K. W. Lim and M. A. Rahman \u201cA Direct Torque Controller for PM Synchronous Motor Drives\u201d IEEE Trans. on Energy Conversion, pp. 637-642,1997. M. F. Rahman, L. Zhong and K. W. Lim, \u201cA Direct Torque Controlled Interior Permanent Magnet Synchronous Motor Drive Incorporating Field Weakening \u201d, IEEE Trans. on Industry Applications, vol. 34, pp. 1246-1253, 1998. S. Ostlund and M. Brokemper, \u201cSensorless Rotor-Position Detection from Zero to Rated Sped for an Integrated PM Synchronous Motor Drive \u201d, IEEE Trans. on Industry Applications, vol. 32, no 5 , pp1158-1165,1996. J. S. Kim and S. K. SUI, \u201cHigh performance PMSM Drives without Rotational Position Sensors Using Reduced order Observers\u201c, IEEE IAS, Annual Meeting, vol 1, pp. 75-82, 1995. J. S. Kim and S. K. SUI, \u201cNew Standstill Position Detection Strategy for PMSM Drive without Rotational Transducers\u201d, Conf. Record of IEEE, APEC, pp.363-369, 1994. P. B. Schmidt, M. L. Gasperi, G. Ray and A. H Wijenayake, \u201cInitial Rotor Angle Detection of a Non-Salient Pole Permanent Magnetsynchronous Machine \u201d, IEEE-IAS, Annual. Meeting, vol 1, pp. 549463, 1997. A. Ferrah, K J. Bradley, P. J Hogben, M. S Woolfson, G.M Asher, \u2018,A Transputer-Basvd Identt3er for Induction Motor Drives uring Real-Time Adoptive Filtering\u201d, IEEE IAS Annual Meeting, voll. pp 194-400, 1996.\nT. S. Low T. H Lee and K. T. Chang, \u201c A non-linear speed observer for Permanent-Magnef Synchronous Mofors \u201d, IEEE Trans. on Ind. Electronics, vol. 40, pp. 307-316, June 1991. T. Noguchi, K. Yamada, S. Kondo, I. Takahashi, \u201cInifial Rofor Position Esfimation Method of Sensorless PM Motor with no Serrsitivity to Armature Resistance\u201d, IEEE Trans. on Ind. Electronics. vol. 45. no. 1. DD. 118-125. Feb. 1998. [IO] J. S. Kim and S. K..Sul, \u201cAighperfor&nce PMSM Drives without Rotational Position Sensors Using Reduced order Observers\u201d, IEEE IAS, Annual Meeting., , pp. 75-82,1995. [ I l l G. Henneberger, B. J Brunsbach, and T. Klepsch,\u201cField Oriented Control of Synchronous and Asynchronous drives without Mechanical Sensors using Kalman filter\u201d, EPE Fierenze, vol 3, pp 664-671,1991. [I21 R. Dhaouadi, N. Mohan, and L. Norum , \u201cDesign and Implementation of an Extended Kalman Filter for the State Estimation of a Permanent magnet synchronous Motor\u201d, IEEE Trans. PE-6, pp 491497,1991. [I31 P. L. Jansen and R. D. Lorenz, \u201cTransducerless Position and Veloci@ Estimation in Induction and salient AC Machines\u201d, IEEE Trans. on Industry Applications, vol. 31, no 2, pp. 240-247, MarcWApriI, 1995. M. W. Degner and R. D. Lorenz, \u201cUsingMult$le Saliencies for the Estimafion of Flux, Position, and Veloci@ in AC Machines\u201d, IEEE-IAS, Annual. Meeting, New Orlans, Louisiana, pp. 760-767, October 1997. [I51 A. Consoli, G. Scarcella and A. Testa, \u201cSensorless Control of AC Motors at Zero Speed\u201d IEEE- ISIE, Bled, Slovenia, pp. 373- 379,1999. [14]\n8 84" ] }, { "image_filename": "designv11_32_0000943_s0997-7538(01)01156-1-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000943_s0997-7538(01)01156-1-Figure1-1.png", "caption": "Figure 1. Orientation of the tensile specimen to the rolling direction.", "texts": [], "surrounding_texts": [ "In order to take into account the dependence of the yield condition on higher powers of stress, a polynomial form of the yield condition is applied. This form was used for the first time by Gol\u2019denblat (1968) as a fracture criterion for polymers.\nTruncating the general form of this equation after the cubic term yields:\nf \u2261K0 ( \u03b5pl\nv\n) +Kij\u03c3ij +Kijkl\u03c3ij \u03c3kl +Kijklmn\u03c3ij \u03c3kl\u03c3mn = 0. (2.8)\nThis yield condition contains material tensors of 2nd, 4th and 6th order and the scalar K0. K0 is a material dependent function of the plastic equivalent strain.\nThe basis for the formulation of the evolution equations forms the approach by Danilov (1971) for a tensor of 4th order:\nKijkl = Iijkl ( \u03b5pl\nv\n) + \u222b \u03b5 pl v\n0 AD\n( \u03b5pl\nv\n)d\u03b5pl ij\nd\u03b5pl v\nd\u03b5pl kl d\u03b5pl v d\u03b5pl v , (2.9)\nwhere AD(\u03b5 pl v ) is a material dependent function and Iijkl is the isotropic tensor of 4th order. By formal extension of this equation the formulation of evolution equations for the cubic yield function is possible:\nKD ij =\n(0) KD ij +\n\u222b \u03b5 pl v\n0 B\n( \u03b5pl\nv\n)d\u03b5pl ij\nd\u03b5pl v\nd\u03b5pl v ,\nKD ijkl =\n(0)\nKD ijkl +\n\u222b \u03b5 pl v\n0 C\n( \u03b5pl\nv\n)d\u03b5pl ij\nd\u03b5pl v\nd\u03b5pl kl d\u03b5pl v d\u03b5pl v ,\nKD ijklmn =\n(0)\nKD ijklmn +\n\u222b \u03b5 pl v\n0 D\n( \u03b5pl\nv\n)d\u03b5pl ij\nd\u03b5pl v\nd\u03b5pl kl d\u03b5pl v d\u03b5pl mn d\u03b5pl v d\u03b5pl v .\n(2.10)\nHere, the initial state is given by the tensors (0)\nKD ... and, unlike in (2.9), an initial anisotropy can be described. The\ntensorial internal variables describe material anisotropy and are therefore functions of the loading path. The evolution of the scalar K0, however, describes a purely isotropic part of hardening. For that reason K0 is only dependent on the amount of plastic strains, represented by \u03b5pl\nv :\nK0 =K0 ( \u03b5pl\nv\n) , (2.11)\nwhere \u03b5pl v for arbitrary loading paths is given by:\n\u03b5pl v =\n\u222b \u03b5 pl v\n0\n\u221a 2\n3 d\u03b5 pl ij d\u03b5 pl ij , (2.12)\n\u03b5pl v is further used as the scalar internal variable. For numerical integration the rate formulation of (2.10) is used, because in the numerical experiments the loading are total strain rates (cf. Section 4.1). With the relations:\nd dt = d\nd\u03b5pl v\nd\u03b5pl v dt = d d\u03b5pl v \u03b5\u0307pl v (2.13)\nand\nd\u03b5pl ij d\u03b5pl v = d\u03b5pl ij dt dt d\u03b5pl v = \u03b5\u0307 pl ij \u03b5\u0307 pl v , (2.14)", "equations (2.10) reduce to:\nK\u0307D ij = B\n( \u03b5pl\nv\n) \u03b5\u0307\npl ij ,\nK\u0307D ijkl = C(\u03b5pl v )\n\u03b5\u0307 pl v\n\u03b5\u0307 pl ij \u03b5\u0307 pl kl,\nK\u0307D ijklmn = D(\u03b5pl v )\n(\u03b5\u0307 pl v )2\n\u03b5\u0307 pl ij \u03b5\u0307 pl kl \u03b5\u0307 pl mn.\n(2.15)\nThe evolution equation for the plastic equivalent strain can be expressed as:\n\u03b5\u0307pl v =\n\u221a 2\n3 \u03b5\u0307\npl ij \u03b5\u0307 pl ij . (2.16)\nBy substituting the flow rule (2.5) into (2.15) and (2.16) the dependence of the rates of the internal variables on plastic strain rates can be replaced by a dependence on \u03bb\u0307 and fij .\nThe anisotropic behaviour of sheet metal can be characterised by the so called r-value. The r-value is defined as the ratio of the logarithmic strain in width direction (\u03d522 or \u03d511, respectively) to the logarithmic strain in thickness direction (\u03d533) during a tensile test. If x1 or x2, respectively, are the directions of tension:\nr1 = \u03d522 \u03d533 and r2 = \u03d511 \u03d533 , respectively. (3.1)\nThis ratio is generally not constant but dependent on plastic deformation and the angle \u03b1 between the axis of the tensile specimen and the rolling direction (Schouwenaars et al., 1994; Lankford et al., 1949):\nr1,2 = r1,2 ( \u03b5pl v , \u03b1 ) . (3.2)\nThe definition of r as ratio of logarithmic strains (3.1) is not sufficient for the consideration of a variable r-value in numerical simulations because this only takes into account the integral dependence on plastic deformation.", "Therefore it makes sense to define the r-value as the ratio of the plastic strain rates in width direction and thickness direction. For specimens parallel and normal to the rolling direction, two different r-values are defined in this way:\nr1 = \u03b5\u0307 pl 22\n\u03b5\u0307 pl 33\n, r2 = \u03b5\u0307 pl 11\n\u03b5\u0307 pl 33\n. (3.3)\nBy substituting the flow rule (2.5), this reduces to:\nr1 = f22 f33 , r2 = f11 f33 . (3.4)\nBy use of the incompressibility condition:\n\u03b5\u0307 pl ii = 0 (3.5)\nand the flow rule (2.5) the equations:\nf22\nf11 \u2223\u2223\u2223\u2223 \u03c322=0 = \u2212 r1 1 + r1 , (3.6a)\nf11\nf22 \u2223\u2223\u2223\u2223 \u03c311=0 = \u2212 r2 1 + r2 , (3.6b)\ncan be formulated which describe the relations between the r-values and the components of the gradient of the yield condition in a plane principal stress state (cf. figure 2). Because of the definitions of r1 and r2, equation (3.6a) is valid for the point of intersection of the yield locus curve with the \u03c311-axis and equation (3.6b) is valid for the point of intersection with the \u03c322-axis. The angles \u03b31 and \u03b32 between the normals of the yield locus curve in these points and the coordinate axes are related to the components of the gradient vector by the relations:\nf22\nf11 \u2223\u2223\u2223\u2223 \u03c322=0 = tan\u03b31, f11\nf22 \u2223\u2223\u2223\u2223 \u03c311=0 = tan\u03b32.\n(3.7)\nBecause of these equations and with (3.6a) and (3.6b), the components fij of the gradient vector are also related to r1 and r2, respectively. For the case of general planar anisotropy, r1 = r2, we have \u03b31 = \u03b32, which leads to changes in position or shape (or both) of the yield locus curve compared with the isotropic state (cf. figure 2b).\nThe following representation is based on the assumption that from an uniaxial tension test in the x1-direction the yield curve \u03c3F(\u03b5 pl v ) and r1(\u03b5 pl v ) are known. The aim of the investigation is to describe the changes of the yield locus curve caused by anisotropic plastic hardening with special regard to a variable planar anisotropy.\nFor isotropic, kinematic and distortional hardening the evolution equations (2.15) are employed. They are, however, not able to take into account a given function r1(\u03b5 pl v ) for the controlled change of planar anisotropy. Therefore they are extended by a term which describes the relation between the gradient vector of the yield locus curve and r1(\u03b5 pl v ). The idea is, that in addition to the evolution of the yield surface because of isotropic, kinematic and distortional hardening, the yield locus curve is rotated. In this way the inclination of the gradient on the yield locus curve at the intersection with the \u03c311-axis is adapted to the function r1(\u03b5 pl v )." ] }, { "image_filename": "designv11_32_0003434_6.2008-4505-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003434_6.2008-4505-Figure8-1.png", "caption": "Figure 8 4.37\" diameter seal with L/R=0.223", "texts": [], "surrounding_texts": [ "Six different configurations of proof of concept foil face seals were fabricated in order to assess the impact of flow path radial length, axial preload and surface velocity on leakage. The six test articles are shown in Figure 5 through Figure 10. Two 9-inch OD thrust foil bearings, two 4.37-inch OD and two 3.82-inch OD configurations were fabricated providing different L/Ro ratios, angular gaps between pads and different flow paths. For each test seal, the outer periphery of the compliantly supported foil pads was open to atmosphere, thereby presenting a leakage path along the radius as opposed to the closed ends shown in Figure 3. Figure 11 and Figure 12 schematically show the tested configurations with the open ends and the primary flow paths. The importance of the open ends for these initial tests was to determine the baseline resistance to flow due to the total axial gap (htotal) in the angular segments between pads, the gap beneath the bump foils (hb) and the gap between the top smooth foil and the disc (hfilm), all without the end flanges and secondary seal elements to restrict flow. This would allow for an assessment of critical design parameters for the fundamental seal shape, such as an assessment of the importance of L/Ro ratio. Additionally, tests of the candidate seals with this arrangement and conducted under rotating conditions would, when compared to static/non-rotating tests, verify that the hydrodynamic pressures were generated and reduce total leakage. As shown in Figure 2 and Figure 3, both the angular gap and open ends will be eliminated in the final configuration, thereby only allowing leakage flow to pass through the minimum film height (hfilm). By eliminating the larger gaps associated with the pad angular spacing and the region beneath the compliant bumps in the face seal configuration, the leakage will be substantially reduced from the measured baseline configuration. It should be noted that during testing the total gap height was on the order of 0.031 inch, whereas hfilm was either zero when static tests were conducted or on the order of 0.001 inch when dynamic testing was conducted at speeds from 24,000 to 60,000 rpm. While hfilm initially increases during dynamic testing (see Figure 11), the generated hydrodynamic film pressure resists the radial inflow/outflow of high pressure air. Thus, the air is forced to flow behind the top smooth foil and through the passages formed by the bumps (approximately 0.021 inch high) as well as the gaps between individual pads. It should also be noted that with the high pressure at the OD, the inward directed pressure driven flow will also be restricted by the inherent outward self pumping action of the disc. Finally, while the gap between pads is approximately 0.031 inches high and between 6\u00b0 and 10\u00b0, flow in this gap is turbulent, even for differential pressures as low as 2 psig. Thus, when the end flanges are introduced at the OD and the pads overlap one another, the primary leakage path will be through the very narrow hydrodynamic film region, which, at about 0.001 inch, will result in leakage rates well below any present technology." ] }, { "image_filename": "designv11_32_0002091_aim.2003.1225147-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002091_aim.2003.1225147-Figure2-1.png", "caption": "Figure 2 Parallel-wire system (C.R.type)", "texts": [ " investigated the mechanism of the parallel-wire drive system and showed some experimental results using a twc-dimensional robot[l]. Osumi et al. developed a crane to move heavy objects . by using the parallel-wire mechanismj21. Kawamura et al. developed a high-speed robot using seven wires for &7803-7759-1/03/$17.00 @ 2003 IEEE 509 six degrees of freedom[%]. The parallel-wire driven system is classified into two types based on the drive principle. One is the incompletely restrained type (I.R. type) as shown in Figure 1, and the ot,her is the completely restrained type (C.R. type) as shown in Figure 2. Distinction between the types is to apply external force as drive means actively or not. The former actively utilizes external force to o p erate, such BS the gravity. The latter u t i l i s only wire tension. Generally speaking, the I.R. type can easily obtain larger work space, and can operate with fewer wires than the C.R. type[6, 71. However, it might be difficult to suppress the vibration problem, because the LR. type can not arbitrarily generate forcemoment at theend-effector. On the other hand, the C" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001182_robot.2002.1014767-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001182_robot.2002.1014767-Figure8-1.png", "caption": "Figure 8: The iteration when the ray of N ( t , ) intersects S.", "texts": [ " We again compare the signs of the antipodal angles at the two endpoints of S . The iteration starts at so = sa and to = t, if the ray of N(t , ) intersects S, or at so = Sb and to = t b if the ray of N(tb) intersects s. In each round, si+l is generated as the intersection of the ray of N ( t i ) and S and ti+1 is generated as its opposite point. The iteration stops if the sequences SO, SI,. . . and t o , t l , . . . reach the other endpoints, in which case no antipodal points exist, or if they converge to a pair of antipodal points. Figure 8(a) illustrates this it- 2.4.1 Endpoint Antipodal Angles with the Same Sign We first determine if one of the rays extending the normals N(t,) and N(tb) intersects s. Under conditions (i)-(v), testing if the ray extending N(t , ) , or simply called the ray of N( t , ) , intersects S can be done by checking whether the cross products (a(&) -a(t,)) x N(t,) and (a ( sb ) - a(t,)) x N ( t , ) have different signs. ,Proposition 5 Suppose S is convex and 7 is concave. Assume that the two antipodal angles 6(s,) and 6(Sb) have the same sign", " To study local convergence rate of the procedure we differentiate equation (8) to obtain the derivative of the iteration function g where si+l = g(si) at S* [6]: 4 s * ) (9) g'(s*) = IC(s*) I Ia(t+) - u ( s * ) l l - - K ( t * ) * Because K ( s * ) > 0 and ~ ( t ' ) < 0, g'(s*) > 0. Because O(si) < 0, fori = 0,1,. . ., we see that in the non-degenerate case. This implies that 0 < g'(s*) < 1. Hence the algorithm converges in linear rate. It also follows from (10) that IIa(t*) - a(s*>ll < & + &. Geometrically, the osculating circle at s* contiuns the osculating circle at t' in its interior, as shown in Figure 8(b). Similar analysis can be performed for the case that the ray of N(tb) intersects S. The convergence rate is still linear and O'(s*) > 0 also holds. If no antipodal points exist on S and T, AntipodalConvex-Concave-March will terminate at the other endpoints of S and 7. 2.4.2 Finding All Pairs of Antipodal Points When the antipodal angles at the two endpoints have different signs, we can use bisection to find one pair of antipodal points. To find all pairs of antipodal points on S and 7, the marching procedure in Section 2" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001601_jmes_jour_1982_024_009_02-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001601_jmes_jour_1982_024_009_02-Figure1-1.png", "caption": "Fig. 1. Squeeze film geometry", "texts": [ " clh D, = (Wy, , - Wy+,)/Wy=o x 100 Non-dimensional roughness parameter = c/h, Function defined by Expectancy operator Probability density distribution function Nominal film height Initial film height Deviation of film height from nominal level Film height Non-dimensional film height = h/ho Thickness of porous facing Integer Pressure in film region Flow component in the x direction Flow component in the y direction Relative time difference Relative load difference Sinkage time Non-dimensional sinkage time = ~ E(w)h:t Instantaneous load capacity Non-dimensional instantaneous load capacity = (Tough - KrnoFth)/Kmooth loo = ( w o u g h - Kmooth)/%nooth loo flA2 E(w)h3 qA2(dh/dt) - _ Rectangular coordinates Plate area Viscosity Permeability of porous facing @H*/h3 Permeability parameter = >= >>; \u20264\u2020\nMoreover, de\u00ae ne the input vector derivatives\nUk t :\u02c6 \u2030u1;t _u1;t \u00a2 \u00a2 \u00a2 u \u2026k\u2020 1;t \u00a2 \u00a2 \u00a2 um;t _um;t \u00a2 \u00a2 \u00a2 u \u2026k\u2020 m;t\u0160T\nThe same way as for S0, for (2) de\u00ae ne the nominal extended system relative to S as\n_\u00b7wt \u02c6 Fw\u2026t; \u00b7wt; ut\u2020; \u00b7wt\u02c60 \u02c6 \u00b7w0\n\u00b7yt \u02c6 hw\u2026t; \u00b7wt; ut\u2020\n9 = ; \u20265\u2020\nThe following de\u00ae nitions are based on concepts and results introduced in Gauthier and Bornard (1981), Tunali and Tarn (1987), Birk and Zeitz (1988) and Borto\u0152and Spong (1990). They will be fundamental throughout this paper.\nDe\u00ae nition 1: The consistent class S0 is said to be completely uniformly locally observable on a set M\u00b1 \u00bb \"g \u00bb 0\nif the observability matrix (8) is \"-non-singular inside this set, that is\ndet Qt > \" \u202613\u2020\nBased on this de\u00ae nition the extended space \u00bd2k\u00a11g \u202614\u2020\n\u00bd2k\u20211 :\u02c6 inf ftjw\u0302s 2 L\"\u2026O\u2020 8s \u00b6 \u00bd2k \u202615\u2020\nDe\u00ae ne also the characteristic function\n\u00c0t :\u02c6 0; \u00bd2k \u00b5 t \u00b5 \u00bd2k\u20211\n1; \u00bd2k\u00a11 < t < \u00bd2k\n(\n\u202616\u2020\nand two gain matrices Kob t , Knob t 2 0 such that\nL\"\u2026O\u2020 6\u02c6 1\nAs it is shown in Krener and Isidori (1983), if the dynamics of S0 are completely uniformly observable, then the new coordinates \u00b1t :\u02c6 F\u00b1\u2026t; zt; U l\u00a4 \u00b1 \u00a11 t ; c\u2020, given by (6) satisfy\nS\u00a4 0 :\n_\u00b1t \u02c6 A\u00b1\u00b1t \u2021 B\u00b1H\u00b1\u2026t; \u00b1t; U l\u00a4\u00b1 t ; c\u2020 \u2021 \u00af\u00b1;1\u2026t; \u00b1t; U l\u00a4\u00b1 \u00a11 t ; c\u2020 \u00b1t\u02c60 \u02c6 F\u00b1\u20260; z0; U l\u00a4\u00b1 \u00a11; c\u2020 yt \u02c6 C\u00b1\u00b1t \u2021 \u00af\u00b1;2\u2026t; \u00b1t; U l\u00a4\u00b1 \u00a11 t ; c\u2020\n8 >>><\n>>:\nwhere\n\u00af\u00b1;1\u2026t; \u00b1t; U l\u00a4\u00b1 \u00a11 t ; c\u2020 :\u02c6 Q\u00b1;t\u00af1\u2026t; zt; ut; c\u2020j\nz\u02c6F\u00a11 \u00b1 \u2026t;\u00b1t;U\nl\u00a4 \u00b1 \u00a11 t ;c\u2020\n\u00af\u00b1;2\u2026t; \u00b1t; U l\u00a4\u00b1 \u00a11 t ; c\u2020 :\u02c6 \u00af2\u2026t; zt; ut; c\u2020j\nz\u02c6F\u00a11 \u00b1 \u2026t;\u00b1t;U\nl\u00a4 \u00b1 \u00a11 t ;c\u2020\nand the vector function H\u00b1\u2026\u00a2\u2020 is de\u00ae ned as\nH\u00b1\u2026t; \u00b1t; U l\u00a4 \u00b1 t ; c\u2020 :\u02c6\nL l1;\u00b1 F\u00b1 h1\u2026t; F\u00a11 \u00b1 \u2026t; \u00b1t ; U l\u00a4\u00b1 \u00a11 t ; c\u2020; U l\u00a4 \u00b1 t ; c\u2020\nL l2;\u00b1 F\u00b1 h2\u2026t; F\u00a11 \u00b1 \u2026t; \u00b1t ; U l\u00a4\u00b1 \u00a11 t ; c\u2020; U l\u00a4 \u00b1 t ; c\u2020\n..\n.\nL lp;\u00b1 F\u00b1 hp\u2026t; F\u00a11 \u00b1 \u2026t; \u00b1t ; U l\u00a4\u00b1 \u00a11 t ; c\u2020; U l\u00a4 \u00b1 t ; c\u2020\n2\n66666666664\n3\n77777777775 2 >=\n>>;\n\u202620\u2020\nwhere, by (3) and (4), the uncertain terms can be expressed as\n\u00a2x;1\u2026t; xt; U l\u00a4x\u00a11 t \u2020 :\u02c6 Qt\u00a2w;1\u2026t; w; ut\u2020jw\u02c6F\u00a11 x \u2026t;xt;U l\u00a4x\u00a11 t \u2020\n\u00a2x;2\u2026t; xt; U l\u00a4x\u00a11 t \u2020 :\u02c6 \u00afw;2\u2026t; w; ut\u2020jw\u02c6F\u00a11 x \u2026t;xt;U l\u00a4x\u00a11 t \u2020\nand the vector function Hx\u2026\u00a2\u2020 is de\u00ae ned as\nHx\u2026t; xt; U l\u00a4x t ; c\u2020 :\u02c6\nL l1;x fx h1\u2026t; F\u00a11 x \u2026t; xt; U l\u00a4x\u00a11 t ; c\u2020; U l\u00a4x t \u2020\nL l2;x Fx h2\u2026t; F\u00a11 x \u2026t; xt; U l\u00a4x\u00a11 t ; c\u2020; U l\u00a4x t \u2020\n..\n.\nL lp;x Fx hp\u2026t; F\u00a11 x \u2026t; xt; U l\u00a4x\u00a11 t ; c\u2020; U l\u00a4x t \u2020\n2\n6666666664\n3\n7777777775 2 E CZ, for 1 Si < j 5 Nrobots and i # j ,\n6:; E {0, l}, 1 5 i < j 5 Nrobotsr 1 5 k 5 Nij tft\"rt 2 0, 1 5 i 5 Nrobota, s$,= 2 si 2 spin, 1 5 i 5 N&,tS.\nThe completion time constraints are necessary for all links of a robot that can potentially have a collision. The collisiontime interval constraints are necessary for only those robots that have one or more lmks involved in a potential collision.\nI time T1 T2\nFig. 4. limelines for mhos dl and dz with multiple collision intervals.\n9 2 L I t ' S t a n time I\nFig. 5. Collision-free time-scaled timelines for mbts dl and dz, with di being delayed at its stan and dz having its timeline shrunk.\nC. lime-Scaled Coordination of Mulri-Link Robots To coordinate manipulator robots with multiple links, we consider motions of the individual links. An aniculated robot A, consists of a set of links {Ail}, where link Ail belongs to robot Ai. For a specified trajectory, the motions of links of an articulated robot are separated by constant time offsets. Let Ail begin moving time T; after the first moving link of A, starts moving. That is, = tftart + T: where t:yt is the start time of Link Ail. The completion time for Ail is tftnPt+T;+T,l, where Til is the motion time of Ail. Note that the start time and motion t i e of a link may depend on the start and motion times of links that precede it in the kinematic chain.\nWhen an articulated robot's trajectory is time scaled, every link Ai, of robot Ai has the same time scaling factor si. Therefore t:Pt = tf'*\" + siT: where t:'Yrt is the start time of robot Ai. The minimum and maximum scaling factors\nD. Specifiing Sequencing Constraints\nIn certain tasks, it may be necessary for one robot to complete a particular operation or reach a certain point before another robot performs a subsequent operation. This can occur in sequenced assembly tasks, or in welding workcells where the primary welds must be completed before secondary welds. Consider the constraint that Ai has to reach qi before Aj reaches q,. For the unmodified trajectories, let the time taken for A, to reach qi be Tq, and for AI to reach qj be 4. The time-scaled sequencing constraint can then be written as tatart + siTp. < tjtart + sjT9, . Such constraints for multiple robots can be easily added to the formulation.\nE. lime-Scaled Coordination Given Input Paths\nConsider the time-scaled coordination task when only the paths for the individual robots are specified. The time-optimal coordination of multiple manipulator robots when only the paths are specified is an open problem. We outline a method to provide feasible and potentially near-optimal coordinated schedules that respect the dynamics constraints. First generate the time-optimal trajectory for each individual robot along its path, following the methods of Bobrow, Dubowsky, and Gibson [20] and Shin and McKay [ZI]. Now the problem can be transformed to the problem of time-scaling the individual time-optimal trajectories. This will result in a feasible solution that respects the dynamics constraints. Further, it provides an upper bound on the time-optimal schedule for the robots given their paths. Note that since at least one of the joint actuators is always saturated along the time-optimal velocity profile, each robot's motion may only be slowed down or remain unchanged.", "Num. of\nVI. IMPLEMENTATION we have implemented time-scaled coordination of manipulators with input trajectories,' and demonstrated the apwhen the scaling range only permits robots to slow down, the completion time is sometimes an improvement over the case with no\nNum. Num.of MlLP MlLP MlLP of collision 1 II 111\nmbots 2 2 6 links zones (secs) (secs) (secs) 3 3 0.04 0.033 0.0367 4 14 0.06 0.07 0.0567 18 24 0.177 0.28 0.3467\nWe have also experimented with time-scaled coordination of up to 12 polyhedral robots modeled as double integrators (since their dynamics are similar to single-link manipulators and Cartesian manipulators). Sometimes the best solutions do not always have all scaling factors at their minimum values (i.e., not all robots move as fast as they can). Further, even\nVII. CONCLUSION We have developed an optimization formulation to enable the uniform time-scaled coordination of multiple manipulators with input trajectories or input paths. The principal advantage of our MILP formulation is that it potentially permits the collision-free coordination of a large number of manipulators, while considering their dynamics. The problem complexity depends primarily on the number of collision zones, and to a lesser extent on the number of robots and their number of degrees of freedom. Although the problem of time-scaled trajectory coordination of multiple robots is NP-hard, the availability of efficient integer programming solvers makes this approach practical for industrial automation problems, which typically involve less than twenty manipulators.\nThis work represents a step towards time-optimal coordination of multiple manipulators. There are several directions for future work. The uniform time-scaling formulation provides an upper bound on the true optimal coordination of a set of manipulators with specified paths. Incorporating less conservative conditions for collision avoidance will improve solution quality. Analyzing the gap between the time-scaled coordination described here and the m e time optimal coordination is important, as is developing techniques for generating the time-optimal coordinated trajectories subject to dynamics constraints. Extending the time-scaled coordination approach to manipulators with elastic joints, based on recent work by De Luca and Farina [37], and exploring extensions to other robot systems would broaden the scope of this approach. Examining alternative solutions generated by the MILP can", "help optimize different actuator performance requirements and improve robot and workcell design. Finally, extensions to online coordination of robots (as in [38]) that involve timing uncertainties would be useful.\nACKNOWLEDGMENTS\nThis work was supported in pan by RPI and by NSF under CAREER Award No. IIS-0093233. Mark Moll\u2019s question sparked this paper. Thanks to Seth Hutchinson for earlier collaboration, and Prasad Akella and Charles Wampler for helpful discussions. Andrew Andkjar implemented animation software that interfaced with PQI?\nREFERENCES\nI11 B. H. Lee and C. S. G. Lee. \u201cCollision-free motion planning of two robots,\u201d IEEE Tmnsocrions on Sysrems. Man, ond Cybernetics, vol. 17, no. 1, pp. 21-32. IanuaryIFebruary 1987. I21 Y. Shin and Z. Bien, \u201cCollision-free trajectory planning for two mbat arms,\u201dRoborica. vol. 7, pp. 205-212, 1989. 131 C. Chang. M. I. Chung. and Z. Bien, \u2018Collision-free motion planning far two articulated robot arms using minimum distance functions,\u201d Robmica. vol. 8, pp. 137-344. 1990. 141 Z. Bien and 1. 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Latombe, \u2018On-line manipulation planning for two robot arms in a dynamic environment,\u201d Inlernorionol Journal of Robotics Research, vol. 16, no. 2, pp. 144-167, 1997." ] }, { "image_filename": "designv11_32_0001829_elan.200503346-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001829_elan.200503346-Figure2-1.png", "caption": "Fig. 2. Schematic representation of the tubular amperometric detector: Ew : working electrode; Eaux: auxiliary electrode; Reference: reference electrode; a: electric contact; b:Perspex support; c: connection to the flow system.", "texts": [ " The cycle endedby replacing the sample and cleansing the manifold. The amperometric detectorwas constructed in such away to permit its application in multicommutated flow systems with internal pressure lower than atmospheric pressure (aspiration of the solutions), basing its construction on a tubular detector recently described in detail [20] but introducing adjustments that facilitate its sealed fixation to the manifold, making viable the aspiration of solutions through its interior without the admission of air bubbles. Its configuration was tubular (Fig. 2), being composed of a Perspex central support, which housed the working and auxiliary electrodes, both of glassy carbon, constructed from a 7 mm diameter glassy carbon rod. The resulting cylinders were of 2 mm thickness and were perforated in the centre creating a 0.8 mm diameter orifice and securely fixed to the support by two rubber rings, also perforated in the centre.As reference electrode, a Methrom electrode was used, (Ag/ AgCl \u2013 KCl 3.0 mol L 1, model 6.0727.000), fixed by a threaded screw and superficially touching the central channel which linked the working electrode to the auxiliary electrode" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002092_1-4020-3393-1_14-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002092_1-4020-3393-1_14-Figure6-1.png", "caption": "Fig. 6. Denavit-Hartenberg notation", "texts": [ " For some set of coordinates previously discussed the constraint equations for the kinematic modeling of a slider-crank are reported in the following. When relative coordinates {q} = { \u03b81 \u03b83 s4 }T are used, loop closure conditions are often imposed. For example, with reference to the nomenclature of Fig. 3, the following equations can be written2 \u03a81 \u2261 a1 sin \u03b81 \u2212 a2 sin \u03b83 \u2212 s4 = 0 (4) \u03a82 \u2261 a1 cos \u03b81 + a2 cos \u03b83 = 0 (5) Let ai, \u03b1i, \u03b8i, si be the Denavit-Hartenberg parameters, and \u03b1\u0302i = \u03b1i + \u03b5ai (6) \u03b8\u0302i = \u03b8i + \u03b5si (7) their dual counterparts (\u03b52 = 0). With reference to Fig. 6, the links coordinate-transformation matrix takes the form [34] 2 With this approach, the coordinate \u03b82 is not involved. [ T\u0302 ]i i+1 = \u23a1\u23a3 cos \u03b8\u0302i \u2212 cos \u03b1\u0302i sin \u03b8\u0302i sin \u03b1\u0302i sin \u03b8\u0302i sin \u03b8\u0302i cos \u03b1\u0302i cos \u03b8\u0302i \u2212 sin \u03b1\u0302i cos \u03b8\u0302i 0 sin \u03b1\u0302i cos \u03b1\u0302i \u23a4\u23a6 (8) The closure condition of the slider-crank chain is expressed by the matrix product[ T\u0302 ]1 2 [ T\u0302 ]2 3 [ T\u0302 ]3 4 [ T\u0302 ]4 1 = [I] (9) where [I] is the unit matrix. The constraint equations (4) and (5) follow by equating appropriate elements of the final matrix products" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001592_aim.2003.1225099-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001592_aim.2003.1225099-Figure4-1.png", "caption": "Figure 4 A pair of wall and matching operations.", "texts": [ " then matching wall information is searched h m other robots information and if received information comes from other robot, matching wall information is searched from information announced by itself. Old information in a database is useless, because the common coordinate system continuously and gradually accumulates odometry errors and changes by itself. Thus such information are purged from a database when they aged enough. 4.3 Find matching walls Examining a bansformation for coordinate redefinition which can be calculated as described later. a pair of walls is determined if they are the same wall in an environment. Following conditions are examined.(see Fig.4.) e A baring direction difference of two walls is less than a threshold. walls is less than athteshold. fined. A difference of distances being from robot to each two Two walls are intersected if a coordinate system is rede- 4.4 Redefining a coordinate system Redefining a coordinate system to match a found wall and a reference wall. In a resulting new coordinate system. two walls could be measured at a same position and pose. At first, rotating around a robot's current position to match a baring direction of two walls" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002999_ramech.2008.4681368-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002999_ramech.2008.4681368-Figure3-1.png", "caption": "Fig. 3. Cartesian robot for capturing flying objects", "texts": [ " * When throwing objects, which are unsymmetrical and not absolute identical, their trajectories are depending on sensitive influences like different conditions during the acceleration by the throwing device, the influence of the gravitation and the aerodynamic resistance. Fig. 2 shows as an example two trajectories of the same electrical terminal block. After 3 m they have in the z-axis a deviation of 120 mm. For other objects it shall be assumed, that they arrive at the robot in a capturing area which is 400 mm x 400 mm. 978-1-4244-1676-9/08 /$25.00 (\u00a92008 IEEE RAM 2008160 * In production systems gantry-robots are often applied to load and unload machines. Therefore a Cartesian robot is used to capture the flying objects. The robot in Fig. 3 has the following technical data: The workingarea in the y-axis is 1000 mm and in the z-axis 800 mm. The maximum acceleration and the maximum speed of this axis are amax = 25 m/s2 and vmax = 4 m/s at a payload ofm = 5 kg. In this paper control algorithms are presented, which allow for this application fast and smooth movements of the Cartesian robot. II. RELATED WORK The visual tracking of flying objects and the tracking of NC-axis of robots have already been realized in several previous research works" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003991_17461390802594243-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003991_17461390802594243-Figure3-1.png", "caption": "Figure 3. Landing efficiency (fxL) is the lost distance due to the athlete falling backwards during landing.", "texts": [ " It was calculated according to equation (4) (Dichwach & Gundlach, 1993): dxL vxL vzL ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi vzL 2 2gzL p g xL (4) where vxL and vzL are the horizontal and vertical velocities of the centre of mass at the instant of landing, xL is the horizontal distance from the heels to the centre of mass at the instant of landing, zL is the height of the centre of mass at the instant of landing, and g is acceleration due to gravity (Figure 2). The second level (fxL) describes the loss accrued due to the athlete falling backwards during landing (Figure 3). It was calculated according to equation (5): fxL (Cx(hill) Cx(last body part) (5) where Cx(hill) is the horizontal coordination of the hill at the instant of landing, and Cx(last body part) is the horizontal coordination of the last body part to leave a mark in the sand during landing that is, where the distance jumped is measured to. Figure 2. The loss accrued due to landing of the pelvis behind the theoretical point where the centre of mass (CM) was supposed to land. D ow nl oa de d by [ U ni ve rs ity o f So ut he rn Q ue en sl an d] a t 1 3: 12 0 9 O ct ob er 2 01 4 The two groups were checked for normal distribution (Kolmogorof-Smirnof test, P 0" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000276_tmag.2003.816499-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000276_tmag.2003.816499-Figure3-1.png", "caption": "Fig. 3. Magnetic flux distribution in the cases of a normal rotor cage and a broken bar.", "texts": [ " The iron core has nonlinear permeability, and the convergence in each time step is examined by the error rate defined as follows: (6) where is the summation of the field intensity of iron-core elements in the th time step. Fig. 2 shows the variation of torque due to the change of error rate in the harsh condition in which the model with a broken rotor bar produces the maximum value of magnetic force. The error rate of 0.03 in this model has been used to ensure the accuracy and convergence in simulation. Fig. 3 shows the magnetic flux distribution of a normal rotor cage and a rotor cage with a broken bar at the transient state. The concentration of magnetic flux is observed around the broken bar and creates asymmetric magnetic flux distribution. Fig. 4 shows the distribution of magnetic flux density along the air gap at an instant of the steady state. It shows that the concentration of magnetic flux is observed around the broken rotor bar even at the steady state and that changes more dominantly than " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003178_s12206-008-0124-3-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003178_s12206-008-0124-3-Figure4-1.png", "caption": "Fig. 4. Contact geometry between cam and rolling follower.", "texts": [ " (8) The entraining velocity of the lubricant varies depending on the curvature of the follower at the contacting point, which, for simplicity, is considered a straight line in this study. For the flat follower, a kinematic study of the valve train system is similarly performed according to the methods (Paranjpe [4]). However, this investigation cannot be the same as the kinematic investigation of a rolling follower, because the contact mechanism of the rolling follower has a different contact geometry from that of a flat follower around the contact spots. The contact locus (Xc, Yc) between cam and rolling follower is computed by the four-linkage system (Fig. 4) by the following vector summation, Eq. (9) [15]. 2 3 4 1 0R R R R (9) Differentiating Eq. (9) with respect to the angle of camshaft rotation gives Eqs. (10) and (11) in x and y components. 3 4 2 2 3 3 4 4sin sin sin 0R R R (10) 3 4 2 2 3 3 4 4cos cos cos 0R R R (11) The center (XCC, YCC) of curvature of the camshaft at the point of contact is obtained as follows: if there is no offset for the roller center from the line to the center of base circle of cam profile, then 3 3cosCC fcX X R (12) 3 3sinCC fcY Y R (13) Assuming that there is no slipping between cam and follower, the relative motion of these two components of contact velocities is described as below", " 3 3f cam fr t t t t (14) Therefore, the entraining velocity of the lubricant is obtained from the following Eq. (15). 3 3f e cam fu r t t t t (15) The cam profile for the rolling follower with the assumption that there is no slipping between cam and rolling follower can be obtained from kinematic simulation after computing the contact point locus (Xc, Yc) as below with zero offset along the camshaftroller line. The traces of the roller center (Xfc, Yfc) as the valve lifts are in the line of the y-axis as shown in Fig. 4 and express the sum of cam radius Rc, valve lift lcam and roller radius Rr. 0fcX (16) fc c r camY R R l (17) Therefore, the cam profile is the transformed trace of the (Xfc, Yfc) as the function of the cam shaft rotation. cos sin sin cos fcc fcc XX YY (18) The generated cam profiles by tracing the contact points from the kinematic investigation of the valve train linkage system for flat and rolling followers are shown in Fig. 5, where the cam for the rolling follower has a unique concaved shape around 70 and 90 of the camshaft angles" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002445_tmag.2006.871421-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002445_tmag.2006.871421-Figure7-1.png", "caption": "Fig. 7. Ratio of eddy current losses in each part of the shield models at 350 kHz. (a) \u201cI\u201d-shield model. (b) \u201cL\u201d-shield model.", "texts": [ " The schematic diagrams of the two shield models are shown in Fig. 5. The thickness of the shields is 2.0 mm. For a basic investigation, it is assumed that the shield is a nonconductor. The relative permeability of the shield is 1000. The sensing index of the proposed models is shown in Fig. 6. It is found that sensing properties of both models are enhanced compared with the actual sensor result. To clarify the cause of the enhancement quantitatively, the eddy current loss values and ratios of each part of the proposed models are shown in Table IV and Fig. 7, respectively. As shown in Tables III and IV, or in Figs. 4 and 7, the housing losses of the shielded models sufficiently decrease while the target losses increase. Especially, the housing loss of \u201cL\u201d-shield Physical parameters of the shield for the numerical experiments are shown in Table V. It is considered that both relative permeability and conductivity affect . Therefore, the 3-D distribution graph of is shown in Fig. 9 to obtain the suitable domain of and . Note that and case means the actual sensor" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003426_tiga.1971.4181272-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003426_tiga.1971.4181272-Figure3-1.png", "caption": "Fig. 3. Flux characteristics (if = 0).", "texts": [ " But this current has generated an armature reaction E(Ia) which magnetizes the poles. Hence if the batteries are disconnected, the remaining voltage can be read. This voltage is subtracted from the previous reading which leads to AU(la) at zero excitation. The curve shown in Fig. 2 has been recorded. Above a certain amount of current, the curve, instead of asymptotically approaching a constant, is beginning to rise. This is due to the assumption that the armature reaction is the remaining voltage. As shown in Fig. 3, this is valid only if the current is in a certain range beyond which the armature reaction increases a lot more. The curve up, to the point of inflexion (lao) is taken, and those data are fitted to the theoretical equation assumed as AU = RIa+ b(l - e-aI,) (5) where R is the linear part of the total resistance seen from the input of the machine and b(1 -e I is the nonlinear part. Determination of the Asymptote: The linear part (around the point of inflexion) is compared to the equation U = RIa + b because if Ia is sufficiently large, e-aa will be negligible" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-FigureA.11-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-FigureA.11-1.png", "caption": "Fig. A.11. Squareness measurement - second axis (vertical plane)", "texts": [ " The second axis measurement is simply a horizontal straightness measurement along the axis on which the reflector was earlier mounted during the first measurement. Figure 5.9 illustrates the concept of obtaining the squareness error from the two straightness measurements. 5.5 Accuracy Assessment 139 The procedure to execute a squareness measurement in the vertical plane is similar to that of the horizontal plane, except for additional requirements in terms of optics. The required set of devices is shown in Figure A.10. The set-up for measurements along the vertical axis (i.e., the z-axis) is given in Figure A.11. Roll measurement refers to the measurement of rotation about its own axis. The measurement of roll tilt about its own axis is quite tedious even with a full set of laser interferometer equipment. Therefore, an electronic level measurement system is usually applied to facilitate this particular measurement. The principles of operation are straightforward: it make use of a pendulum in conjunction with an electronic detection system to sense precisely the attitude of the pendulum with respect to a reference" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002142_bf03546353-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002142_bf03546353-Figure3-1.png", "caption": "FIG. 3. Spring Pendulum.", "texts": [ " These terms are shown without derivation in equations (37) and (38) respectively, as translation 1 ( 0 2 0 2) 1 0 0 0 1 0 0T1 = -ml XA + YA - -mIL1xAOI SIn 01 + -m1L1yAOl cos 01 2 2 2 - XA0 1 cos 01qTb1 - XA sin 01qTbl - yAOl sin 01qTb1+ YA cos 01qTb i (37) (38) T translation 1 ( 0 2 + 0 2) 1 L 0 li . Ll + 1 L 0 iJ Ll p+1 = \"2 m p+1 XA YA - \"2 m p+1 p+1 XAUp+1 SIn Up+1 \"2 m p+1 p+IYAUp+1 cos Up+1 P P - m p+1 XA L LiOi sin Oi + m p+1YA L LiOi cos Oi i=l i=l - XAOp+1 cos Op+1q~+lbp+1 - XA sin Op+1q~+lbp+1 - yAOp+1 sin Op+1q~+lbp+1 + YA cos Op+1q~+lbp+1 (39) First, we present an illustrative example of a problem in which the equations of motion are automatically generated and integrated by explicitly forming the La grangian function. The spring pendulum, as shown in Fig. 3, is a simple two-degree of freedom system which can be readily solved by hand. However, we present it here in order to demonstrate the method, which can be applied generally to solving additional problems. As was mentioned previously, in order to solve this type of problem we need to simply specify the Lagrangian function, the constraint relations (if they exist), and the generalized forces, and as well, the system physical parameters and initial conditions. The Lagrangian function is L = T - V, where 1 " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000519_robot.1997.619363-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000519_robot.1997.619363-Figure1-1.png", "caption": "Figure 1. A Planar 3 Degrees of Freedom Mechanism", "texts": [ " Based on the compliance model, a load distribution method is proposed to create the desired 0-7803-361 2-7-4197 $5.00 0 1997 IEEE 2663 RCC characteristics. Simulations for both cases are carried out to corroborate the proposed theory. Lastly, we draw conclusions. 11. Modulation of Output Compliance Matrix Using Redundant Joint Compliances 2.1 Kinematics of A Planar 3 DOF Parallel Mechanism C41 The mechanism proposed in this paper consists of three subchains which connect the platform to the ground as shown in Fig. 1. Each subchain possesses three joints and two links. .dn denotes the joint angle of nth joint of the r th subchain. Also, .l, denotes the link length of nth link of the r t h subchain. Let U = (x y fi) represents the center location of the upper platform, and let yq5==( ydl y4z yq53)T represents the joint angles of the r th serial subchain. Then, the first- and second-order kinematic relations between the two vectors are described by [el U = [,G$l rd, r=1,2,3 (1) U = [,G,\u201dl P$+ .d\u2018[.H\u201d,I rd (2) where [ " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000487_59.962404-Figure9-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000487_59.962404-Figure9-1.png", "caption": "Fig. 9. Graphical construction for finding the saturation correction voltageE", "texts": [ " Magnetic saturation also produces odd order harmonics due to the distortion of the air gap flux corresponding to Potier voltage E . wave. However, saturation harmonics are small and can be ignored from synchronous generator steady state studies. A1. 100 MVA Generator Data kV s s s. A2. Benmore Generator Data (112.5 MVA) kV s s s. Generator Open Circuit Saturation Characteristic (kA) (kV rms) (kA) (kV rms) The Potier reactance technique uses a saturation correction voltage , obtained from the open-circuit saturation curve and the Potier voltage as shown in Fig. 9, to determine the excitation voltage , and indicates the position of the q-axis under saturation. In order to eliminate the manual calculation of , the saturation curve is represented by a mathematical expression that can be obtained by using curve fitting technique such as cubic splines interpolation. Thus can be directly expressed as a function of , and consequently a function of . In reference to Fig. 10, the variation of rotor angle under saturation condition, , is obtained from as: (25) where (26) The rotor angle under saturation is therefore: (27) where and are given in (1) and (25)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001416_robot.2003.1241672-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001416_robot.2003.1241672-Figure2-1.png", "caption": "Fig. 2: Overview of the master manipulator", "texts": [], "surrounding_texts": [ "Then we propose an impedance controller to cope with this problem. In the proposed system, the position controller for the slave manipulator is also constructed by means of a velocity-control-based impedance controller. This feature makes it possible to shorten the dead time taken by the slave manipulator to respond for the contact force input. This paper also reports the result of a clinical w e of the remote ultrasound diagnostic system. The result of the experiments demonstrates that a medical doctor can diagnose patients as well as the conventional diagnosis.\n1 Introduction Medical treatment has increasingly changed from consultation in the hospital to home care and medical treatment in the arriving \u201caged society\u201d and differentiation and specialization in medical field also goes on. As a result, the number of medical specialists who can diagnose a disease is limited. For example, the number of medical specialists who can diagnose shoulder disease such as dialysis-related amyloid arthropathy (DRAA) by ultrasonographic images of shoulder is limited[l][Z][3]. Therefore, it is necessary to realize\n0-7803-7736-2/03/$17.00 02003 IEEE\nmedical systems to support efficient medical care. Therefore, we have developed a remote medical system for ultrasound diagnosis in the \u201caged society\u201d [4][5][6]. In general, reality-sensation is necessary to diagnose efficiently in remote medical systems. This paper presents the impedance controller for a master-slave type remote ultrasound diagnostic system.\nAn impedance control is a method t o control the mechanical impedance of the tip of the manipulator according to tasks and to regulate the response characteristics properly regarding to the motion of the manipulator[\u2019l].\nThis paper proposes and evaluates impedance controller for the remote ultrasound diagnostic system. Specifically we evaluated our proposed impedance controller by comparing the proposed impedance controller with the conventional impedance controller in the remote ultrasound diagnosis.\nGenerally, there is only one impedance controller in the conventional impedance controller that is located in the master site or the slave site or the relay point. Therefore, the effect of the time lag in transmitting force and position data becomes large. Specifically, the response time between the force input in the slave site and the slave motion output is large in the conventional system. Then we proposed an impedance controller to cope with this problem. In the proposed system, each site has its own velocity control based impedance control. Therefore, the effect of the time lag to transmit force and position data can be lessened. The proposed impedance control allows the master and the slave ma,\n676", "nipulators to move autonomously according to the motion control law for the remote ultrasound diagnosis, and allows the medical doctor to feel feedback force as the result of the change in velocity.\nFirst, this paper presents the configuration of this system and position controller. Second, we illustrates an impedance controller based on velocity control. Then, we explain the characteristic of the proposed controller. Third, we evaluate the proposed impedance controller by comparing it with the conventional impedance controller. we also discuss the efficiency of position feedback compensation between the master manipulator and the slave manipulator for the remote ultrasound diagnostic system. Fourth, we report the result of remote ultrasound diagnostic experiments conducted by using the proposed system and controller when i t is clinically used. Then we compare the results of the remote ultrasound diagnosis with those of the conventional diagnosis.\n2 Related work\nRecently, a remote diagnostic system bas become a topic of conversation in the medical field. However, it is mainly advisory to the medical doctor with patients, from a doctor in the remote site, referring to diagnostic image and other data (X-ray film, computed tomography (CT) image, magnetic resonance imaging (MRI), electro-cardio graphy, electromyography (EMG), ultrasonography, endoscopy, arteriography, venography, ultrasonography and phonocardiogram). Therefore, it is necessary to realize a remote diagnostic system with robot a r m that can input and realize medical doctors\u2019 motion in diagnosis for efficient home care.\nTachi\u2019s group studies a bilateral remote control with high reality sensation including force feedbackIS]. S.E.Salcudean\u2019s and Koyama\u2019s group study remote ultrasound diagnostic system[9][10][11]. Furthermore, a remote ultrasound diagnostic system using pantograph mechanism is also developed(lZ]. The control system of our system is based on impedance control. The control law and impedance controlled master-slave system whose impedance parameter is variable feature our study. This makes it possible for the medical doctor to diagnose efficiently according to tasks in the remote ultrasound diagnosis. Furthermore, we discuss the method and device to input an impedance parameter.\n3 Remote ultrasound diagnostic system\nThe system configuration is shown in Fig.1. Specifically, a medical doctor diagnoses a patient from a", "/\nremote site by manipulating the master manipulator. During diagnosing the patient, the medical doctor refers to the ultrasound diagnostic image, the ultrasound probe, the patient and the slave manipulator displayed on TV monitor. Position, orientation, force, image and audio information are,transmitted between the multimedia cockpit with the medical doctor and the consulting morn with the patient. The overview and degree-of-freedom configuration of the master and the slave manipulators are shown in Figs.2 and 3 respectively.\n4 Impedance controller\n4.1 Controllers for the master and the slave manipulators\nPosition controllers for the master and the slave manipulators are implemented using an impedance controller based on velocity control.\nFirst, we illustrate the controller for the master manipulator. A driving force of the master manipulator is calculated by Eq.(l).\nHere, Fmd(t) is the driving force of the master manipulator. Fm(t) is the measured force of the master manipulator, F,(t) is the measured force of the slave manipulator. S, is the force-scale ratio and td is the time lag.\nThe desired velocity can be calculated by solving Eq.(2) using Eqs.(3) -(IO) by Runge-Kutta method. Here, vmd is the desired velocity of the master manipulator and At represents the sampling time of force information. In Eq.(4), ko - 8 3 are calculated from Eqs.(5) - (8).\nTo compensate the dead time caused by sampling time, F(t, + 9) and F(t, + At) are calculated using the master force F(t,) and the previous one F(In-l) in Eqs.(S) - (10). Those forces are used in Eqs.(G) and (E). Based on the desired velocity sent to the motor driver, this system can control proper angular velocity.\n. .\nand Fm(t) ' Fs(t - t d ) ? 0 (1) if F,,,(t) < SfF,( t - I d ) and Fm(t) .F,(t - td) < 0 Second, we illustrate the controller for the slave manipulator. Same as the master manipulator, the slave manipulator is also controlled by velocity control based impedance controller (Eqs.( 11) - (13)).\nHere, F,d(t) is the driving force of the master ma-\nF m ( t )\nFmd(t) = hfdZmd + CdZmd\ndumd c d\ndt .Md\nnipulator and umd is desired velocity of the master ma(3) nipulator. -\nThen position error hetween the master and the slave manipulators is compensated by position feedback\n1 6 \"md,+i = \"md, + -(ko + 2 k l + 2k2 + IC3) (4)" ] }, { "image_filename": "designv11_32_0001763_025-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001763_025-Figure3-1.png", "caption": "Figure 3. Fibre rotating over a pin, indicating frictional forces F, torque Mt, bending moment M b , and tension T.", "texts": [ " More details of this work will be reported elsewhere, but an example is shown in figure 2(b) (plate). Real twist is impossible since the two clamps are geared together. However the rotation of the centre point of the fibre lags behind the rotation of the clamps giving right-handed twist on one side and left-handed twist on the other, as shown in figure 2(b). Frictional drag between the fibre and the surface of the pin would give rise to an effect of this sort. The forces and moments would vary in the way indicated in figure 3 with the torque being zero at the centre point and rising to a constant value where the fibre leaves the pin. This variation in torque would explain the fact that in coarse fibres the splitting occurs in opposite senses in two separated positions where the torque is higher. Torque in fatigue testing ofjibres 727 When there is rotation over a pin, there is clearly an external frictional force which would cause torque to develop, although, on reflection, the levels of twist developed appear to be high, especially as tensions are low and the surface damage caused by any friction is very slight" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002826_j.jfranklin.2006.12.003-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002826_j.jfranklin.2006.12.003-Figure1-1.png", "caption": "Fig. 1. Feasibility region for suboptimal H2 observer design.", "texts": [], "surrounding_texts": [ "Example 1. This example is provided to show the regions in the P and Y coordinates in which the LMIs (12) and (15) have solutions for a one-dimensional system and various design parameters. These parameters are given in Table 1 for three different cases of performance criteria involving H2 suboptimal, HN suboptimal, and output strict passivity results. LMI (12) and LMI (15) are initially solved for a as well as P40 and Y and then this avalue is kept fixed as d (in Figs. 1 and 3) and A (in Fig. 2) are changed. The feasibility A B C Cz D Dz Af Bf a d b A Suboptimal H2 observer .5 0 1 1 0 0 .0099 0 1.4652 .1, .3, .7, .9 0 0 Suboptimal HN observer .5 .5 1 1 .5 1 .0099 0 3.1075 1 0 4.5, 4, 3.5, 3, 2.5 Output strict passivity .5 .5 1 1 .5 1 .0099 0 2.403 .1, .3, .5, .7, .8 1 0 regions corresponding to various parameter values and performance criteria are shaded differently in Figs. 1\u20133 to indicate how the shape of the regions changes as the design parameter d or A changes. Large areas should be interpreted as including the smaller areas. So, as the d or A value increases the feasibility region gets smaller. Higher values in this range will result in lower bounds on the energy of the performance output in Figs. 1 and 2 and higher dissipativity in Fig. 3. Example 2. This example is provided to present some simulation results on the time responses of various observer designs proposed in this work. Again, three different design cases including the suboptimal H2 observer (wk 0, kX0), with e0 6\u00bc0 and suboptimal HN observer together with output strict passivity (with e0 \u00bc 0 wk 6\u00bc0, kX0) are chosen. ARTICLE IN PRESS E.E. Yaz et al. / Journal of the Franklin Institute 344 (2007) 918\u2013928 925 For the design parameters given in Table 2, when the LMIs (12) and (15) are used, the sub-optimal H2 observer gain is found to be K \u00bc 0:8630 7:9065 . For the case of the suboptimal HN observer, K is found to be K \u00bc 0:93428 10:815 , and the gain K for the output strict ARTICLE IN PRESS E.E. Yaz et al. / Journal of the Franklin Institute 344 (2007) 918\u2013928926 passivity case is found to be K \u00bc 0:85927 7:9532 . The estimation error norm plots for all cases are given in Fig. 4 and they show the difference between the time responses of observers designed based on these criteria. Example 3. Chaotic synchronization is chosen to demonstrate one of the possible applications of the proposed observer design. Chua\u2019s circuit [26] has become almost a benchmark for design involving chaotic systems because of its strong nonlinear dynamical behavior. The discretized (with sampling time T \u00bc .01 s) version of the example in Ref. [8] was chosen for this demonstration. The design is done for boundedness of the estimation error. The state and measurement equation of this model is written as follows: _x1 _x2 _x3 2 64 3 75 \u00bc aC aC 0 1 1 1 0 bC m 2 64 3 75 x1 x2 x3 2 64 3 75 aCf \u00f0x1\u00de 0 0 2 64 3 75; y \u00bc \u00bd 1 0 0 x1 x2 x3 2 64 3 75, where f \u00f0x1\u00de \u00bc bxx1 \u00fe 0:5\u00f0a b\u00de\u00f0jx1 \u00fe 1j \u00fe jx1 1j\u00de. And we use the following parameters in the simulation with a randomly chosen initial state: aC \u00bc 9.1, bC \u00bc 16.5811, m \u00bc .138083, a \u00bc 1.39386, b \u00bc .75590. For the given system, the observer gain is found to be K \u00bc 0:8285 1:3421 4:2815 2 64 3 75. The simulation results involving co-plots of state variables together with their estimates (Figs. 5(a)\u2013(c)) and the norm of the error vector (Fig. 5(d)) show that the proposed observer is able to estimate the state successfully. Figs. 5(e)\u2013(g) are included to clearly depict the transient response of the observer state variable estimates." ] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-FigureA.9-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-FigureA.9-1.png", "caption": "Fig. A.9. Squareness measurements - second axis (horizontal plane)", "texts": [ " The main cause of a squareness deviation is probably the constraints during the manufacture or assembly of the machine to fix two axes exactly perpendicular to each other. The squareness measurement will be useful to allow the small angular difference to be measured and compensated for. The optics required for squareness measurements are given in Figure A.7. The main procedure for squareness measurement on a horizontal plane is to carry out a measurement along the first axis as shown in Figure A.8 using an optical square, and subsequently to carry out a measurement along the second axis according to the set-up in Figure A.9. The second axis measurement is simply a horizontal straightness measurement along the axis on which the reflector was earlier mounted during the first measurement. Figure 5.9 illustrates the concept of obtaining the squareness error from the two straightness measurements. 5.5 Accuracy Assessment 139 The procedure to execute a squareness measurement in the vertical plane is similar to that of the horizontal plane, except for additional requirements in terms of optics. The required set of devices is shown in Figure A" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001332_iecon.1998.722910-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001332_iecon.1998.722910-Figure4-1.png", "caption": "Fig. 4: Heyland circle diagram for R, = 0", "texts": [ " Only at low stator frequencies with a rotor frequency with opposite sign of the stator frequency the open-loop gain is positive; this causes stability problems when (14) is used for speed identification. To explain this behaviour at low stator frequencies it is first assumed that the stator resistance can be neglected: R, = 0 3 p = 0. Under this condition the estimation of stator flux is ideal (!l'F='\u20ac'Fw) even if there is a difference An between model and machine speed, so that model and machine can be described with the same Heyland circle diagram. A speed difference leads to different operating points on this circle with different stator currents, as shown in Fig. 4. For small speed differenms An<< 1 the space vector of the stator current difference A is is nearly perpendicular to the corresponding diameter of the Heyland circle. For all operating points used in practice with Gr< 1 it is almost perpendicular to the rotor flux space vector, too. So the sign of the transfer function Gil, describing the relation between the speed difference and the component of the stator current difference perpendicular to rotor flux, is only dependent on the sign of An. This can also be seen if Gil is calculated with (14): - - Gil (p = 0) = -' LO ' ( l+Kr2 ) 3 signkyl (p = 0)) = -1 v ns, n, (15) - The absolute value of G1l , which i s responsible for the gain of speed estimation, only depends on the leakage inductance and the load conditions" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000457_978-3-642-55848-1-Figure2.11-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000457_978-3-642-55848-1-Figure2.11-1.png", "caption": "Fig. 2.11. Simplification ofthe bond graph of Fig. 2.10", "texts": [ " Direct processing can be used to eliminate some, or all, of the algebraic variables (i.e., variables that are not differentiated). We can also simplify the bond graph first, then write the corre sponding equations. We consider the second approach in more detail, as it leads to the sort of bond graphs usually found in the literature. We can simplify the model by substituting every component at the top of Fig. 2.10 by its corresponding model, given at the bottom part of the same figure. The resulting bond graph is shown in Fig. 2.11 a. The source flow on the left imposes zero wall velocity; thus, we can remove the effort junction and the source flow, as well as the two bonds connecting the junction to the flow junctions. We also re move the corresponding ports at the flow junctions. This yields a bond graph rep resented by Fig. 2.11 b. We should also eliminate these flow junctions, for they are trivial, having only one power input port and one power output port. Thus, the C and R element ports can be connected directly to the right-hand effort junction ports. This results in the bond graph of Fig. 2.11c. The model in Fig. 2.llc is much simpler than that in Fig. 2.10. The resulting equations now consist of Vm = Xs Fs = k ,xs Fd =b,vm Fm =Pm Pm = m,vm F = (t) -Fs-Fd-Fm+F=O Xm =Vm (2.56) We have reduced the system to eight equations with eight variables F s, xs, F d, Fm, Vm, Pm, F, and Xm\u2022 This was achieved, however, by eliminating some variables that can be of interest, e.g. total force transmitted to the wall. This bond graph can be developed directly from Fig. 2.9a by the application of classical methods of bond graph modelling, as explained in [1]" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003156_20080706-5-kr-1001.02585-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003156_20080706-5-kr-1001.02585-Figure1-1.png", "caption": "Fig. 1. Rotary wing vehicle", "texts": [ " However, in this paper the problem is solved by introducing fractional order derivative controllers that guarantees the robustness of the system to variations in its dynamics and parameters, giving a constant phase margin in the frequency response. Since the approach here presented is specifically tailored to our particular rotorcraft dynamics, the control design problem becomes much simpler and gives very straightforward tuning rules. A similar strategy, though with a different application, has been also used in Feliu et al. [2005]. 978-3-902661-00-5/08/$20.00 \u00a9 2008 IFAC 15285 10.3182/20080706-5-KR-1001.3638 The rotary wing vehicle is shown in Figure 1. It is powered by four non-tilting rotors attached to a rigid frame. The dynamical model of the rotary wing vehicle considered can be obtained as follows. Let 0xeyeze denote a righthand inertial frame (earth frame) such that ze points downwards into the centre of the earth and 0xbybzb a right-hand frame fixed to the center of mass of the aircraft structure (body frame). The vehicle dynamics in the body frame is described by (Roskam [1982]) m V\u0307 b CM + m \u2126 \u00d7 V b CM = F b e I \u2126\u0307 + \u2126 \u00d7 I \u2126 = M b e (1) where m represents the vehicle mass, V b CM = [ u v w ] \u22a4 denotes the linear velocity of the vehicle center of mass expressed in the body frame, \u2126 = [ p q r ] \u22a4 denotes the angular velocity of the body frame, I is the vehicle inertia matrix 1 , F b e represents the external applied forces expressed in the body frame, and M b e represents the external applied moments expressed in the body frame" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000271_robot.1994.351376-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000271_robot.1994.351376-Figure1-1.png", "caption": "Figure 1: A generic manipulation system", "texts": [ " Examples of the presented technique are given in section 5, while section 0 concludes with some final comments. 2 Kinematic Model The manipulation systems we deal with may be composed of a generic number of 'arbsA, i.e. serial kinematic chains, each one in ContactIwith an object with one or more links. More than a contact is possible for each kinematic chain, and each kinematic chain may not have full mobility in the task space (for example, the fingers of a robotic hand usually have three or four degrees of freedom), see Fig. 1. Moreover, since the mobility of the system (and the applicable forces) are influenced by the contact models between the object have to be taken into ing it is assumed that the contact positions, located on the arms, are known. This implies that a distributed sensoriality is used in the manipulation system, for example skin-like sensors or force sensors of the intrinsic tactile type, [S In order to o tain the kinematic relationships for the system, define for each of the ra contacts two reference frames \"Ci and \"Ci, i = 1," ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001933_05698190590948232-Figure13-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001933_05698190590948232-Figure13-1.png", "caption": "Fig. 13\u2014Particle abrasion scratch.", "texts": [ " 8\u2014Relationship curve of seal power consumption versus rotating speed: 1, total power consumption including test seal and test rig; 2, calibrated test rig power consumption without test seal; 3, gross power consumption of test seal; and 4, seal net power consumption, considering test rig\u2019s transmission efficiency. y coordinate is enlarged 1,000 times and one unit is 2 \u00b5m. From the detection, the mean wear of the two primary rings is 0.4 \u00b5m, which means the wear for each start-up and shut-down process of 25 times is about 0.015 \u00b5m. The herringbone spiral-groove pattern was studied when the seal was designed at first. High wear was observed after every test. As shown in Fig. 13, a deep scratch abraded on the primary ring after a 4-h test can be seen clearly. This is typical particle abrasion, caused by the particles from the oil system and oil pipeline accumulated at the meeting line of upstream pumping and downstream pumping. Two effective measures to settle the problem are taken. One is changing the groove pattern from a herringbone D ow nl oa de d by [ E rc iy es U ni ve rs ity ] at 1 5: 28 2 9 D ec em be r 20 14 Fig. 12\u2014Diagram of wear detection on the face of the outboard primary ring: 1, scratch near the outside diameter (OD); 2, scratch near the mid-diameter (MD); and 3, scratch near the inner diameter (ID); (left: before test; right: after test)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001519_j.matdes.2004.09.005-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001519_j.matdes.2004.09.005-Figure1-1.png", "caption": "Fig. 1. (a) Schematic illustration of the half polygonal disc. (b) OC cross-section of the polygonal disc.", "texts": [ " Good correlation was seen between theoretical and experimental results. The difficulty in solving such problems arises from the fact that the three-dimensional changes in the configuration of workpieces must be solved through nonlinear equations of plastic deformations and these take such long time, which is not acceptable in automation. Therefore, fast and accurate numerical solutions are required. The axes of Cartesian coordinate system (x,y,z) are chosen and their origin is located at the centre of mid-section of polygonal block as shown in Fig. 1. During forging of polygonal discs, the flow of metal is nonuniform both in the plane section of the workpiece and along its thickness. The workpiece is compressed along the z-direction between moving upper die with velocity of \u2013U0 as bottom die is held stationary. As deformation proceeds thickness of workpiece is shortened, while the workpiece elongates along the x and y directions. Barrelling along the thickness and bulging through sideways take place as a consequence of non-uniform metal flow caused by friction between two flat dies as the workpiece is completely covered by the dies and the material being deformed", " For this a kinematically admissible velocity field was constructed for incompressible material and used to analyse many metal forming problems by different researchers [14\u201320]. By using dual stream function (DSF) method, three unknown velocity components are reduced to two unknown stream functions and incompressibility condition and boundary velocity conditions are satisfied as a property of stream function. Due to symmetry of the workpiece, only a triangular segment OBCC 0B 0O 0 is considered for upper bound solution as shown in Fig. 1. Since normal velocity across the OO 0BB 0, OO 0CC 0 and OO 0EE 0 surfaces is zero therefore no metal flow occurs through these surfaces. v and w are dual stream function, therefore, these surfaces are defined as stream surfaces and the following conditions are then obtained: v and=or w \u00bc C1 at h \u00bc 0; v and=or w \u00bc C2 at h \u00bc a; \u00f01\u00de where C1 and C2 are constants. Velocity boundary conditions at the top and bottom surfaces are V z \u00bc _U 0 at z \u00bc t and V z \u00bc 0 at z \u00bc 0 \u00f02\u00de and V x \u00bc V y \u00bc 0 at x \u00bc y \u00bc 0: \u00f03\u00de By using boundary conditions given in Eqs", " (15) is a parabolic equation and governing equations are in exponential form. Therefore, optimisation curve and consequently optimisation interval must be determined. To do this, a computer code has been developed to optimise equation (15). In the analysis, a, b and B values have been used as optimisation parameters. AISI 5454 aluminium alloy was chosen as the working material for the experiments and its mechanical and chemical descriptions are given in Table 1. Polygonal discs were machined from the alloy sheet having a thickness of 20\u201315 mm as illustrated in Fig. 1(a). Each of them had the same height and cross-sectional area. The aluminum discs were fully annealed for about 2.5 h at 450 C and then furnace cooled. Experiments for open-die forging of regular polygonal discs were carried out in a 110 ton PLC controlled hydraulic press at room temperature and for slightly oily conditions. In Fig. 2(a), the picture of simple flat tooling and in Fig. 2(b) few polygonal forged discs are shown. The specimens were cold forged at ram speed of 0.5 cm/s by giving various deformations from 2% to about 50%", " Dual stream function method is introduced by Yih [13] to construct the kinematically admissible velocity field for incompressible material and used to analyse many metal forming problems by different researchers [14\u201320]. By using dual stream function method, three unknown velocity components are reduced to two unknown stream functions and incompressibility condition and boundary velocity conditions are satisfied as a property of stream function. Due to symmetry of the workpiece, only a triangular segment OBCC 0B 0O 0 is considered for upper bound solution as shown in Fig. 1. Since normal velocity across the OO 0BB 0, OO 0CC 0 and OO 0EE 0 surfaces is zero, therefore, no metal flow occurs through these surfaces. v and w are dual stream functions, therefore, these surfaces are defined as stream surfaces and following conditions are obtained. v and=or w \u00bc C1 at h \u00bc 0; v and=or w \u00bc C2 at h \u00bc a; \u00f0A:1\u00de where C1 and C2 are constants. Velocity boundary conditions at top and bottom surfaces are V z \u00bc _U 0 at z \u00bc t and V z \u00bc 0 at z \u00bc 0 \u00f0A:2\u00de and V x \u00bc V y \u00bc 0 at x \u00bc y \u00bc 0: \u00f0A:3\u00de By using boundary conditions given in Eqs" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003850_gt2009-60186-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003850_gt2009-60186-Figure1-1.png", "caption": "Figure 1. Foil bearing schematic", "texts": [ " NOMENCLATURE \u03c9 Frequency \u03c3u Standard deviation associated with u Ai Acceleration, frequency domain bi j Damping coefficient fi Force, time domain Fi Force, frequency domain Guv Power spectral density of arbitrary functions u and v Hi j Frequency response function i Directional index (x corresponds to horizontal direction, y corresponds to vertical) j Directional index (x corresponds to horizontal direction, 1 roceedings.asmedigitalcollection.asme.org/ on 02/01/2016 T y corresponds to vertical) ki j Stiffness coefficient mb Mass of the test bearing assembly si Positional coordinate, time domain Si Positional coordinate, frequency domain t Time u Function index (placeholder) v Function index (placeholder) Foil bearings are self-acting, compliant-surface hydrodynamic rotor supports made from multiple layers of sheet metal foils. A generalized bearing, depicted in Figure 1, features a top-foil supported by one or more elastic sub-foils. The top-foil, which is typically coated with a wear-resistant, anti-friction material, traps an air film that supports a load. As the gas pressure on the top-foil changes, the force is transmitted to the elastic subfoils, which vary by bearing design but are most often corrugated, spring-temper sheet metal. Deflection of the top-foil (under the influence of the gas film pressure) causes the sub-foils to compress radially and expand circumferentially" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003394_peds.2007.4487699-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003394_peds.2007.4487699-Figure1-1.png", "caption": "Fig. 1. A 3D view of a 16 pole RFAPM machine with concentrated coils.", "texts": [ "ndex Terms-air-cored, concentrated coil, permanent magnet, radial fluxtheoretically LIST OF SYMBOLS Roman Symbols the number of parallel circuits per phase peak fluxdensity of the first harmonic machine constant peak sinusoidal phase voltage height/thickness of the stator coils magnet height/thickness yoke height/thickness peak sinusoidal phase current fill factor flux-linkage factor coil per phase to pole ratio torque factor active copper length of the stator conductors end turn length of the stator conductors air gap length number of turns per coil number of poles copper losses electrical power mechanical power number of coils per phase total number of coils (Q = 3q) nominal stator radius copper resistance total copper resistance per phase total copper volume of the stator coil side-width of the stator coils Greek Symbols a A A1 A Pcu Op oq relative angle between the rotor and the stator the angle measured from the centre of the coil side 1 coil side-width angle of the stator coils2 flux-linkage of a single turn flux-linkage copper conductance pole pitch angle coil pitch angle end turn to active copper length ratio I. INTRODUCTION In this paper two different concentrated coil configurations for Radial Flux Air-cored Permanent Magnet (RFAPM) machines are analysed and evaluated against a RFAPM machine that utilises overlapping coils. The construction of RFAPM machines, as shown in Fig. 1, is similar to that of dual rotor radial flux toroidal-wound permanent magnet machines, [1]. The difference are that the stator of the RFAPM consists of air-cored coils, instead of iron-cored toroidal coil, and that the rotor uses a north-south magnet polarity configuration, instead of a north-north configuration. Concentrated coils are also sometimes referred to in the literature as concentrated windings [2]. The main reasons for using concentrated coils above overlapping coils is to reducing the manufacturing costs of the machine and still be able to produce the same amount of torque" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000474_b:elas.0000005548.36767.e7-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000474_b:elas.0000005548.36767.e7-Figure1-1.png", "caption": "Figure 1. Reference configurations \u03ba and \u03ba\u2217 in the change of frame from \u03c6 to \u03c6\u2217.", "texts": [ " We call \u2217 = \u03c6\u2217 \u25e6 \u03c6\u22121: E \u00d7 R \u2192 E \u00d7 R a change of frame from \u03c6 to \u03c6\u2217. In general, the change of frame \u2217, which maps (x, t) to (x\u2217, t\u2217), is a Euclidean transformation of the following form, x\u2217 = Q(t)(x \u2212 x0) + c(t), t\u2217 = t + a, (2.1) for some a \u2208 R, x0 \u2208 E , c(t) \u2208 E , and Q(t) \u2208 O, where O is the group of orthogonal transformations on the translation space of E . In particular, \u03c6\u2217 t \u25e6 \u03c6\u22121 t : E \u2192 E is given by x\u2217 = \u03c6\u2217 t (\u03c6 \u22121 t (x)) = Q(t)(x \u2212 x0) + c(t). (2.2) Let \u03ba\u0303: B \u2192 Wt0 be a reference placement of the body at some instant t0, then (see Figure 1) \u03ba = \u03c6t0 \u25e6 \u03ba\u0303 and \u03ba\u2217 = \u03c6\u2217 t0 \u25e6 \u03ba\u0303 (2.3) are the two corresponding reference configurations of B in the frames \u03c6 and \u03c6\u2217 at the same instant, and X = \u03ba(X), X\u2217 = \u03ba\u2217(X), X \u2208 B. Let us denote by \u03b3 = \u03ba\u2217 \u25e6 \u03ba\u22121 the change of reference configuration from \u03ba to \u03ba\u2217 in the change of frame, then it follows from (2.3) that \u03b3 = \u03c6\u2217 t0 \u25e6 \u03c6\u22121 t0 and by (2.2), we have X\u2217 = \u03b3 (X) = K(X \u2212 x0) + c(t0), (2.4) where K = Q(t0) is a constant orthogonal tensor. On the other hand, the motion in referential description relative to the change of frame is given by x = \u03c7\u03ba(X, t), x\u2217 = \u03c7\u2217 \u03ba\u2217(X\u2217, t\u2217), and from (2" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure2.2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure2.2-1.png", "caption": "Fig. 2.2. Laminar design", "texts": [ " To derive maximum performance from PAs, a variety of configuration can be designed to adapt to various requirements. The most common design for PAs is a stack of ceramic layers (see Figure 2.1). Such devices are capable of achieving high displacements and holding forces. Standard designs which can withstand pressures of up to 100kN are available in commercial products (e.g., products from Physik Instrumente), and preloaded actuators can also be operated in a push-pull mode. This design uses thin laminated ceramic sheets (see Figure 2.2). When a voltage is applied to the device, the actuator sheet contracts. The displacement in the device is caused by the contraction in the material being perpendicular to the direction of polarization and electric field application. The maximum travel of the laminar actuators is a function of the length of the sheets, while the number of sheets arranged in parallel will determine the stiffness and force generation of the ceramic element. Laminar actuators are easily integrated in conventional composite layers" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001839_tia.1979.4503695-Figure10-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001839_tia.1979.4503695-Figure10-1.png", "caption": "Fig. 10. SCI/reluctance motor elementary sequences.", "texts": [ " INSTANTANEOUS VALUES IN STEADY STATE CONDITION The vector diagram tied to the fundamental gives satisfactory results with regard to the average value in steady-state conditions but does not provide an accurate means of showing the evolution of the instantaneous values of the characteristic variables. We therefore tum to a simulation of the inverterreluctance motor drive system by a numerical computer. The The rotor winding is taken into consideration by means of two windings in short circuit positioned in the d and q axes. For reasons of symmetry and periodicity only one-sixth of the total period has to be described. A switching function may therefore be described by the circuits shown in Fig. 10. Transition from one sequence to another is conditioned by the voltage and current levels across semiconductors. This provides an accurate means of simulating the behavior of the converter associated with the machine. The computer resolution method is by Runge Kutta. The experimental curves of Fig. 5 are then used to account for saturation. Two different ways, each of which differs appreciably in complexity, may be used. * In the inductance method the inductances are assumed to be constant for an operating point defined by I and IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001796_physrevlett.95.207801-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001796_physrevlett.95.207801-Figure7-1.png", "caption": "FIG. 7. Schematic drawing of the few surface layers in modulated film of the Sm-C phase. The change of the film thickness without bending of bulk layers requires the edge dislocations being close to the film surface. In the slope area, additional tilt of the molecules is allowed in the surface layer. Energy of elastic deformation is minimal if, around each dislocation defect, the director is tilted along the defect line (y direction), and the c vector (arrows) is uniform through the film thickness. Below the critical temperature, the edge dislocation lines curve, giving rise to the stripe/labyrinth texture. The c vector remains along the defect line and has to rotate by between the neighboring edge dislocation lines. Rotation of the c vector in the -wall region is indicated by thick arrows, ds is the stripe width, d0 is the smectic layer thickness, and is the surface inclination angle.", "texts": [ " 6), while tilting the sample in the direction perpendicular to the stripes shows that, in the narrow regions between the broad stripes, the c-vector direction is identical. Thus, it was concluded that the c vector rotates by between the stripes. The rotation is not uniform in space, the broad stripes with nearly uniformly oriented c vector are connected by narrow regions over which the c vector rotates ( walls), and rotations in the negative and the positive sense interchange between the 1-2 neighboring stripes (Fig. 5). The walls are located at the crests and the valleys of the film surface (Fig. 7). The modulated structure is observed in thin and in very thick films alike. The stripe width and the -wall width depend on the thickness of the film. The transition to the labyrinth structure is observed also in films that have almost uniform thickness above the transition temperature. Since the effect is observed for the intercalated smectic phase, we suggest that it is driven by the mass density difference in the surface and the bulk layers. In order to decrease the intermolecular distances and, thus, increase the density of the surface layers, which are \u2018\u2018half empty,\u2019\u2019 the molecules increase the tilt in the layer or the layers tilt", " Because of the entropic effects, the reduction of density is possible only at a sufficiently low temperature, and, for dimers, the tilt of the layers is energetically more favorable than the tilt of one-half of a dimer. In a uniform thickness film, one possibility to reduce the volume of the surface layer is the undulation of the whole film; however, undulation of the bulk layers should be extremely expensive in the intercalated system. Another possibility is to undulate only the surface layer, keeping the bulk layers flat, which leads to the modulation of the film thickness. This scenario involves formation of edge defects close to the film surface (Fig. 7). The position of the edge defects depends on the ratio between the surface tension ( 10 2 J=m2) and the bulk elasticity, which is determined by the smectic layer compressibility constant (B 106 J=m3) and the elastic constant for the layer bending (K). If < KB p , dislocation is attracted to the surface [7,8]. In ordinary smectics K 10 12 J=m, so the ratio = KB p > 1 and edge defects are repelled from the surface [7,9]. However, in the intercalated structure, K should be larger (strong interlayer interactions) and smaller (low mass density in the surface layer) than in ordinary smectic, so it might be expected that edge defects are attracted to the surface", " If, at a certain temperature, the system reduces the free energy by enlarging the sloped regions more than it pays for the elongation of the edge dislocation lines associated with increasing the sloped areas, surfaces start to deform; this leads to the transition between the uniform and the modulated structure. Deformation of the film surface requires the 1-3 flow of the material, which in liquid crystals is the easiest in the direction of the c vector [10]. The elastic deformation across the edge dislocation defect in the Sm-C phase is the lowest if the c vector is tilted along the defect line [11] (y direction in Fig. 7). Thus, the flow is tangential to the dislocation line. This enhances the dislocation line curvature inhomogeneity and finally creates the labyrinth pattern in the film [Fig. 2(a)]. The initially approximately straight edge dislocation line begins to curl, but the c vector remains along the line. As a result, the c vector has to rotate by between the neighboring edge dislocation lines, and the walls are formed (Fig. 7). The transition to the labyrinth structure occurs when the energy associated with the formation (or elongation) of the edge defects and the walls is compensated by the reduction of the surface energy. The contribution (FS) to the surface energy per unit length of a stripe that privileges a finite tilt 0 of the surface layers is assumed to be: FS 1 2WS 1 2= 2 0 2dS, where WS WS T is the surface strength which increases with lowering temperature, is the tilt of the surface layers, and dS is the stripe width" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000184_pime_proc_1986_200_140_02-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000184_pime_proc_1986_200_140_02-Figure3-1.png", "caption": "Fig. 3 Forces in an open bearing during articulation", "texts": [ " Therefore, the analysis predicts stick and slip motion accounted for by the elementary rule of friction-the distribution of frictional stress at the interface is everywhere proportional to the normal contact pressure. Under this assumption, if the inclination of the contact force exceeds the angle of friction, sliding begins and the frictional traction is everywhere equal to its limiting value. The mechanics of the narrow bearing during articulation is different from that of the open bearing. Hence it is necessary to analyse both types as they articulate on to the driver sprocket. 2.1 Open end forward The schematic of the bearing (Fig. 3) shows the forces and motion occurring during articulation. As the roller engages with the sprocket tooth, the tooth force is transmitted to the bush. The bush is press-fitted into the preceding link L,. This link turns with the sprocket and at any given instant during the articulation is at an angle 8 with the succeeding link Lo. 0 IMechE 1986 at UNIV OF PITTSBURGH on February 8, 2015pic.sagepub.comDownloaded from The pin making contact with the bush is press-fitted into the succeeding link Lo which essentially remains parallel to, and equal to, the tight span tension Po during the articulation" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001614_1464419042035953-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001614_1464419042035953-Figure1-1.png", "caption": "Fig. 1 Rotor cross-section", "texts": [ " The bearing and rotor system simulated a proposed design of grinding machine tool spindle and grind-wheel mounting arrangement [3]. The grind-wheel (i.e. rotor) was belt driven and supported by fluid film bearings on a stationary central shaft or stator. There were two hydrodynamic bearings of the novel adjustable configuration, separated along the shaft, and a single four-pocket hydrostatic bearing in between. The purpose of the hydrostatic bearing was to support the rotor for zero speed and all other conditions when the hydrodynamic bearings were not operating. The same oil was used for all bearings. Figure 1 shows a longitudinal cross-section of the rotor and shaft arrangement. The steel shaft had a nominal diameter of 70 mm and housed the hydrostatic bearing pockets, their feeds and restrictors, the hydrodynamic bearings, their oil feeds, adjustment devices and a combined scavenge oil return. Figure 2 depicts the shaft used. Oil supply was via end blocks containing galleries and O ring seals to minimize pipework and allow efficient access to the adjuster controls and other items. There were four adjustable segments associated with each hydrodynamic bearing, each controlled by a steel adjuster pin", " Four contact thermocouples indicated temperatures of the oil in the main tank, hydrodynamic feed, hydrostatic feed and central gallery output. In addition, a roving thermocouple head could be positioned through access holes to record the temperature of oil on immediate exit of the hydrodynamic bearings. The instrumentation system is shown outlined in Fig. 7. Rotor radial displacement was sensed by four non-contacting inductive type transducers mounted in pairs orthogonally at each end. One of each pair is visible in Fig. 1. The gaps, and changes in gap, between the ends of the transducers and adjacent rotor surface were sensed. Outputs were low-voltage d.c. signals fed to digital voltmeters and an oscilloscope which provided a summative visual indication of the position and locus of the rotor centre of rotation. The main advantage of this inductive type of transducer is that it is not affected by the varying presence of any oil in the gap. The main disadvantage, based on experience with a variety of different sizes and types, is that during an experiment the effective position of the electrical origin may drift over a period of time" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001439_12.584626-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001439_12.584626-Figure4-1.png", "caption": "Fig. 4. An image of embryos immobilized at a sample patterned arrays of with 200 m x 200 m cross-shaped and 200 m x 100 m truncated cross-shaped sites. The immobilization yield was 72 % and the number of misplaced embryos less <5%.", "texts": [ " Samples completely covered with oil were immersed in water, leaving oil only at the hydrophobic sites. Finally Drosophila embryos were dispensed onto the surface keeping the sample submerged in water. As a result embryos were immobilized only at the oil-covered pads forming a well ordered 2-D array. The process flow is shown schematically in Fig. 3. Samples with 200 m x 200 m cross-shaped and 200 m x 100 m truncated cross-shaped immobilization sites with a pitch of 800 m x 800 m were fabricated. An image of one of these samples after embryo array formation is shown in Fig. 4. The immobilization yield was 72 % and the number of misplaced embryos was less than 5%. [10]. Proc. of SPIE Vol. 5641 69 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 05/19/2015 Terms of Use: http://spiedl.org/terms Although their orientation varies the self-assembly process facilitates rotational alignment to some degree. An average of ~ 40 % of 760 embryos align within 9 of the symmetry axis of the immobilization sites. The presented microassembly technique enables realization of 2-D arrays of immobilized embryos, and opens for manipulation of a large number of embryos in parallel", " An estimate was achieved by investigation of water flow induced detachment of the embryos; By directing a water flow at immobilized embryos and measure the flow rate at which the embryo detaches from the pad, rough estimates of the corresponding drag force, FD, acting at the embryo were obtained using : 2 2 1 AFDDD vACF (1) where CD is the drag coefficient, AD is the cross-section of an embryo, f is the density of water, A is the average flow velocity, Q is the measured flow rate. The adhesion force of immobilized embryos was estimated at 14 N 5.5 N [10], which is substantially lower than the required penetration force [11]. More precise measurements were carried out by means of a micromachined force sensor [12]. The sensor is based on an optical phase encoder for high-resolution displacement measurement. The basic operation principle of the optical force sensor is shown in Fig. 4. The sensor comprises two identical, vertically aligned phase gratings. When a force is applied horizontally along the probe the upper index grating is displaced. The relative position of the two gratings can then be determined by Fraunhofer diffraction theory. The first diffraction mode intensity I1(d) is a function of the injector displacement [12]: )(sin] 4 )(sin)[() 2 sin 2 sin ()( 0 22 2 2 2 1 dG L dLcdL L dc L dNc NdI (2) where, ]2,[ 4 )3(sin ],0[ 4 )(sin )( 2 2 LLd L dL Ld L dL dG (3) where I0 is the illuminating light intensity, N the number of grating periods, 2L the period of the grating, and d the displacement of the injector modulus 2L" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002384_02286203.2006.11442380-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002384_02286203.2006.11442380-Figure3-1.png", "caption": "Figure 3. Approximate bending of an asperity due to the tangential component of the contact force.", "texts": [ " For interaction of two asperities in contact: \u2202Pt \u2202r = 4 3 E\u2032\u03b21/2 ( \u2202(w1 cos\u03b1)3/2 \u2202r sin\u03b1+ (w1 cos\u03b1)3/2 \u00d7\u2202(sin\u03b1) \u2202r ) (6) where: sin\u03b1 = r/\u03b2 \u221a 4 + r2 \u03b22 (7) cos\u03b1 = 2/ \u221a 4 + r2 \u03b22 (8) The total normalized tangential contact stiffness K\u0303t can be written as: K\u0303t =H \u222b 6 128 (s\u2212 h)3/2\u03c33/2 4\u03b22(s\u2212 h)\u03c3 + 13(s3 \u22123s2h+ 3sh2 \u2212 h3)\u03c33 \u03b22 + ([ (72\u03b2(s3 \u2212 3s2h+ 3sh2 \u2212 h3)\u03c33 + 36\u03b22(s2 + sh\u2212 h2)\u03c32 ] + [ 55(s4 \u2212 4s3h+ 6s2h2 \u2212 4sh3 + h4)\u03c34)(s\u2212 h)\u03c3 ] 1 \u03b2 5 2 )] \u03c6(s) ds (9) Later in this paper the surface parameters are used in conjunction with the density function for a Gaussian distribution to examine contact stiffness and force. The above formulations are employed with: \u03c6(s) = 1\u221a 2\u03c0\u03c3 e \u2212s2 2 (10) Fig. 3 illustrates an asperity under the action of a tangential force, F . X1 is the asperity height and Xf is the distance of the tangential force from the peak. The moment at X is: M = F (X \u2212Xf ), Xf < X < X1 (11) where: M = EI d2y dx2 (12) The second area moment, I, is: I = \u03c0\u03c14 4 (13) and from the assumed shape of an asperity: x = \u03c12 2\u03b2 , or \u03c14 = 4\u03b22x2 \u21d2 I = \u03c0\u03b22x2 (14) Equation (12) becomes: d2y dx2 = F \u03c0\u03b22E 1 x \u2212 Fzf \u03c0\u03b22E 1 x2 , (15) Integrating (15) gives: dy dx = F \u03c0\u03b22E ln |x| + Fzf \u03c0\u03b22E 1 x + C (16) The constant C can be obtained by applying the boundary condition (dy)/(dx)|X=X1 = 0", " This yields: C = F \u03c0\u03b22E ( Xf X1 + ln |X1| ) (17) Substituting (17) in (16) and simplifying, we obtain: dy dX = F \u03c0\u03b22E [ ln \u2223\u2223\u2223\u2223 XX1 \u2223\u2223\u2223\u2223 +Xf ( 1 X \u2212 1 X1 )] (18) Integrating (18): y = FX1 \u03c0\u03b22E [ X X1 ln \u2223\u2223\u2223\u2223 XX1 \u2223\u2223\u2223\u2223\u2212 X X1 ] + F \u03c0\u03b22E \u00d7 [ Xf ln |X| \u2212 Xf X1 X ] + C (19) The expression for the constant C may be found by letting y(X1) = 0, leading to: y = F \u03c0\u03b22E [ X ln \u2223\u2223\u2223\u2223 XX1 \u2223\u2223\u2223\u2223\u2212X ] + FXf \u03c0\u03b22E [ ln \u2223\u2223\u2223\u2223 XX1 \u2223\u2223\u2223\u2223 ] + FXf \u03c0\u03b22E [ 1 \u2212 X X1 ] + FX1 \u03c0\u03b22E (20) The stiffness corresponding to the scenario shown in Fig. 3 may be obtained as follows: K = F y(Xf ) = \u03c0\u03b22E 2zf ln \u2223\u2223\u2223Xf X1 \u2223\u2223\u2223\u2212 X2 f X1 +X1 (21) As z represents the expected sum of asperity heights of the two mating rough surfaces, for two similar surfaces in contact, Xf = (z\u2212 d)/2 and X1 = z/2. The stiffness now may be rewritten in terms of z and d as: K = \u03c0\u03b22E (z \u2212 d) ln \u2223\u2223 z\u2212d z \u2223\u2223\u2212 (z\u2212d)2 z + z 2 (22) The expected total bending stiffness is then given by: K\u0303b = 2\u03c0\u03b72A \u222b z \u222b r K(z, d)\u03c6(z)r dr dz (23) Defining the result of r-integration as: Kb0 = 2\u03c0\u03b7 2 \u221a \u03b2(z\u2212d)\u222b 0 \u03c0\u03b22E (z \u2212 d) ln \u2223\u2223 z\u2212d z \u2223\u2223\u2212 (z\u2212d)2z z + z 2 r dr = 4\u03c02\u03b7E\u03b23 ln \u2223\u2223 z\u2212d z \u2223\u2223\u2212 (z\u2212d) z + z 2(z\u2212d) (24) The normalized form of the expected contact stiffness due to asperity bending is: K\u0303b = 4\u03c0\u03b72E\u03b23 \u221e\u222b h 1 ln((s\u2212 h)/s) \u2212 ((s\u2212 h)/s) + (s/2(s\u2212 h)) \u03c6(s) ds (25) Equation (25) is the macroscopic expected stiffness of the surfaces due to bending effects of surface asperities" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000298_20.42369-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000298_20.42369-Figure3-1.png", "caption": "Figure 3 shows a portion (excluding air) of a finite element model of a planar reluctance motor, assumed made of constant permeability steel. Table 1 lists the torque calculated by the new and old methods. Again they agree within approximately 0.01 percent.", "texts": [], "surrounding_texts": [ "A vector potential finite element method of calculating magnetic force or torque by direct analytic differentiation of coenergy is derived and applied to two- and three-dimensional actuators. The results are shown to agree well with calculations using the conventional difference between coenergies at two positions, and to also agree well with experimental measurements. Another method o f force calculation, Maxwell's stress tensor, is also derived by differentiating coenergy, resulting in a new formula applicable on the surface of nonlinear materials.\nIntroduction\nMagnetic force or torque must be calculated for a wide variety of devices such as motors or actuators and is known to equal the derivative of coenergy with respect to position at constant current. Past work has approximated the derivative by performing two finite element analyses at two positions spaced by a finite distance [1],[2]. To avoid analyzing two models and the error associated with taking the difference in coenergies, a number of recent papers have presented a1 ternative onestep approaches. One alternative, Maxwell's stress tensor [ 21, [3], is usual ly accurate for determi n 1 ng normal forces but inaccurate for torqties and tangential forces. Coulomb has presented a derivation of a method of one-step differentiation of coenergy [3],[4], which has been evaluated by others [5]. Istfan [61 has described a method which uses differentiation of stored energy [6], not coenergy. The direct differentiation method described here appears similar in concept to Coulomb's, but the derivation here is different. The method can be extended to estimate model sensitivity to any desired parameter. Force and torque calculations with the method are compared with two-position calculations and with measurements. Finally, Maxwell's stress tensor is derived for nonlinear materials by differentiating coenergy .\nMatrix Theory of Direct Differentiation\nMagnetic coenergy C is a function of grid point positions P in a finite element model and of the magnetic vector potential A, that is:\nC = C(P,A) (1)\nThe desired force or torque for a given motion 'parameter m is given by the derivative of C with respect to m for constant current. However, because both P and A depend on m the derivative is:\ndC/dm = (aC/dP) (dP/dm) t (bC/dA) (dA/dm) (2)\nThe quantities aC/bP and K/aA can be computed analytically, and dP/dm is given by the motion desired. It remains to find dA/dm. Let gi be the ith component of the finite element functional minimization equation [21:\nfr A gi = (d/dai)[Z(/H dB -) J dA ) dVt ] (3) P c 0\nThe customary solution for the case where H is a nonlinear function of B is Newton iteration, where at each iteration n\n(4)\nwhere the matrix elements of Kn are second derivatives of gn with respect to the elements of A [2], so that\nKn = (d2gn/daida.) J (5)\nAt the solution of (3) we have gi = 0-for all degrees of freedom i. Since gi is a function of P and A, the total derivative of gi with respect to m is\ndgi/dm = (dgi/dP)(dP/dm) tX(dgi/daj)(daj/drn) (6)\nObserve that dA/dm = (daj/dm) and from (5) that the matrix K = (dgi/daj). Thus dA/dm is the solution of the linear matrix equation\nI\nK (dA/dm) = -G' = -[(bgi/aP)(dP/dm), . . . I (7)\nwhere K is exactly the K obtained at the solution o f the field, the components of dA/dm are the desired gradients, and G' is evaluated, in closed form, at the solution values of A. The values o f dA/dm are then substituted into (2) to compute the force or torque. Note that (7) has the same matrix K as the final iteration of (4). Thus, once the B field is found K need not be recomputed; that is, the solution of (7) i s the same as the final solution of (4) with a new right hand side vector. Hence no additional matrix decomposition is required, saving considerable computer time compared with the two-position method of force or torque calculation.\nComDarison of Calculated Results\nResults obtained by the above method are here compared with those calculated by the customary twoposition method.\nFigure 1 shows a rotary actuator with complex Three example problems are analyzed.\nFigure 1 . Exploded vi- of a three-dimensional rotary actuator.\n0018-9464/89/0900-3578$01 .00@1989 IEEE", "3519\nthree-dimensional geometry and highly three-dimensional flux paths [l]. Figure 2 shows the steel finite elements used to model one quadrant of Figure 1, consisting of isoparametric hexahedrons and pentahedrons. In this example the steel is assumed to have constant-permeability (linear BH) steel. Table 1 lists its torque calculated for the rotor in the 30 degree position. The torque T calculated by the new method is seen in Table 1 to agree with that calculated by the customary two-position method within 0.01 percent.\nboth methods. In this case the two methods disagree by approximately 1 percent. One possible explanation is that the force is highly nonlinear with air gap length for such small air gap lengths. Hence the force obtained by the new method is more accurate than that obtained by the old two-position method.\nTab1 e 1. Comparison of Cal cul ations\n2.T(N-m) -7.966E-3 -7.967E-3 3.T(N-m) -29.6998E-3 -29.6966E-3 4.F(N) 467.6 463.3\nComparison with Measurements\nThe rotary actuator shown in Figures 1 and 2 was subjected to torque measurements and to comparative calculations using the above method of direct differentiation.\nThe torque measurements were made with an INSTRON instrument. Due to measurement details, a finite range of torque is measured instead of a fixed value. Here the torque was measured at the 10 and 30 degree positions for 0.4 amps current. This current was chosen so that the magnetic material was operating in the linear region of its B-H curve. The linearity was tested by observing that the torque increased with the square of the current, as expected for no saturation in this type of actuator. The model has dimensions taken from parts drawings; because of tolerances the solenoid will actually have different dimensions than those of the drawings. The relative permeability of the solenoid steel was assumed as 6100 as suggested by the steel suppl i er. Table 2 lists the calculated torques versus the number o f grid points in the finite element model of Figure 1. Note that as the model size increases, the calculated torque a1 so increases. The largest size model obtained a torque lying at the center of the measured torque band within 1.0 percent at 10 degrees and 3.6 percent at 30 degrees.\nFiqure 2-Position Direct\nWhile the above method can accurately calculate torque and force, it does not calculate the distribution of the magnetic vector forces. Distribution of the force is required for many mechanical stress and/or vibration calculations.\nMaxwell's stress tensor obtains force distributions over a surface. However, the formula for the stress tensor is derived for linear materials only, that is, the surface must not be on or within saturable steel. In order to calculate force distributions for nonlinear materials we present here a derivation that differs from any previous derivation or formula [7]. As in the first part of this paper, we begin by examining the differential of coenergy\n6C =fbdB dH)dV =/[H 6B - b ( / HdB)]dV (8)\nwhere dV is a differential volume fixed in space. During a virtual displacement om, the material reluctivity 3=H/B can change; what was at x-6m is now at X, thus\n6 \\I = J(x-bm)-V(x) = -6m.n) (9)\nSubstituting (9) in (8) gives\nbC = ) (H bB t/ 6 m . d B dB) dV (10)", "3580\nD i f f e r e n t i a t i n g w i t h respect t o t ime t gives:\nw a t = /[ii (ai/bt) +f;.wB.dB]dv\nv x e = - aR/bt + v x ( i B)\n(11)\nwhere bveloc i ty=bm/bt . Now from Maxwell's equations w i t h a v e l o c i t y V:\n(12)\nM u l i t i p l y i n g (12) by v x H = 3 and i n t e g r a t i n g over V:\nE . j dV = -/ [ i .(bB/at) - ~ . v x ( ~ x B ) ] dV (13)\nwhich i s t h e Law o f Conservation o f Magnetostat ic Energy. Using vector i d e n t i t i e s , (13) becomes\n(14) /p. (b j /b t ) dV =\nS u b s t i t u t i n g (14) i n (11) g ives\n-E.J dV +/ ( B x v X ~ ~ ) .i dV\ndC/dt = -/t.sdV +/ [ ( i~vXH)+f&.dB] :GdV (15)\nRecognizing r a t e o f energy change as power,\nX / d t = -l(F.i) dV (16)\nwhere 7 i s fo rce per u n i t volume. Combining (16) and (15) wh i le ignor ing the E.J heat generation term gives:\nT = -ExvX~~ - J VJE.di\nf=-(1/2)dv(B2) + V( i .v)B -/VQi.dE (18)\nf = (B.v)A - (1/2)[Vv(B2) + 1 v? d(B2)]\n(17)\nExpanding the f i r s t term by vector i d e n t i t y gives:\n(19)\n7 = (6.vfi - v 3 i . d i (20)\nf = ( B . P ) ~ t ( V . E ) i - V J VBdB\nThis equation becomes symmetric by adding V.i=O: -\n(21)\nwhich can be w r i t t e n as - f = t r . T\nwhere f i s Maxwell's Stress Tensor w i t h terms B\nTij = HiBj - dij H dB (23)\nF = $ ? . d s (24)\n0\nI n t e g r a t i n g (22) over a volume r e s u l t s i n t o t a l force:\nwhere 3 i s the surface o f t h e volume, which may be the surface o f an armature made o f nonl inear s tee l . The i n t e g r a l o f HdB i n (23) accounts f o r t h e non l inear i ty , and i s a new term t h a t reduces t o t h e o l d when l i n e a r . The non l inear s t ress tensor o f (23) has been implemented i n 2D and 3D software [8]. Results on many problems such as i n Figure 4 show t h a t t o t a l normal fo rce agrees w i t h i n b e t t e r than 5 percent w i t h the twop o s i t i o n o r d i r e c t d i f f e r e n t i a t i o n force. The advantage o f Maxwell s t ress , i s t h a t the d i s t r i b u t i o n o f the vector fo rce i s a lso obtainable, on the surfaces o f i n t e r s e c t i o n o f any two f i n i t e elements.\nConclusions\nThe method o f d i r e c t d i f f e r e n t i a t i o n has been appl ied t o two- and three-dimensional magnetic vector p o t e n t i a l f i n i t e element analys is . I t s ca lcu la ted torques and forces i n several t y p i c a l problems compare very c l o s e l y w i t h those obtained by the conventional\ntwo-pos i t ion method, and a lso agree we l l w i t h measurements. The method i s app l i cab le t o c a l c u l a t i o n of any parameter r e q u i r i n g a der iva t ive .\nAlso der ived i s a new Maxwell Stress Tensor which determines both t o t a l fo rce and fo rce d i s t r i b u t i o n . The new tensor enables the fo rce d i s t r i b u t i o n t o be evaluated d i r e c t l y on o r w i t h i n nonl inear mater ia ls .\nReferences\n[l] J. R. Brauer, E. A. Aronson, K. G. McCaughey, and W. N. Sul l ivan, \"Three-Dimensional F i n i t e Element So lu t ion o f Saturable Magnetic Fluxes and Torques o f an Actuator\" , IEEE Trans. on Maqnetics, January 1988, pp.\n[2] John R. Brauer (ed.), What Everv Enqineer Should Know About F i n i t e Element Analysis, New York: Marcel Dekker, Inc., 1988. [3] J . L. Coulomb, \"A Methodology f o r the Determination o f Global Electromechanical Q u a n t i t i e s from a F i n i t e Element Analys is and i t s App l ica t ion t o the Evaluat ion o f Magnetic Forces, Torques, and St i f fnesses\" , Trans., vo l . MAG-19, November 1983, pp. ?514-2519. [4] J. L. Coulomb and 6. Meunier, F i n i t e Element Implementation o f V i r t u a l Work P r i n c i p l e f o r Magnetic or E l e c t r i c Force and Torque Computation\", IEEE Trans., vo l . MAG-20, Sept. 1984, pp. 1894-1896. [5] S. McFee and D. A. Lowther, \"Towards Accurate and\n455-458.\nConsistent Force Ca lcu la t ion i n F i n i t e Element Based Computational Magnetostat ics\", IEEE Trans., vo l . MAG23, Sept. 1987, PP. 3771-3773. 161 Basim F. Is t fan, \"Extensions t o the F i n i t e Element Method fo r Nonlinear Magnetic F i e l d Problems\", Ph.D. thes is , Rennselaer Polytechnic I n s t i t u t e , August 1987. [7] T. K. Khoe and R. J. Lar i , \"Forgy\", Proceedinqs o f Fourth I n t e r n a t i o n a l Conference on Maqnet Technoloqy, Brookhaven (NY) Nat ional Magnet Lab, 1972. [8 ] MSC/MAGNUM and MSC/MAGNETIC are p r o p r i e t a r y products of The MacNeal -Schwendler Corp., 9076 N. Deerbrook T r a i l , Milwaukee, W I 53223.\nAPPENDIX. Solenoid Dynamics\nI n f a s t - a c t i n g solenoids, motion creates eddy currents and a back vo l tage i n the c o i l . The back vo l tage i s t h e l a s t term i n K i r c h o f f ' s equation:\nv ( t ) = R c ( t ) + N [@(x,c)/dt] (A1 1 where v i s the appl ied voltage, R i s t h e c i r c u i t ( inc lud ing c o i l ) res is tance, N i s t h e c o i l turns, and a' i s t h e f l u x l i n k i n g the c o i l t h a t i s a func t ion o f cur ren t c and p o s i t i o n ( l i n e a r o r r o t a r y ) x. Then\nv ( t ) = R c ( t ) + P(C,X) c ' ( t ) + q(c,x) x ' ( t ) (A21\nwhere p(c,x) = N dJT(c,x)/dc = Nf(dE/dc).dT (A31\nq(c,x) = N dg(c,x)/dx = N/ (d i /dx ) .d i (A4)\nThe grad ien t dA/dx i s computed i n (7) w i t h the symbol m replaced by x, and i s the same gradient used i n the fo rce ca lcu la t ion . The gradient dA/dc i s computed as fo l lows. Since gi i s a func t ion o f P, A(P,c), and c, where P i s independent o f c, then\ndgi/dc = dgi/dc + Ej(dgi/daj)(da./dc) J = 0 (A51\nThe l a s t gradients i n (A5) are t h e des i red p a r t i a l der iva t ives . Hence the vector dA/dc i s the s o l u t i o n o f\nK (dA/dc) = 6 1 = gci = [-(bgi/6c, . . . I (A61\nwhere K i s t h e same K as i n (7). e a s i l y computed i n a n a l y t i c a l form. The vector GL can be" ] }, { "image_filename": "designv11_32_0000140_s0025579300015230-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000140_s0025579300015230-Figure1-1.png", "caption": "Figure 1. Velocity profiles for ve evaluated on the z-axis for representative values of c. (a) l3.", "texts": [ " As c increases from c, the repeated roots separate, one increasing and the other decreasing, and setting r = 1 in (29) shows that the decreasing root becomes unity when c satisfies the equation (c + l ) 2 ( c -3 ) = 0, (32) i.e., when c = 3. For values of c > 3 , the decreasing root of (29) is less than 1, the stagnation point disappearing from the flow field, whilst the remaining point moves outwards along the negative z-axis towards -oo with increasing c. Typical velocity profiles for ve(r, 0,0) and ve(r, v, 0) are sketched in Fig. 1 for the ranges 1< c < c,, c, < c < 3 and c> 3. We next investigate the possibility of flow separation in the plane y = 0 at the surface of the sphere. Such points of separation are determined by the vanishing of the vorticity curl v at a point of the sphere r = 1 in the half-planes \nSo defined in a corotational triad the stress vector 6 is objective. It is not modified by a rigid\nrotation.\nThe stress rate is associated to a strain rate \u00a3 defined in the same triad. It is the time derivative\nof the distance between the two elements faces.", "If A is a point of the solid boundary and B is the point of intersection between the tool bound-\nary and the solid normal e R at A the distance u is expressed in the local triad by\nu = R(z B - z ~)\nIt is objective i.\u00a2. independent of a rigid rotadon of the two bodies together. The strain rate\nvector is then\ndu = R dzB dzA d R . B ~.a\n= -d-f ( - ~ d~- + -d-i - ( ~ - )\nwhere the second term is an objectivity correction due to the rigid rotationR Finally thc virtual power developed on the solid boundary is\nwith ~s\n~s = - R 6 x \"4\nCONSTITUTIVE LAW OF CONTACT WITH FRICTION\nThe relation bctw~n the generaliscd stress rate ~ and the generalised strain rate 8 is depending on the interface rheology: surface state, special material in the interface, special bchaviour of one body along the interface .... This point was studied by a large number of authors: DIETERICH [5,6], GHABOUSSI[7], SHAFER[8], CHANDRA and MUKHERTE[9], AL", "KHATI'AT[10], NAGTEGAAL AND REBELO[ll]... For metals in contact, rheology is depending on cleanliness and finish of surface and on lubricant properties (GODET[12]). For soils and rocks the theological problem is perhaps more complex as shown by BOULON[13] and\nNOVA[14].\nWe are supposing here the interface to be thin with regard to the finite elements and body size as it is done in plasticity rheology when one supposes the metal to be homogeneous and not a crystal assembly. Therefore the constitutive law is a \"mean\" law, what is the opposite of the local concept proposed by ODEN and PIRES [15,16,17].\nWe will develop hereafter the constitutive law following the elastoplastic formalisms as done by CURNIER [18,19] and thermodynamically justified by SIDOROFF[20]: slipping is an irreversible mechanical phenomenon described as plasticity in metals.\nA gap between the two bodies implies null contact stresses :\ntr = < 0,0,0 >\nIn the stress space, we are supposing an elastic field (which has essentially a numerical meaning) bounded by a plasticity surface. Elasticity implies sticking contact. Real rigid and sticking contact is difficult to introduce in a classical finite element code. The elastic formalisms is in fact a penalty of the rigid contact and sticking condition. From a geometrical point of view elasticity of contact implies a interpenetration of the two bodies in contact. The elastic constitutive law is a diagonal one :\nKp 0 0 ) 6\" = 0 Kt 0\n0 0 K,\nKp et K t are the penalty coefficients; they must be as large as possible in order to reduce the penetration of the bodies, but there is a limitation due to the decrease of the numerical convergence. The code user unfortunately is not completely free of choosing these coefficients. Therefore it seems unprofitable to search a physical meaning to these parameters.\nAt the present time we have only implemented a COULOMB yield surface (figure 4.):" ] }, { "image_filename": "designv11_32_0002269_j.engfracmech.2006.04.002-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002269_j.engfracmech.2006.04.002-Figure6-1.png", "caption": "Fig. 6. Finite element model of the cracked zone: (a) the whole model; (b) particular of the model showing the crack.", "texts": [ " The results obtained by the previous step are used as boundary conditions of a three-dimensional finite element model of the zone surrounding the crack: in particular, the displacements at the points corresponding to the nodes of the boundary surface of the FE model are applied to these latter and are used as boundary conditions of the analysis. In this way it is simple to accurately evaluate the SIF for Mode I, II and III along the crack front. The FE model consists in a cylinder of radius R and height H containing the three-dimensional crack whose front can be circular or elliptical (Fig. 6); a is the half-length of the crack. The dimensions of the FE model are critical parameters. In fact, it is necessary to verify that the dimensions are large enough to guarantee that the boundaries of the model are not influenced by the presence of the crack; doing so, it is possible to apply the displacements analytically calculated in the uncracked half-space to the FE model. After a trial and error procedure, the chosen dimensions were the following ones: R = 4.5a and H = 3a. Brick elements with 20 nodes and second order shape functions were used" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002215_1.2387164-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002215_1.2387164-Figure2-1.png", "caption": "FIG. 2. In the case depicted, the director is not anchored at the boundaries of the system and the cholesteric pitch is larger than the sample thickness d. The external electric field E induces a rotation of the director from its ground state conformation n\u03020 solid lines to its end position n\u0302 dashed lines .", "texts": [ " We note that dielectric effects result from contributions quadratic in E to the energy density of the system. What we observe in the regime linear in E=Ez\u0302 is rather different from these dielectric effects. As denotes the phase shift of the director orientation around the helical axis, Eqs. 11 and 14 describe a rotation of the director around the cholesteric helical axis when compared to the ground state of E=0, no matter whether a 0 or a 0. Without any boundary conditions for the director, this rotation occurs homogeneously over the whole sample as given by Eq. 11 and depicted in Fig. 2, where the situation is sketched for a sample of a cholesteric pitch larger than the sample thickness d. If strong anchoring of the director prevails at the surfaces, the rotation is hindered at the boundaries as given by Eq. 14 . In both cases the amplitude of the rotation is proportional to the amplitude of the external electric field, to the rotatoelectric coefficient R , as well as to the wave number of the cholesteric helix q0. We also note that the larger the coupling between the director and the polymer network of the respective SCLSCE, reflected by the coefficient D1, the smaller is the amplitude of the rotatoelectric rotation", " Such a behavior is reminiscent of the precession during a gyroscopic motion in the gravitational field, where the resulting mechanical force inducing the motion of precession is also oriented perpendicular to the external field direction. In the last section we have shown that rotatoelectricity implies very interesting effects, which should be observable in an experiment using a rather simple setup. Therefore we present in this section some expressions that might be helpful for a comparison with experimental results. The setup we propose is identical with the geometry depicted in Fig. 2. If thin films of cholesteric SCLSCEs are investigated, for which the cholesteric pitch is large compared to the sample thickness d, then the mean orientation of the director in such samples should be observable by optical measurements using polarizing microscopy. The viewing direction is assumed to be parallel to the helical axis and thus parallel to the direction of the external electric field. Since we think that the condition of strong anchoring of the director to the sample surfaces leads to more realistic boundary conditions, we will use the result given by Eq" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002299_14644207jmda107-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002299_14644207jmda107-Figure1-1.png", "caption": "Fig. 1 Experimental testing of the cricket bats: (a) modal analysis test setup and (b) grid of impact points on the bat blade", "texts": [ " The work also uses the same measurements to consider the effects of blade profile (i.e. shape) and bat mass on the performance. The final part of the work describes a simplified two-part beam model of a cricket bat and uses this to assess the influence of changing blade and handle stiffness and mass on the natural frequencies and resulting performance of the bat. The primary objective of the experimental work is to measure the mode shapes and frequencies of a cricket bat subject to impact excitation when under boundary conditions typical of those used in practice. Figure 1(a) shows the general layout of the test setup which is based on the use of an instrumented hammer to excite the bat over a range of frequencies simultaneously. The frequency range is dictated by the duration of the impulse. In practice, impact with a cricket ball, a relatively compliant object, only excites a comparatively low range of frequencies (typically 0\u20131200 Hz based on a lowest contact time of 0.8 ms [9]). This frequency range can easily be generated using an impact hammer with an appropriately compliant plastic head. The main advantage of the method is the speed with which a test can be performed and the ability to improve the signal to noise ratio by averaging the response from a number of repeat tests. Each of the cricket bats tested has a series of impact points laid out in a grid on the blade front and handle of the bat, as shown in Fig. 1(b). The points are numbered as indicated in the figure. An accelerometer is fixed to a flat surface cut into the back face of the bat directly behind point 1. This position was chosen as it is likely to be an antinode for all the modes of vibration of the bat and thus will yield a suitably high vibration signal over the whole frequency range. To perform a test, each of the points is impacted by the hammer in turn and a frequency response function (FRF) is calculated from the input and response signals using Data Physicsw signal analysis PC software [10]", " The clamped condition involved clamping tightly around the rubber grip at two positions along the handle corresponding to the approximate hand positions. Frequencies and Proc. IMechE Vol. 220 Part L: J. Materials: Design and Applications JMDA107 # IMechE 2006 at UNSW Library on July 24, 2015pil.sagepub.comDownloaded from mode shapes were determined for the first fourmodes of vibration (not including rigid bodymodes) for these boundary conditions. Figure 4 shows the FRFs for the driving point no. 1 (Fig. 1(b)) for the freely suspended, clamped, and hand held support conditions. The peaks in the figure represent the natural frequencies of the different modes of vibration. It can be seen that the FRF for the hand held bat is of a lower quality of test data due to the difficulties in performing the hand held test. The peaks are also rounded and of much lower magnitude. However, central frequency values can still be determined from this data. Figure 5 gives the corresponding frequencies for the modes for each type of support" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003253_20070625-5-fr-2916.00091-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003253_20070625-5-fr-2916.00091-Figure1-1.png", "caption": "Fig. 1. The scanning pattern of given targets", "texts": [ "eywords: agile spacecraft, guidance, robust attitude control The dynamic requirements to the attitude control systems (ACSs) for remote sensing SC are: \u2022 guidance the telescope\u2019s line-of-sight to a pre- determined part of the Earth surface with the scan in designated direction; \u2022 stabilization of an image motion at the onboard optical telescope focal plane. Moreover, for the remote sensing spacecraft these requirements are expressed by rapid angular manoeuvering and spatial compensative motion with a variable vector of angular rate, Fig. 1. Increased requirements to such information satellites (lifetime up to 10 years, exactness of spatial rotation manoeuvers with effective damping the SC flexible structure oscillations, robustness, fault-tolerance as well as to reasonable mass, size and energy characteristics) have motivated intensive development the gyro moment clusters (GMCs) based on excessive number ? The work was supported by Presidium of Russian Academy of Sciences (RAS) (Pr. 22), Division on EMMCP of the RAS (Pr. 16 and 18) and RFBR (Grants 04-01-96501, 07-08-97611) of gyrodines (GDs) \u2014 single-gimbal control moment gyros" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002092_1-4020-3393-1_14-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002092_1-4020-3393-1_14-Figure5-1.png", "caption": "Fig. 5. Example of natural coordinates", "texts": [ " The points are chosen on the basis of the following criteria [18]: 1. Each link must have at least two basic points. 2. A basic point must be located at the center of revolute kinematic pairs. The point is shared by the two kinematic elements. 3. In a prismatic pair one point is positioned on the line of action of the relative motion among the two kinematic elements. The other point is attached on the second kinematic element. 4. Other points whose motion needs to be monitored can be chosen as basic points. Fig. 5 shows the slider-crank mechanism modeled with natural coordinates. Due to the elimination of angular coordinates, the number of natural coordinates required for the analysis is usually less than the number of Cartesian generalized coordinates. de Jalo\u0301n and Bayo [18] reported a thoughful discussion between these types of coordinates and their influence in the simulation process. The convenience of using sets of dependent coordinates has been already stated. These are related by the equations of constraints of the form \u03a8i (q1, q2, ", " Using Cartesian generalized coordinates, with reference to the nomenclature of Figure 4, the scleronomic constraints are expressed by the following equations \u03a81 \u2261 X (1) A0 \u2212X (4) A0 = 0 (10) \u03a82 \u2261 Y (1) A0 \u2212 Y (4) A0 = 0 (11) \u03a83 \u2261 X (2) A \u2212X (3) A = 0 (12) \u03a84 \u2261 Y (2) A \u2212 Y (3) A = 0 (13) \u03a85 \u2261 X (3) B \u2212X (4) B = 0 (14) \u03a86 \u2261 Y (3) B \u2212 Y (4) B = 0 (15) \u03a87 \u2261 Y (4) B = 0 (16) where X(i) P , Y (i) P are the absolute coordinates of point P on the ith body. Such coordinates are related to the generalized Cartesian coordinates by the transform{ X (i) P Y (i) P } = [ cos q3i \u2212 sin q3i sin q3i cos q3i ]{ x (i) P y (i) P } + { q3i\u22122 q3i\u22121 } (17) Using the natural coordinates (see Fig. 5, A0, A, B and C are basic points. The coordinates of A0 and C are fixed and known. Thus, {q} = { XA YA XB YB }T is the vector of variable coordinates. The constraints exquations are espressed by the following equations \u03a81 \u2261 (XA \u2212XA0) 2 + (YA \u2212 YA0) 2 \u2212 a2 1 = 0 (18) \u03a82 \u2261 (XA \u2212XB)2 + (YA \u2212 YB)2 \u2212 a2 2 = 0 (19) \u03a83 \u2261 det \u2223\u2223\u2223\u2223\u2223\u2223 XA0 YA0 1 XB YB 1 XC YC 1 \u2223\u2223\u2223\u2223\u2223\u2223 = 0 (20) The constraints equations (2) e (3) are differentiated for velocity analysis3 3 Dots denote differentiation w.r.t. time. [\u03a8q] {q\u0307} = \u2212{\u03a8t} (21) and acceleration analysis, [\u03a8q] {q\u0308} = {\u03b3} (22) where [\u03a8q] is the Jacobian of the constraint system and {\u03b3} = \u2212 ([\u03a8q] {q\u0307})q {q\u0307} \u2212 2 [\u03a8qt] {q\u0307} \u2212 {\u03a8tt} (23) The Newton-Euler treatment is based on the consideration of a free rigid body, in the sense that, if constrained, the forces of constraint are included" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003745_tpwrd.2010.2068567-Figure9-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003745_tpwrd.2010.2068567-Figure9-1.png", "caption": "Fig. 9. Schematic drawing of the porcelain insulator (XP1-300). (a) Appearance of porcelain insulator. (b) Section of porcelain insulator.", "texts": [ " However, experiments of insulator buckling showed that the broken stress is about 850\u20131000 MPa [4]. As illustrated in Fig. 8, stress calculation results (maximal value 681.5 MPa) are less than the average broken stress values of the core rod. 2) Porcelain Insulator Strings: The adjacent insulators may happen to rotate relatively because of the connection relationship. The bound angle (maximal angle rotated in the axial direction of adjacent insulators) is related to the position of the joint. As shown in Fig. 9, the bound angle is different when the insulator goes around a different orientation [A, B, and C in Fig. 9(a)]. The practice showed that the bound angle in orientation A was larger than the other two orientations (B, C). The displacements calculation of the V-shape insulator string with different bound angles (11, 18, and 24 ) has been investigated. The type of porcelain insulator used in the calculation is XP1-300. The result displayed in Fig. 10 is for the V-string with an included angle of 70 . With different bound angles (11, 18, and 24 ), the calculation results have no obvious difference. However, the bound angles have an influence on the deformation of the V-shape insulator string" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000324_robot.2002.1014786-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000324_robot.2002.1014786-Figure4-1.png", "caption": "Figure 4: Models of the rover body, suspension, and manipulator. The rover suspension and steering joints are in their zero positions.", "texts": [ " Each of the 4- DOF manipulator\u2019s links has one high-level OBB encompassing all of the link\u2018s geometry, and the second through fourth links have lower-detail OBBs and OBPs representing more detailed geometry. The rover body is represented by several high-level OBBs and more detailed children. The front part of the rover\u2019s suspension is slightly more complex, since it is articulated. Each of the front wheel assemblies is represented by an OBP for the wheel and an OBB for the steering arm that can be moved to match the current steering angles. These parts, along with the bogie tube (the horizontal link leading towards the front wheel in Figure 4) and steering actuator housing are also affected by the rocker and bogie joint angles. All suspension parts for each side of the rover are enclosed in an OBB that moves with the rocker and bogie angles, but which is large enough to contain all parts for all steering angles. The rear portion of the suspension is not modeled since it is not in the manipulator\u2019s workspace. Because of the kinematics of FIDO\u2019s manipulator, no self-collisions are possible within the links of the manipulator; however, self-collisions with other parts of the rover body or suspension are possible" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000373_int.10025-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000373_int.10025-Figure5-1.png", "caption": "Figure 5. Fuzzy segments built from the sensor data in a real environment.", "texts": [ " This central segment can be identified with the one \u03b1-cut of the fuzzy segment. Likewise, Septotal is the distance that separates each of the lateral segments from the central segment, which cover the region of possibility of the fuzzy segment representing the support. Additionally, the perpendicular distance of the central segment to the origin of the coordinate frame is represented by the fuzzy set: \u03c1fuz = {\u03c1 \u2212 Septotal, \u03c1, \u03c1 + Septotal} The angle that forms the normal to the segment with the X axis is represented by the fuzzy set: \u03b8fuz = {\u03b8 \u2212 Sep\u03b1, \u03b8, \u03b8 + Sep\u03b1}. Figure 5 shows the result of the described process to determine the fuzzy seg- ments in a room of a real office-like environment. This room contains tables, chairs, and boxes near the walls. In the figure, the small crosses represent the perceived points with a high value of belief in a possible wall perpendicular to some sensor. BEHAVIOR-BASED ROBOTS 349 These points have been computed following the contour of walls and objects in the real environment. The lines represent the fuzzy segments that cover the perceived points" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003825_j.triboint.2010.02.018-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003825_j.triboint.2010.02.018-Figure2-1.png", "caption": "Fig. 2. Polar load diagram of engine bearing [9].", "texts": [ " The external load applied was assumed to be of the form W \u00bcW a 1\u00fesin t 2 n o \u00f010\u00de where Wa is the steady state load corresponding to the eccentricity ratio e0\u00bc0.8. Eq. (10) is used to calculate the load value at each time step. Using the values of W , F r and Ff and the value of M , the equations of motion are solved for e,_e, f and _f for the next time step. The journal centre locus is obtained by repeating the above procedure for various operating conditions. The variable rotating load is simulated using the Ruston and Hornsby 6VEB-X MKIII engine connecting rod bearing load data. Fig. 2 shows the polar load diagram for the bearing relative to the cylinder axis [8]. Appendix 4.1 of Ref. [9] gives the magnitudes of the load at 101 crank angle intervals. The resultant load was calculated and then non-dimensionalized using the relation W \u00bcWC2=ZUR2L. Appendix 4.1 of Ref. [9] also gives other related data which are presented in suitable units in Table 1. These were used in the equations of motion along with the mass parameter and steady state load to get the journal centre trajectory" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003407_cdc.2007.4434738-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003407_cdc.2007.4434738-Figure2-1.png", "caption": "Fig. 2. Sketch of the nonsmooth nonlinearity.", "texts": [ " The nonlinear system is assumed to be preceded by an actuating device (see figure 1) whose dynamics are described by: x\u0307A = fA(xA) + \u2206fA(xA) + gA(xA)v + dA(xA) (2) w = hA(xA) (3) where xA(t) \u2208 R nA is the actuator state vector at time t, v(t) \u2208 R is the input signal of the actuator, gA(xA) : R nA \u2192 R nA is the smooth actuator state-input map, fA(xA) : R nA \u2192 R nA is a smooth function describing the known plant dynamics, and finally \u2206fA(xA) and dA(xA) describe eventual uncertain terms in the actuator. The actuator output w(t) \u2208 R is connected to the system input u(t) by a nonsmooth block (see figure 2). Following the idea introduced in [8], a compact analytical description of the hysteresis has the following structure: u(t) = Fi(w(t), w(tk), u(tk), tk) if w(\u00b7) is increasing over [tk, tk+1] Fd(w(t), w(tk), u(tk), tk) if w(\u00b7) is decreasing over [tk, tk+1] (4) where Fi(\u00b7) and Fd(\u00b7) are two different piecewise linear functions aimed at describing the memory effect associated to the hysteretic behavior of the interconnection between actuator and system. Indeed, they describe the relation between the actuator output w and system input u for (respectively) positive or negative increments starting from the point (w(tk), u(tk)) at time tk" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002091_aim.2003.1225147-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002091_aim.2003.1225147-Figure3-1.png", "caption": "Figure 3: Definition of Coordinate Systems", "texts": [ " Therefore it is important for the parallel-wire robots with more than n + 1 wires to guarantee the stability and the motion In this paper, first, I explain the principle of orthogonalization for the completely restrained parallel-wire driven system, which plays a very important role to investigate the relation between force-moment at the endeffector and wire tension. Next, a Lyapunov function using results obtained from the principle of orthogonalization is introduced to prove the motion convergence of wire length feedback scheme for the general case with more than n wires. . convergence as well. Vector Closure In this paper, I consider a completely restrained parallelwire driven robot as shown in Figure 3, of which object or end-effector is suspended by m wires. Since wires can generate only tension, redundant actuation is necessary. This feature is similar to that of multi-finger robots. In fact, the concept \u201cVector Closure\u201d which was remarked in the research of multi-finer robots plays a very impor- tant role in the research of parallel-wire dirven robots[b]. Here, let us define wire vector w, in order to make clear the relation between Vector Closure and the completely restrained wire driven robot. As shown in Figure 3, the wire vector w, is given by where a vector p , denotes a directional vector, ri means a vector between the center of gravity on the object and a connected point of the wire. The mark x represents vector product. When the wire tension vector and the resultant force-moment acting on the object are set at at = (atlot*.. .am)T and f = ( f ~ f z . . .fn)= respectively, the relation between the wire tension vector at and the forcemoment vector f is expressed by f = Wat, (2) where the matrix W E LnXm denotes wire matrix which is defined by w = (W1WZ", " (19) FromEquations (5), (12), (13), (15), (16), (17), (18) and (19), the closed loop equation is expressed by - Mq + (B+W+Mo*++W+ ( B . -Ma+So ) W+T 1 q +KpAq + KvAq - v;, + v = 0. (20) where, (21) - M = ( A + W'MoW\"). And then substituting the projection relation described by Equations (10) and (11) into Equation (20) yields - M(Q4 + Qii) + { B + W + M o W + + W + ( i&fo + S o ) W+') Qq +KpAq + KvAq - ~ t n + v = 0. (22) where MO E 8\"'\": inertia matrix, SO(Z, k) E Rnx\": skew-symmetric matrix, I E 32% position-orientation of the center of gravity, go E 32\": gravitational vector, f E R\": force-moment vector. As seen Figure 3, the Wire tension at generates motion of.the end-effector. Hence, the force-moment vector f is given by Equation (2) and the inverse relation is given vector Q and the vector x, it is given by the following equations[3], Q = W x, (14) j. = W + T Q . (15) V is given by In the next section, it is investigated whether the wire length vector q converges to the desired one qd or not. Motion Convergence Now, We are at the position to prove stability of parallelwire drive robots. Consider a candidate of Lyapunov function which includes the projection matrix Q follows: by Equation (5)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002176_11505532_4-Figure4.4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002176_11505532_4-Figure4.4-1.png", "caption": "Fig. 4.4. The transient behavior of 3 agents utilizing guided formation path following to assemble and maintain a V-shaped formation while tracking a virtual leader.", "texts": [ " seabed mapping, ship replenishment, or formation flying. To illustrate the dynamic performance of the proposed guided formation control scheme, a simulation is carried out in which three agents assemble and maintain a V-shaped formation while chasing a virtual leader along a sinusoidal path in the plane. Specifically, the desired path is parametrized as xp( ) = 10 sin(0.2 ) and yp( ) = ; the control parameters are chosen as \u03b3i = 100, e,i = \u02dc ,i = 1 and \u03c3i = 0.9, \u2200i \u2208 {1, 2, 3}; and the speed of the virtual leader is fixed at Ul = 0.25. Figure 4.4 illustrates the transient behavior of the formation agents as they assemble and maintain a V-shaped formation defined by \u03b5f,1 = [\u22121,\u22121] , \u03b5f,2 = [0, 0] and \u03b5f,3 = [\u22121, 1] , while synchronizing with the virtual leader, as is further illustrated in Figure 4.5. This paper has addressed fundamental kinematic aspects of formation control. A socalled guided formation control scheme based on a guided path following approach was developed by combining guidance laws with synchronization algorithms and collision avoidance techniques" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003675_oca.955-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003675_oca.955-Figure6-1.png", "caption": "Figure 6. Two-link robot.", "texts": [ " AN ILLUSTRATIVE EXAMPLE Consider the unknown nonlinear input\u2013output time-delay system (1) consisting of N =2 interconnected MIMO subsystems shown as \u2211 1 : x\u03071(t) = f1(x1(t))+g1(x1(t))[u1(t \u2212 i1)+h\u2032 12(x2(t \u2212 s2 \u2212 i1))] (74a) y1(t) = C1x1(t \u2212 o1) (74b) \u2211 2 : x\u03072(t) = f2(x2(t))+g2(x2(t))[u2(t \u2212 i2)+h\u2032 21(x1(t \u2212 s1 \u2212 i2))] (75a) y2(t) = C2x2(t \u2212 o2) (75b) where u1(t)= [ u1,1(t) u1,2(t) ] , u2(t)= [ u2,1(t) u2,2(t) ] , x1(t)= \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a3 x1,1(t) x1,2(t) x1,3(t) x1,4(t) \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a6 , x2(t)= \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a3 x2,1(t) x2,2(t) x2,3(t) x2,4(t) \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a6 The first subsystem 1 of the large-scale system is given by two-link robot, which is described is Figure 6. The dynamic equation of the two-link robot system can be expressed as follows: M(q)q\u0308 +C(q, q\u0307)q\u0307 +G(q)= (76) Copyright 2010 John Wiley & Sons, Ltd. Optim. Control Appl. Meth. 2011; 32:433\u2013475 DOI: 10.1002/oca where M(q) = [ (m1 +m2)l2 1 m2l1l2(s1s2 +c1c2) m2l1l2(s1s2 +c1c2) m2l2 2 ] C(q, q\u0307) = m2l1l2(c1s2 \u2212s1c2) [ 0 \u2212q\u03072 \u2212q\u03071 0 ] G(q) = [\u2212(m1 +m2)l1gr s1 \u2212m2l2gr s2 ] and q = [q1 q2]T , q1, q2 are the angular positions, M(q) is the moment of inertia, C(q, q\u0307) includes coriolis and centripetal forces, G(q) is the gravitational force, is the applied torque vector" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003877_acc.2010.5531082-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003877_acc.2010.5531082-Figure1-1.png", "caption": "Fig. 1. The inverted pendulum on a cart.", "texts": [ " Thus, if \u03c3 > 0, then the reduced order closed-loop system (23) is exponentially stable [8]. Remark 2.1: As will be shown in the next section, in specific cases when the system dynamics are known it is possible to add a nonquadratic term to a Lyapunov function candidate in order to significantly simplify the matrix R(y) so that it only depends on a part of the state vector y. In this section, we apply the methodology developed in Section II to the example of an inverted pendulum studied in [4]. The system is shown in Figure 1 and the equations of motion are given by (M + m)x\u0308(t) + ml\u03b8\u0308(t) cos \u03b8(t) = ml\u03b8\u03072(t) sin \u03b8(t) +u(t), (35) mlx\u0308(t) cos \u03b8(t) + ml2\u03b8\u0308(t) = mgl sin \u03b8(t), (36) where m and M are pendulum and cart masses, respectively, q(\u00b7) is the cart position, \u03b8(\u00b7) is the pendulum angular position, l is the pendulum length, and u(\u00b7) is the control force acting on the cart. Note that equations (35), (36) can be written in the form of (1) with Maa(x, \u03b8) = M + m, Mau(x, \u03b8) = ml cos \u03b8, Muu(x, \u03b8) = ml2, fa(x, \u03b8, x\u0307, \u03b8\u0307) = ml\u03b8\u03072 sin \u03b8, fu(x, \u03b8, x\u0307, \u03b8\u0307) = mgl sin \u03b8" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002657_0041-2678(73)90005-5-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002657_0041-2678(73)90005-5-Figure4-1.png", "caption": "Fig 4 Through-shaft mounting", "texts": [ " The quantity of grease to fill a bearing depends upon its internal features but as a guide the following expressions may be used: P _ K(D + B)(D - B)W 5200 where P is the full charge, g; B the bearing bore, mm;D the bearing outside diameter, mm; W the bearing width, mm. If B, D and W are in inches then P = 3.1K(D + B)(D -B)W The value of K depends upon the type of bearing and Table 1 sets out some values. Enclosure design Figs 2 and 3 show typical arrangements for shaft-end mountings, the closing covers or caps being either blind or TRIBOLOGY February 1973 23 bored. Through-shaft mountings are shown with lips at the bores turned outwards, making it possible to lengthen the shaft seal (Fig 4) or inwards (Fig 5). For ordinary work they can be omitted altogether (Fig 2). The covers are easily dimensioned diametrally because the diameters A and C, Fig 2, can be found from the bearing manufacturer's catalogue under the heading of abutment depths or shoulder heights, dimension H; then A = D - 2H and C = B + 2H. The general thickness, E, of the covers is open to the designer but an inwardly pointing lip should not be too thick since it will reduce the volume of the grease recess in the cover; use F ~ 0.07(D - B), Fig 3. This leaves only the depth, T, of a cover, Fig 4, to be dimensioned. The depth may be dependent on the general design of the machine particularly on those parts which have to be accommodated within the enclosure. It will certainly depend upon the volume of grease to be packed into the enclosure. This volume is part of the design and has to be determined. Its size will depend on the size of the bearing and its service duty. The grease packed into a mounting is usually divided into three parts - the part to charge the bearing and the parts to charge each cover cavity" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002467_jmes_jour_1975_017_038_02-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002467_jmes_jour_1975_017_038_02-Figure1-1.png", "caption": "Fig. 1. Topography of surfaces under lubrication", "texts": [ "1 Notation Width of bearing Expected value or statistical mean Frictional force Nominal film thickness Stochastic film thickness Total film thickness Step position Length of step bearing Real numbers Pressure Flow flux Radial co-ordinate Inlet radius Torque Surface velocity components in x and y directions Load capacity Lubricant viscosity (constant) Variance Friction coefficient Random variable the flow of an incompressible lubricant stationarv rouah surface and a mouinq smooth Y Y surface (see Fig. 1). The equation governing the pressure in the film is : (1) . . . where the pressure P can, in principle, be determined for a given film thickness H . Since the film thickness function H is a stochastic process, the pressure also becomes a stochastic process and can only be determined by an averaging procedure (6)(8). Thus, for a given random input H , equation (1) is a stochastic differential equation for determining the random function P (5). Now, by taking the statistical average or expected value of each term of equation (1) we have : Journal Mechanical Engineering Science OIMechE 1975 Vol 17 No 5 1975 at University of Birmingham on June 4, 2015jms" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001577_iros.2003.1250740-Figure9-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001577_iros.2003.1250740-Figure9-1.png", "caption": "Fig. 9. over eighty cycles. Looping c u e s in roll-yaw space produced by Gait 3", "texts": [ " Table III shows the parameters of Gait 3\u2019s sinusoidal leg trajectories of the form asin( rot + f l ) + y. An envelope function ramps the legs from zero velocity to sinusoidal paths and ensures continuity in (4, , &) space. To eliminate any drift in roll and yaw due to the initial transients, we add damping of the TABLE in Gait 3 parameters. Leg1 Leg2 Frequency o (rad/s) Phase (rad) Offset y (rad) n/2 Damping k -1 -I form -kiO,,ki > 0 to the roll and yaw axis equations. Under Gait 3, the body settles down into a steady rocking pattern after initial transients (see Fig. 9). Note that this motion is similar to the roll-yaw attitude oscillations in Fig. 3 that produce RRRobot translation. IV. DISCUSSION Suppose RRRobot has large pitch inertia so that pitch configuration changes are negligible compared to roll-yaw changes. Then, RRRobot is similar to 884 a unicycle, with yaw corresponding to unicycle direction, and body roll corresponding to forward motion. We can compute RRRobot XY-plane translation kinematically using: AX= vsinO2dt, AY= -vcosB,dt, (4) where v = b e , is the body center velocity" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure4.1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure4.1-1.png", "caption": "Fig. 4.1. Example of a precision gantry stage", "texts": [ " Clearly, with the friction compensator, the root-mean-square (RMS) value of the tracking error can be drastically reduced from 11.2 \u03bcm to around 1.01 \u03bcm. U 3.4 Experiments 99 100 3 Automatic Tuning of Control Parameters 4 Among the various configurations of long travel and high precision Cartesian robotic systems, one of the most popular is the H-type which is more commonly known as the moving gantry system. In this configuration, two motors which are mounted on two parallel slides move a gantry simultaneously in tandem. An example of this stage is shown in Figure 4.1. This gantry system consists of four sub-assemblies, viz., the X and Y-axis sub-assemblies, the planar platform, and two orthogonal guide bars. When positioning precision is of the primary concern, direct drive linear motors are usually used and fitted with aerostatic bearings for optimum performance. Another setup of H-type gantry stage is shown in Figure 4.2. It consists of two X-axis servo motors: SEMs MT22G2-10 and a Y-axis servo motor: Yaskawa\u2019s SGML-01AF12. This gantry configuration has been in use for large overhead travelling cranes in ports, rolling mills and flying shear" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003655_978-90-481-9262-5_29-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003655_978-90-481-9262-5_29-Figure1-1.png", "caption": "Fig. 1 Prototype of the H4 robot.", "texts": [ " If t denotes the twist system order, then the wrench system order is w = 6\u2212t. Any twist in T is reciprocal to any wrench in W and vice versa [15]. Two screws are reciprocal to each other if their orthogonal product is equal to zero. Two zero pitch screws are reciprocal to each other if and only if their axes are coplanar. A zero pitch screw is reciprocal to an infinite pitch screw if their directions are orthogonal to each other. Two infinite pitch screws are always reciprocal to each other. The H4 robot shown in Fig. 1 belongs to a new family of 4-DOF parallel robots designed for highspeed pick and place operations [17, 18]. A kinematic graph of the H4 robot was given in [19]. The H4 robot is composed of four identical legs li = Ri\u2013 (4S)i, (i = 1, . . . , 4), attached to a common base (B) and linked to the end effector (E) by means of an articulated nacelle. The nacelle is composed of three bodies: (i) bI , connecting l1 and l2 in parallel and giving a resulting chain l12; (ii) bII connecting l3 and l4 in parallel and giving a resulting chain l34; and (iii) (E), linked to bI and bII with two revolute joints RI and RII respectively, and carrying the end effector of the robot" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003648_iccas.2010.5669710-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003648_iccas.2010.5669710-Figure4-1.png", "caption": "Fig. 4 Mobile robot position and heading angle.", "texts": [ " RF Transmitters transmit signal in regular the intervals of 0.4sec, and the system calculate TOF(Time of Flight), and then, the distance between transmitters and receivers can be measured.. Using 2 receivers the absolute position based on 3 dimensional space(X,Y,Z) and angle of direction\u03b8 can be measured. Fig. 2. shows way of measuring position (X,Y,Z ) and angle of direction \u03b8 using PUS . and Fig. 3. shows the test model. Getting information about where the vehicle is moving to is important as well as getting to know the position of it. As you see on Fig. 4 the vehicle is equipped with 2 Ultra sonic receiver to get information of angle of direction as well as of position of the vehicle. After the position of the vehicle is decided, an angle of direction of the vehicle can be calculated by below equation (2.6) 1tan ( )front rear front rear y y x x \u03b8 \u2212 \u2212 = \u2212 (2.6) Herein, \u03b8 is angle between X axis and the direction the vehicle is forwarded to. Degrees of Angle increases in a clockwise direction from X axis 978-89-93215-02-1 98560/10/$15 \u00a9ICROS 1126 Getting data from Gyro sensor and PUS, adopted Kalman filter estimates more precise angle of direction than before using the filter To acquire angle of direction, let state variable as below x \u03b8 \u03d5 \u23a1 \u23a4= \u23a2 \u23a5 \u23a3 \u23a6 (2" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000283_ipemc.2000.885354-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000283_ipemc.2000.885354-Figure5-1.png", "caption": "Fig. 5 Buried maganet PMSM cross section", "texts": [ " Since the carrier frequency and the angle of the carrier signal voltage injection is precisely known the order and kiandwidth of the synchronous reference frame filter does not have to be very high in order to completely eliminate the positive sequence component. In addition, the negative sequence component is at twice the carrier frequency in this reference frame, reducing the effects of the filter bandwidth on it. 4. Experimental Results The motor used in the experimental system is a buried PM motor. The elecbical and mechanical data for this motor are given in Table 1. A cross section of the motor used in the test is given m Fig.5. The sensorless control was implemented on a Motorola 560001 DSP system. The DSP U0 interface system consisted of four digital-to-analog (D/A) outputs four analog-to-digital (A/D) inputs, one sine-triangle PWM output and optical encoder input. The self-sensing control software was written in 56000 assembly language to minimize the execution time. A 2000 line optical encoder was attached to an Electrocraft AC PM synchronous servo motor. The encoder was used for evalu,ation of the position estimate from self-sensing" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003796_1.3206730-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003796_1.3206730-Figure1-1.png", "caption": "FIG. 1. An idealized algal cell. Representation of the orientation vector p by means of spherical-polar angles and relative to a right-handed system of Cartesian coordinates with origin at the center. Here h denotes the distance of the center of gravity from the center of the cell.", "texts": [ "18 Similarly, the mean swimming direction and the cell diffusivity tensor are calculated from the probability density function for the orientation of the cells.18 Closed form solutions using Fokker\u2013Planck equation are available for some flows2,19,20 but these are not readily amenable for analysis purposes. The simplified ad hoc model is thus a good first model for gyrotaxis and experience with numerical simulations13\u201316 suggests that essential features of the problem will be captured. For simplicity, algal cells such as Chlamydomonas whose shape closely approximates a spheroid are idealized here as spheres of radius a see Fig. 1 . Let the unit vector p point in the swimming direction of the cell. The cells are bottom heavy so that the center of mass is displaced by h from the center of buoyancy. Balance of torques due to gravity and viscosity leads to the equation for the reorientation rate,21 p\u0307 = 1 2B z\u0302 \u2212 z\u0302 \u00b7 p p + p 2 , 6 where is the local vorticity field and B=4 a3 /mgh is called the gyrotactic reorientation parameter. The equations describing the equilibrium orientation in terms of Euler angles , are \u2212 1 sin + 2 cos = sin /B 7 1 cos + 2 sin = 3 tan " ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001653_978-3-642-81589-8_11-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001653_978-3-642-81589-8_11-Figure5-1.png", "caption": "Figure 5c: Bending Moments M2 , M3 at M", "texts": [ "~ M= ;mEl 2L ~ M -Jill. - l analytical numerical (10 elements 160 load-stepsl F1gure 4 5.2 Two span beam under bending and torsion In th1S example a two-span beam loaded by a slngle load 1n midspan, a constant d1str1buted load as well as a d1str1buted torsional moment 1S analyzed. It was chosen to demonstrate that warp1ng constra1nts over the central support may be important, and that near the load caus1ng sidesway buckl1ng the torsional rotat1ons are no longer small. The configurat1on is shown in Figure 5. The cross M ~ = - 0.088 m, EF = 2 1 6902. 9 kN m , EF ww sectional parameters were taken as follows: 6 2 1.008 \u00b710 kN, EFnn 1575 kNm , EF~~ = 15.057 kNm 4 , GJT 9.882 kNm 2 . The boundary condit1ons are ObV10US from the f1gure and all loads were o - 0 increased proportionally, i.e. E = A\u00b7 E, where the values o\u00a3 E were taken o 0 a / as: P~1 = 5kN/m, P~2 = 1kN/m, m1 = 0.2 kNm m 10 kN. 208 cross-section R -1 II 1111111101 jJ II I H II I 0 II H t ~2 \"g;\" 6: 1\" om 1c \"~rf~ 10cm~ Figure S The numerical results are given in F1gS" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001602_robot.2004.1308769-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001602_robot.2004.1308769-Figure2-1.png", "caption": "Fig. 2. Two single-link manipulators, with paths and collision Zone (in bald) indicated.", "texts": [ " Ai(y;(C)) nAj(Yi(5j)) # 01 PBij is the set of all points on the path of robot A; at which Ai could collide with Aj, and can be represented as a set of intervals PBij = I[I. Conceptually, intersection regions of the swept volumes of pairs of robots give the collision zones. Figure 2 is an example of two single-link manipulators with paths that overlap in a collision zone. Here PE12 = { [al , a2]} and PB21 ={ [bl , b?]} . Collisions can occur only when ). C. Collision Zones: liming The collision zones describe the geometry of possible collisions, but for scheduling the robots, we must describe the timing of the collisions. For a specified parameterization 7;. the set of times at which it is possible that robot A; could collide with robot A, is given by: TBij(7i) = It I Ai(ri(ri(t))) nAj (y j (5 j ) ) # 0, for some O. Observe that by Corollary 6.9, in order for the exterior o f C1 to be mapped to the interior of C2 it is necessary that Ir -< ~/2. Assume that the perpendicular to L1 and L2 makes an angle r + r with the x-axis, Ir -< ~/2. D e f i n i t i o n 6.1@. Let DL = DL (05, ~) denote the Euclidean distance between L1 and L2. D e f i n i t i o n 6.11. Let Dc = De(t, 05, ~b) be the distance between the parallel lines L] and L~, where L[ is tangent to C1 and parallel to L1 and L~ is tangent to C2, with L~ and L~ chosen so that C1 and C2 lie between L~ and L~. We emphasize that the cond/t/on that we have a T-Schottky configuration is thus precisely that De < Dr. In what follows, we progressively describe how best to choose the geometr/c parameters t, 05, ~. Essentially, we minimize D e - DL as a function of t, then ~b, and then ~b." ] }, { "image_filename": "designv11_32_0000022_00218468608074940-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000022_00218468608074940-Figure3-1.png", "caption": "FIGURE 3 A ball rolling on a pressure sensitive adhesive.", "texts": [], "surrounding_texts": [ "Equations of motion of a ball rolling on a pressure sensitive adhesive are as follow^:^.^ M j = - F M y = 0 = N - Mg Z 6 = RF - f N x = R@ + constant where M , R, Z(=2MR2/5) are mass, radius and moment of inertia of a ball, respectively, and F is static frictional force, N normal force, CP angle of rotation of a ball, and f is rolling friction coefficient of a pressure sensitive adhesive. From Eqs. (1)-(4), we get Because f depends on the physical properties of the material, it must be expressed as a function of velocity (v) for viscoelastic D ow nl oa de d by [ N ew Y or k U ni ve rs ity ] at 0 0: 45 1 8 Fe br ua ry 2 01 5 88 H. MIZUMACHI AND T. SAITO materials. We proposed the following equation in the previous report2: f = #o+ 4 l V (6) Then, we get v = u , e x p ( - y t ) %#I -2 ( I - e x p ( - T r ) ) %#I (7) 7R (x - x,) = - 5g# 1 (% + t)( 1 - exp( - $ I ) ) - 2 r (8) 1R (x - x& = - { 21, - 5 log( 1 + ; vO)] 5g#1 $1 (9) where ( x - x,) is rolling distance at time t and ( x - x& is ( x - xo) at LJ = 0, namely rollout distance. If we neglect rolling friction of the solid material of the curved path, initial velocity of a ball in the pressure sensitive adhesive zone is expressed as a function of H. 1/2 v, = ( T g H ) Then, 7R We can analyze our data on rolling distance and those on rollout distance according to Eqs. (8) and (11), respectively. D ow nl oa de d by [ N ew Y or k U ni ve rs ity ] at 0 0: 45 1 8 Fe br ua ry 2 01 5 ROLLING BALL ON PSA 89 (A) Rolling distance Some of the typical data are shown in Figure 4. Not only rollout distance, but also the shape of a curve of ( x - x o ) vs t is different from specimen to specimen. Initial velocity of a ball must be the same for every case, regardless of R of a ball. From initial gradients of the curves in Figure 4, we get vo = 150 cm/sec, which is close to the calculated value. Equation (8) was applied to these data and values of @o and were determined so as to minimize the sum of deviations of experimental data from the curve in every case. Value of @o and @1 thus determined were substituted in Eqs. (7), (8) and (9), in order to obtain theoretical curves of velocity and rolling distance of a ball as a function of time, and rollout distance, which were compared with experimental ones. Some of the results of these analysis are given in Figure 5 and Figure 6, and they are summarized in Table 1 %O I % 1 t S E C FIGURE 4 Some typical data of rolling distance of balls as a function of time. 1. T a p e C , R = 0 . 8 0 c m , 2 . T a p e C , R = 0 . 6 4 c m , 3 . T a p e D , R = 0 . 8 0 c m , 4 . TapeB, R =0.96cm, 5. Tape D, R =0.56cm. D ow nl oa de d by [ N ew Y or k U ni ve rs ity ] at 0 0: 45 1 8 Fe br ua ry 2 01 5 90 H. MIZUMACHI AND T. SAITO 0 . 0 2 . 0 4 . 0 6 . 0 6 . 1 . 1 2 . 1 4 . 1 6 . 1 8 . 2 t S E C FIGURE 5 Comparison between experimental points (0) and a theoretical curve (-) of rolling distance. Velocity is also shown by a broken line (- - - - -1. Tape B, R=0.80cm, +,=2.01, -0.0116. 1 4 1 4 0 \\ \\ y ''1 1 0 \\ \\ \\ \\ \\ I I I I \\ l I I I I 0 .O1 , 0 2 . 0 3 . 0 4 - 0 5 . 0 6 . 0 7 .0E . 0 9 . 1 t S E C FIGURE 6 Comparison between experimental points (0) and a theoretical curve (-) of rolling distance. Velocity is also shown by a broken line (-----). Tape D, R=0.56cm, +,=8.95, +,=-0.0579. D ow nl oa de d by [ N ew Y or k U ni ve rs ity ] at 0 0: 45 1 8 Fe br ua ry 2 01 5 ROLLING BALL ON PSA 91 TABLE I1 Results of analysis of rolling distances R $0 $1 DEV\" DIST,,, DIST,,, Sample (cm) (cm) (sec) (cm') ( 4 (cm) B 0.96 6.74 -0.0396 5.90X lo-' 7.37 7.68 B 0.96 4.10 -0.0150 1.30X lo-' 6.35 6.51 C 0.96 2.38 -0.0137 2.88x lo-' 19.45 19.74 C 0.80 2.01 -0.0116 6.62X lo-' 19.49 19.22 C 0.64 2.72 -0.0166 1.46X lo-' 13.90 14.23 C 0.64 2.62 -0.0159 7.63 X lo-' 14.42 14.67 D 0.80 3.48 -0.0195 8.57X lo-' 10.48 10.79 D 0.80 4.26 -0.0257 8.01 x 10.61 10.98 D 0.56 6.00 -0.0356 1.19X lo-' 4.99 5.33 D 0.56 8.95 -0.0579 2.14X 5.44 5.87 E 0.80 1.47 -0.0066 2.25 X lo-' 17.32 17.62 E 0.80 1.32 -0.0053 2.59x lo-' 17.22 17.46 F 0.80 2.37 -0.0086 1.31 X lo-' 8.84 9.13 F 0.80 2.26 -0.0073 1.09X lo-' 8.64 8.93 G 0.80 3.44 -0.0212 1.12X lo-' 14.55 14.90 F 0.80 2.18 -0.0075 1.96X lo-' 9.29 9.49 a DEV = C 01 - yj)' DIST = ( X - x&, 11, where data of Tape A are lacking, because we could not determine time/position of the ball on the tape by photography. Because deviations are very small in all the runs, and calculated values of rollout distance are almost the same as the observed ones, we believe that rolling motion of a ball can satisfactorily be described by these equations. However, &, and are not necessarily the same for two runs of the same condition. For example, in the case a ball of radius 0.56cm rolling on Tape D, (&, is (8.95, -0.0579) at the first run, and (6.00, -0.0356) at the second, in spite of the fact that deviations for individual runs are very small. The reason is not known exactly. A specimen of a pressure sensitive adhesive tape is prepared by unwinding a roll and cutting it, and then it is a set on a tester by apparently the same procedure. But there could be some differences in the fine states of specimens which we usually do not recognize. There is always a scatter of points in this kind of experiment, but it is a very interesting fact that any individual run can be described at full length according to a very simple mechanical principle. If we want to obtain data on D ow nl oa de d by [ N ew Y or k U ni ve rs ity ] at 0 0: 45 1 8 Fe br ua ry 2 01 5" ] }, { "image_filename": "designv11_32_0000781_0898-1221(86)90093-3-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000781_0898-1221(86)90093-3-Figure1-1.png", "caption": "Fig. 1. Undeformed and deformed blade segment, and rotating unit vector triads.", "texts": [ " and \u00a2IX0= are the cyclic pitch first harmonics , with Ix being the advance ratio for the rotor. For the case of hover , where Ix = 0, eqn ( lb ) reduces to 0 = 00. The e lements of the t ransformat ion matrix [T] relating the unit vector triads (~, ~1, ~) and (.f, .f, ~), as [~, ~ , ~]r = [T]. [.f, 3~, ~]r are readily obtained f rom Fig. 3 and are given as shown in eqn (2a). Also, if r denotes arc length measured along the b lade ' s elastic axis. nondimensionalized by R, the partial der ivat ive of x with respect to r follows direct ly by inspection of Fig. 1 and is given as shown in eqn (2b). Here ( ) ' denotes partial differentiat ion with respect to x, and 0~ = 0(x, tb) + 0x(x, 0): T ( I , 1) = cOS 0y COS 0:, T ( I , 2 ) = cOS 0y Sin 0:, T(2, 1) = - cos0~ s i n 0 : - s i n 0 t sin 0,. cos 0:, T(2, 2) = cos 0~ cos 0: - sin 0t sin 0y sin 0.., T(3, 1) = sin 0t sin 0: - cos 0~ sin 0,. cos 0:, T ( 3 , 2 ) = - s i n 0 t c o s 0 : - cos0~ sin 0y sin 0:, T ( l , 3 ) = sin0,. , T ( 2 , 3 ) = s in0~cos0~ . , T ( 3 , 3 ) = c o s 0 t cos0, . , (2a) Ox/Or = 1/[(1 + \u00a2- 'u ') 2 + (\u00a2v ' ) 2 + ( \u00a2 w ' ) ' ] 1'2" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001614_1464419042035953-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001614_1464419042035953-Figure4-1.png", "caption": "Fig. 4 Electromagnet positioning Fig. 5 Electromagnet and cradle assemblies", "texts": [ " The tapered portion bore against the under surface of the adjustable segment, providing a radially stiff load path. Turning the adjuster caused a longitudinal wedging action. The effect was to lift or lower the segment surface slightly in a controlled and continuous manner, thereby changing the hydrodynamic conditions, irrespective of any loads. This concept and the effect on the hydrodynamic action have been reported [4]. The rotor is shown in Fig. 3. It was of composite construction and designed to interact with large adjacent electromagnets positioned schematically as in Fig. 4. The rotor core comprised a central steel collar upon which were keyed a large number of steel disc blanks, each 0.65 mm thick. These provided the majority of the interaction between the rotor and the electomagnets and were of the BS-specified power loss rating of 10 W/kg at 1.5 T 50 Hz [5]. They were clamped by large nuts threaded to the rotor collar doubling as crowned pulleys for drive belts. The nuts in turn were locked in place with keyed lock rings and aluminium belt guides, visible in Fig", " Each electromagnet was energized by a singlephase variable transformer unit. Rotary control potentiometers allowed each magnet force to be changed smoothly and continuously and held at any required value within range. Resolution was +0.1 kgf throughout the range. Each whole cradle assembly was located on two circular mountings set concentrically with the central shaft to provide the series of angular positions from horizontal to vertical. Alternatively, setting both magnets at the same angle of 22.58 above horizontal, as shown in Fig. 4, allowed a load equivalent to the rotor weight to be vectored in virtually any radial direction by suitable adjustment of the magnet forces, without the need for physical repositioning. K01003 # IMechE 2004 Proc. Instn Mech. Engrs Vol. 218 Part K: J. Multi-body Dynamics at CARLETON UNIV on June 18, 2015pik.sagepub.comDownloaded from Figure 6 shows an overall view of the complete test rig, with the magnets set at 22.58 above horizontal. The rotor drive power was supplied by a variable-speed three-phase d" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003188_j.mechmachtheory.2007.07.001-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003188_j.mechmachtheory.2007.07.001-Figure1-1.png", "caption": "Fig. 1. Sketch for moulding surface.", "texts": [ " Obviously, the basic frame isn\u2019t unique, and it can be determined in accordance with the requirements; (2) when the trihedron moves along the directrix, respective loci of e2-axis and e3-axis are developable surfaces, thus it follows that when a straight-line passes the origin of the frame and has a constant crossing angle with e2-axis, its locus along the directrix is also a developable surface. Now the kinematic behaviors of the basic frame are developed. Suppose that qn = 1/kn is the radius of normal curvature at considered point P of the directrix Cp, and qg = 1/kg is the radius of geodesic curvature. In Fig. 1, let the origin P of the basic frame be the starting point, we can obtain the geodesic curvature center Og by intercepting qg along e2-axis and the normal curvature center On by intercepting qn along e3-axis, thus the line OgOn becomes the axis of curvature of the directrix at this instant and has a same direction as the vector x. The ruled surface, generated by the axes of curvature at every instant, is a developable surface and, meanwhile, it is also a directing surface of moulding surface. The normal plane Rn (i", " In other words, the shape of the directrix at the neighborhood of point P can be deemed as the locus generated by the rotation of point P around the axis of curvature. The foot Oc of the perpendicular POc of OgOn is the instantaneous center of rotation of point P, i.e. the center of curvature of the directrix Cp, and the length jPOcj denotes the radius of curvature. As described above, the spatial motion of normal plane of the directrix depends on the directrix and its basic frame. When the normal plane Rn moves along the directrix Cp, the resulting locus R of an arbitrary planar generator Cm, attached on the normal plane, is moulding surface, as shown in Fig. 1. The generator Cm is represented in the basic frame fP ; e1; e2; e3g of the directrix by vector function: Cm : q \u00bc q\u00f0h; s\u00de \u00bc r\u00f0h\u00de\u00f0e2 cos h\u00fe e3 sin h\u00de \u00f04\u00de where r, h are the polar radius and the polar angle at considered point on the generator. e2; e3 are unit normal vectors of basic frame, and are the functions of parameter s. According to the definition and Fig. 1, moulding surface R is represented by vector function: R : R \u00bc Rp\u00f0s\u00de \u00fe q\u00f0h; s\u00de \u00bc Rp \u00fe r\u00f0h\u00de\u00f0e2 cos h\u00fe e3 sin h\u00de \u00f05\u00de Obviously, moulding surface is a special structural surface with the following geometric properties: (1) Parametric curve. When s is a constant, the resulting curve from Eq. (5) is the generator (the meridian) Cm of the surface R; when h is a constant, another resulting curve is a parametric curve (the parallel) Cn on the surface R, and is also an affiliated curve of Cp. The partial derivative of Eq" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure7.10-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure7.10-1.png", "caption": "Fig. 7.10. Box-structure derived from tetrahedron-structure", "texts": [], "surrounding_texts": [ "Next, space-structures or three-dimensional structures will be considered. These are structures that are of interest in most applications. In a very general sense, space-structures can be perceived as a combination of many plane-structures, arranged in a manner that all the planes are not coplanar. Therefore, for a space-structure to be rigid, every plane-structure that makes up the space-structure must be rigid in its own right. This is one reason to have a good understanding of plane structural rigidity. Since machine structures are stationary, the sum of the forces and moments acting on it must be zero; which is in accordance with Newton\u2019s second law. Mathematically, this implies \u2211 F = 0, (7.5) \u2211 M = 0, (7.6) where F and M are three-dimensional force and moment vectors, respectively. The sign conventions as depicted in Figure 7.1 will be used. As before, each structural configuration can be tested to verify if the planestructure satisfies the equation 3j = m + 6, (7.7) where j denotes the number of joints and m denotes the number of members; then, there are three possible cases, namely 7.1 Mechanical Design to Minimise Vibration 203 2. If 3j > m + 6, then the structure is unstable 3. If 3j < m + 6, then the structure is statically indeterminate In the plane-structure, the triangle is the basic shape, which is rigid and statically determinate. In a space-structure, the basic form for rigidity and statically determinant is the tetrahedron, which is depicted in Figure 7.8. Adding a new non-coplanar joint to the three existing joints of a triangular plane-structure derives the tetrahedron-structure. This new joint is connected to the existing joints with three new members. By following this procedure, rigid and statically determinate space-structure can be derived. Other space-structures are shown in Figures 7.9 and 7.10. It is also noteworthy that the members are connected with ball-joints. 1. If 3j = m + 6, then the structure is statically determinate" ] }, { "image_filename": "designv11_32_0003623_9780470567319.ch5-Figure5.13-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003623_9780470567319.ch5-Figure5.13-1.png", "caption": "Figure 5.13 Top and bottom views of the Dexcom transmitter that is inserted into the skin patch. Copyright 2008 Abbott. Used with permission.", "texts": [ " The patch is applied to the skin by removing plastic tabs that cover the adhesive in a manner similar to an adhesive bandage. The user then pushes on the inserter and then pulls on the inserter, thus driving an approximately 24 gauge needle into the skin with the sensor contained within the needle and then removing the needle leaving the sensor in the skin. The used inserter is removed from the patch and discarded (Figure 5.12). The STS transmitter is inserted into the patch that causes it to make electrical contact with the sensor (Figure 5.13). The transmitter is powered by a nonreplaceable battery. The transmitter is in radio frequency communicationwith the STS receiver (Figure 5.14). The glucose results are displayed on the receiver. Once the sensor is inserted, the user is instructed to wait 2 h before they are prompted to calibrate the sensor. The user must run duplicate blood glucose measurements using a specific brand of glucose meter and download the fingerstick data into the receiver. The calibrated sensor will transmit data from the transmitter to the receiver every 5min" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure2.12-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure2.12-1.png", "caption": "Fig. 2.12. U-shaped linear motor", "texts": [ " To compensate for poor flux utilisation, these motors draw more current while entailing significant heat loss to achieve a given force level in comparison to other architectures. Consistency of the force output is dependent upon maintaining a close consistent air gap (\u2264 0.5 mm); fluctuations in the air gap over the length of travel cause flux variations, and hence force output variations. These variations in force output must be compensated for in order to maintain good trajectory tracking performance. The high attractive forces between the forcer and platen, coupled with the precise air gap requirements, also lead to a relatively complex installation process. Figure 2.12 shows another popular linear motor design used today\u2014 the Ushaped linear motor. U-shaped linear motors are widely used in high precision operations requiring smoothness of motion. The U-shaped motor armature consists a planar winding epoxy bonded to a plastic \u201cblade\u201d which projects between a double row of magnets. The permanent magnetic fields generated by the track works in conjunction with the electromagnetic fields in the blade to produce linear motion. This design is advantageous for its zero detent force and resultant smoothness as well as the absence of attractive forces between armature and stator" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001608_j.medengphy.2004.04.005-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001608_j.medengphy.2004.04.005-Figure1-1.png", "caption": "Fig. 1. Simple schematic of components of a loading machine.", "texts": [ " Although it is not the intent of this manuscript to endorse a particular company or brand and we acknowledge that the components purchased for this loading machine can be provided by a multitude of companies, the specific model numbers and companies used have been provided to assist researchers wishing to duplicate this loading system for their testing needs. Also, interested researchers are encouraged to open a dialogue with these companies as their expertise may point in an alternate direction that will more optimally suit a particular investigator\u2019s testing needs. As is typical of testing platforms, the basic components of this mechanical/materials testing machine are: planar (xy) motion; automated vertical (z) motion; a power source; load and displacement sensors; data collection (scanner and computer); and, bend fixtures, Fig. 1. Planar motion was accomplished with a relatively inexpensive milling machine table (Palmgren) with a 100 150 mm travel. The widespread use of these tables in machine shops resulted in the affordability of the table ($ 500.00) and the required planar movement accuracy (0.0127\u20130.0254 mm) for high precision mill work is more than adequate for our loading system. Using the milling machine table, the x and y positions can be independently dialed in to a resolution of 0.0254 mm. Once in place, the positions can be locked with a set screw while etched dials enable reproducible placement" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001249_fuzzy.2000.839157-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001249_fuzzy.2000.839157-Figure3-1.png", "caption": "Fig. 3. 'Tlic input varinblcs; U and d", "texts": [ " 'The other line segments consist of S and other vertices must be longer. With this method, the nuniber of the reduced vertices is four (vertex 2-5). For the case o f concave obstacle, we can exploit the method in [6] to avoid the AMR going into a trap. , ~~~~~ ~~~~~ ~ AI I j .... ,.. ,._' .................. a . I .. '.,, G i i A1 I 1 Pig. I. The shonest pnth , , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. The L VDM and FLDM Schemes 'l'he input variables of the decision mechanism are shown in Fig. 3, where d presents the distance of the robot at S and thc vertcx A , , and 8 deiiotes ttie angle between the robot at S , the vertex A, and the goal G . The LVDM scheme is basically an importance quotient (iQ) decisioii method and can be detcrmincd by the following equation, where 0 5 A 5 I , IQ is ihe importance quotient. It is seen that the bigger value the IQ is (that is, 0 and d are small), the higher priority t l i e vertex i s selected to reach for. Fig. 4 illustrates the flow chart of LVDM scheme" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002328_tpas.1973.293606-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002328_tpas.1973.293606-Figure2-1.png", "caption": "Fig. 2. Four-pole machine rotor", "texts": [ " Some of the essential features of the reluctance motor are reviewed elsewhere by Cruickshank et al, in a paper containing an exhaustive bibliography3 That paper, and an earlier one4, describe the advantages, construction, testing, and firstorder analysis of a machine with a rotor consisting of laminations of anisotropic material with planes parallel to the axis of rotation. Menzies , and with co-workers Mathur and Lee in a companion paper , reported on a discretized, equivalent-magnetic-circuit approach for the analysis of flux in the air gap, prediction of machine performance, and subsequent experimental verification. An axially laminated anisotropic rotor, for a two-pole machine, can be made by stacking sheets of cold-rolled, grain-oriented steel and machining to a circular form as indicated in Fig. 1. For the fourpole machine, of Fig. 2, the steel strip is first wound on a form by standard C corewinding techniques. It is then cut, reassembled, and machined to a circular shape. The intervening region generally con- Paper T 72 422-4, recommended and approved by the Rotating Machinery Committee of the IEEE Power Engineering Society for presentation at the IEEE PES Summer Meeting, San Francisco, Calif., July 9-14, 1972. Manuscript submitted February 17, 1972; made available for printing April 20, 1972. sists of aluminum except for the shaft that would likely be made of a non-magnetic nickel steel", " Inspection of Figs. 1 and 2 indicate clearly that at any point within the rotor, the local high and low reluctance directions (i.e. the principal axes) are perpendicular to one another. As the laminations (indicated by hatched lines) are very thin, we are justified in replacing the actual rotor structure by a locally averaged permeability tensor P at each point. The numerical values depend upon material properties and the stacking factor. Clearly, the rotor of Fig. 1 is homogenleous while that of Fig. 2, because the laminations change direction from point-to-point, is inhomogeneous. As a further simplification in this work, fine details of the pole-face geometry are ignored by assuming a sinusoidal variation of magnetic potential 4 about the inner periphery of the stator. Thus, stator tooth saturation effects are neglected. However, this restriction is not essential and the resulting computer program can be altered to include nonlinearities as described elsewhere2. Also, it is assumed that end effects and the magnetic field outside of the machine are negligible", " The previous program8 had facilities for polynomial multiplication and so these operations were easily performed. Existing routines within the program were employed to represent accurately the curved boundary and the continuous variation of boundary condition along the outer periphery of the rotor. The curve along the inner portion of the anisotropic rotor material was represented simply by shifting triangleside nodes to the curve and performing all integrations up to and along the edge. RESULTS Fig. 2 is a scale drawing of the case tested numerically. The radius of the rotor is 2.985 in and the rotor-stator gap is 0.3 mm (about 0.012 in ). The maximum scalar magnetic potential, of the stator wave, is taken to be 250 At, and the principal axes permeabilities are 10-2 and 10-5 H/m. Figs. 3 - 6 present potential contours within the rotor and magnetic flux density at the air gap plotted against mechanical degrees. All computations employed cubic polynomials. The air gap flux was computed by dividing the gap potential difference by the reluctance", " This was found to agree, as it should, with the computation of flux obtained by differentiation of the potential function at all points - except in the immediate vicinity of the gap edges. This is because the gradient is poorlybehaved there. Potentials are, on the other hand, not unduly affected. Note the element positioning, shown in Fig. 3, with a special arrangement to cater for the fields near the gap edges. There is a small bump in the flux plots between the 350 to 400 points. The reason is unclear, but it is thought to result from problems associated with using a triangle with a small angle. cas e. Note the flux reversal in the quadrature-axis From Fig. 2, one can infer the path of the laminations within the magnetic part of the rotor. Note that, in Fig. 3, the potential contours are not quite perpendicular to the laminations. The main design problem is to enhance the anisotropic properties. Judicious variation of design parameters could, with the aid of such plots, help to bring this about. On the other hand, the potential contours appear to correspond closely to the laminations in the quadrature-axis position. The potential plots were all obtained with the Dirichlet boundary condition enforced" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003287_1.3591505-Figure9-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003287_1.3591505-Figure9-1.png", "caption": "Fig. 9 Gear noise patterns for transverse plane for 14 DP gears", "texts": [], "surrounding_texts": [ "12 SO H.P.M\nII50 R.P.M\n450 overall wise\nLEVEL\nFig. 5 Gear noise patterns in transverse plane for 6 DP gears\n450 R.P.U\nNOUC AT\nT.C.F\nR. P.M.\n450 R.RM.\nFig. 6 Gear noise patterns in a plane inclined 45 deg to the transverse plane for 6 DP gears\n45 OR.P.M\nI\n1250 P. .P.M\nOVERALL\nLEVEL\nd\nc NOISE\nLEVEL AT 2X-T.C-F\nat 450 and 1250 rpm. The values given are the average overall noise levels and (he noise levels around the twice-tooth contact frequency component in the planes given in the figures.\nFigs. 9 and 10 show the noise patterns of 14 DP-l'/a-in-wide nickel chrome steel gears of finished, ground, and shaved teeth, running at 450 and 1250 rpm and lead equivalent to K = 80. The values given are the overall noise levels, and the noise levels of the main noise containing component of frequency equals that of the tooth contact and measured in the transverse plane of the gears and in a plane inclined 45 deg to it, respectively.\nFigs. 11 and 12 show the noise patterns around the driving and driven 14 DP-l ' /Vm. nickel crome steel gears of finished, shaved, and ground teeth running at 450 and 1250 rpm, respectively. The values given are the average overall noise levels and the noise levels around the tooth contact frequency component iu the given planes.\nFig. 13 shows the changes of the total average noise level with speed for different facewidths of the gear under constant transmitted load equivalent to I\\ \u2014 80 for 6 DP helical involute gears. Fig. 14 is similar to Fig. 13, but showing the noise levels around twice the tooth contact frequency component which is the main noise-containing harmonic.\nFig. 15 shows the changes of the total average overall noise level with transmitted load at different running speeds fig^ 7 Gear noise patterns for 6 DP driving gaars for the same gears. Fig. 10 is similar to Fig. 15, but showing the noise levels around twice the tooth contact frequency component. Fig. 17 shows the changes of the total average noise levels of 0 DP helical gears at different speeds with the change of facewidfh, overlap ratio, and number of teeth in contact.\nFig. 18 shows the change of total average overall noise level with speed of 14 1)P helical involute gears made of nickel steel, and transmitting constant load equivalent to K = 80. Fig. 19 is similar to Fig. 18, but the values of total average noise level are those around the tooth contact frequency component which contains the main noise.\nFig. 20 shows the change of total average overall noise level of 14 DP helical gears at different speeds with the change of the transmitted load. Fig. 21 shows the same changes for the total average noise level around the tooth frequency component.\nFig. 22 shows typical noise spectra for 6 DP-3-in. facewidth running at speeds of 450 and 1250 rpm.\nDiscussion of Results Noise Patterns for Involute Helical Gears . The directional behavior of noise of test gears for different facewidths, speeds,\nSCALE REFERENCE\nLEVEL 70 DB 7 8\nAVERAGE OVERALL\nNOISE LEVEL 8 8\n92\n450 R.P.M\nIZSO R.RM\n99\n1250 R.RM.\n450 R.RM-\nNOISE LEVEL\nAT 2 XT.C.F.\n1250 R-P.M.\n4 5O fl.P.M. NOISE LEVEL\nAT 2XT-C.F\nFig. 8 Gear noise patterns for 6 DP driven gears\n450 R.P.N.\nAVERAGE OVERALL NOISE LEVEL\nI ISO R.RM.\nJournal of Engineering for Industry F E B R U A R Y 1 9 6 9 / 1 6 7\nDownloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use", "and transmitted loads were studied on three-dimensional patterns formed by projecting rods representing the measured values of noise levels at 68 points on the surface of wooden spheres. For all the test gear combinations, these patterns have shown directivities exhibiting rotational symmetry about a direction of maximum radiation along the vectorial resultant of the direction of the helix and that of the line of pressure between the contacting teeth. Thus each of the three-dimensional noise patterns is mainly composed of a sphere centered on the noise source with four lobes at its corners. These lobes are shown at points a, b, c, and d in Figs. 5, 6, 9, and 10.\nThe results have also shown that the directivity of the driving gear is more than that of the driven and the indexes calculated from the three-dimensional patterns are 12 db and 6 db for the driving 6 OP and 14 DP gears, respectively, compared with 6 db and 4 db for the driven gears measured in the directions of the pattern axes.\nIt has also been noticed that the four lobes become more defined and the directional gain increases with the increase of speed.\nFig. 12 Gear noise patterns for 14 DP driven gear\nThe directional gain also increases with the increase of facewidth of the gear. This is mainly due to the increase of the length of the rectangular area of contact and the friction between contacting teeth with the increase of facewidth.\nFor 14 DP nickel steel ground gears the noise patterns (Figs. 11, 12) are more uniform with less directional gain than those of 6 DP commercial gears.\nThe Largest Single Frequency Component. For 6 DP involute helical gears the largest single component of noise is that of double the tooth contact frequency. For 14 DP nickel steel ground gears the largest, component has a frequency equal to that of the tooth contact. This was found to be consistent in all the gear combinations tested at different speeds and loads. This also agrees with the corresponding load distribution curves previously recorded in a strain-gage investigation on dynamic loads on gear teeth [7].\nFig. 23 shows the load distribution curves for involute gear teeth. For commercial gears the curve has four peaks along a length of contact equal to the base pitch, and two peaks for ground and shaved gears. The effect of shock loading due to impact between teeth usually appears at these bumps where the tips of teeth come into or leave contact [8].\n450 R.P.M.\nI AVERAGE OVERALL\n/VO/.S5 LF.VEL\ntf.ac r..r.\\:.\n1250 R P.M.\nA50 RP.M.\nNOISE LEVEL AT T.C.r\nSCALE RTFERERENCE 10 OB\n1 6 8 / F E B R U A R Y 1 9 6 9 Transactions of the AS M E\nDownloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use", "95\n34 S3 32 SI 90 > 1 |> I 1 iS ! 87 i 8 6 !\u00ab5 j 81 : 83 [ 82 E 8 ' > 80\n79\nWs2 / / /\nw.-l/ A t /\n/ / / A / /\nw*3 >/ /\n>5 V / / / } \\! t\ny\nif /\n1 w\nh w- lj\ni / 400 600 600 IOOO ,ZO0 tfOO\nSPEED R.P.M.\nFig. 13 C h a n g e of total a v e r a g e n o i s e l e v e l w i t h s p e e d for g e a r s of different f a c e w i d t h s for 6 DP g e a r s\n160 too K .FACTOR\nF ig . 15 C h a n g e of total a v e r a g e o v e r a l l n o i s e l eve l w i t h a p p l i e d l o a d a different s p e e d s for 6 DP g e a r s\n5 Q 9o\nI \" \"> 8 2\nl \" * 76\nW-i / > / , / 'A /\nA F f\nl< t\n/ / i .\u2014 i-*\n7 400 1000 1200 Moo\nSPEED R.PM.\nFig. 14 C h a n g e of total a v e r a g e n o i s e l e v e l w i t h s p e e d for g e a r s of different f a c e w i d t h s a r o u n d d o u b l e the tooth contact f r e q u e n c y c o m p o n e n t for 6 DP g e a r s F ig . 16 C h a n g e of total a v e r a g e n o i s e l eve l w i t h a p p l i e d l o a d at different s p e e d s a r o u n d d o u b l e the tooth contact f r e q u e n c y c o m p o n e n t for 6 DP g e a r s\nC h a n g e of G e a r N o i s e Wi l l i S p e e d . Figs. 13 aild 18 show that the overall noise level increases rapidly at first with speed and then tends at higher speeds to reach a maximum.\nThe rise in total average overall noise level over the same range of speed variation is found to be 4 db higher for 6 DP commercial gears than for nickel steel ground gears under the same running conditions. The maximum noise level is also expected to be reached at a lower speed for the ground gears.\nC h a n g e of G e a r N o i s e With T r a n s m i t t e d L o a d . With increasing transmitted load, the teeth deflect radially, which results in reduced contact ratio. The gears are also tilted under load due to the deflections of their shafts which produce end loading and loss of helical contact ratio which can be a major factor of noise generation.\nFig. 15 shows that the overall noise level of 6 DP gears increases with the increase of transmitted load and tends to reach a maximum which is expected when the amount of tooth deflection under load is equal to the transmission error between the teeth.\nC h a n g e of G e a r N o i s e With N u m b e r of Teeth in Contac t . T h e number of teeth in contact in involute helical gears depends on involute contact and helical contact ratios. The involute contact ratio is the length of the line of action per unit base pitch. The helical contact ratio is the amount which the line\nNUMBER or TEETH IN CONTACT ei 3 a\n9 5 94 97 9J\nn'9l\nQ 00 \u00a7 87 O\n| 85\nkj 83 U 5 82 ^ r \" a so\nov. RU P R QTIO\n/ s / \\ ieso R.P.M\n/ \\ \u2022v / \\ S 900 R.P.M\n/ \\ ^ 1 / 150 R.P.M.\n1 / 1 h N V\n. 60 ORf.M.\n! ASO R.r.M.\no i 4 1 3\nFACE WIDTH IN. Fig . 17 C h a n g e of total a v e r a g e n o i s e l eve l w i t h f a c e w i d t h a n d n u m b e r of teeth in contact at different s p e e d s for 6 DP g e a r s\nJournal of Engineering for Industry F E B R U A R Y 1 9 6 9 / 1 6 9\nDownloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use" ] }, { "image_filename": "designv11_32_0000235_cdc.1996.574537-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000235_cdc.1996.574537-Figure1-1.png", "caption": "Fig. 1. S C A M robot : frames and joint variables.", "texts": [], "surrounding_texts": [ "6.1. Data acquisition Torques are calculated using the relation : r mJ . = G T ~ vT~ (13) VT~ is the current reference of the amplifier current loop which is directly the control data at a sample rate w, in the case of using a numerical controller. In the case of analog control it must be analog lowpass filtered to prevent aliasing before to be sampled at w, with an analog to digital converter. GT, is the gain of the joint j drive chain, which is taken as a constant in the frequency range [0 wdp] of the robot. Accurate determination of GT, using methods described in [ 161 is essential for the success of the identification. Usually, robot sensors provide discrete joint position measurements from encoders or resolvers. Then the use of an analog antialiasing filter is not possible and the sample rate w, must be large enough to avoid high frequency noise aliasing in the bandwidth [0 wdp] of the joint position closed loop. The rule W,=1oo*wdp is generally used to get an acceptable sample rate for the control input VT. Calculating the L.S. solution of (Eq. 12) from noisy discrete measurements or estimations of (9, q , q , Tm ) may lead to bias because W and Y are non independent random matrices [l]. Then it is essential to filter data in Y and W, before computing the L.S. solution. 6.2. Filtering the explicit dynamic model Samples of VT and q at rate w, allow to calculate samples of (Eq.5) at times f, i=l, ...,&, to get the (lxr) measurement vectorY(T,) and the (rxNp) observation matrix W(q, q, i i) , with r=nx~>Np : r m ( i ) = r m ( t i ) is calculated with (Eq.13) D(i) = D(q(ti ), q(ti ). q(ti )) , is calculated with (Eq.6) or with it's customized Newton Euler formulation [13]. In order to avoid distortion in the dynamic regressor which is composed of non linear h c t i o n s of (9, q, ii) (Eq.6), the joint velocity and acceleration are calculated without phase shift by central difference of q. The drawback of this derivation is a dramatic increase of high eequency noise effect in (q, q) estimations [ 171. Then the matrix W is very perturbed and has to be lowpass filtered. The torque Tm is perturbed by the rejection of perturbations (high frequency torque ripple of the joint drive chain) of the closed loop control and has also to be filtered. Then Tm and D(q, q, q) in (Eq.14) are both filtered by a lowpass filter fp(s), with s a derivative operator, to get a new filtered linear system : It is to be noted that no error is introduced by this filtering process in the linear relation (Eq.15) compared with (Eq. 12). The only point is to approximately choose the cutoff frequency wfp around 5*wdp in order to keep useh1 signal of the dynamic behavior of the robot in the filter bandwidth. Because there is no more signal in the range [wa wc/2], Yfpand Wfpare resampled at a lower rate, keeping one sample over nd. The decimate procedure of Matlab is used to easily calculate a filtered and decimated linear system : Yfpd wfpd(q, ($3 4) x +Pfpd (16) with : n&wc/2)/wfp for a FIR filter, and nd=O.8*(wc/2)/wf, for an IIR filter. Taking w,'1oo*wdy, and wfp=5*wdp gives a value of n, c IO. In order to decrease noise in W, it is better to prefilter the joint position q before calculating the derivatives, but it is to be noted that this prefiltering is sensitive to the choice of the cut-off frequency wfs. The filtered data (qf,, qfq, qf,) must be equal to (9, q, ii) in the range [0, wfq] in order to avoid distortion in the dynamic regressor : yfp =Wfp(q, 4, W + F \u20ac p (15) Q,i (9, q>$ = Mi (4 6 + Ni (979 = Mi (Sfq ) 6fq + Ni (9 fq 9 'Ifs ) Mi(qfq) 'ifq + Ni(qfq,qfq)= D:,i(qfq,qfq,qfq)= Dfq:,i The derivatives qfq, qfq are obtained without phase shift using a central difference algorithm of the filtered positionqfq . In order to eliminate high frequency noise differentiation, the order of the lowpass filter fq(s) must be greater than 2 to et a passband filter s*fq(s) to calculate the velocity and $*fq(s) to calculate the acceleration. The filter fq(s) must have a flat amplitude characteristic without phase shifl in the range [0 wfq], with the rule of thumb wfq> 1 o*wd,. Considering an off-line identification, this is easily obtalned with a non causal zero-phase digital filtering by processing the input data through an IIR lowpass buttenvorth filter in both the forward and reverse direction using a filtfilt procedure from Matlab. Then the parallel filtering process is carried out to get the linear system : (17) y fpd = Wfpd(qfq, qfq, qfq) X+Pfpd 6.3. Filtering the implicit dynamic model The same decimate procedure fpd as that of previous section is applied to get a parallel filtered and decimated linear system : yfpd = Wfpd('lfq, qfq)x+@d (18) It is composed of a sampling of the filtered torque Tm (Eq. 13) and regressor F (Eq.9) as following : (E,i )fpd (qfq > qfq = ( S'i(qfq ) qfq)fpd 4- (Pi )fpd(qfq 9 fq (F,i )fpd(qfq 9 4 fq = s( (4 fq qfq)fpd + (pi )fpd This expression shows an advantage of the implicit dynamic model over the explicit one, because it allows to proceed to the second derivative s(Ml(qfq) 4fq),, (using a central difference algorithm) without any distortion compared with the expression(Mi(qfq) qfq)fpd in the regressor of the explicit dynamic model, where the second derivative of filtered position can introduce distortion depending on the choice of fq(s). In order to eliminate high frequency noise differentiation, the order of the lowpass filter f p ( s ) in the decimate procedure fpd must be greater than 1 to get a passband filter s*fp(s) to calculate the derivative s(M;(qfq) qfq)fpd . 6.4. Filtering the energy model The energy model has been used by sampling (Eq.11) at different times t,(i), tb(i)=ta(i+l), i=l, ..., r, r>Np, as following [6,9,18] : Y = ... , y(i)= tb(i) qfqTymfqdt , W = [?.:I (20) [I:] ta(1) Ah(r) (21) Ah(i) = h(qfq,qfq)(tb(i))-h(qfq,qfq)(t,(i)) One point is how to choose the times ta(i). In order to avoid offset in y(i) due to constant perturbation in (qfqT rmfq ) , tb(i)-ta(i) must be bounded. In [15,18], sampling times are optimized to get a well conditioned observation matrix W (Eq.20). This formulation needs a lower resampling of the energy function h at times ta(i), ta(i). Then the function h calculated at the acquisition rate w, must be lowpass filtered with fp(s) in order to avoid aliasing. So it is easier and natural to associate the sampling times with the decimate procedure with a ratio nd, which results in choosing tb(i) and ta(i) with a constant value tb(i)ta(i)=~*2*n/wC. As a result, the parallel decimate procedure fpd must be applied to (Eq. 20,2 1) as following : This is equivalent to parallel filter and decimate the differential expression of the energy model (Eq. lo), which is the power model : The derivative dhfpd is calculated without phase shiR using a central difference algorithm. This formulation clearly defines the choice of the sampling times ta(i) which depends on Q = 10 and shows that the power model is the scalar formulation of the filtered implicit dynamic model (Eq.19). The main advantage of this model is the simplicity of the energy functions h. 7. VALIDATION 7.1. Description of the robot The comparison is carried out on a 2 joints planar direct drive prototype robot (Fig. l), without gravity effect. The description of the geometry of the robot uses the modified Denavit and Hartenberg notation [9,13]. The robot is direct drived by 2 DC permanent magnet motors supplied by PWM choppers. The dynamic model depends on 8 minimal dynamic parameters, considering 4 friction parameters : X=[ZRI Fvl Fsl rZ, LMX2 M 2 Fv2 F3lT ZZRl= ZZ1+ M2 L2 L is the length of the first link, M2 is the mass of the link 2, ZZ1 and ZZ2 are the drive side moment of inertia of link 1 and 2 respectively, MX2 and MY2 are the first moments of link 2. The simulation is carried out with the supposed true values (SI Units) : X=[3.5 0.05 0.5 0.06 0.12 0.005 0.01 O.1IT The columns of the regressors are the following : -explicit dynamic model (Eq.5,6) : -implicit dynamic model (Eq.7,8,9) : - energy model (Eq. 10) : hl = hZZR, = 112 a t , a 2 =&FV, =q1 9 &3 = &Fsl = (41) 7 . 2 h4 = hZZ, = 1 / 2 (4: +&), h5 = hLMX2 = 41(4l+ 4 2 ) cosq2 7 h6 =hLMY2 =-41(41+42) sinq2 9 2 d h 7 = & F v 2 =42 , = &Fs, = 1421 7.2. Comparison by simulation The robusmess of the 3 methods with respect to the systematic errors introduced by the filtering and derivative processes, without any noise, is investigated using the 3 models to estimate the dynamic parameters of the robot and compare them to the true values. This stage is important to check that filtering doesn't introduce distortion in the identification process. The sampled torque is calculated with the dynamic model and a sampling of a successive point to point trajectories using a classical 5' order polynomial trajectory generator, with a sample rate wC=2*.rr* 100rd/s, (Nyquist fiequency = wC/2=2*n*5Ord/s). Starting with ne=8000 samples, and nd=10 (w~=0.8*(wc/2)/10), we get 1-800 equations and a condition number of W Cond(W)=28, for the dynamic model and ~ 4 0 0 with Cond(W)=93, for the energy model. Joint positions and torques are prefiltered using a butterworth filter with a cut-off frequency Results given in Tab.1 show that errors are close for the 3 models which can be considered equivalent from the filtering systematic error point of view, with a little advantage for the dynamic model with explicit acceleration. wfg=O.8*(wc/2)/5. The 3 models and the same filtering process as defined for simulation have been used to calculate the L.S estimation k o f the dynamic parameters of the prototype robot. In order to get the same number of equations ~ 1 6 0 0 , 2 independent realizations of the trajectory have been used for the dynamic models and 4 realizations for the energy model. Standard deviations o~~ are estimated using classical and simple results from statistics, considering the matrix W to be a deterministic one, and p to be a zero mean additive independent noise, with standard deviation oP such that C,, = E(pTp) = o: I,, where E is the expectation operator. The variance-covariance matrix of the estimation error and standard deviations can be calculated by : Cj,, =E(X-k) (X-k)T =o;iW'W)-' oki = Ckkii , the diagonal coefficient of CA, [ 1 2 An unbiased estimation o fop is used to get the relative standard deviation okri by the expression : 0 * . -2 , '%0kri = 1 o o * x ' Ai OP= r -Np Results given in Tab.2 are exactly the same for both dynamic models. This study confms that there is no advantage in using the dynamic identification model with implicit acceleration, because it's symbolic expression is more complicated than that of the dynamic model with explicit acceleration, and because experimental results are the same [l]. Another result is to show that the new formulation of the energy model, with a filtered power model, gives the same accuracy than that obtained with the dynamic models, using the same number r of rows in W and the same filters (wfp, wfq). So, it is possible to take advantage of a very simple identification model which is less sensitive to the use of exciting trajectories compared to it's integral formulation [ 181. 8. CONCLUSION This paper presents a unified approach of 3 identification models which are used to estimate the dynamic parameters of robots. A new formulation of the energy model, based on a filtered power model, is proposed. Theoretical, simulation and experimental studies show that the 3 models give close estimations and accuracy, providing to use the same filters and the same number of equations of the overdetermined linear systems. Our conclusion is that the filtered power model is very attractive for it's simplicity and accuracy. The 2 dynamic models give the same results, then there is no advantage in using the dynamic model with implicit acceleration because it's expression is more complicated than that of the dynamic model with explicit acceleration. REFERENCES [ 11 M. Gautier, P.P. Restrepo, W. Khalil, \"Identification of an industrial robot using filtered dynamic model 'I, Proc. 3rd ECC, Rome, Sept. 1995, pp. 2380-2385. [2] R.H. Middleton, G. Goodwin, \"Adaptative computed torque control for rigid link manipulators\", Proc. IEEE Conf. on Decision and Control, Athen, 1986, pp. 68-73. [3] J.J.E. Slotine, W. Li, \"On the adaptative control of robot manipulators\", Int. J. of Robotics Research, [4]P. Hsu, M. Bodson, S. Sastry, B. Paden, \"Adaptative identification and control for manipulators without V01.6, NO 3, 1987, pp. 49-59. using joint accelerations\", IEEE Conf.-on Robotics and Automation, Raleigh, pp. 12 10-12 15. C. Canudas de Wit, A. Aubin, \"Parameters identification of robots manipulators via sequential hybrid estimation algorithms\", IFAC Congress, Tallin, M. Priifer, C. Schmidt, F. Wahl, \"Identification of Robot Dynamics with Differential and Integral Models : a Comparison\", IEEE Conf. on Robotics and Automation, San Diego, 1994, pp. 340-345. C.H. An, C.G. Atkeson, J.M. Hollerbach, \" Estimation of inertial parameters of rigid body links of manipulators\". Proc. 24th Conf. on Decision and control, 1985, pp. 990-995. 1990, pp. 178-183. [8] P.K. Khosla, T . Kanade, \"Parameter identification of robot dynamics \", 24th CDC, 1985, pp. 1754-1760. [9] Gautier, W. Khalil, \"On the identification of the inertial parameters of robots\", 27th CDC, 1988, pp. 2264-2269. [lo] M. Gautier, W. Khalil, Direct calculation of minimum inertial parameters of serial robots\", IEEE Trans. on Robotics and Automation, Vol. 6, No 3, [l 13 H. Mayeda, K. Yoshida, K. Osuka, \"Base parameters of manipulator dynamics\", Proc. IEEE Conf. on Robotics and Automation, 1988, pp. 1367-1373. [ 121 M. Gautier, \"Numerical calculation of the base inertial parameters\", Journal of Robotics Systems, Vol. 8, No 4, [13] W. Khalil, \"SYMORO+ : A system for generating the symbolic models of robots\", SYROCO, Capri, Sept. 1994. [14] S.Y. Sheu, M. Walker, \"Estimating the essential parameter space of the robot manipulators dynamics\", Proc. 28 th CDC, 1989, pp. 2135-2140. [15] M. Gautier, \"Optimal motion planning for robot's inertial parameters identification\", 3 1 st CDC, Tucson, [ 161 P. P. Restrepo, M. Gautier, \"Calibration of drive chain of robot Joints\", 4th IEEE Conf. on Control Applications, Albany, 1995, pp. 526-53 1 . [ 171 P.R. Belanger, X. Meng, P. Dobrovolny, \"Estimation of angular velocity and acceleration from equallyspaced shaft encoder measurements\", IEEE Conf. on Robotics and Automation, Nice, 1992. [18] M. Gautier, W. Khalil, C. Presse, P.P. Restrepo, \"Experimental Identification of dynamic Parameters of robot\", 4th SYROCO, Capri, Italy, Sept. 1994, pp. 625- 630. [19] C. PressB, M. Gautier, \"New Criteria of exciting trajectories for Robot Identification\", Proc. IEEE Conf. on Robotics and Automation, Atlanta, 1993, pp. 907- 912. 1990, pp. 368-373. 1991, pp. 485-506. 1992, pp.70-73." ] }, { "image_filename": "designv11_32_0002510_cnt.1975.19.3.207-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002510_cnt.1975.19.3.207-Figure2-1.png", "caption": "Figure 2", "texts": [ " So Camot, when faced with the same problem in 1824, ingeniously took recourse to the hypothesis of conservation of heat, originating from Lavoisier and Laplace\u2022, and applied it to the following situation 1o: Suppose a closed cycle 1-2-3, consisting of an isothermal expansion 1-2, followed by a compression under constant pressure 2-3 and an adiabatic compression 3-1. Then according to conservation of heat (5) ~: dq = ~: dq + ~: dq, (6) ~: dq = 0, whence follows (7) Now, the specific heat of air had been measured by Delaroche and Berard (8) Cp = 0.267 kcal. So, by assuming the small, though finite temperature difference of the points 2 and 3 to be (9) Carnot could calculate the heat absorbed on the isotherm from 1 to 2: (10) ~: dq = mcp = Aq. Completing the process 1-2-3 of figure 1 by the Carnot cycle 1-2-4-3 of figure 2 he, in 1824, also calculated the mechanical work (11) done in this cycle by the approximative equation (12) AA= Ap.AV and arrived at the following relation of work gained to heat absorbedll (13) M 11( At = 1 \u00b0C) = Aq = 1.395 kgmfkcal for air at 0\u00b0C. Here it is important to keep in mind that according to Camot's cal culation the result (10) is based on the assumption of the conservation of heat and that therefore Mach's suggestion is not applicable without further consideration. Before doing this let us turn to the third suggestion, put forward by Louis Decombe12 in 1919" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000457_978-3-642-55848-1-Figure2.4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000457_978-3-642-55848-1-Figure2.4-1.png", "caption": "Fig. 2.4. Revolute joint. (a) Scheme of joint, (b) Word model representation", "texts": [], "surrounding_texts": [ "Ports, as explained in Sect. 2.2, are places where interactions between components take place. These interactions can be looked on as power or information transfer. Thus, two types of ports are defined. Ports characterised by power flow into or out of a component are termed power ports. Such ports are depicted by a half arrow (Fig. 2.2). The half arrow pointing to the component describes power inflow. It is assumed that at such a port there is positive power transfer into the component. Similarly, a half arrow pointing away from the component depicts power outflow from the component and the corresponding power transfer is then taken as negative. Another type of port is characterised by negligible power transfer, but high in formation content. These are termed control ports and are depicted by a full ar row. The arrow pointing to the component denotes transfer of information into the component (control input). Similarly the port arrow pointing away from the com ponent denotes information extracted from the component (control output). The word model, i.e. the component represented by the name and the ports, is taken as the lowest level of component abstraction (Fig. 2.2). Components interact with other components through their ports. These interactions are looked on as power or information transfer between components and are depicted by lines con necting corresponding component ports (Fig. 2.3a). The lines that connect power ports are termed bond lines, or bonds for short. A bond line joins a power outflow port of one component and a power inflow port of the other and clearly shows the assumed direction of power transfer between components. Similarly, lines con necting control output ports and control input ports are termed active or control bonds. These lines show the direction of information transfer between compo- 2.3 Ports, Bonds, and Power Variables 25 nents. When a bond line is drawn, ports and connecting lines appear as a single line with a half or full arrow at one of its ends (Fig. 2.3b). In the bond graph litera ture emphasis is put on the bonds, with ports playing a minor role. In our approach just the opposite point of view is taken: Ports, the places where inter-component interactions take place, receive emphasis. Power or information exchange between component ports can be quite com plex. It generally depends on the processes taking place in the components. In the simplest case the process in the component as seen at a power port can be de scribed by a pair of power variables, the effort and flow variables. Their product is the power through the port (Sect. 1.3). Connecting such ports by a bond simply implies that effort and flow variables of interconnected ports are equal. Similarly, information at component control ports can be described by a single control vari able (signal). Connecting an output port of a component to an input port of the other just means that these two control variables are equal. In general, the situation is not this simple. Thus, the revolute joint illustrated schematically in Fig. 2Aa may be used to connect robot links or, a door in a door frame. The joint can be represented by a word model (Fig. 2Ab), with ports repre senting the parts of the joint provided for the connection. The function of the joint is to enable rotation of the connected bodies about the joint axis. To describe the interactions at the joint connection properly, pairs of ef fort and flow vectors are used. The effort vector can be represented by three rec tangular components of the forces and torques, and likewise the flow vector by the rectangular components of linear and angular velocities. The meaning of these 26 2 Bond Graph Modelling Overview variables can be explained by defining a detailed model of the joint and the bodies in question. Hence the connection of a body to the joint can be represented by a bond, which denotes again that the efforts and flows of connected parts are equal. This time the power variables are not simple one-dimensional variables, but vector quantities. Complex interactions at the ports can also be represented using multidimen sional bond notation known as multibonds [3, 4]. We do not use this approach here, but instead treat the component ports as compounded. This means that the component ports are not simply objects, but define the structure of the mathemati cal quantities that describe the processes taking place inside the component. The bond lines simply define which port is connected to which, and hence which mathematical quantities should be equal. To define the structure of the ports the component model is developed in more detail." ] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure7.11-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure7.11-1.png", "caption": "Fig. 7.11. Gantry space-structure", "texts": [ " If 3j = m + 6, then the structure is statically determinate Thus far, the approach to obtain the tetrahedron space-structure from the triangle plane-structure, the pyramid from the tetrahedron, and the box from the tetrahedron has been illustrated. The next aspect of the design is to combine some of these structures. The structures can be treated as being coupled together as rigid bodies, and a rigid body in space has six degrees of freedom, i.e., the structure is capable of translations in the x, y and z directions, and rotation about the x, y and z axes. Therefore, six members are needed providing six reactive forces to exactly constrain the structure in space. Figure 7.11 shows a typical gantry configuration, which is used extensively in many coordinate-measuring machines (CMM). However, one of the members is bearing a bending load, which has been shown earlier to be very detrimental 7.1 Mechanical Design to Minimise Vibration 205 to the stiffness of the structure. There are alternative structure configurations as shown in Figures 7.12 and 7.13, although some redesign maybe needed if such a configuration is utilized. If the ground is perceived as another rigid body in which the spacestructure is to be coupled, then the design of the supports for a space-structure is similar to those of coupling two space-structures together, i" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002361_jps.2600621115-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002361_jps.2600621115-Figure3-1.png", "caption": "Figure 3-Estimutes of the ionization interrul obtained from lines drawn tangent to the infecrion point and through p o i ~ ~ r s on the mobility-pHprofileatpH- p K a = ~k0.5and +l.O.", "texts": [ " The relationship of this ionization interval to the shape of the mobility-pH profile may be seen by dilferentiating Eq. 2 with respect to pH and evaluating the resulting equation in terms of u at the point of inflection or pKa, where U = u - U = u / 2 , which gives: [gH)lpKa = $F$oy) = l% = slope at pKa (Eq. 5 ) This implies that. irrespective of molecular weight. a line drawn tangent to a continuous plot of the mobility-pH profile at the pKa will intercept the values of minimum and maximum mobility with an intervening distance of 1.74 pH units for a monoprotic acid or baze (Fig. 3). However. a line drawn through discontinuous experimental data points obtained at increments of 0.5-1.0 pH unit will have a slightly lower slope. For instance, the line drawn through points spaced 0.5 pH unit above and below the pKa will form intercepts with the minimum and maximum mobilities with an intervening distance of 1.92 pH units, and the intercepts derived from a line through points spaced 1.0 pH unit above and below the pKa will be 2.44 units apart (Fig. 3). A diprotic acid will possess two electrical charges when fully ionized. The acid will be 50% ionized at a hydronium-ion concentration. [H+], given by Eq. 6: [H\u2019] = dZF.2 (Eq. 6) where K , and K? are the apparent dissociation constants of the two ionizable groups. In logarithmic form, Eq. 6 becomes: The ionization and, consequently, the electrophoretic mobility of a diprotic acid may be conveniently expressed as: percent ionized = 100 (i) = H) (-\\/x.$L.--) (Eq. 8) A z + A d X + 1 where: The mobility of a zone of a diprotic acid at a particular pH will be proportional to the charge on the acid at that pH" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003554_978-1-84800-021-6-Figure7.3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003554_978-1-84800-021-6-Figure7.3-1.png", "caption": "Fig. 7.3. a Unstable structure. b Extra member", "texts": [ " In the event of thermal expansion of its member, due to a rise in temperature, statically determinate structures allow expansion of their members, without inducing any stress resulting from an over-constrained condition due to the redundant members. 7.1 Mechanical Design to Minimise Vibration 199 The triangle is the basic shape for a plane structure as shown in Figure 7.2a. Statically determinate plane structure can be expanded from this basic structure simply by linking two new members to two different existing joints for every new joint added, as shown in Figure 7.2b. However, the axis of the two new members must not form a line; in other words, the three joints must not be in the same line as shown in Figure 7.3a. It should also be remembered that the ground constitutes one member as well, and all joints are pin-joints, as shown in Figure 7.3b. The second part of structure design lies in its supports. From this aspect, the whole structure can be treated as a rigid body. For a plane-structure, it has three degrees of freedom, i.e., the plane-structure is capable of motion in the x and y directions, and rotation about the z-axis. Therefore, three members are needed providing three reactive forces to constrain exactly the plane-structure in the plane. Figure 7.4a\u2013c shows some possible support for plane structure, while Figure 7.4d shows an unstable support scenario" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003975_gt2009-59260-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003975_gt2009-59260-Figure1-1.png", "caption": "Fig. 1 Schematic view of gas foil bearing", "texts": [ " DellaCorte and Valco [5] divided all foil bearings into three generations classified by their structure and introduced a simple method to estimate the load capacity of foil bearings based on published bearing load capacity data. The bump-type foil bearings and foil bearings with similar structures have been of increasing interest in recent years for the obvious advances in their performances. The bump-type foil bearing consists of two parts, a smooth top foil acting as the bearing surface and a flexible corrugate bump foil supporting the top foil to provide elastic deflection and frictional damping. The configuration of bump-type foil bearings is shown in Fig.1. 1 Copyright \u00a9 2009 by ASME erms of Use: http://www.asme.org/about-asme/terms-of-use Downlo Accurate analytical models to predict the performance of gas foil bearings can release the designers form the prototype investigation, which is time-consuming and expensive. Since the first theoretical model of a single bump introduced by Wallowit and Anno [6], numerous researchers are of great interest to develop analytical models that provide accurate performance prediction. However, the mechanical complexity of support elastic structure increases the difficulty to predict the performance of gas foil bearings" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000021_bf02442819-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000021_bf02442819-Figure2-1.png", "caption": "Fig. 2 The structure of the multigas sensor with a flow cell. l :pH sensor; 2: pO 2 sensor; 3: pCO 2 sensor; 4: epoxy rod; 5: pin; 6: insulation resin; 7: connector body; 8: screw part; 9: O-ring; 10: flow cell body; 11: male part; 12: female part; 13: Luer-lock", "texts": [ " The pH-ISFET that has been used for the pH and pCO2 sensors in the present work has the size and the structure shown in Fig. 1 (SHIMADA et al., 1978). The drain region (n) is surrounded by the source region (n) with the U-formed gate region exposed from the channel stopper (p+). A p+ region connects the source bonding pad to the substrate (p), to which the n region of the diode as a temperature sensor is contacted, resulting in a circuit of a drain-sourcediode in series. The whole surface of the tip part of the sensor is insulated with a double layer of silicon oxide and nitride. 2.2 Multigas sensor Fig. 2 shows a whole view of the multigas sensor including a flow cell. The multigas sensor embodied with an eight-pin connector is screwed into a flow cell, which has a male part with a Luer-lock for connecting to an indwelling cannula, and a female part for connection of an administration tube of lactate Ringer. The total dead space of the 3 / / \\ %'%'~ /~' ( \"4 Fig. 3 cell including the indwelling cannula (21 gauge) is about 250 #1. Fig. 3 shows the relative placement of a pH sensor, a reference electrode, a pCO 2 sensor and a pO2 sensor moulded in an epoxy rod with a rectangular cross-section" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002855_07ias.2007.334-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002855_07ias.2007.334-Figure5-1.png", "caption": "Figure 5. Mode 2 of the stator with magnetic excitation, 8200 Hz", "texts": [ " These resonant frequencies and associated mode shapes depend on SRM geometries, Young modulus and the considered mode. In this case, stator design is chosen in order to have only one resonance in audible spectrum corresponding to mode 2 at 8200 kHz. A finite element model developed with Ansys\u00ae software confirms that only one vibration mode (resonant frequency) exists in the audible spectrum (Figure 4.). Yoke frame and end shields are necessary to SRM functioning. In order to reduce influence of yoke frame and end shields on the stator resonance and mode shape, joining are placed on vibration antinodes (Figure 5.). Indeed, yoke frame and end shields have their own resonant frequencies but have in this way low influences on stator strain (Figure 6.). Figure 7. shows the experimental spectrum of vibratory acceleration measured on stator, yoke frame and end shields excited by symmetrical piezoelectric actuators. In respect with yoke frame and end shields location, stator vibratory acceleration spectrum has only one resonance. Vibratory acceleration spectra of the yoke frame and the end shields have multiple spectral lines due to different part of them (bolt, teeth \u2026)", "5V and 5V amplitude) applied to piezoelectric inserts. These excitation are synchronized in order to the more piezoelectric voltage increase, the more vibratory acceleration is reduced. Figure 9. Mode 2 resonance for a magnetic excitation and a synchronous piezoelectric excitation Piezoelectric inserts are able to reduce the spectrum of vibratory acceleration and so, decrease the resonance. Table II. shows the relative vibration damping for sinusoidal excitations (magnetic and piezoelectric) at stator mode 2 resonance (Figure 5.) at 8200 Hz. Like Figure 7. has shown, piezoelectric actuators have a great influence on stator vibration but also on 3D part (Yoke frame and End shields). Note that piezoelectric actuators have been supplied in order to generate 2D forces (and consequently 2D strain) and at this frequency, the nodal strain is essentially 2D. Table III. shows the relative vibration damping for sinusoidal excitations (magnetic and piezoelectric) at yoke frame resonance (Figure 6.) at 6600 Hz. Contrary to the stator mode 2 resonance, the strain generated on this frequency is essentially 3D" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000240_s0263574701004027-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000240_s0263574701004027-Figure1-1.png", "caption": "Fig. 1. Stewart platform [8].", "texts": [ " They are not suitable for practical use in a production environment, where the measurement and calibration method should be simple and robust. Using an external laser measuring device to determine the actual accuracy of a Stewart platform, a practical and simple leg length compensating calibration method, that improves the accuracy of the Stewart platform by a magnitude of around 7, is proposed. The procedures and computation algorithms of the calibration method are shown. KEYWORDS: Stewart platform; Calibration; Parallel robot; Numerical analysis. The Stewart platform1 shown in Figure 1 is a six degrees of freedom parallel manipulator composed of six extensible legs connecting a moving platform to a fixed base platform. It has received considerable attention in numerous applications2\u20136 as it is anticipated that parallel manipulators should have some advantages compared with serial link manipulators including greater accuracy. However, J. Wang and Oren Masory7 indicate through simulation results that the Stewart Platform is no more accurate than a serial manipulator with similar nominal dimensions" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000364_robot.1988.12028-Figure16-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000364_robot.1988.12028-Figure16-1.png", "caption": "Figure 16: Changes in Regions with Contact Length.", "texts": [ " The effect of the extra contact is that now T is a range of possible contact angles at the vertex. If the kinematics of the hand allow the second finger to contact the object in T while maintaining contacts 1 and 5, then squeezing will cause the object to break both support contacts. Importantly, this results in a stable force closure grasp [18]. It is also important to note that the length of the translation window has a direct effect on the size of T. Therefore an attempt should always be made to make the translation window as large as possible. Figure 16 shows how the size of the translation region grows with the length of the contact along a flat finger. 3. MANIPULATION PLANNING An object may be manipulated in an infinite number of ways to achieve a desired grasp. One way to begin is by choosing an initial grasp in the translation region. During the first instant of manipulation, i . e . lift-off, the second finger could be moved toward the object with the first finger held fixed. After lift-off, the translation window and the translation regions still exist and can be used for manipulation planning" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001864_13873950412331318071-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001864_13873950412331318071-Figure3-1.png", "caption": "Fig. 3. x-y-trajectory of the play (a) and the one-sided dead-zone operator (b).", "texts": [ " It is defined as the concatenation of a Prandtl-Ishlinskii hysteresis operator H and a Prandtl-Ishlinskii superposition operator S and in vector notation is given by G\u00bdx \u00f0t\u00de \u00bc S\u00bdH\u00bdx \u00f0t\u00de \u00bc wS T SrS \u00bdwH T HrH \u00bdx; zH0 \u00f0t\u00de: \u00f0104\u00de The operator H consists of a weighted linear superposition of d\u00fe 1 elementary play operators HrH, which are included in Equation (104) in the d\u00fe 1-dimensional vector HrH . The rate-independent characteristic of the play is characterised by the thresholddependent x-y-trajectory; see Figure 3a. The weights wHi, the thresholds rHi and the IDENTIFICATION OF LINEAR ERROR-MODELS 79 D ow nl oa de d by [ FU B er lin ] at 0 2: 05 1 4 M ay 2 01 5 initial values zH0i, i \u00bc 0 : : d of the play operators are considered in the vector notation (104) by the vector of weights wH T \u00bc \u00f0wH0 wH1 : :wHd\u00de, the vector of thresholds rH T \u00bc \u00f0rH0 rH1 : : rHd\u00de with rH0 \u00bc 0 and the vector of the initial values zH0 T \u00bc zH00 zH01 : : zH0d\u00de. The outputs of the elementary operators zHi \u00bc HrH \u00bdx; zH0i , i \u00bc 0 : : d represent the inner system state or the memory of the discrete-threshold PrandtlIshlinskii hysteresis operator. The memoryless superposition operator S describes the deviation of the real characteristic from the odd symmetry property of the operator H [2]. It consists of the weighted linear superposition of 2l\u00fe 1 one-sided dead-zone operators SrS, which are included in Equation (104) in the 2l\u00fe 1-dimensional vector SrS. The rate-independent transfer characteristic is characterised by the threshold-dependent x-y-trajectory shown in Figure 3b. The weights wSi and the thresholds rSi, i \u00bc l : : \u00fe l of the onesided dead-zone operators are considered in the vector notation Equation (104) by the vector of weights wS T \u00bc \u00f0wS l : :wS0 : :wSl\u00de and the vector of thresholds rS T \u00bc \u00f0rS l : : rS0 : : rSl\u00de with rS0\u00bc 0. The corresponding compensator G 1\u00bdy \u00f0t\u00de \u00bc H 1\u00bdS 1\u00bdy \u00f0t\u00de \u00bc w0 H T Hr0 H \u00bdw0 S T Sr0 S \u00bdy ; z0H0 \u00f0t\u00de \u00f0105\u00de exists uniquely in the convex polyhedron O \u00bc wH wS 2 Rd\u00fe1 R2l\u00fe1 UH O O US wH wS uH uS o o \u00f0106\u00de and follows from the inversion ofH and S and the concatenation of S 1 andH 1 [2]" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002500_12.11.710-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002500_12.11.710-Figure1-1.png", "caption": "Figure 1. Amount injected vs height of peak for methylamine (EI), ethylamine (0), propylamine (Q). Flame ionization detector; range 1, attenuation 1. Size of injection samples, 0.5 I. Column, 1.4 x 2 mm; Carbopack + 0.3% KOH + 0.5% PEI 40 M; temperature, 68\u00b0C; linear carrier gas velocity, 8.5 cm/sec.", "texts": [ " The chromatographic apparatus was connected to a Leeds and Northrup Speedomax Model G recorder operating with a 1 millivolt, full-scale response. At the maximum sensitivity of the amplifier system (1 x 1) about 1.5 pA gave a full-scale response of the re- corder. The artificial mixtures of eluted compounds were prepared from various commercial sources. Because columns were altered upon contact with aceton or methanol, non-aqueous mixtures were prepared by using diethyl ether. A 10 \u00b5l SGE syringe (Melbourne, Australia) was used. Resuits and Discussion In Figure 1 calibration curves ranging from 0.5 to 10 nanograms of methylamine, ethylamine and propylamine eluted on 0.5% PEI 40 M + 0.3% KOH modified GCB are shown. As can be seen, correct straightline curves passing through the origin were obtained, thus making evident the absence of anomalous effects of adsorption. As a first attempt, only PEI 40 M was added to Carbopack. Untailed peaks for amines gave evidence that PEI by itself was able to deaotivate the carbon surface. There was also evidence, however, of a certain chemical instability in this kind of column, as tiny amounts of oxygen injected into the column provoked the appearance of a decomposition peak of the liquid phase" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000457_978-3-642-55848-1-Figure9.56-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000457_978-3-642-55848-1-Figure9.56-1.png", "caption": "Fig. 9.56. Scheme of the robot arm with the coordinate frames", "texts": [ " The robot is controlled by a hybrid law: the PD position con trol law in the unconstrained sub-space, and by the I force control law in the con strained subspace. For simplicity, we assume that the control is applied to the first three joints only. Thus, we model a three-link robot arm as a multibody system. The wrist and tool together are modelled as a point body. Compliance is modelled in the direction orthogonal to the wall by a Contact component of Sec 6.4.1. A schematic diagram of the robot arm is given in Fig. 9.56. This is an anthro pomorphic arm with three revolute joints powered by servo-actuators. The co ordinate frames used for description of the motion are also given in the figure. The geometrical and and inertial parameters are given in Fig. 9. 57 and Table 9.12 and are based on [23, 24]. The distance of the wrist centre to the wall is w = 0.1 m. 386 9 Multibody Dynamics 9.6.2 Model of the Robot System We next give a brief description of the model. The complete model is held in the BondSim program library under the project name Robot Hybrid Control", " The joint components are created as copies of the 3D joint component of Sect. 9.5.4 (Figs. 9.48 - 9.51). But there are some differences from joint to joint. The general structure is the same as given in Fig. 9.48, but the Joint rotation compo nents differ because the rotation matrices of the body (link) frames change from joint to joint. For every joint a specific transformer component is used. We show this for Joint 2, which rotates the frame of Link 2 with respect to the frame of Link1. The rotation matrix of these two frames is given by (Fig. 9.56) [ COSQ2 -sinQ2 0] R21 = sinQ2 cosQ2 0 o 0 1 The corresponding transformations are given by (Fig. 9.51) f1 = R21f2 } e 2 = R~1e 1 (9.132) (9.133) These transformations are represented by the components shown in Fig. 9.60. There are four transformers corresponding to the four nonzero elements in the first two rows of the rotation matrix in Eq. (9.132). 388 9 Multibody Dynamics Every effort and flow vector component in Eq. (9.133) is represented by a sepa rate effort or flow junction, and the transformers are connected between them", " Starting from the port where the feedback is connected we need to separate first the joint position signals from the velocity. This is achieved by two components n composed of nodes only that are used to extract the signals and then pack them again as 3D vectors of, respectively, joint angles (9.134) and velocities The positional part is converted to the vector of tool tip coordinates with re spect to the base frame using the relations of direct kinematics of the manipulator. For the anthropomorphic configuration of Fig. 9.56, these are given by [ L2 cosq1 cosq2 + L3 cosq1 sin(q2 + q3) 1 rtool = L2 sin q1 cos q2 + L3 sin q1 sin( q2 + q3) L2 sinq2 -L3 COS(Q2 +Q3) (9.136) These relationships are represented by the component DK that is composed of function elements and summators that express the coordinates of the tool tip in the base frame as a function of the joint coordinates. 9.6 Motion of an Anthropomorphic Robot Arm Under Hybrid Control 393 We also need the transformation of the joint velocities to the velocity of the tool tip with respect to the base frame" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002145_s0065-2911(08)60046-6-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002145_s0065-2911(08)60046-6-Figure8-1.png", "caption": "FIG. 8. Diagram showing how the sphere of influence results in large volumes of fluid being affected during the effective stroke (a), while smaller volumes are affected in the recovery stroke (b). Fig. 8(c) shows how the near-field effects contribute to fluid flow within the ciliary layer. Modified from Blake (1972).", "texts": [ " Near-field effects concern the behaviour of fluid within the field of cilia, while far-field effects contribute to the propulsive velocity of an organism. For an element of a cylinder on an infinite plane surface, the near-field is a sphere of radius 0.5h where h is the height of the element above the surface. Hence, in the effective stroke, an individual cilium influences a relatively large volume of fluid in terms of near-field effects but this volume is considerably reduced during the recovery stroke, when much of the cilium is close to the surface (Fig. 8) . By considerations of the near-field effects, a qualitative assessment of the fluid flow for a field of cilia can be obtained. Near the surface to which the cilia are attached, near-field effects due to both the effective and recovery strokes contribute, so that an oscillatory motion of the fluid is to be expected in this region. Further from the surface, the fluid is affected by the effective stroke only so that unidirectional flow should be observed. More detailed hydrodynamic analysis of both models suggests that there should be a net back-flow of fluid close to the surface to which the cilia are attached" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000925_0266-352x(90)90029-u-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000925_0266-352x(90)90029-u-Figure5-1.png", "caption": "FIGURE 5. Incremental objectivity problem.", "texts": [ " At the opposite for the three-dimensionai case the yield surface is conical and a refined integration scheme is needed. We have implemented a division of the time step in some subincrements and in each sub-increment we arc performing a two step generalised mid-point integration scheme. This scheme is second order accurate (RICE and TRACEY[21], MARQUES[22], CHARLIER[1]) An other point to be discussed in the incremental objectivity: for a finite time step what is the reply of the time integration scheme under a rigid body rotation (implying of course the two bodies) ? As one can see on the figure 5 if constant velocity of the nodal points is supposed during the step, some strains will appear in the interface for a rigid body rotation. More precisely no tangential displacement will occurs but some normal displacement. For undilatant interface (metal contact) this normal displacement will produce reversible stresses returning at the end of the step to their initial value. But for dilatant material, this could induce some irreversible behaviour. Therefore it seems to be better to use a mean normal strain" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002595_tpas.1973.293637-Figure7-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002595_tpas.1973.293637-Figure7-1.png", "caption": "Fig. 7. A connection diagram of A-Y transformer banks", "texts": [ " (Appendix II) do s 4' - 4' q sinb ) - x id (15) q0s ( wdt sin' + Yqtcosb ) xi (16) Plyd0s Woj(r+rt+rs) do 4'qosV (17) P qes w0 (r+rt+rs)iqo - 'dos+ es (18) The differential equation of motion for the machine is -Hp2b+-Dpb -T T(I9 w w m e (19) o o The second-order differential equation is written as two firstorder equations as follows: p( ) T Te D A (20) pb \u00b0 (21) And then, the electrical torque is computed from the following equation: T i4IV i4' - i ' - i4' (2e q d d tq q dt d qt (22) If the A-Y transformer banks exist as shown in Fig. 7, the phase currents at the generator terminals are calculated in terms of d- and q-axis quantities from equations 23 to 25. (2) Four Line-to-Ground Fault The performance equations, which are different from those for steady-state, are given in equations 26 to 35. The new variables, 4d f and Oqof, are do and qCaxis components of flux linkages at grounded point through an impedance, Zf at the fault, respectively. (Appendix II) v m (4v cosb -PY sinb) -x idoa3dt o qt s idos v = ('v sinb +'vcos)) -x i qos dt qt s qoS Plydo s {(r+r t)i + rid + yr qo4 qos r+ t dio+8 qod los qs eJ -V" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000793_s0022112001004037-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000793_s0022112001004037-Figure3-1.png", "caption": "Figure 3. Coordinate systems used in the analysis of squid locomotion.", "texts": [ " The time-varying outline of the squid profile from each squid swimming sequence was extracted automatically with a PC, frame-by-frame, using a peak grey-level gradient searching algorithm (Anderson 1998). The algorithm subjects images to a standard Prewitt grey-level gradient filter, and then searches the gradient matrix for the contour of maximum gradient that represents the outline of the squid. This works well for high-contrast image sequences. Good contrast was achieved with front lighting and a black felt background. 3. Fluid dynamic model 3.1. Coordinate systems Three coordinate systems were used in this analysis (figure 3). The x- and z-axes represent the fixed reference frame of the camera field of view and flume. The flume flow velocity, U, is in the negative x-direction. The squid swam into the flow in the positive x-direction. The z-axis is the vertical position in the water column. The second coordinate system, the \u03be- and \u03b6-axes, has its origin at the apex of the mantle. Recall that this is the end of the squid which usually leads in sustained swimming and escape responses. The \u03be-axis is the long axis of the squid" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003700_1.4002456-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003700_1.4002456-Figure1-1.png", "caption": "Fig. 1 Cutting width orthogonal to the feeding direction is maximized in point milling", "texts": [ " 132, OCTOBER 2010 om: http://manufacturingscience.asmedigitalcollection.asme.org/ on 01/29 determined based on the relative position of the tool swept curve at the sampled positions with the ideal part surface. There are two requirements for this positioning: \u2022 First, the material, as large as possible, is removed at each local region. This requirement is transformed into two different objectives for two main types of milling, respectively: a For point milling, the cutting width orthogonal to the feeding direction should be maximized see Fig. 1 ; b for flank milling, the tool is orientated as close as possible to the part surface, or the maximal deviation between the tool swept curve and the part surface is minimized see Fig. 2 . \u2022 Second, the tool has no collision or local gouges with either the part surface or the environment. The optimization problem can now be formulated as for point milling max i, i i W li,S 2 such that li where i , i , i=1,2 , . . . ,m is a set of parameter pairs specifying ITAs, li is the ith swept curve, and S is the ideal part surface" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001247_robot.1990.126127-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001247_robot.1990.126127-Figure1-1.png", "caption": "Figure 1", "texts": [], "surrounding_texts": [ "Two applications need to determine the minimum inertial parameters: -The determination of the set of minimum inertial parameters of robots contributes at reducing the computational cost of the dynamic models [ 1,. . .,5], -The minimum inertial parameters constitute also the identifiable inertial parameters. Its determination simplifies the identification of the inertial parameters of robots and increases the robustness of the identification process [5 , .... 101. These two applications are directly related to the implementation of control laws based on the dynamic model of robots [ 1 1,12,13]. We have presented a general method to determine the set of minimum inertial parameters of serial or tree structured robots [14,15,16]. At the same time similar results concerning the special case of serial robots whose successive axes are perpendicular or parallel have been given by Mayeda et al.[ 17.1 81. Numerical method conceming this problem have also been presented [19,20]. The aim of this paper is to extend our symbolic algorithm to calculate the minimum inertial parameters for robots with parallelogram closed-loops.\nThe system to be considered is a closed-loop mechanism. The description of the system will be carried out by the use of the notation given in [21,22]. The system is composed of n+l links and L joints, link 0 is the base while link n is an end effector. The number of closed-loops denoted B is equal to L - n. The number of motorized joints is denoted m. To describe this system we construct, at first, an equivalent tree structure system by virtually cutting each closed-loop at one of its joints, then the constraint equations of the closed loops will be derived.\n2-1 Description of the equivalent tree structure\nA coordinate frame j is assigned fixed with respect to iink j. The Zj axis is along the axis of joint j, the Xj axis is along the common perpendicular of z* and one of the succeeding joint axes on the same link. We use the symbol a(i) to indicate the link antecedent to link j.\nCH2876-1/90/0000/1026$01.00 0 1990 IEEE\nThe frame j coordinate will be defined wi-th respect to frame i. with i =a(j), by the following (4x4) matrix 'Tj :\n'Tj = Rot (2.3) Trans (Z.bj) Rot (x. aj) Trans (x. dj) Rot (z, ej) Trans (2, rj)\n'Tj {oi:o i y ] =\ncyjcej-syjcajsej -cyjsejsrjca,cej Srjsaj djCyj+rjSrjSaj\nSy,Cej+Cy,Ca,SO, srjSej+Cy,Ca,\u20acej -QjSaj d,Srj+y,Saj\nSajSO, sajce, Caj rjCaj+bj 0 0 0 1 [ (1) where: The geometric parameters : bj, yj, aj, dj, e j and rj can be deduced from figure (l), 'Aj defines the orientation of frame j with respect to frame i, it is given as:\nwith A(z, 8) is the (3x3) upper left matrix of Rot@. 3) and iPj defines the position of the origin of frame j with respect to frame\nIf Xi is the common perpendicular on zi and Z j then the parameters bi and yi will be equal to zero, this is always the case in serial robots. The joint variable j is denoted qj such that:\nwhere: o j = 0 if joint j is rotational. o j = 1 for j translational,\n'Aj = 8) A(x, aj) A@, Oj) (2)\n1.\nqj = Oj ej + oj rj\n1026\n--", "and Gj = (1-j ). The vector.of the joint variables of the equivalent tree structure system IS given as:\n2-2 Description of the closed-loop structure\nThe opened joints are numbered f\" n+l to L. For each opened joint k, we define a frame k fixed on one of the links i or j connected by this joint. The axis Zk is along the axis of the joint k, while xk is along the common perpendiculair of zk and q. where i the link on which this frame is supposed fixed. Frame k will be defined with respect to frames i and j using the same parameters defined in section 2-1. The parameters defining frame k with respect to frame j will get the subscript k as usual. The parameters defining frame k with respect to frame i are constant and will get the subscript k+B. Thus a(k) = j and a(k+B)= i. This is equivalent to the definition of a frame k+B aligned with frame k. Thus two more frames per loop will be defined. The constaint equations can be obtained by equating the product of the transformation matrices along the loop by the identity matrix [22,23].\n3- D e t t\nThe minimum inertial parameters are defined as the minimum set of constant inertial parameters to calculate the dynamic model of the robot. They can be obtained from the standard inertial parameters by eliminating those which have no effect on the dynamic model and by regrouping some other parameters. The dynamic model of a closed-loop structured robot can be obtained as function of the equivalent tree structure dynamic model using the following relation [22,23]:\nwhere: rm i s the (mxl) vector of the torques (or forces) of motorized joints, qm is the (mxl) vector of the motorized joint variables,\nC - \"' is the jacobian matrix of the joint variables qe with\nqtf:[91 92 * * e %IT (3)\n. . . . . .\nr,,, = GT rtr (4)\n-6 E S p e C t tO qm rtr is the (nxl) vector of the joint torques (or forces) of the equivalent tree smcture. The torque rtr can be obtained from the dynamic model of the equivalent tree structure as a linear relation with respect to the inertial parameters by [4] :\n(5 ) X is the standard link inertial parameters vector. Since C is function of the geometric parameters only, we conclude from (4) and (5) that the relations defining the minimum inertial parameters of the equivalent tree structure system will be conserved. Supplementary elimination or regrouping of parameters may take place for the parameters of the links belonging to the closed-loops owing to the constraint equations between its variables. In the following we recall the results obtained for the tree structure systems [15,16] and then we illustrate how to take into account the closed-loops.\n3-1- The minimum inertial parameters of the equivalent tree structure\nThe standard inertial parameters are composed of the elements\n- JJj the inertia matrix of link j about the origin of frame j,\nrtr = w (qtr. i t rgtr) x\nof:\nreferred to frame j, - JMSj the first moments of link j about the origin of frame j. referred to frame j. - Mj the mass of linkj. We denote:\nXXj XYj XZj\n(6)\n(7) The total energy of the structure is given as: H = E + U (8) with E and U denote the kinetic and potential energy jMSj = [ MXj MYj MZj]T\nloj the angular velocity of link j, referred to frame j. JV. the velocity of the origin of the link j fixed frame, reiemd to frame j. og is the acceleration of gravity referred to frame 0. The energy H is linear in the inertial parameters, so we can\nwhere Xi is an inertial parameter, and c the number of standard inertial parameters.\n3-1-1- Parameters having no effect on the dynamic model\nAn inertial parameter Xi has no effect on r, i.e it is not an element of the minimum inertial parameters [14, 15, 161, if the corresponding:\nThe inertial parameters satisfying this condition belong to the links near the base side. They can be detemined easily by hand or automatically by computer. Simple rules to determine most of them without calculating the dynamic model nor the energy are given in [15,16]. For the sake of the application of section (5 ) we just give the following two rules: i- If joint k is translational and if a(k)=O then XXk, XYk, XZk,\ndynamic model. ii- If joint k is rotational and a(k)=O then the parameters XXk, XYk, xzk , YYk, Yzk, W k , MZk and Mk have no effect On\nthe dynamic model. If the axis of this link is along the gravity. the parameters h'lxk, MYk will have no effect also.\n3-1-2- Regrouping the inertial parameters\nThe regrouping of an inertial parameter Xi to some other parameters Xil, ..., Xk can be carried out by detecting the linear dependence of the function DHi. So if [14,15,16]:\nDHi = constant (12)\nYYk, Yzk. zzk, m k , MYk and MZk have no effect On the\nr DHi=tirDHil+ ... +tiDHir= Ctik DHik (13)\nk=l with tik = constant, then Xi does not belong to the set of minimum inertial parameters, it will be regrouped to the parameters Xik . The new value of X& will be denoted XR& where:" ] }, { "image_filename": "designv11_32_0001195_s0263574700003593-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001195_s0263574700003593-Figure2-1.png", "caption": "Fig. 2. Two convex polyhedra (most of the nf, n,r are not shown).", "texts": [ ") The sum of the number of vertices w, in face F,, over all faces i of a convex polyhedron, is M 1 = 1 f = Af \u2022 (average number of vertices per face) where M is the number of polygonal faces on the polyhedron. As stated above, we shall calculate the minimum distance between pairs of convex polyhedra. If As is the M x 3 matrix of normal vectors defining S = {s | As s s d5} in (1), and AT is a matrix defining another convex polyhedron T, with N faces, then we wish to minimize LUi(sk-tk) 2, where As ssd s , As(Mx3), s(3 x 1), AS{M x 1); and AT t < dr, .4r(iV x 3), t(3 x 1), dT(N x 1). See Figure 2. If we view x = as a vector in R6, the minimisation problem stated above is min (C \u2022 x) where C is a 6 x 6 matrix: C = 1 0 0 - 1 0 . 0 0 1 0 0 - 1 0 0 0 1 0 0 - 1 - 1 0 0 1 0 0 0 - 1 0 0 1 0 0 0 - 1 0 0 1 The matrix \\AS 0.1. IS L 0 AT\\ (M + N) x 6, and the right hand side Td5l r is a vector with M + N components: together they define a linear constraint set. The objective function x \u2022 (C \u2022 x) = \u00a3*_! (sk \u2014 tk) 2 is positive semi-definite, and the minimization problem can therefore be solved using a quadratic programming method, such as Lemke's method" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002158_ias.2005.1518846-FigureA-3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002158_ias.2005.1518846-FigureA-3-1.png", "caption": "Fig. A-3: Test set-up", "texts": [], "surrounding_texts": [ "Three motors were used for the analysis and the tests: Motor # 1: 4 phase; 8/6; rated torque: 2.0 Nm; base speed: 2,500 rpm; 42V. Motor # 2: 3 phase; 12/8; rated torque: 1.0 Nm; base speed: 3,000 rpm; 42 V (Fig. A-1). Motor # 3: 4 phase; 8/6; rated torque: 0.8 Nm; base speed: 2,500 rpm; 12V; 8 turns per pole (Fig. A-2). IAS 2005 2740 0-7803-9208-6/05/$20.00 \u00a9 2005 IEEE" ] }, { "image_filename": "designv11_32_0002092_1-4020-3393-1_14-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002092_1-4020-3393-1_14-Figure3-1.png", "caption": "Fig. 3. Example of relative coordinates", "texts": [ " Thus, independent coordinates are not suitable of unequivocally determine the position of the multibody system. Another problem involved with the use of independent coordinates is the variation of F during simulation. This is not a remote possibility and may happen, for instance, in linkages with particular dimensions or when modeling stiction in kinematic pairs. The most common types of coordinates currently used to describe the motion of multibody systems are: - Relative coordinates. The position of each element is defined with respect to the previous one (e.g. Fig. 3). These coordinates allow numerical efficiency due to their reduced number, but lead to small order and expensive to evaluate dense matrices. They are specially suited for open kinematic chain systems. The control of movement between adjacent parts is easy. The choice of variables requires a preprocessing, whereas a postprocessing is needed to determine the absolute motion of all the parts. The set of coordinates used by the well known Denavit-Hartenberg notation [35] belong to this cathegory. Noteworthy multibody dynamics formulations based on relative coordinates are reported in [17, 32]", " The algebraic structure of the constraint equations depends on the type of coordinates implemented. The conditions used to generate the equations of constraints depend also on the type of coordinates used. For some set of coordinates previously discussed the constraint equations for the kinematic modeling of a slider-crank are reported in the following. When relative coordinates {q} = { \u03b81 \u03b83 s4 }T are used, loop closure conditions are often imposed. For example, with reference to the nomenclature of Fig. 3, the following equations can be written2 \u03a81 \u2261 a1 sin \u03b81 \u2212 a2 sin \u03b83 \u2212 s4 = 0 (4) \u03a82 \u2261 a1 cos \u03b81 + a2 cos \u03b83 = 0 (5) Let ai, \u03b1i, \u03b8i, si be the Denavit-Hartenberg parameters, and \u03b1\u0302i = \u03b1i + \u03b5ai (6) \u03b8\u0302i = \u03b8i + \u03b5si (7) their dual counterparts (\u03b52 = 0). With reference to Fig. 6, the links coordinate-transformation matrix takes the form [34] 2 With this approach, the coordinate \u03b82 is not involved. [ T\u0302 ]i i+1 = \u23a1\u23a3 cos \u03b8\u0302i \u2212 cos \u03b1\u0302i sin \u03b8\u0302i sin \u03b1\u0302i sin \u03b8\u0302i sin \u03b8\u0302i cos \u03b1\u0302i cos \u03b8\u0302i \u2212 sin \u03b1\u0302i cos \u03b8\u0302i 0 sin \u03b1\u0302i cos \u03b1\u0302i \u23a4\u23a6 (8) The closure condition of the slider-crank chain is expressed by the matrix product[ T\u0302 ]1 2 [ T\u0302 ]2 3 [ T\u0302 ]3 4 [ T\u0302 ]4 1 = [I] (9) where [I] is the unit matrix" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000364_robot.1988.12028-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000364_robot.1988.12028-Figure3-1.png", "caption": "Figure 3: Quantities for Edge Liftability Regions.", "texts": [ " Note that in the Figure, T only occurs at the boundaries between B3 t2 c o s ( v i ) + t 3 sin(yr1 - ~ 2 ) . C24 = 2.2 Liftabil i ty Regions of Polygons A polygon can be used to approximate any twod imens iona l ob jec t with arbitrary prec is ion . Therefore we will discuss their liftability regions in detail and then generalize the results to arbitrary cu rves . The region S may be determined by realizing that it is the portion of the perimeter for which the inward contact normal has a horizontal component with the same sense as that of f l . In Figure 3, S is comprised of edges 1, 2, and 3, vertices 2 and 3, and a portion of vertex 4 (What is meant by a portion of a vertex will be made clear later). If the second finger contacts the polygon in S, squeezing will cause the polygon to slide to the left. The regions, J, B3, B4, and T are restricted to the remaining perimeter. Consider the kth edge of the polygon in Figure 3. The points, p, lying on the line [k through the edge can be written in parametric form as (6) where s is the fraction of the distance along the edge from vk to v k + l . The line, I p p d . is the unique line which contains the summing point, q , and is perpendicular to Ik. The intersection is the point on the kth edge where the moment arm, 12. of the second contact force is zero. The variables s and t2 are linearly related by where a is the value of s at the intersection of l k and Ippd. Along the edge, c23 and c24" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002400_j.mechmachtheory.2006.01.005-Figure6-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002400_j.mechmachtheory.2006.01.005-Figure6-1.png", "caption": "Fig. 6. Experimental layout with drive and brake wheel.", "texts": [ " ; \u00f025\u00de where kig \u00bc givb gi and fs is the correction factor. Elimination of F 0t by combining Eqs. (23)\u2013(25) gives the following correction factor: fs \u00bc apEh 4\u00f01 m2\u00dep ; p \u00bc g0 2 a\u00fe b\u00f0 \u00de2 \u00fe vb Xn i\u00bc1 gi a\u00fe b kig 1 exp a\u00fe b kig : \u00f026\u00de The stiffness of the model is compensated by scaling the Maxwell parameter with the factor of Eq. (26). Experiments were conducted to measure the actual relationship between traction and slip at a drive station in the E\u2013BS and validate the presented model. During the experiments two wheels were used, see Fig. 6. One wheel made from steel represents the drive wheel and is driven by an electric drive motor. The other wheel, representing the belt cover, has a rubber layer (h = 30 mm) vulcanised to it. It is also connected to an electric motor that is used as an adjustable brake. Strain gauges on each motor shaft measure the produced torque. An adjustable spring was also used to pull the brake wheel onto the drive wheel, making it possible to control the contact force. The diameters (Dd = Db = 500 mm) of both wheels were chosen such that their contact patch, created when pressed against each other, is comparable with the patch between the drive wheel (D = 250 mm) and the belt in the E\u2013BS" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0001183_cdc.1989.70628-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001183_cdc.1989.70628-Figure4-1.png", "caption": "Fig. 4 Collision Free Trajectories", "texts": [ " Let the preassumed paths be: r1 = 1 + S I , p1 = (1 - 2sl)n/2 and r2 = l+sz, pz = (2s*-l)n/2, 0 5 s1 5 1, 0 5 sz 5 1. Clearly, two paths intersect and collisions may occur between the two robots moving along these two paths. For simplicity, the torque constraints are assumed to be Idzrl/dtzl 5 l (mz/s) , IdZPl/dtZI 5 3, ld2rz/dtZI 5 The outputs of PLANNER are plotted in Figs. 2 and 3. RI was delayed by 0.81 sec. and the resulting total finish time was 2.86 sec. To see how the two robots avoid collision more clearly, their movements along the optimal collision-free trajectories are plotted in Fig. 4 and their movements along the minimum time trajectories obtained in Step 1 of Algorithm 1 (i.e., without delaying RI) are plotted in Fig. 5. Note that a collision occurred in the latter case. Clearly, both assumptions of the theorem are satisfied for this example. Thus, from the optimality of Algorithm 1, the trajectories obtained will ensure that two robots reach their ending positions along the preassumed paths in minimum time. However, because of the path-velocity decomposition used in the algorithm, the trajectories may not be overall optimal" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002939_s11071-007-9215-4-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002939_s11071-007-9215-4-Figure8-1.png", "caption": "Fig. 8 Experimental setup", "texts": [ " Then, by keeping the excitation frequency constant and varying the offset of the excitation \u03b81off from 0 to \u03c0/4 (from (a) to (a)\u2032 along the arrows in Fig. 7), the minimum value of the distance rtip = rmin at the point (a)\u2032 can be realized. The magnitude of the minimum value for the Springer parameters of the after-mentioned experimental apparatus is rtip = 0.6373. In this way, the tip can reach any point in the clarified reachable area described in Fig. 4. 4 Experiments 4.1 Experimental setup The validity of the proposed control method is experimentally examined by using an apparatus shown in Fig. 8. The base is levitated above a planar glass by air bearings [New Way Air Bearings, Flat air bearing (40 mm Dia.)] and the links are configured to be horizontal so that there is no gravity effect. Compressed air is supplied to the air bearings from the air tanks on the base. The first link is mounted on the base through a DC motor with an encoder [Maxon Motor, RE40 + MR Encoder (maximum torque: 2.29 Nm)], and the angle of the first link with respect to the base is controlled under state feedback with respect to \u03b81 and d\u03b81/dt (active joint)" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002238_s00170-006-0517-3-Figure5-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002238_s00170-006-0517-3-Figure5-1.png", "caption": "Fig. 5 Single point-line meshing gear", "texts": [ " The curvature radius of the contact point When a pair of gears reach meshing terminal point J, the curvature radius of the small and big gear wheel in the mesh point must be smaller than that of the big gear wheel in point J so as to enlarge the contact area in protruding and concave gears meshing and to avoid the interference. \u03c1f 1 \u03c1f 2 Point-line meshing gear accomplish the following three kinds of forms according to the teeth meshing principle: 1. Single point-line meshing gear\u2014usually called just point-line meshing gear\u2014can accomplish the oblique tooth, or the straight tooth, as shown in Fig. 5. 2. Double point-line meshing gear, namely, half of the concave tooth outline of the transition curve, the other involute part is protruding tooth outline. After meshing the teeth mutually, they form double point meshes and the thread meshes. The double point-line meshing gear can also be accomplished as straight tooth and oblique tooth, as shown in Fig. 6. 3. \u2018Few tooth number\u2019 of point-line meshing gear. Lowest tooth number of its small gear wheel can achieve 2\u20133 teeth, thus its drive ratio can be very large (see Fig" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002073_s00366-005-0008-4-Figure12-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002073_s00366-005-0008-4-Figure12-1.png", "caption": "Fig. 12 Single frame of fourbar animation for the first branch", "texts": [ " Another difference is that there is an additional argument in member function setCouplerPoint(). This third argument, TRACE_ON, is a macro used to specify tracing of the coupler point. Note that the member function animation() contains a single integer argument. This number refers to the branch number of the fourbar linkage. Depending on its type, a fourbar linkage may have up to four branches. Since the fourbar defined in the problem statement is a Grashof crank-rocker, it has only two branches. Figure 12 shows one frame of animation for the first branch of the fourbar mechanism, whereas Fig. 13 is an overlay of all the frames of animation. Likewise, Fig. 14 is one frame of animation of the second branch, and Fig. 15 shows all of the animation frames. An object-based mechanism toolkit has been developed. The toolkit consists of animation program QuickAnimationTM and a collection of classes for design and analysis of commonly used planar mechanisms. Written in Ch, a C/C++ interpreter, the Ch Mechanism Toolkit is useful for solving practical engineering problems in design and analysis of mechanisms" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003998_09544062jmes1329-Figure8-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003998_09544062jmes1329-Figure8-1.png", "caption": "Fig. 8 The contact area and notations for the collet geometries of a gas spindle system", "texts": [ " The contact area of the tool-holder can be calculated using equations (4) and (5) A1 = 1 2 R2 1\u03b8 = 1 2 ( D/2 sin \u03b1 )2 \u00d7 2\u03c0 sin \u03b1 = D2\u03c0 4 sin \u03b1 (4) A2 = 1 2 R2 2\u03b8 = 1 2 ( d/2 sin \u03b1 )2 \u00d7 2\u03c0 sin \u03b1 = d2\u03c0 4 sin \u03b1 (5) where A1 and A2 are conic areas with lengths R1 and R2, respectively, \u03b8 is the conic angle, D and d are the larger and smaller base diameters of the conic section of the tool-holder, and \u03b1 is half of the taper angle. Note that all the taper angle terms in this article refer to angle \u03b1 instead of the full taper angle. Typically, as indicated in Fig. 8, four slots cut into the collet of the high-speed gas spindle system allow the collet to expand when a drill bit is inserted. This study disregarded the area of these slots when calculating the contact area of the collet\u2013spindle interface. By disregarding the slot area, the actual contact area can then be obtained using equation (6), which is derived from equations (4) and (5) A = \u03c0(D + d)L 2 cos \u03b1 \u2212 mlL cos \u03b1 (6) where A (mm2) is the true contact area of the collet\u2013 spindle interface, L (mm) the axial length of the cone, m the number of slots, and l (mm) the width of each slot", " However, the difference gradually increased as the deflection increased, reaching 8.4 per cent at a deflection of 0.8 mm (75 per cent of free height) of the stacked disc springs where the Proc. IMechE Vol. 223 Part C: J. Mechanical Engineering Science JMES1329 \u00a9 IMechE 2009 at UNIVERSITE DE SHERBROOKE on April 11, 2015pic.sagepub.comDownloaded from forces were 1888 and 1730 N for the experiment and FEA, respectively. The contact pressure on the collet\u2013 spindle interface with a variety of taper angles (refer to angle \u03b1 in Fig. 8) from 7 to 3\u25e6 was calculated by taking each of the forces up to 1888 N in the experimental data into equation (9) to obtain the results presented in Fig. 14. The load applied to the disc spring after being transmitted through the drawbar mechanism was the drawbar force acting on the collet. Thus, Fig. 14 shows that the contact pressure on the collet\u2013 spindle interface was higher for smaller taper angles under a specific drawbar force. The increase in the contact pressure became more notable when the taper angle was incrementally reduced from 7 to 3\u25e6" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000001_s0389-4304(01)00108-4-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000001_s0389-4304(01)00108-4-Figure1-1.png", "caption": "Fig. 1. Measuring bench.", "texts": [ "r 2001 Society of Automotive Engineers of Japan, Inc. and Elsevier Science B.V. All rights reserved. In this study, we established a technique for precisely measuring sliding loss in the timing chain and the loss in the meander-preventive timing chain guides of an engine to classify timing chain sliding loss into components attributable to sliding friction in the guides and in other parts. We also studied the effect of main oil hole pressure and camshaft torque on friction in each engine part. Fig. 1 shows a measuring bench designed to measure overall friction in the timing chain of an actual engine driven by a motor [1,2]. Pistons, valve system and oil pump have been removed from the engine. Hydraulic pressure and temperature are controlled by the oil pump and oil heater installed outside the engine. Water temperature is controlled by the circulating-water heater, also installed outside the engine. The camshaft torque controls torque load by means of the powderbrake, which is directly connected to the camshaft [3]" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002855_07ias.2007.334-Figure4-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002855_07ias.2007.334-Figure4-1.png", "caption": "Figure 4. Mode 2 of stator, 8200 Hz", "texts": [ "([ =+ XKXM (1) Where [M] and [K] are respectively the mass and stiffness matrix, (X) the coordinates vector. These resonant frequencies and associated mode shapes depend on SRM geometries, Young modulus and the considered mode. In this case, stator design is chosen in order to have only one resonance in audible spectrum corresponding to mode 2 at 8200 kHz. A finite element model developed with Ansys\u00ae software confirms that only one vibration mode (resonant frequency) exists in the audible spectrum (Figure 4.). Yoke frame and end shields are necessary to SRM functioning. In order to reduce influence of yoke frame and end shields on the stator resonance and mode shape, joining are placed on vibration antinodes (Figure 5.). Indeed, yoke frame and end shields have their own resonant frequencies but have in this way low influences on stator strain (Figure 6.). Figure 7. shows the experimental spectrum of vibratory acceleration measured on stator, yoke frame and end shields excited by symmetrical piezoelectric actuators" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002185_amc.2006.1631633-Figure1-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002185_amc.2006.1631633-Figure1-1.png", "caption": "Fig. 1. Layout of Helicopter and CCD camera", "texts": [ " So it is an absolutely example to development a new control technique. And it is available to utilize for general force control applications using forces of wind as actuators. According to the above consideration, this paper introduces the controller design process including system modeling, simulation results, and experimental results. The presented helicopter control system has two control modes. The first mode is to position control for flights and the second is force control for takeoff and landing. They are utilized alternately. Fig.1 shows a system layout example for flights. A CCD camera as a position sensor detects the helicopter. By assume a virtual screen, a controller can calculates the position data of the helicopter. In order to identificate a mathematical model related to the helicopter, the relation from the operational voltage of controller to the force sensor output voltage is utilized. The 0-7803-9511-5/06/$20.00 \u00a92006 IEEE AMC\u201906-Istanbul, Turkey62 input operational voltage consists of M sequence time series data that has the offset corresponding to the half of gravity of the helicopter" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0002947_978-3-540-75103-8_18-Figure9-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0002947_978-3-540-75103-8_18-Figure9-1.png", "caption": "Fig. 9b. Topologically aligned seams introduced with its 2D domain in the background source and target cylindrical surfaces.", "texts": [ " Firstly, if the parameter spaces of these surfaces are overtly distorted, it is difficult to generate a good quality mesh; let alone the morphed mesh on the target face. Secondly, even if the parameter space is good, there is no guarantee that the seam/pole(s) of the target face will align with those of the source face, thus distorting the mesh on the target. With a discrete representation, there is an advantage. Arbitrary seams (cuts) could be introduced at desired locations on the tessellated faces (both source and target) as shown below in Figure 9a-9b. The generated 2D domain is thus geometrically more uniform and congruent resulting in good quality meshes on both the source and the target face. The algorithmic details for a cylinder are given below \u2013 Cylindrical faces are cut so that the facets can be unzipped to get a flattened domain. Essentially a two-loop cylinder becomes a one-loop cylinder with the cut edge being repeated twice in the loop (edge e3 as shown in Fig. 9a). Each cut edge in the loop is represented as a \u201cdummy\u201d edge (edge e4 as shown in Fig. 9a) and an edge dependency relationship is established between these edges. For the purpose of mapping the source nodes on the target, duplicate nodes (as shown in Fig. 10a) are introduced in the master mesh along the cut edge. This enables a one-to-one mapping with the source and the target edges. At this point, a periodic surface is treated just like a non-periodic face and the mapping of boundary and interior nodes is done as described in 5.1(e). At the point of creation of elements on the target face, duplicate nodes are eliminated based on the edge-dependency relation ship between the cut edges of the target loop" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003806_icelmach.2010.5608274-Figure9-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003806_icelmach.2010.5608274-Figure9-1.png", "caption": "Fig. 9. Magnitude of the third harmonic of magnetic flux density.", "texts": [], "surrounding_texts": [ "The four-pole energy-saving small induction motor with core made from the non-oriented silicon steel M600-50A was examined. The supply voltage was 230 V for the frequency 50 Hz. Stator windings were delta connected. The number of series turns of stator windings was 368. The external diameter of the stator core was 120 mm, the internal diameter is 70.5 mm, and stator core lengths is 102 mm." ] }, { "image_filename": "designv11_32_0001933_05698190590948232-Figure3-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0001933_05698190590948232-Figure3-1.png", "caption": "Fig. 3\u2014Structure drawing of the early test seal: 1, primary ring; 2, case; 3, retainer; 4, spring; 5, rotating seat; and 6, 0-ring secondary seal.", "texts": [ " Presented at the 59th Annual Meeting in Toronto, Ontario, Canada May 17-20, 2004 Final manuscript approved December 14, 2004 Review led by Jim Netzel The main target of research on oil-film-lubricated spiral-groove face seals is to develop noncontacting spiral-groove face seals with zero leakage and long life, mainly for use in high-speed turbocompressors of the oil refinery and petrochemical industries. So, the development of a high-speed test rig is very important and essential. Figure 1 is a drawing of the early high-speed test rig (Wang, et al. (2)), where a two-stage speed-increasing gear box was used. Figure 2 is the structure sketch of latest high-speed test rig, where a high-speed variable-frequency motor with rotating speed up to 20,000 r/min is used. This has reduced noise in the laboratory and increased the driving torque. Figure 3 is a drawing of the early test spiral-groove face seal. It is a face-to-face, double seal with a closed circulation system of sealing oil using a self-circulating screw pump. Figure 4 shows the principle of the supporting system for the test rig. It consists of a sealing-oil system and a sealed-gas system. Figures 5 and 6 are the latest seal designs. The former is also a face-to-face double seal without a self-circulating screw pump, and the latter is a combined single seal with a floating bushing seal, which is more suitable for high-pressure conditions than the former. The conventional outside sealing-oil circulating system is adopted by both of them. Two kinds of oil-film-lubricated face seals with spiral grooves, including double-row herringbone spiral grooves and single-row spiral grooves, have successfully passed tests not only in the laboratory but also in the field. Experimental Investigation The face seal with double-row spiral grooves, shown in Fig. 3, was tested in the lab for 300 h. During the last run of 145 h, the time with speed of more than 10,000 r/min is 121 h, and the time of startup and shutdown is 25 h. Test speed is shown in Fig. 7. At 10,000 r/min, the corresponding average face speed is 93 m/s. The maximum rotating speed is 12,090 r/min, and the corresponding average face speed is up to 113 m/s. In the standard test, the sealed gas pressure is 0.5\u20130.6 MPa, so the sealing oil pressure is 0.6\u20130.8 MPa. In the comparison test of 589 D ow nl oa de d by [ E rc iy es U ni ve rs ity ] at 1 5: 28 2 9 D ec em be r 20 14 Fig", " spiral-groove parameters, the sealed gas pressure is 1.0\u20131.2 MPa, so the sealing oil pressure is up to 1.2\u20131.5 MPa. Theoretically speaking, noncontacting face seals with spiral grooves can realize zero leakage. However, it is common knowledge that for screw seals, called viscoseals, a \u201csecondary leakage\u201d problem, called \u201csealing breakdown,\u201d will occur (Wang, et al. (3)). The same problem cannot be eliminated completely for spiralgroove face seals, particularly under high-speed conditions. In the first experiment, the primary ring, item 1 in Fig. 3, made of bronze, and the rotating ring, item 5, made of tungsten carbide, were used. The result showed that the leakage rate, primarily secondary leakage, was about 100 ml/h at a rotating speed of 10,000 r/min. Next, a carbon-graphite primary ring was used. The leakage rate was greatly reduced, less than 10 ml/h, under the same rotating speed. No wear of the seal faces in either experiment was observed. Because the thermal expansion coefficient of bronze is great, the thermal deformation of the seal face is large, and therefore the interface deviation from the ideal parallel state and the sealing gap becomes convergent", " To solve the problem completely, a section of wind-back screw designed on the inner bore of the primary ring seat that fits together with the seal sleeve is adopted. When this design was tested for 300 h D ow nl oa de d by [ E rc iy es U ni ve rs ity ] at 1 5: 28 2 9 D ec em be r 20 14 with rotational speed changes from 3000 to 12,000 r/min, there was no visible drop leakage. A small amount of evaporating sealing oil was observed on the seal parts. The relationship of the power consumption of the test seal shown in Fig. 3 and rotating speed is shown in Fig. 8. Curve 1 is the total power consumption, including the test seal and test rig. Curve 2 is the calibrated test-rig power without the test seal. Curve 3 is the power consumption of the test seal, that is, the difference between curve 1 and curve 2. Curve 4 is the corrected seal net power consumption, considering the test rig\u2019s transmission efficiency. Seal power consumption is composed of friction power of two faces and power consumption of the screw pump. From curve 4 in Fig", " So the power consumption rise is reduced because of the increase in film thickness and the decrease of viscosity. A well-designed noncontacting seal with spiral grooves will not contact during normal operation. However, instantaneous contact will occur during startup and shutdown. To determine the amount of wear at these conditions, the seal was subjected to 25 startups and shutdowns. During this time, the speed was decreased gradually 19 times and abruptly 4 times. To measure the wear of the sealing face, three scratches were made on the face of the primary ring, item 1 in Fig. 3, made of carbon graphite, near the outside diameter (OD), inner diameter (ID), and mid-diameter (MD). The depths of those scratches were measured before and after the test using a surface roughness measuring apparatus. The depth would decrease after the test and the difference would be the wear. Figure 12 shows the diagram of wear detection on the face of the outboard primary ring. The left one is measured before test and the right one is measured after test. The three rows are the scratches near OD, MD, and ID in turn" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0003845_speedam.2010.5544958-Figure2-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0003845_speedam.2010.5544958-Figure2-1.png", "caption": "Fig. 2. Bearing by SKF.", "texts": [ " The induction motor (Fig. 1) tested had the following specifications: \u2022 Rated Power: 0.75 kW. \u2022 Rated Voltage: 400 V. \u2022 Rated Current: 1.86 A. \u2022 Rotor Slots: 26. \u2022 Pole Pairs: 2. \u2022 Mains frequency: 50 Hz. One of the original bearings of the motor was replaced by other bearing by SKF. The mounted open cage ball bearing belongs to the 6004 series (The q values, characteristic of this bearing were consulted in SKF charts). It was lubricated with grease filling completely all open spaces between the balls (Fig. 2). The grease was manufactured by Kraft and had the following specifications: MOLYKOTE BR 2 Plus with MoS. The motor was coupled to a magnetic powder brake which acted as load (Fig. 1), and was driven by utility voltage. A small number of tests were performed at two different load levels: no-load (10 tests) and full-load (10 tests). A Yokogawa 701933 hall-effect current probe (Fig. 3) was used to register stator current with a PCI-6250 M DAQ board by National Instruments. Data acquisition resolution was 80 kHz and data was analyzed with Matlab, where the Power Spectral Density of the stator current was computed using a Hanning window" ], "surrounding_texts": [] }, { "image_filename": "designv11_32_0000457_978-3-642-55848-1-Figure9.28-1.png", "original_path": "designv11-32/openalex_figure/designv11_32_0000457_978-3-642-55848-1-Figure9.28-1.png", "caption": "Fig. 9.28. Scheme of the reciprocating mechanism", "texts": [ " How important these variations are is difficult to comprehend a priori and requires detailed analy sis of the complete system [16, 17]. There are also some non-linear effects that lumped parameter models cannot predict, e.g. the so-called secondary resonance [17]. Hence, a more detailed model of the engine in the time domain is important. 356 9 Multibody Dynamics In this section we develop a model of a complete single-cylinder engine based on multibody models of the reciprocating mechanism. The analysis is based on the plane body motion models of Sec. 9.2 [18,19]. The scheme of the reciprocating mechanism is given in Fig. 9.28. It consists of a crank that rotates about the bearing at 0 and which is connected to the engine piston by the connecting rod AB. All connections of reciprocating members are by bearings. We treat bearings as frictionless revolute joints. The pis ton slides in the cylinder bore and is acted upon by pressure forces developed by the combustion processes in the cylinder chamber. The piston friction is neglected. There is friction in the mechanism however, but this is quite difficult to predict. Thus its overall effect is represented by a linear resistive element (see later)", "29) is modelled simply by an inertial element connected to an effort junction, from which information on the flywheel angular velocity is obtained. This is fed to the display component (at the right bottom in the docu ment). The Crank and Conrad components are modelled as rigid bodies in plane mo tion using the general model for plane motion bodies of Sec. 9.2.1. The compo nents are created simply by copying the Body component from the library. The main difference is the change of name. The ports are moved to the upper and lower parts of the components in order to represent the connections as depicted in Fig. 9.28. Thus, the model of the Crank is as depicted in Fig. 9.31. 9.4 Engine Torsional Vibrations 359 Note that, because of the connection through the frictionless bearings, there is no transfer of external moments to the crank. The SE connected to the mass centre joint describes the weight of the component. It can be seen in the lower part of the model that signals of the crank rotation angle and the angular velocity are ob tained. These are used to display the crank motion, as well as for simulating the shaft load torque (Fig" ], "surrounding_texts": [] } ]